DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP262^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n029.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 09:13:34 AM UTC 2026

% Result   : Theorem 32.77s 9.02s
% Output   : Refutation 33.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   59 (  23 unt;   0 typ;   2 def)
%            Number of atoms       :  219 (  93 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  657 (  50   ~;  31   |;  12   &; 550   @)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :   95 (  94 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 3919 (3916 usr;  63 con; 0-8 aty)
%            Number of variables   :   46 (   0   ^;  35   !;  11   ?;  46   :)

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

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

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

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

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

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

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

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

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

thf(type_def_15,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_16,type,
    produc8923325533196201883nteger: $tType ).

thf(type_def_17,type,
    set_fi4554929511873752355omplex: $tType ).

thf(type_def_18,type,
    filter6041513312241820739omplex: $tType ).

thf(type_def_19,type,
    set_fi7789364187291644575l_real: $tType ).

thf(type_def_20,type,
    filter2146258269922977983l_real: $tType ).

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

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

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

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

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

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

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

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

thf(type_def_29,type,
    filter1242075044329608583at_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_Product_unit: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_47,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

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

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

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

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

thf(type_def_57,type,
    list_P4002435161011370285od_o_o: $tType ).

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

thf(type_def_59,type,
    list_P3795440434834930179_o_int: $tType ).

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

thf(type_def_61,type,
    list_P6285523579766656935_o_nat: $tType ).

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

thf(type_def_63,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(type_def_64,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(type_def_65,type,
    list_P7333126701944960589_nat_o: $tType ).

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

thf(type_def_67,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(type_def_68,type,
    produc8025551001238799321T_VEBT: $tType ).

thf(type_def_69,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(type_def_70,type,
    produc334124729049499915VEBT_o: $tType ).

thf(type_def_71,type,
    list_P4547456442757143711BT_int: $tType ).

thf(type_def_72,type,
    produc4894624898956917775BT_int: $tType ).

thf(type_def_73,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(type_def_74,type,
    produc9072475918466114483BT_nat: $tType ).

thf(type_def_75,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(type_def_76,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(type_def_77,type,
    option4927543243414619207at_nat: $tType ).

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

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

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

thf(type_def_81,type,
    option6357759511663192854e_term: $tType ).

thf(type_def_82,type,
    produc8763457246119570046nteger: $tType ).

thf(type_def_83,type,
    produc7773217078559923341nt_int: $tType ).

thf(type_def_84,type,
    produc4953844613479565601on_nat: $tType ).

thf(type_def_85,type,
    produc2233624965454879586on_nat: $tType ).

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

thf(type_def_87,type,
    produc3447558737645232053on_num: $tType ).

thf(type_def_88,type,
    produc7036089656553540234on_num: $tType ).

thf(type_def_89,type,
    produc1193250871479095198on_num: $tType ).

thf(type_def_90,type,
    produc6241069584506657477e_term: $tType ).

thf(type_def_91,type,
    produc1908205239877642774nteger: $tType ).

thf(type_def_92,type,
    produc8551481072490612790e_term: $tType ).

thf(type_def_93,type,
    produc2285326912895808259nt_int: $tType ).

thf(type_def_94,type,
    produc6121120109295599847at_nat: $tType ).

thf(type_def_95,type,
    produc5491161045314408544at_nat: $tType ).

thf(type_def_96,type,
    produc5542196010084753463at_nat: $tType ).

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

thf(type_def_98,type,
    produc4411394909380815293omplex: $tType ).

thf(type_def_99,type,
    produc2422161461964618553l_real: $tType ).

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

thf(func_def_1,type,
    produc1908205239877642774nteger: $tType ).

thf(func_def_2,type,
    produc5491161045314408544at_nat: $tType ).

thf(func_def_3,type,
    produc2285326912895808259nt_int: $tType ).

thf(func_def_4,type,
    produc8763457246119570046nteger: $tType ).

thf(func_def_5,type,
    produc7773217078559923341nt_int: $tType ).

thf(func_def_6,type,
    produc1193250871479095198on_num: $tType ).

thf(func_def_7,type,
    produc8306885398267862888on_nat: $tType ).

thf(func_def_8,type,
    produc6121120109295599847at_nat: $tType ).

thf(func_def_9,type,
    produc7036089656553540234on_num: $tType ).

thf(func_def_10,type,
    produc2233624965454879586on_nat: $tType ).

thf(func_def_11,type,
    produc6241069584506657477e_term: $tType ).

thf(func_def_12,type,
    set_fi4554929511873752355omplex: $tType ).

thf(func_def_13,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(func_def_14,type,
    produc8551481072490612790e_term: $tType ).

thf(func_def_15,type,
    option6357759511663192854e_term: $tType ).

thf(func_def_16,type,
    produc3447558737645232053on_num: $tType ).

thf(func_def_17,type,
    produc4953844613479565601on_nat: $tType ).

thf(func_def_18,type,
    set_fi7789364187291644575l_real: $tType ).

thf(func_def_19,type,
    filter6041513312241820739omplex: $tType ).

thf(func_def_20,type,
    list_P7037539587688870467BT_nat: $tType ).

thf(func_def_21,type,
    list_P4547456442757143711BT_int: $tType ).

thf(func_def_22,type,
    list_P5647936690300460905T_VEBT: $tType ).

thf(func_def_23,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(func_def_24,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(func_def_25,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_26,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(func_def_27,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(func_def_28,type,
    filter2146258269922977983l_real: $tType ).

thf(func_def_29,type,
    option4927543243414619207at_nat: $tType ).

thf(func_def_30,type,
    filter1242075044329608583at_nat: $tType ).

thf(func_def_31,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(func_def_32,type,
    produc9072475918466114483BT_nat: $tType ).

thf(func_def_33,type,
    produc4894624898956917775BT_int: $tType ).

thf(func_def_34,type,
    produc8025551001238799321T_VEBT: $tType ).

thf(func_def_35,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(func_def_36,type,
    produc4411394909380815293omplex: $tType ).

thf(func_def_37,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(func_def_38,type,
    list_P6285523579766656935_o_nat: $tType ).

thf(func_def_39,type,
    list_P3795440434834930179_o_int: $tType ).

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

thf(func_def_41,type,
    produc334124729049499915VEBT_o: $tType ).

thf(func_def_42,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(func_def_43,type,
    produc6271795597528267376eger_o: $tType ).

thf(func_def_44,type,
    produc2422161461964618553l_real: $tType ).

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

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

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

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

thf(func_def_49,type,
    list_P4002435161011370285od_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_92,type,
    nat: $tType ).

thf(func_def_93,type,
    int: $tType ).

thf(func_def_94,type,
    archim7802044766580827645g_real: real > int ).

thf(func_def_95,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_96,type,
    archim6058952711729229775r_real: real > int ).

thf(func_def_97,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_98,type,
    archim8280529875227126926d_real: real > int ).

thf(func_def_99,type,
    binomial: nat > nat > nat ).

thf(func_def_100,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_101,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_102,type,
    bit_concat_bit: nat > int > int > int ).

thf(func_def_103,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_104,type,
    bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).

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_se545348938243370406it_int: nat > int > int ).

thf(func_def_122,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_123,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_124,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_125,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_126,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_127,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_128,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_129,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_130,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_131,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_132,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_133,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_134,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_135,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(func_def_136,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_137,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_138,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_139,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_140,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_141,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_142,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_143,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_144,type,
    code_negative: num > code_integer ).

thf(func_def_145,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_146,type,
    code_positive: num > code_integer ).

thf(func_def_147,type,
    code_Target_negative: num > int ).

thf(func_def_148,type,
    code_Target_positive: num > int ).

thf(func_def_149,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(func_def_150,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(func_def_151,type,
    comple4887499456419720421f_real: set_real > real ).

thf(func_def_152,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_153,type,
    complete_Sup_Sup_int: set_int > int ).

thf(func_def_154,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(func_def_155,type,
    comple1385675409528146559p_real: set_real > real ).

thf(func_def_156,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(func_def_157,type,
    arg: complex > real ).

thf(func_def_158,type,
    cis: real > complex ).

thf(func_def_159,type,
    cnj: complex > complex ).

thf(func_def_160,type,
    complex2: real > real > complex ).

thf(func_def_161,type,
    im: complex > real ).

thf(func_def_162,type,
    re: complex > real ).

thf(func_def_163,type,
    csqrt: complex > complex ).

thf(func_def_164,type,
    imaginary_unit: complex ).

thf(func_def_165,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(func_def_166,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(func_def_167,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(func_def_168,type,
    adjust_div: product_prod_int_int > int ).

thf(func_def_169,type,
    adjust_mod: int > int > int ).

thf(func_def_170,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_171,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_172,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_173,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_174,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_175,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_176,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_177,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_178,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_179,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_180,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_181,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(func_def_182,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_183,type,
    semiri2265585572941072030t_real: nat > real ).

thf(func_def_184,type,
    invers8013647133539491842omplex: complex > complex ).

thf(func_def_185,type,
    inverse_inverse_rat: rat > rat ).

thf(func_def_186,type,
    inverse_inverse_real: real > real ).

thf(func_def_187,type,
    at_bot_real: filter_real ).

thf(func_def_188,type,
    at_top_nat: filter_nat ).

thf(func_def_189,type,
    at_top_real: filter_real ).

thf(func_def_190,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_191,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(func_def_192,type,
    eventually_real: ( real > $o ) > filter_real > $o ).

thf(func_def_193,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(func_def_194,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

thf(func_def_195,type,
    filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).

thf(func_def_196,type,
    filtermap_real_real: ( real > real ) > filter_real > filter_real ).

thf(func_def_197,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(func_def_198,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(func_def_199,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(func_def_200,type,
    finite_card_o: set_o > nat ).

thf(func_def_201,type,
    finite_card_complex: set_complex > nat ).

thf(func_def_202,type,
    finite_card_int: set_int > nat ).

thf(func_def_203,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_204,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_205,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(func_def_206,type,
    finite_card_char: set_char > nat ).

thf(func_def_207,type,
    finite_finite_o: set_o > $o ).

thf(func_def_208,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(func_def_209,type,
    finite_finite_int: set_int > $o ).

thf(func_def_210,type,
    finite_finite_list_o: set_list_o > $o ).

thf(func_def_211,type,
    finite8712137658972009173omplex: set_list_complex > $o ).

thf(func_def_212,type,
    finite3922522038869484883st_int: set_list_int > $o ).

thf(func_def_213,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(func_def_214,type,
    finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).

thf(func_def_215,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_216,type,
    finite_finite_num: set_num > $o ).

thf(func_def_217,type,
    finite_finite_rat: set_rat > $o ).

thf(func_def_218,type,
    finite_finite_real: set_real > $o ).

thf(func_def_219,type,
    finite6551019134538273531omplex: set_set_complex > $o ).

thf(func_def_220,type,
    finite6197958912794628473et_int: set_set_int > $o ).

thf(func_def_221,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(func_def_222,type,
    finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).

thf(func_def_223,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(func_def_224,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(func_def_225,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_226,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_227,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_228,type,
    comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).

thf(func_def_229,type,
    comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).

thf(func_def_230,type,
    id_o: $o > $o ).

thf(func_def_231,type,
    id_nat: nat > nat ).

thf(func_def_232,type,
    map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).

thf(func_def_233,type,
    map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).

thf(func_def_234,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_235,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_236,type,
    map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).

thf(func_def_237,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_238,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

thf(func_def_239,type,
    gcd_Gcd_int: set_int > int ).

thf(func_def_240,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_241,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_242,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_243,type,
    gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_244,type,
    gcd_gcd_int: int > int > int ).

thf(func_def_245,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(func_def_246,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_247,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_248,type,
    abs_abs_complex: complex > complex ).

thf(func_def_249,type,
    abs_abs_int: int > int ).

thf(func_def_250,type,
    abs_abs_rat: rat > rat ).

thf(func_def_251,type,
    abs_abs_real: real > real ).

thf(func_def_252,type,
    minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).

thf(func_def_253,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_254,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(func_def_255,type,
    minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_256,type,
    minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).

thf(func_def_257,type,
    minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(func_def_258,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_259,type,
    minus_minus_complex: complex > complex > complex ).

thf(func_def_260,type,
    minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_261,type,
    minus_minus_int: int > int > int ).

thf(func_def_262,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_263,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_264,type,
    minus_minus_real: real > real > real ).

thf(func_def_265,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(func_def_266,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_267,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_268,type,
    minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).

thf(func_def_269,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(func_def_270,type,
    minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(func_def_271,type,
    one_one_Code_integer: code_integer ).

thf(func_def_272,type,
    one_one_complex: complex ).

thf(func_def_273,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(func_def_274,type,
    one_one_int: int ).

thf(func_def_275,type,
    one_one_nat: nat ).

thf(func_def_276,type,
    one_one_rat: rat ).

thf(func_def_277,type,
    one_one_real: real ).

thf(func_def_278,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_279,type,
    plus_plus_complex: complex > complex > complex ).

thf(func_def_280,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

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

thf(func_def_282,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_283,type,
    plus_plus_num: num > num > num ).

thf(func_def_284,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_285,type,
    plus_plus_real: real > real > real ).

thf(func_def_286,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_287,type,
    sgn_sgn_complex: complex > complex ).

thf(func_def_288,type,
    sgn_sgn_int: int > int ).

thf(func_def_289,type,
    sgn_sgn_rat: rat > rat ).

thf(func_def_290,type,
    sgn_sgn_real: real > real ).

thf(func_def_291,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_292,type,
    times_times_complex: complex > complex > complex ).

thf(func_def_293,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_294,type,
    times_times_int: int > int > int ).

thf(func_def_295,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_296,type,
    times_times_num: num > num > num ).

thf(func_def_297,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_298,type,
    times_times_real: real > real > real ).

thf(func_def_299,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_300,type,
    uminus1482373934393186551omplex: complex > complex ).

thf(func_def_301,type,
    uminus_uminus_int: int > int ).

thf(func_def_302,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_303,type,
    uminus_uminus_real: real > real ).

thf(func_def_304,type,
    uminus8566677241136511917omplex: set_complex > set_complex ).

thf(func_def_305,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(func_def_306,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_307,type,
    uminus612125837232591019t_real: set_real > set_real ).

thf(func_def_308,type,
    uminus613421341184616069et_nat: set_set_nat > set_set_nat ).

thf(func_def_309,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_310,type,
    zero_zero_complex: complex ).

thf(func_def_311,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(func_def_312,type,
    zero_zero_int: int ).

thf(func_def_313,type,
    zero_zero_nat: nat ).

thf(func_def_314,type,
    zero_zero_rat: rat ).

thf(func_def_315,type,
    zero_zero_real: real ).

thf(func_def_316,type,
    groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(func_def_317,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(func_def_318,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(func_def_319,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(func_def_320,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(func_def_321,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(func_def_322,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_323,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(func_def_324,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_325,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_326,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_327,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(func_def_328,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_329,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(func_def_330,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_331,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_332,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_333,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(func_def_334,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(func_def_335,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(func_def_336,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(func_def_337,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(func_def_338,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(func_def_339,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(func_def_340,type,
    groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).

thf(func_def_341,type,
    groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(func_def_342,type,
    groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).

thf(func_def_343,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_344,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_345,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_346,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

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_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_352,type,
    if_complex: $o > complex > complex > complex ).

thf(func_def_353,type,
    if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).

thf(func_def_354,type,
    if_int: $o > int > int > int ).

thf(func_def_355,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_356,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(func_def_357,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_358,type,
    if_num: $o > num > num > num ).

thf(func_def_359,type,
    if_option_nat: $o > option_nat > option_nat > option_nat ).

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,
    if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

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

thf(func_def_370,type,
    rep_Integ: int > product_prod_nat_nat ).

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

thf(func_def_372,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_373,type,
    nat2: int > nat ).

thf(func_def_374,type,
    ring_1_Ints_complex: set_complex ).

thf(func_def_375,type,
    ring_1_Ints_real: set_real ).

thf(func_def_376,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_377,type,
    ring_17405671764205052669omplex: int > complex ).

thf(func_def_378,type,
    ring_1_of_int_int: int > int ).

thf(func_def_379,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_380,type,
    ring_1_of_int_real: int > real ).

thf(func_def_381,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_382,type,
    sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_383,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_384,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_385,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(func_def_386,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_387,type,
    bfun_nat_real: ( nat > real ) > filter_nat > $o ).

thf(func_def_388,type,
    at_infinity_real: filter_real ).

thf(func_def_389,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_390,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_391,type,
    distinct_int: list_int > $o ).

thf(func_def_392,type,
    distinct_nat: list_nat > $o ).

thf(func_def_393,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

thf(func_def_394,type,
    cons_int: int > list_int > list_int ).

thf(func_def_395,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_396,type,
    nil_int: list_int ).

thf(func_def_397,type,
    nil_nat: list_nat ).

thf(func_def_398,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_399,type,
    set_o2: list_o > set_o ).

thf(func_def_400,type,
    set_complex2: list_complex > set_complex ).

thf(func_def_401,type,
    set_int2: list_int > set_int ).

thf(func_def_402,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_403,type,
    set_real2: list_real > set_real ).

thf(func_def_404,type,
    set_set_nat2: list_set_nat > set_set_nat ).

thf(func_def_405,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_406,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(func_def_407,type,
    list_update_o: list_o > nat > $o > list_o ).

thf(func_def_408,type,
    list_update_complex: list_complex > nat > complex > list_complex ).

thf(func_def_409,type,
    list_update_int: list_int > nat > int > list_int ).

thf(func_def_410,type,
    list_update_nat: list_nat > nat > nat > list_nat ).

thf(func_def_411,type,
    list_update_real: list_real > nat > real > list_real ).

thf(func_def_412,type,
    list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).

thf(func_def_413,type,
    list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_414,type,
    nth_o: list_o > nat > $o ).

thf(func_def_415,type,
    nth_complex: list_complex > nat > complex ).

thf(func_def_416,type,
    nth_int: list_int > nat > int ).

thf(func_def_417,type,
    nth_nat: list_nat > nat > nat ).

thf(func_def_418,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(func_def_419,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(func_def_420,type,
    nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).

thf(func_def_421,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(func_def_422,type,
    nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).

thf(func_def_423,type,
    nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).

thf(func_def_424,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(func_def_425,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(func_def_426,type,
    nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).

thf(func_def_427,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(func_def_428,type,
    nth_real: list_real > nat > real ).

thf(func_def_429,type,
    nth_set_nat: list_set_nat > nat > set_nat ).

thf(func_def_430,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_431,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(func_def_432,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(func_def_433,type,
    product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).

thf(func_def_434,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(func_def_435,type,
    product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).

thf(func_def_436,type,
    produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).

thf(func_def_437,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(func_def_438,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(func_def_439,type,
    produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).

thf(func_def_440,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(func_def_441,type,
    remdups_nat: list_nat > list_nat ).

thf(func_def_442,type,
    replicate_o: nat > $o > list_o ).

thf(func_def_443,type,
    replicate_complex: nat > complex > list_complex ).

thf(func_def_444,type,
    replicate_int: nat > int > list_int ).

thf(func_def_445,type,
    replicate_nat: nat > nat > list_nat ).

thf(func_def_446,type,
    replicate_real: nat > real > list_real ).

thf(func_def_447,type,
    replicate_set_nat: nat > set_nat > list_set_nat ).

thf(func_def_448,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_449,type,
    upt: nat > nat > list_nat ).

thf(func_def_450,type,
    upto: int > int > list_int ).

thf(func_def_451,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_452,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_453,type,
    suc: nat > nat ).

thf(func_def_454,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_455,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(func_def_456,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_457,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_458,type,
    pred: nat > nat ).

thf(func_def_459,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_460,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(func_def_461,type,
    semiri4216267220026989637d_enat: nat > extended_enat ).

thf(func_def_462,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_463,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_464,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_465,type,
    semiri5074537144036343181t_real: nat > real ).

thf(func_def_466,type,
    size_size_list_o: list_o > nat ).

thf(func_def_467,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(func_def_468,type,
    size_size_list_int: list_int > nat ).

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

thf(func_def_470,type,
    size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).

thf(func_def_471,type,
    size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).

thf(func_def_472,type,
    size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).

thf(func_def_473,type,
    size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).

thf(func_def_474,type,
    size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).

thf(func_def_475,type,
    size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).

thf(func_def_476,type,
    size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).

thf(func_def_477,type,
    size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).

thf(func_def_478,type,
    size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).

thf(func_def_479,type,
    size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).

thf(func_def_480,type,
    size_size_list_real: list_real > nat ).

thf(func_def_481,type,
    size_s3254054031482475050et_nat: list_set_nat > nat ).

thf(func_def_482,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(func_def_483,type,
    size_size_num: num > nat ).

thf(func_def_484,type,
    size_size_option_nat: option_nat > nat ).

thf(func_def_485,type,
    size_size_option_num: option_num > nat ).

thf(func_def_486,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(func_def_487,type,
    size_size_char: char > nat ).

thf(func_def_488,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(func_def_489,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_490,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_491,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_492,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_493,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_494,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_495,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_496,type,
    nat_triangle: nat > nat ).

thf(func_def_497,type,
    root: nat > real > real ).

thf(func_def_498,type,
    sqrt: real > real ).

thf(func_def_499,type,
    bitM: num > num ).

thf(func_def_500,type,
    inc: num > num ).

thf(func_def_501,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_502,type,
    neg_nu7009210354673126013omplex: complex > complex ).

thf(func_def_503,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_504,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_505,type,
    neg_numeral_dbl_real: real > real ).

thf(func_def_506,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_507,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(func_def_508,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_509,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_510,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(func_def_511,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_512,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(func_def_513,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_514,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_515,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(func_def_516,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_517,type,
    bit0: num > num ).

thf(func_def_518,type,
    bit1: num > num ).

thf(func_def_519,type,
    one: num ).

thf(func_def_520,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_521,type,
    size_num: num > nat ).

thf(func_def_522,type,
    num_of_nat: nat > num ).

thf(func_def_523,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_524,type,
    numera6690914467698888265omplex: num > complex ).

thf(func_def_525,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(func_def_526,type,
    numeral_numeral_int: num > int ).

thf(func_def_527,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_528,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_529,type,
    numeral_numeral_real: num > real ).

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

thf(func_def_531,type,
    pred_numeral: num > nat ).

thf(func_def_532,type,
    sqr: num > num ).

thf(func_def_533,type,
    none_nat: option_nat ).

thf(func_def_534,type,
    none_num: option_num ).

thf(func_def_535,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(func_def_536,type,
    some_nat: nat > option_nat ).

thf(func_def_537,type,
    some_num: num > option_num ).

thf(func_def_538,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(func_def_539,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(func_def_540,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_541,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_542,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_543,type,
    size_option_nat: ( nat > nat ) > option_nat > nat ).

thf(func_def_544,type,
    size_option_num: ( num > nat ) > option_num > nat ).

thf(func_def_545,type,
    size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).

thf(func_def_546,type,
    the_nat: option_nat > nat ).

thf(func_def_547,type,
    the_num: option_num > num ).

thf(func_def_548,type,
    the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_549,type,
    bot_bo4199563552545308370d_enat: extended_enat ).

thf(func_def_550,type,
    bot_bot_nat: nat ).

thf(func_def_551,type,
    bot_bot_set_complex: set_complex ).

thf(func_def_552,type,
    bot_bo7653980558646680370d_enat: set_Extended_enat ).

thf(func_def_553,type,
    bot_bot_set_int: set_int ).

thf(func_def_554,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_555,type,
    bot_bot_set_num: set_num ).

thf(func_def_556,type,
    bot_bot_set_rat: set_rat ).

thf(func_def_557,type,
    bot_bot_set_real: set_real ).

thf(func_def_558,type,
    bot_bot_set_set_int: set_set_int ).

thf(func_def_559,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(func_def_560,type,
    bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).

thf(func_def_561,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_562,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(func_def_563,type,
    ord_less_int: int > int > $o ).

thf(func_def_564,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_565,type,
    ord_less_num: num > num > $o ).

thf(func_def_566,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_567,type,
    ord_less_real: real > real > $o ).

thf(func_def_568,type,
    ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_569,type,
    ord_less_set_complex: set_complex > set_complex > $o ).

thf(func_def_570,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_571,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_572,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(func_def_573,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_574,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_575,type,
    ord_less_set_set_int: set_set_int > set_set_int > $o ).

thf(func_def_576,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_577,type,
    ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).

thf(func_def_578,type,
    ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).

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

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

thf(func_def_581,type,
    ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_582,type,
    ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(func_def_583,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_584,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(func_def_585,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(func_def_586,type,
    ord_le4104064031414453916r_real: filter_real > filter_real > $o ).

thf(func_def_587,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_588,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_589,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_590,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_591,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_592,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(func_def_593,type,
    ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_594,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(func_def_595,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_596,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_597,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(func_def_598,type,
    ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_599,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(func_def_600,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_601,type,
    ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).

thf(func_def_602,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_603,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_604,type,
    ord_max_Code_integer: code_integer > code_integer > code_integer ).

thf(func_def_605,type,
    ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).

thf(func_def_606,type,
    ord_max_int: int > int > int ).

thf(func_def_607,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_608,type,
    ord_max_num: num > num > num ).

thf(func_def_609,type,
    ord_max_rat: rat > rat > rat ).

thf(func_def_610,type,
    ord_max_real: real > real > real ).

thf(func_def_611,type,
    ord_max_set_int: set_int > set_int > set_int ).

thf(func_def_612,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(func_def_613,type,
    order_9091379641038594480t_real: ( nat > real ) > $o ).

thf(func_def_614,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(func_def_615,type,
    order_mono_nat_real: ( nat > real ) > $o ).

thf(func_def_616,type,
    top_top_set_o: set_o ).

thf(func_def_617,type,
    top_top_set_nat: set_nat ).

thf(func_def_618,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_619,type,
    top_top_set_real: set_real ).

thf(func_def_620,type,
    top_top_set_char: set_char ).

thf(func_def_621,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_622,type,
    power_power_complex: complex > nat > complex ).

thf(func_def_623,type,
    power_power_int: int > nat > int ).

thf(func_def_624,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_625,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_626,type,
    power_power_real: real > nat > real ).

thf(func_def_627,type,
    produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).

thf(func_def_628,type,
    produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).

thf(func_def_629,type,
    produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).

thf(func_def_630,type,
    produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).

thf(func_def_631,type,
    produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).

thf(func_def_632,type,
    produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).

thf(func_def_633,type,
    produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).

thf(func_def_634,type,
    produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).

thf(func_def_635,type,
    produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).

thf(func_def_636,type,
    produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).

thf(func_def_637,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(func_def_638,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(func_def_639,type,
    product_Pair_o_nat: $o > nat > product_prod_o_nat ).

thf(func_def_640,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(func_def_641,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_642,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_643,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_644,type,
    product_Pair_nat_o: nat > $o > product_prod_nat_o ).

thf(func_def_645,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_646,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_647,type,
    produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).

thf(func_def_648,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_649,type,
    produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).

thf(func_def_650,type,
    produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).

thf(func_def_651,type,
    produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).

thf(func_def_652,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(func_def_653,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(func_def_654,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(func_def_655,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(func_def_656,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_657,type,
    produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).

thf(func_def_658,type,
    produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).

thf(func_def_659,type,
    produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).

thf(func_def_660,type,
    produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).

thf(func_def_661,type,
    produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).

thf(func_def_662,type,
    produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).

thf(func_def_663,type,
    produc7959293469001253456omplex: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > produc7773217078559923341nt_int > set_complex ).

thf(func_def_664,type,
    produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).

thf(func_def_665,type,
    produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).

thf(func_def_666,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_667,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_668,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_669,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_670,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_671,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(func_def_672,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_673,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_674,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_675,type,
    produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).

thf(func_def_676,type,
    produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).

thf(func_def_677,type,
    produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).

thf(func_def_678,type,
    produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).

thf(func_def_679,type,
    produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).

thf(func_def_680,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_681,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_682,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_683,type,
    produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).

thf(func_def_684,type,
    produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).

thf(func_def_685,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_686,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_687,type,
    produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).

thf(func_def_688,type,
    produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).

thf(func_def_689,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_690,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(func_def_691,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_692,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_693,type,
    produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).

thf(func_def_694,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(func_def_695,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(func_def_696,type,
    fract: int > int > rat ).

thf(func_def_697,type,
    frct: product_prod_int_int > rat ).

thf(func_def_698,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_699,type,
    of_int: int > rat ).

thf(func_def_700,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_701,type,
    real_V2521375963428798218omplex: set_complex ).

thf(func_def_702,type,
    real_V5970128139526366754l_real: ( real > real ) > $o ).

thf(func_def_703,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(func_def_704,type,
    real_V975177566351809787t_real: real > real > real ).

thf(func_def_705,type,
    real_V1022390504157884413omplex: complex > real ).

thf(func_def_706,type,
    real_V7735802525324610683m_real: real > real ).

thf(func_def_707,type,
    real_V4546457046886955230omplex: real > complex ).

thf(func_def_708,type,
    real_V2046097035970521341omplex: real > complex > complex ).

thf(func_def_709,type,
    real_V1485227260804924795R_real: real > real > real ).

thf(func_def_710,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_711,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(func_def_712,type,
    divide_divide_int: int > int > int ).

thf(func_def_713,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_714,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_715,type,
    divide_divide_real: real > real > real ).

thf(func_def_716,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_717,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(func_def_718,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_719,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_720,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_721,type,
    dvd_dvd_real: real > real > $o ).

thf(func_def_722,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_723,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_724,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_725,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_726,type,
    zero_n1201886186963655149omplex: $o > complex ).

thf(func_def_727,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_728,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_729,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(func_def_730,type,
    zero_n3304061248610475627l_real: $o > real ).

thf(func_def_731,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(func_def_732,type,
    suminf_real: ( nat > real ) > real ).

thf(func_def_733,type,
    summable_real: ( nat > real ) > $o ).

thf(func_def_734,type,
    sums_real: ( nat > real ) > real > $o ).

thf(func_def_735,type,
    collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).

thf(func_def_736,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(func_def_737,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_738,type,
    collect_list_o: ( list_o > $o ) > set_list_o ).

thf(func_def_739,type,
    collect_list_complex: ( list_complex > $o ) > set_list_complex ).

thf(func_def_740,type,
    collect_list_int: ( list_int > $o ) > set_list_int ).

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

thf(func_def_742,type,
    collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).

thf(func_def_743,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_744,type,
    collect_num: ( num > $o ) > set_num ).

thf(func_def_745,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(func_def_746,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

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_complex: ( set_complex > $o ) > set_set_complex ).

thf(func_def_751,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(func_def_752,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(func_def_753,type,
    pow_nat: set_nat > set_set_nat ).

thf(func_def_754,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_755,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_756,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_757,type,
    image_nat_real: ( nat > real ) > set_nat > set_real ).

thf(func_def_758,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_759,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_760,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(func_def_761,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(func_def_762,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(func_def_763,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_764,type,
    insert_complex: complex > set_complex > set_complex ).

thf(func_def_765,type,
    insert_int: int > set_int > set_int ).

thf(func_def_766,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_767,type,
    insert_num: num > set_num > set_num ).

thf(func_def_768,type,
    insert_rat: rat > set_rat > set_rat ).

thf(func_def_769,type,
    insert_real: real > set_real > set_real ).

thf(func_def_770,type,
    insert_set_nat: set_nat > set_set_nat > set_set_nat ).

thf(func_def_771,type,
    insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).

thf(func_def_772,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_773,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_774,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_775,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(func_def_776,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_777,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(func_def_778,type,
    set_or370866239135849197et_int: set_int > set_int > set_set_int ).

thf(func_def_779,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_780,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_781,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_782,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_783,type,
    set_ord_atLeast_real: real > set_real ).

thf(func_def_784,type,
    set_ord_atMost_int: int > set_int ).

thf(func_def_785,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_786,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_787,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(func_def_788,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_789,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(func_def_790,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(func_def_791,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_792,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(func_def_793,type,
    set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).

thf(func_def_794,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_795,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_796,type,
    set_ord_lessThan_num: num > set_num ).

thf(func_def_797,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_798,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(func_def_799,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

thf(func_def_800,type,
    ascii_of: char > char ).

thf(func_def_801,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_802,type,
    size_char: char > nat ).

thf(func_def_803,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_804,type,
    integer_of_char: char > code_integer ).

thf(func_def_805,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_806,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(func_def_807,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(func_def_808,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(func_def_809,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(func_def_810,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(func_def_811,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(func_def_812,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(func_def_813,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(func_def_814,type,
    arccos: real > real ).

thf(func_def_815,type,
    arcosh_real: real > real ).

thf(func_def_816,type,
    arcsin: real > real ).

thf(func_def_817,type,
    arctan: real > real ).

thf(func_def_818,type,
    arsinh_real: real > real ).

thf(func_def_819,type,
    artanh_real: real > real ).

thf(func_def_820,type,
    cos_real: real > real ).

thf(func_def_821,type,
    cos_coeff: nat > real ).

thf(func_def_822,type,
    cosh_real: real > real ).

thf(func_def_823,type,
    cot_real: real > real ).

thf(func_def_824,type,
    exp_complex: complex > complex ).

thf(func_def_825,type,
    exp_real: real > real ).

thf(func_def_826,type,
    ln_ln_real: real > real ).

thf(func_def_827,type,
    log: real > real > real ).

thf(func_def_828,type,
    pi: real ).

thf(func_def_829,type,
    powr_real: real > real > real ).

thf(func_def_830,type,
    sin_real: real > real ).

thf(func_def_831,type,
    sin_coeff: nat > real ).

thf(func_def_832,type,
    sinh_real: real > real ).

thf(func_def_833,type,
    tan_real: real > real ).

thf(func_def_834,type,
    tanh_complex: complex > complex ).

thf(func_def_835,type,
    tanh_real: real > real ).

thf(func_def_836,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(func_def_837,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_838,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(func_def_839,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(func_def_840,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(func_def_841,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(func_def_842,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(func_def_843,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(func_def_844,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_845,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(func_def_846,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_847,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(func_def_848,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_849,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(func_def_850,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_851,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(func_def_852,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(func_def_853,type,
    vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_854,type,
    vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_855,type,
    vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_856,type,
    vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_857,type,
    vEBT_VEBT_bit_concat: nat > nat > nat > nat ).

thf(func_def_858,type,
    vEBT_VEBT_minNull: vEBT_VEBT > $o ).

thf(func_def_859,type,
    vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_860,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(func_def_861,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(func_def_862,type,
    vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_863,type,
    vEBT_VEBT_add: option_nat > option_nat > option_nat ).

thf(func_def_864,type,
    vEBT_VEBT_greater: option_nat > option_nat > $o ).

thf(func_def_865,type,
    vEBT_VEBT_less: option_nat > option_nat > $o ).

thf(func_def_866,type,
    vEBT_VEBT_lesseq: option_nat > option_nat > $o ).

thf(func_def_867,type,
    vEBT_VEBT_max_in_set: set_nat > nat > $o ).

thf(func_def_868,type,
    vEBT_VEBT_min_in_set: set_nat > nat > $o ).

thf(func_def_869,type,
    vEBT_VEBT_mul: option_nat > option_nat > option_nat ).

thf(func_def_870,type,
    vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).

thf(func_def_871,type,
    vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).

thf(func_def_872,type,
    vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).

thf(func_def_873,type,
    vEBT_VEBT_power: option_nat > option_nat > option_nat ).

thf(func_def_874,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

thf(func_def_875,type,
    vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_876,type,
    vEBT_vebt_mint: vEBT_VEBT > option_nat ).

thf(func_def_877,type,
    vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_878,type,
    vEBT_is_pred_in_set: set_nat > nat > nat > $o ).

thf(func_def_879,type,
    vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).

thf(func_def_880,type,
    vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_881,type,
    vEBT_is_succ_in_set: set_nat > nat > nat > $o ).

thf(func_def_882,type,
    vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).

thf(func_def_883,type,
    vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(func_def_884,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_885,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_886,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_887,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_888,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_889,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(func_def_890,type,
    accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(func_def_891,type,
    fChoice_real: ( real > $o ) > real ).

thf(func_def_892,type,
    member_o: $o > set_o > $o ).

thf(func_def_893,type,
    member_complex: complex > set_complex > $o ).

thf(func_def_894,type,
    member_int: int > set_int > $o ).

thf(func_def_895,type,
    member_list_o: list_o > set_list_o > $o ).

thf(func_def_896,type,
    member_list_int: list_int > set_list_int > $o ).

thf(func_def_897,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_898,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(func_def_899,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_900,type,
    member_num: num > set_num > $o ).

thf(func_def_901,type,
    member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_902,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_903,type,
    member_real: real > set_real > $o ).

thf(func_def_904,type,
    member_set_int: set_int > set_set_int > $o ).

thf(func_def_905,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_906,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(func_def_907,type,
    deg: nat ).

thf(func_def_908,type,
    m: nat ).

thf(func_def_909,type,
    ma: nat ).

thf(func_def_910,type,
    maxs: nat ).

thf(func_def_911,type,
    mi: nat ).

thf(func_def_912,type,
    na: nat ).

thf(func_def_913,type,
    summary: vEBT_VEBT ).

thf(func_def_914,type,
    treeList: list_VEBT_VEBT ).

thf(func_def_915,type,
    xa: nat ).

thf(func_def_934,type,
    sP0: num > rat > rat > $o ).

thf(func_def_935,type,
    sP1: option_nat > option_nat > ( nat > nat > nat ) > option_nat > $o ).

thf(func_def_936,type,
    sP2: real > real > num > $o ).

thf(func_def_937,type,
    sP3: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > $o ).

thf(func_def_938,type,
    sP4: ( real > real ) > set_real > $o ).

thf(func_def_939,type,
    sP5: ( complex > real ) > ( real > complex ) > set_real > set_real > $o ).

thf(func_def_940,type,
    sP6: ( complex > real ) > set_real > set_real > set_complex > set_complex > $o ).

thf(func_def_941,type,
    sP7: set_real > ( real > real ) > ( complex > real ) > ( real > complex ) > $o ).

thf(func_def_942,type,
    sP8: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_943,type,
    sP9: set_set_nat > set_nat > set_set_nat > $o ).

thf(func_def_944,type,
    sP10: set_real > set_real > ( real > int ) > set_int > set_int > $o ).

thf(func_def_945,type,
    sP11: set_real > ( real > real ) > $o ).

thf(func_def_946,type,
    sP12: ( int > real ) > ( real > int ) > set_real > set_real > $o ).

thf(func_def_947,type,
    sP13: ( int > real ) > set_real > set_real > set_int > set_int > $o ).

thf(func_def_948,type,
    sP14: list_nat > nat > $o ).

thf(func_def_949,type,
    sP15: vEBT_VEBT > nat > $o ).

thf(func_def_950,type,
    sP16: ( nat > real > real ) > nat > real > $o ).

thf(func_def_951,type,
    sP17: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_952,type,
    sP18: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_953,type,
    sP19: $o > list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_954,type,
    sP20: $o > $o > nat > $o ).

thf(func_def_955,type,
    sP21: $o > $o > nat > $o > $o ).

thf(func_def_956,type,
    sP22: $o > vEBT_VEBT > nat > $o ).

thf(func_def_957,type,
    sP23: vEBT_VEBT > $o > nat > $o ).

thf(func_def_958,type,
    sP24: vEBT_VEBT > $o > nat > $o ).

thf(func_def_959,type,
    sP25: $o > vEBT_VEBT > nat > $o ).

thf(func_def_960,type,
    sP26: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).

thf(func_def_961,type,
    sP27: $o > $o > nat > $o ).

thf(func_def_962,type,
    sP28: $o > $o > nat > $o > $o ).

thf(func_def_963,type,
    sP29: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_964,type,
    sP30: list_VEBT_VEBT > nat > nat > nat > nat > $o > $o ).

thf(func_def_965,type,
    sP31: $o > vEBT_VEBT > $o ).

thf(func_def_966,type,
    sP32: vEBT_VEBT > $o > $o ).

thf(func_def_967,type,
    sP33: nat > nat > ( nat > int ) > int > $o ).

thf(func_def_968,type,
    sP34: ( int > $o ) > ( int > $o ) > set_int > int > $o ).

thf(func_def_969,type,
    sP35: set_int > int > ( int > $o ) > $o ).

thf(func_def_970,type,
    sP36: ( int > $o ) > ( int > $o ) > int > set_int > $o ).

thf(func_def_971,type,
    sP37: ( int > $o ) > int > set_int > $o ).

thf(func_def_972,type,
    sP38: real > real > real > $o ).

thf(func_def_973,type,
    sP39: ( real > real ) > real > real > $o ).

thf(func_def_974,type,
    sP40: ( option_num > option_num > $o ) > option_num > option_num > $o ).

thf(func_def_975,type,
    sP41: ( int > $o ) > int > int > $o ).

thf(func_def_976,type,
    sP42: ( int > $o ) > int > int > $o ).

thf(func_def_977,type,
    sP43: ( int > $o ) > int > int > $o ).

thf(func_def_978,type,
    sP44: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_979,type,
    sP45: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_980,type,
    sP46: nat > list_VEBT_VEBT > nat > nat > nat > $o ).

thf(func_def_981,type,
    sP47: nat > list_VEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_982,type,
    sP48: vEBT_VEBT > nat > $o ).

thf(func_def_983,type,
    sP49: vEBT_VEBT > nat > $o ).

thf(func_def_984,type,
    sP50: nat > vEBT_VEBT > $o ).

thf(func_def_985,type,
    sP51: nat > vEBT_VEBT > $o ).

thf(func_def_986,type,
    sP52: nat > vEBT_VEBT > $o ).

thf(func_def_987,type,
    sP53: rat > rat > rat > $o ).

thf(func_def_988,type,
    sP54: vEBT_VEBT > nat > $o ).

thf(func_def_989,type,
    sP55: vEBT_VEBT > nat > $o ).

thf(func_def_990,type,
    sP56: real > real > ( real > real ) > $o ).

thf(func_def_991,type,
    sP57: ( real > real ) > ( real > real ) > ( real > real ) > real > ( real > real ) > real > $o ).

thf(func_def_992,type,
    sP58: real > ( real > real ) > ( real > real ) > real > $o ).

thf(func_def_993,type,
    sP59: real > real > ( real > real ) > $o ).

thf(func_def_994,type,
    sP60: num > rat > rat > $o ).

thf(func_def_995,type,
    sP61: int > int > int > $o ).

thf(func_def_996,type,
    sP62: int > int > int > $o ).

thf(func_def_997,type,
    sP63: int > int > int > $o ).

thf(func_def_998,type,
    sP64: complex > set_complex > set_complex > $o ).

thf(func_def_999,type,
    sP65: int > int > int > $o ).

thf(func_def_1000,type,
    sP66: vEBT_VEBT > option_nat > $o ).

thf(func_def_1001,type,
    sP67: option_nat > vEBT_VEBT > $o ).

thf(func_def_1002,type,
    sP68: ( set_nat > $o ) > set_nat > $o ).

thf(func_def_1003,type,
    sP69: rat > rat > rat > $o ).

thf(func_def_1004,type,
    sP70: nat > nat > ( nat > $o ) > $o ).

thf(func_def_1005,type,
    sP71: vEBT_VEBT > nat > $o ).

thf(func_def_1006,type,
    sP72: vEBT_VEBT > nat > $o ).

thf(func_def_1007,type,
    sP73: nat > option_nat > vEBT_VEBT > $o ).

thf(func_def_1008,type,
    sP74: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1009,type,
    sP75: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1010,type,
    sP76: nat > vEBT_VEBT > $o ).

thf(func_def_1011,type,
    sP77: vEBT_VEBT > nat > $o ).

thf(func_def_1012,type,
    sP78: vEBT_VEBT > nat > $o ).

thf(func_def_1013,type,
    sP79: vEBT_VEBT > nat > $o ).

thf(func_def_1014,type,
    sP80: set_int > ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_1015,type,
    sP81: ( int > $o ) > set_int > int > $o ).

thf(func_def_1016,type,
    sP82: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_1017,type,
    sP83: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > $o ).

thf(func_def_1018,type,
    sP84: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1019,type,
    sP85: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1020,type,
    sP86: $o > $o > nat > $o ).

thf(func_def_1021,type,
    sP87: $o > vEBT_VEBT > $o ).

thf(func_def_1022,type,
    sP88: $o > vEBT_VEBT > $o ).

thf(func_def_1023,type,
    sP89: $o > vEBT_VEBT > $o ).

thf(func_def_1024,type,
    sP90: $o > vEBT_VEBT > $o ).

thf(func_def_1025,type,
    sP91: rat > num > rat > $o ).

thf(func_def_1026,type,
    sP92: real > real > real > $o ).

thf(func_def_1027,type,
    sP93: set_int > int > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1028,type,
    sP94: set_int > int > ( int > $o ) > $o ).

thf(func_def_1029,type,
    sP95: rat > rat > rat > $o ).

thf(func_def_1030,type,
    sP96: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1031,type,
    sP97: $o > vEBT_VEBT > nat > $o ).

thf(func_def_1032,type,
    sP98: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1033,type,
    sP99: $o > vEBT_VEBT > nat > $o ).

thf(func_def_1034,type,
    sP100: ( int > $o ) > int > set_int > ( int > $o ) > $o ).

thf(func_def_1035,type,
    sP101: real > nat > real > ( nat > real > real ) > $o ).

thf(func_def_1036,type,
    sP102: rat > rat > rat > $o ).

thf(func_def_1037,type,
    sP103: real > nat > real > $o ).

thf(func_def_1038,type,
    sP104: rat > rat > rat > $o ).

thf(func_def_1039,type,
    sP105: num > real > real > $o ).

thf(func_def_1040,type,
    sP106: nat > nat > nat > $o ).

thf(func_def_1041,type,
    sP107: nat > nat > nat > $o ).

thf(func_def_1042,type,
    sP108: nat > nat > nat > $o ).

thf(func_def_1043,type,
    sP109: ( real > real ) > ( real > real ) > set_real > set_real > $o ).

thf(func_def_1044,type,
    sP110: ( real > real ) > ( real > real ) > set_real > set_real > $o ).

thf(func_def_1045,type,
    sP111: ( real > real ) > set_real > set_real > set_real > set_real > $o ).

thf(func_def_1046,type,
    sP112: set_real > ( real > real ) > ( real > real ) > ( real > real ) > $o ).

thf(func_def_1047,type,
    sP113: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).

thf(func_def_1048,type,
    sP114: ( int > $o ) > $o ).

thf(func_def_1049,type,
    sP115: num > num > num > $o ).

thf(func_def_1050,type,
    sP116: num > num > num > $o ).

thf(func_def_1051,type,
    sP117: num > num > num > $o ).

thf(func_def_1052,type,
    sP118: num > num > num > $o ).

thf(func_def_1053,type,
    sP119: num > num > num > $o ).

thf(func_def_1054,type,
    sP120: num > num > num > $o ).

thf(func_def_1055,type,
    sP121: num > num > num > $o ).

thf(func_def_1056,type,
    sP122: num > num > num > $o ).

thf(func_def_1057,type,
    sP123: ( int > real ) > ( real > int ) > set_real > set_real > $o ).

thf(func_def_1058,type,
    sP124: set_real > set_real > ( real > int ) > set_int > set_int > $o ).

thf(func_def_1059,type,
    sP125: ( int > real ) > set_real > set_real > set_int > set_int > $o ).

thf(func_def_1060,type,
    sP126: set_int > set_int > ( real > int ) > ( int > real ) > $o ).

thf(func_def_1061,type,
    sP127: rat > rat > rat > $o ).

thf(func_def_1062,type,
    sP128: rat > rat > rat > $o ).

thf(func_def_1063,type,
    sP129: rat > rat > rat > $o ).

thf(func_def_1064,type,
    sP130: nat > vEBT_VEBT > $o ).

thf(func_def_1065,type,
    sP131: vEBT_VEBT > nat > $o ).

thf(func_def_1066,type,
    sP132: ( complex > real ) > set_complex > $o ).

thf(func_def_1067,type,
    sP133: set_int > ( int > real ) > ( complex > real ) > ( int > complex ) > $o ).

thf(func_def_1068,type,
    sP134: set_complex > set_complex > ( int > complex ) > ( complex > int ) > $o ).

thf(func_def_1069,type,
    sP135: set_int > set_int > ( int > complex ) > set_complex > set_complex > $o ).

thf(func_def_1070,type,
    sP136: option_nat > vEBT_VEBT > $o ).

thf(func_def_1071,type,
    sP137: ( set_int > $o ) > set_int > $o ).

thf(func_def_1072,type,
    sP138: real > real > real > $o ).

thf(func_def_1073,type,
    sP139: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).

thf(func_def_1074,type,
    sP140: ( int > real ) > set_int > $o ).

thf(func_def_1075,type,
    sP141: set_int > ( int > real ) > ( int > real ) > ( int > int ) > $o ).

thf(func_def_1076,type,
    sP142: set_int > set_int > ( int > int ) > ( int > int ) > $o ).

thf(func_def_1077,type,
    sP143: set_int > set_int > ( int > int ) > ( int > int ) > $o ).

thf(func_def_1078,type,
    sP144: nat > vEBT_VEBT > $o ).

thf(func_def_1079,type,
    sP145: nat > vEBT_VEBT > $o ).

thf(func_def_1080,type,
    sP146: option_num > option_num > option_num > $o ).

thf(func_def_1081,type,
    sP147: set_int > ( int > real ) > ( real > real ) > ( int > real ) > $o ).

thf(func_def_1082,type,
    sP148: ( int > real ) > set_int > $o ).

thf(func_def_1083,type,
    sP149: set_int > set_int > ( int > real ) > set_real > set_real > $o ).

thf(func_def_1084,type,
    sP150: ( real > real ) > set_real > $o ).

thf(func_def_1085,type,
    sP151: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1086,type,
    sP152: ( real > complex ) > set_real > $o ).

thf(func_def_1087,type,
    sP153: set_int > ( real > complex ) > ( int > real ) > ( int > complex ) > $o ).

thf(func_def_1088,type,
    sP154: set_real > set_real > ( real > int ) > set_int > set_int > $o ).

thf(func_def_1089,type,
    sP155: ( int > complex ) > set_int > $o ).

thf(func_def_1090,type,
    sP156: real > real > ( real > real > real ) > $o ).

thf(func_def_1091,type,
    sP157: real > num > real > $o ).

thf(func_def_1092,type,
    sP158: num > real > real > $o ).

thf(func_def_1093,type,
    sP159: real > real > real > $o ).

thf(func_def_1094,type,
    sP160: rat > rat > rat > $o ).

thf(func_def_1095,type,
    sP161: ( real > real ) > real > ( real > real ) > real > $o ).

thf(func_def_1096,type,
    sP162: real > real > ( real > real ) > $o ).

thf(func_def_1097,type,
    sP163: ( real > real ) > real > real > $o ).

thf(func_def_1098,type,
    sP164: real > ( real > real ) > real > $o ).

thf(func_def_1099,type,
    sP165: rat > rat > rat > $o ).

thf(func_def_1100,type,
    sP166: vEBT_VEBT > nat > $o > $o ).

thf(func_def_1101,type,
    sP167: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1102,type,
    sP168: $o > nat > vEBT_VEBT > $o ).

thf(func_def_1103,type,
    sP169: ( real > real ) > real > real > $o ).

thf(func_def_1104,type,
    sP170: vEBT_VEBT > nat > $o ).

thf(func_def_1105,type,
    sP171: ( int > complex ) > set_int > $o ).

thf(func_def_1106,type,
    sP172: set_int > set_int > ( int > int ) > set_int > set_int > $o ).

thf(func_def_1107,type,
    sP173: ( int > int ) > ( int > int ) > set_int > set_int > $o ).

thf(func_def_1108,type,
    sP174: ( int > complex ) > set_int > $o ).

thf(func_def_1109,type,
    sP175: $o > $o > nat > $o ).

thf(func_def_1110,type,
    sP176: $o > $o > $o > nat > $o ).

thf(func_def_1111,type,
    sP177: vEBT_VEBT > nat > $o > $o ).

thf(func_def_1112,type,
    sP178: nat > $o > vEBT_VEBT > $o ).

thf(func_def_1113,type,
    sP179: vEBT_VEBT > option_nat > $o ).

thf(func_def_1114,type,
    sP180: vEBT_VEBT > option_nat > $o ).

thf(func_def_1115,type,
    sP181: nat > vEBT_VEBT > $o ).

thf(func_def_1116,type,
    sP182: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1117,type,
    sP183: ( option_nat > option_nat > $o ) > option_nat > option_nat > $o ).

thf(func_def_1118,type,
    sP184: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1119,type,
    sP185: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_1120,type,
    sP186: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_1121,type,
    sP187: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1122,type,
    sP188: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_1123,type,
    sP189: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_1124,type,
    sP190: option_nat > nat > vEBT_VEBT > $o ).

thf(func_def_1125,type,
    sP191: real > real > real > $o ).

thf(func_def_1126,type,
    sP192: vEBT_VEBT > option_nat > $o ).

thf(func_def_1127,type,
    sP193: vEBT_VEBT > nat > $o ).

thf(func_def_1128,type,
    sP194: vEBT_VEBT > nat > $o ).

thf(func_def_1129,type,
    sP195: ( set_set_nat > $o ) > set_set_nat > $o ).

thf(func_def_1130,type,
    sP196: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1131,type,
    sP197: ( real > real ) > ( real > real ) > real > real > $o ).

thf(func_def_1132,type,
    sP198: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).

thf(func_def_1133,type,
    sP199: set_int > int > set_int > $o ).

thf(func_def_1134,type,
    sP200: product_prod_int_int > int > int > $o ).

thf(func_def_1135,type,
    sP201: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1136,type,
    sP202: $o > nat > list_VEBT_VEBT > option4927543243414619207at_nat > vEBT_VEBT > nat > $o ).

thf(func_def_1137,type,
    sP203: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1138,type,
    sP204: rat > num > rat > $o ).

thf(func_def_1139,type,
    sP205: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).

thf(func_def_1140,type,
    sP206: set_real > real > set_real > $o ).

thf(func_def_1141,type,
    sP207: nat > vEBT_VEBT > $o ).

thf(func_def_1142,type,
    sP208: num > num > num > $o ).

thf(func_def_1143,type,
    sP209: num > num > num > $o ).

thf(func_def_1144,type,
    sP210: num > num > num > $o ).

thf(func_def_1145,type,
    sP211: ( nat > real > real ) > nat > real > real > $o ).

thf(func_def_1146,type,
    sP212: num > rat > rat > $o ).

thf(func_def_1147,type,
    sP213: $o > vEBT_VEBT > $o ).

thf(func_def_1148,type,
    sP214: $o > vEBT_VEBT > $o ).

thf(func_def_1149,type,
    sP215: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > $o ).

thf(func_def_1150,type,
    sP216: rat > num > rat > $o ).

thf(func_def_1151,type,
    sP217: ( nat > real > real ) > real > nat > $o ).

thf(func_def_1152,type,
    sP218: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_1153,type,
    sP219: nat > vEBT_VEBT > list_VEBT_VEBT > $o ).

thf(func_def_1154,type,
    sP220: set_complex > ( set_complex > $o ) > $o ).

thf(func_def_1155,type,
    sP221: ( int > $o ) > int > $o ).

thf(func_def_1156,type,
    sP222: real > num > real > $o ).

thf(func_def_1157,type,
    sP223: ( int > $o ) > int > int > $o ).

thf(func_def_1158,type,
    sP224: int > int > ( int > $o ) > $o ).

thf(func_def_1159,type,
    sP225: ( real > real ) > ( nat > real > real ) > nat > real > real > $o ).

thf(func_def_1160,type,
    sP226: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1161,type,
    sP227: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1162,type,
    sP228: nat > vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1163,type,
    sP229: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1164,type,
    sP230: ( option4927543243414619207at_nat > option_num > $o ) > option_num > option4927543243414619207at_nat > $o ).

thf(func_def_1165,type,
    sP231: vEBT_VEBT > nat > $o ).

thf(func_def_1166,type,
    sP232: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1167,type,
    sP233: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1168,type,
    sP234: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1169,type,
    sP235: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1170,type,
    sP236: ( option_num > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option_num > $o ).

thf(func_def_1171,type,
    sP237: ( option_num > option_nat > $o ) > option_nat > option_num > $o ).

thf(func_def_1172,type,
    sP238: nat > nat > list_VEBT_VEBT > nat > nat > $o ).

thf(func_def_1173,type,
    sP239: num > num > num > $o ).

thf(func_def_1174,type,
    sP240: num > num > num > $o ).

thf(func_def_1175,type,
    sP241: num > num > num > $o ).

thf(func_def_1176,type,
    sP242: num > num > num > $o ).

thf(func_def_1177,type,
    sP243: num > num > num > $o ).

thf(func_def_1178,type,
    sP244: num > num > num > $o ).

thf(func_def_1179,type,
    sP245: num > num > num > $o ).

thf(func_def_1180,type,
    sP246: num > num > num > $o ).

thf(func_def_1181,type,
    sP247: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1182,type,
    sP248: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_1183,type,
    sP249: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1184,type,
    sP250: nat > option_nat > vEBT_VEBT > $o ).

thf(func_def_1185,type,
    sP251: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1186,type,
    sP252: real > real > real > $o ).

thf(func_def_1187,type,
    sP253: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > $o ).

thf(func_def_1188,type,
    sP254: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > $o ).

thf(func_def_1189,type,
    sP255: rat > num > rat > $o ).

thf(func_def_1190,type,
    sP256: set_real > set_real > ( real > real ) > set_real > set_real > $o ).

thf(func_def_1191,type,
    sP257: set_real > ( real > complex ) > $o ).

thf(func_def_1192,type,
    sP258: ( real > complex ) > ( real > real ) > ( real > complex ) > set_real > $o ).

thf(func_def_1193,type,
    sP259: ( real > real ) > ( real > real ) > set_real > set_real > $o ).

thf(func_def_1194,type,
    sP260: rat > num > rat > $o ).

thf(func_def_1195,type,
    sP261: real > ( real > real ) > real > $o ).

thf(func_def_1196,type,
    sP262: real > num > real > $o ).

thf(func_def_1197,type,
    sP263: real > ( real > real ) > ( real > real > real ) > real > $o ).

thf(func_def_1198,type,
    sP264: ( set_real > $o ) > set_real > $o ).

thf(func_def_1199,type,
    sP265: $o > nat > $o > $o ).

thf(func_def_1200,type,
    sP266: $o > $o > nat > $o > $o ).

thf(func_def_1201,type,
    sP267: $o > nat > vEBT_VEBT > $o ).

thf(func_def_1202,type,
    sP268: real > real > real > $o ).

thf(func_def_1203,type,
    sP269: list_VEBT_VEBT > nat > nat > nat > nat > $o ).

thf(func_def_1204,type,
    sP270: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).

thf(func_def_1205,type,
    sP271: ( int > $o ) > int > set_int > ( int > $o ) > $o ).

thf(func_def_1206,type,
    sP272: real > real > ( real > real > $o ) > $o ).

thf(func_def_1207,type,
    sP273: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1208,type,
    sP274: ( real > real ) > real > real > $o ).

thf(func_def_1209,type,
    sP275: $o > nat > $o > $o ).

thf(func_def_1210,type,
    sP276: nat > vEBT_VEBT > $o ).

thf(func_def_1211,type,
    sP277: nat > vEBT_VEBT > $o ).

thf(func_def_1212,type,
    sP278: nat > vEBT_VEBT > $o ).

thf(func_def_1213,type,
    sP279: ( nat > real > real ) > real > nat > $o ).

thf(func_def_1214,type,
    sP280: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1215,type,
    sP281: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1216,type,
    sP282: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1217,type,
    sP283: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_1218,type,
    sP284: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_1219,type,
    sP285: nat > vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_1220,type,
    sP286: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_1221,type,
    sP287: vEBT_VEBT > nat > $o > $o ).

thf(func_def_1222,type,
    sP288: rat > rat > rat > $o ).

thf(func_def_1223,type,
    sP289: int > ( int > $o ) > int > $o ).

thf(func_def_1224,type,
    sP290: ( int > $o ) > int > int > $o ).

thf(func_def_1225,type,
    sP291: num > real > real > $o ).

thf(func_def_1226,type,
    sP292: ( option4927543243414619207at_nat > option_nat > $o ) > option_nat > option4927543243414619207at_nat > $o ).

thf(func_def_1227,type,
    sP293: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > $o ).

thf(func_def_1228,type,
    sP294: set_nat > nat > set_nat > $o ).

thf(func_def_1229,type,
    sP295: real > num > real > $o ).

thf(func_def_1230,type,
    sP296: nat > ( nat > $o ) > nat > $o ).

thf(func_def_1231,type,
    sP297: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_1232,type,
    sP298: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_1233,type,
    sP299: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_1234,type,
    sP300: option_nat > nat > vEBT_VEBT > $o ).

thf(func_def_1235,type,
    sP301: option_nat > vEBT_VEBT > nat > $o ).

thf(func_def_1236,type,
    sP302: real > real > real > $o ).

thf(func_def_1237,type,
    sP303: nat > ( nat > nat ) > $o ).

thf(func_def_1238,type,
    sP304: ( option_nat > option_num > $o ) > option_nat > option_num > $o ).

thf(func_def_1239,type,
    sP305: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_1240,type,
    sK306: ( num > $o ) > num ).

thf(func_def_1241,type,
    sK307: real > real > ( real > real ) > real ).

thf(func_def_1242,type,
    sK308: nat > nat > nat > nat ).

thf(func_def_1243,type,
    sK309: ( real > nat ) > set_real > ( real > nat ) > real ).

thf(func_def_1244,type,
    sK310: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).

thf(func_def_1245,type,
    sK311: int > set_int > int > int ).

thf(func_def_1246,type,
    sK312: int > set_int > int > int ).

thf(func_def_1247,type,
    sK313: ( set_nat > nat ) > set_set_nat > ( set_nat > nat ) > set_nat ).

thf(func_def_1248,type,
    sK314: real > ( real > real ) > real ).

thf(func_def_1249,type,
    sK315: ( real > complex ) > set_real > set_real > real ).

thf(func_def_1250,type,
    sK316: ( real > complex ) > set_real > set_real > real ).

thf(func_def_1251,type,
    sK317: ( real > real > $o ) > real ).

thf(func_def_1252,type,
    sK318: ( real > real > $o ) > real ).

thf(func_def_1253,type,
    sK319: ( real > real > $o ) > real ).

thf(func_def_1254,type,
    sK320: ( real > real > $o ) > real ).

thf(func_def_1255,type,
    sK321: set_int > ( int > real ) > ( int > real ) > ( real > real > $o ) > int ).

thf(func_def_1256,type,
    sK322: set_real > ( real > real ) > real ).

thf(func_def_1257,type,
    sK323: int > int > set_int > int ).

thf(func_def_1258,type,
    sK324: int > int > set_int > int ).

thf(func_def_1259,type,
    sK325: ( num > int ) > num ).

thf(func_def_1260,type,
    sK326: ( num > int ) > num ).

thf(func_def_1261,type,
    sK327: produc2285326912895808259nt_int > int ).

thf(func_def_1262,type,
    sK328: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_1263,type,
    sK329: produc2285326912895808259nt_int > int ).

thf(func_def_1264,type,
    sK330: ( real > rat ) > ( set_real > $o ) > real ).

thf(func_def_1265,type,
    sK331: ( real > rat ) > ( set_real > $o ) > set_real ).

thf(func_def_1266,type,
    sK332: real > real ).

thf(func_def_1267,type,
    sK333: ( produc1908205239877642774nteger > $o ) > code_integer ).

thf(func_def_1268,type,
    sK334: ( produc1908205239877642774nteger > $o ) > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_1269,type,
    sK335: ( produc1908205239877642774nteger > $o ) > code_integer ).

thf(func_def_1270,type,
    sK336: ( int > int > $o ) > int ).

thf(func_def_1271,type,
    sK337: ( int > int > $o ) > int ).

thf(func_def_1272,type,
    sK338: rat > rat ).

thf(func_def_1273,type,
    sK339: option_nat > option_nat > ( nat > nat > nat ) > option_nat > nat ).

thf(func_def_1274,type,
    sK340: option_nat > option_nat > ( nat > nat > nat ) > option_nat > nat ).

thf(func_def_1275,type,
    sK341: option_nat > nat ).

thf(func_def_1276,type,
    sK342: produc8763457246119570046nteger > complex > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > code_integer > option6357759511663192854e_term ).

thf(func_def_1277,type,
    sK343: produc8763457246119570046nteger > complex > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8923325533196201883nteger ).

thf(func_def_1278,type,
    sK344: int > int > set_int > int ).

thf(func_def_1279,type,
    sK345: int > int > set_int > int ).

thf(func_def_1280,type,
    sK346: ( product_prod_int_int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > int ).

thf(func_def_1281,type,
    sK347: ( product_prod_int_int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > int ).

thf(func_def_1282,type,
    sK348: nat > nat > nat ).

thf(func_def_1283,type,
    sK349: int > int ).

thf(func_def_1284,type,
    sK350: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1285,type,
    sK351: product_prod_int_int > ( int > $o ) > ( int > int > int ) > int ).

thf(func_def_1286,type,
    sK352: product_prod_int_int > ( int > $o ) > ( int > int > int ) > int ).

thf(func_def_1287,type,
    sK353: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_1288,type,
    sK354: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1289,type,
    sK355: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1290,type,
    sK356: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1291,type,
    sK357: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).

thf(func_def_1292,type,
    sK358: ( nat > $o ) > nat > nat ).

thf(func_def_1293,type,
    sK359: ( nat > $o ) > nat > nat ).

thf(func_def_1294,type,
    sK360: nat > ( nat > $o ) > nat ).

thf(func_def_1295,type,
    sK361: ( nat > $o ) > nat ).

thf(func_def_1296,type,
    sK362: ( rat > rat ) > rat ).

thf(func_def_1297,type,
    sK363: ( rat > rat ) > rat ).

thf(func_def_1298,type,
    sK364: set_nat > ( nat > real ) > ( nat > real ) > nat ).

thf(func_def_1299,type,
    sK365: set_num > num > num ).

thf(func_def_1300,type,
    sK366: real > nat > real ).

thf(func_def_1301,type,
    sK367: set_int > ( int > rat ) > int ).

thf(func_def_1302,type,
    sK368: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_1303,type,
    sK369: produc1908205239877642774nteger > produc8923325533196201883nteger ).

thf(func_def_1304,type,
    sK370: set_nat > ( nat > rat ) > ( nat > rat ) > nat ).

thf(func_def_1305,type,
    sK371: set_real > set_real > ( real > nat ) > real ).

thf(func_def_1306,type,
    sK372: set_real > ( real > nat ) > ( real > nat ) > real ).

thf(func_def_1307,type,
    sK373: set_real > ( real > nat ) > set_real > real ).

thf(func_def_1308,type,
    sK374: nat > vEBT_VEBT > nat ).

thf(func_def_1309,type,
    sK375: set_real > ( real > real ) > ( complex > real ) > ( real > complex ) > real ).

thf(func_def_1310,type,
    sK376: ( complex > real ) > set_real > set_real > set_complex > set_complex > complex ).

thf(func_def_1311,type,
    sK377: ( complex > real ) > ( real > complex ) > set_real > set_real > real ).

thf(func_def_1312,type,
    sK378: ( real > real ) > set_real > real ).

thf(func_def_1313,type,
    sK379: set_real > set_complex > set_real > set_complex > ( real > complex ) > real ).

thf(func_def_1314,type,
    sK380: ( complex > real ) > set_complex > complex ).

thf(func_def_1315,type,
    sK381: ( complex > real ) > set_complex > set_complex > ( real > complex ) > complex ).

thf(func_def_1316,type,
    sK382: ( ( product_prod_nat_nat > $o ) > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).

thf(func_def_1317,type,
    sK383: ( ( product_prod_nat_nat > $o ) > $o ) > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).

thf(func_def_1318,type,
    sK384: nat > real > real ).

thf(func_def_1319,type,
    sK385: set_complex > set_complex > ( complex > int ) > complex ).

thf(func_def_1320,type,
    sK386: set_int > ( int > real ) > ( int > complex ) > int ).

thf(func_def_1321,type,
    sK387: ( nat > num ) > nat ).

thf(func_def_1322,type,
    sK388: ( nat > num ) > nat ).

thf(func_def_1323,type,
    sK389: list_int > ( int > $o ) > int ).

thf(func_def_1324,type,
    sK390: ( real > rat ) > ( real > rat ) > set_real > real ).

thf(func_def_1325,type,
    sK391: nat > nat ).

thf(func_def_1326,type,
    sK392: num > num ).

thf(func_def_1327,type,
    sK393: ( nat > rat ) > set_nat > nat ).

thf(func_def_1328,type,
    sK394: real > real > nat ).

thf(func_def_1329,type,
    sK395: code_integer > code_integer > code_integer ).

thf(func_def_1330,type,
    sK396: ( complex > real ) > set_complex > set_complex > complex ).

thf(func_def_1331,type,
    sK397: set_complex > set_complex > ( complex > real ) > complex ).

thf(func_def_1332,type,
    sK398: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1333,type,
    sK399: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1334,type,
    sK400: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1335,type,
    sK401: ( set_real > $o ) > set_real ).

thf(func_def_1336,type,
    sK402: ( set_real > $o ) > real ).

thf(func_def_1337,type,
    sK403: ( rat > nat ) > rat ).

thf(func_def_1338,type,
    sK404: ( rat > nat ) > rat ).

thf(func_def_1339,type,
    sK405: ( int > nat ) > ( int > nat ) > int ).

thf(func_def_1340,type,
    sK406: real > real ).

thf(func_def_1341,type,
    sK407: ( set_set_nat > $o ) > set_nat ).

thf(func_def_1342,type,
    sK408: ( set_set_nat > $o ) > set_set_nat ).

thf(func_def_1343,type,
    sK409: ( nat > $o > $o ) > nat > list_o ).

thf(func_def_1344,type,
    sK410: ( nat > $o > $o ) > nat > nat ).

thf(func_def_1345,type,
    sK411: nat > ( nat > $o > $o ) > $o ).

thf(func_def_1346,type,
    sK412: list_o > ( nat > $o > $o ) > nat > nat ).

thf(func_def_1347,type,
    sK413: ( real > real ) > real > real ).

thf(func_def_1348,type,
    sK414: ( int > int > $o ) > int ).

thf(func_def_1349,type,
    sK415: ( int > int > $o ) > int ).

thf(func_def_1350,type,
    sK416: num > num ).

thf(func_def_1351,type,
    sK417: int > int ).

thf(func_def_1352,type,
    sK418: ( int > real ) > set_real > set_real > set_int > set_int > int ).

thf(func_def_1353,type,
    sK419: ( int > real ) > ( real > int ) > set_real > set_real > real ).

thf(func_def_1354,type,
    sK420: set_real > ( real > real ) > real ).

thf(func_def_1355,type,
    sK421: set_real > set_real > ( real > int ) > set_int > set_int > real ).

thf(func_def_1356,type,
    sK422: set_int > ( int > real ) > int ).

thf(func_def_1357,type,
    sK423: set_real > ( real > real ) > ( real > int ) > ( int > real ) > real ).

thf(func_def_1358,type,
    sK424: set_int > ( int > real ) > set_int > ( real > int ) > int ).

thf(func_def_1359,type,
    sK425: ( real > real ) > real > real > real ).

thf(func_def_1360,type,
    sK426: list_nat > nat > nat ).

thf(func_def_1361,type,
    sK427: list_nat > nat > list_nat ).

thf(func_def_1362,type,
    sK428: vEBT_VEBT > nat > nat ).

thf(func_def_1363,type,
    sK429: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1364,type,
    sK430: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1365,type,
    sK431: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_1366,type,
    sK432: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1367,type,
    sK433: vEBT_VEBT > nat > $o ).

thf(func_def_1368,type,
    sK434: vEBT_VEBT > nat > $o ).

thf(func_def_1369,type,
    sK435: ( rat > rat ) > rat ).

thf(func_def_1370,type,
    sK436: ( rat > rat ) > rat ).

thf(func_def_1371,type,
    sK437: set_real > ( real > nat ) > set_real > real ).

thf(func_def_1372,type,
    sK438: set_real > ( real > nat ) > set_real > real ).

thf(func_def_1373,type,
    sK439: ( nat > nat ) > set_nat > nat ).

thf(func_def_1374,type,
    sK440: nat > ( nat > nat ) > set_nat > nat ).

thf(func_def_1375,type,
    sK441: rat > rat ).

thf(func_def_1376,type,
    sK442: real > int ).

thf(func_def_1377,type,
    sK443: ( nat > real ) > real > nat > nat ).

thf(func_def_1378,type,
    sK444: set_nat > nat > nat ).

thf(func_def_1379,type,
    sK445: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).

thf(func_def_1380,type,
    sK446: real > ( int > int > set_real ) > product_prod_int_int > int ).

thf(func_def_1381,type,
    sK447: real > ( int > int > set_real ) > product_prod_int_int > int ).

thf(func_def_1382,type,
    sK448: set_int > int ).

thf(func_def_1383,type,
    sK449: set_int > ( int > rat ) > int ).

thf(func_def_1384,type,
    sK450: real > real ).

thf(func_def_1385,type,
    sK451: set_int > ( int > nat ) > int ).

thf(func_def_1386,type,
    sK452: ( set_nat > real ) > ( set_nat > complex ) > set_set_nat > set_nat ).

thf(func_def_1387,type,
    sK453: set_real > set_real > ( real > nat ) > real ).

thf(func_def_1388,type,
    sK454: set_real > set_real > ( real > nat ) > real ).

thf(func_def_1389,type,
    sK455: ( complex > real ) > set_complex > complex ).

thf(func_def_1390,type,
    sK456: list_nat > nat > nat ).

thf(func_def_1391,type,
    sK457: $o > list_o > nat ).

thf(func_def_1392,type,
    sK458: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_1393,type,
    sK459: produc1908205239877642774nteger > code_integer ).

thf(func_def_1394,type,
    sK460: produc1908205239877642774nteger > code_integer ).

thf(func_def_1395,type,
    sK461: ( real > nat ) > set_real > real ).

thf(func_def_1396,type,
    sK462: set_int > ( int > code_integer ) > int ).

thf(func_def_1397,type,
    sK463: ( int > code_integer ) > code_integer > set_int > code_integer > int ).

thf(func_def_1398,type,
    sK464: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_1399,type,
    sK465: produc7773217078559923341nt_int > int ).

thf(func_def_1400,type,
    sK466: produc7773217078559923341nt_int > int ).

thf(func_def_1401,type,
    sK467: nat > real > real ).

thf(func_def_1402,type,
    sK468: set_complex > ( complex > rat ) > complex ).

thf(func_def_1403,type,
    sK469: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).

thf(func_def_1404,type,
    sK470: ( nat > real > real ) > nat > real > real ).

thf(func_def_1405,type,
    sK471: ( nat > real > real ) > nat > real > nat ).

thf(func_def_1406,type,
    sK472: real > ( real > real ) > ( nat > real > real ) > nat > real ).

thf(func_def_1407,type,
    sK473: int > nat > ( int > $o ) > int ).

thf(func_def_1408,type,
    sK474: ( set_rat > $o ) > set_rat ).

thf(func_def_1409,type,
    sK475: ( set_rat > $o ) > rat ).

thf(func_def_1410,type,
    sK476: nat > nat > nat > nat ).

thf(func_def_1411,type,
    sK477: nat > nat > nat > nat ).

thf(func_def_1412,type,
    sK478: set_int > ( int > rat ) > int ).

thf(func_def_1413,type,
    sK479: int > nat ).

thf(func_def_1414,type,
    sK480: nat > nat ).

thf(func_def_1415,type,
    sK481: int > nat ).

thf(func_def_1416,type,
    sK482: rat > int ).

thf(func_def_1417,type,
    sK483: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1418,type,
    sK484: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1419,type,
    sK485: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1420,type,
    sK486: set_nat > ( nat > int ) > set_nat > nat ).

thf(func_def_1421,type,
    sK487: nat > real > real ).

thf(func_def_1422,type,
    sK488: ( real > rat ) > set_real > real ).

thf(func_def_1423,type,
    sK489: real > nat ).

thf(func_def_1424,type,
    sK490: ( complex > real ) > ( complex > real ) > set_complex > complex ).

thf(func_def_1425,type,
    sK491: ( real > real ) > set_real > real ).

thf(func_def_1426,type,
    sK492: ( int > $o ) > list_int > int ).

thf(func_def_1427,type,
    sK493: ( int > real ) > set_int > int ).

thf(func_def_1428,type,
    sK494: ( int > rat ) > set_int > set_int > int ).

thf(func_def_1429,type,
    sK495: $o > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1430,type,
    sK496: $o > vEBT_VEBT > nat > nat ).

thf(func_def_1431,type,
    sK497: $o > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1432,type,
    sK498: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1433,type,
    sK499: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1434,type,
    sK500: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1435,type,
    sK501: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_1436,type,
    sK502: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_1437,type,
    sK503: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_1438,type,
    sK504: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_1439,type,
    sK505: vEBT_VEBT > $o > nat > product_prod_nat_nat ).

thf(func_def_1440,type,
    sK506: $o > vEBT_VEBT > nat > product_prod_nat_nat ).

thf(func_def_1441,type,
    sK507: $o > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1442,type,
    sK508: $o > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1443,type,
    sK509: nat > vEBT_VEBT > $o > $o ).

thf(func_def_1444,type,
    sK510: nat > vEBT_VEBT > $o > $o ).

thf(func_def_1445,type,
    sK511: nat > real > ( real > real ) > ( nat > real > real ) > real ).

thf(func_def_1446,type,
    sK512: ( nat > real > real ) > nat ).

thf(func_def_1447,type,
    sK513: ( nat > real > real ) > real ).

thf(func_def_1448,type,
    sK514: nat > nat ).

thf(func_def_1449,type,
    sK515: complex > list_complex > nat ).

thf(func_def_1450,type,
    sK516: ( int > int > set_set_nat ) > product_prod_int_int > set_nat > int ).

thf(func_def_1451,type,
    sK517: ( int > int > set_set_nat ) > product_prod_int_int > set_nat > int ).

thf(func_def_1452,type,
    sK518: ( nat > $o ) > nat ).

thf(func_def_1453,type,
    sK519: nat > ( nat > $o ) > nat ).

thf(func_def_1454,type,
    sK520: set_int > ( int > real ) > int > int ).

thf(func_def_1455,type,
    sK521: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1456,type,
    sK522: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1457,type,
    sK523: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_1458,type,
    sK524: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1459,type,
    sK525: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1460,type,
    sK526: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1461,type,
    sK527: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1462,type,
    sK528: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1463,type,
    sK529: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1464,type,
    sK530: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1465,type,
    sK531: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1466,type,
    sK532: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_1467,type,
    sK533: vEBT_VEBT > $o > nat > nat ).

thf(func_def_1468,type,
    sK534: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_1469,type,
    sK535: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1470,type,
    sK536: vEBT_VEBT > $o > nat > $o ).

thf(func_def_1471,type,
    sK537: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1472,type,
    sK538: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1473,type,
    sK539: vEBT_VEBT > nat ).

thf(func_def_1474,type,
    sK540: ( int > rat ) > ( set_int > $o ) > set_int ).

thf(func_def_1475,type,
    sK541: ( int > rat ) > ( set_int > $o ) > int ).

thf(func_def_1476,type,
    sK542: list_o > $o > $o ).

thf(func_def_1477,type,
    sK543: nat > vEBT_VEBT > nat > nat ).

thf(func_def_1478,type,
    sK544: rat > rat ).

thf(func_def_1479,type,
    sK545: nat > nat > ( nat > int ) > int > nat ).

thf(func_def_1480,type,
    sK546: ( nat > int ) > nat > nat > nat ).

thf(func_def_1481,type,
    sK547: set_complex > ( complex > nat ) > complex ).

thf(func_def_1482,type,
    sK548: real > real > ( real > real ) > real ).

thf(func_def_1483,type,
    sK549: ( num > rat ) > num ).

thf(func_def_1484,type,
    sK550: ( num > rat ) > num ).

thf(func_def_1485,type,
    sK551: ( real > real ) > real > real > real ).

thf(func_def_1486,type,
    sK552: int > int ).

thf(func_def_1487,type,
    sK553: complex > produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8923325533196201883nteger ).

thf(func_def_1488,type,
    sK554: complex > produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > code_integer > option6357759511663192854e_term ).

thf(func_def_1489,type,
    sK555: int > int > set_int > int ).

thf(func_def_1490,type,
    sK556: int > int > set_int > int ).

thf(func_def_1491,type,
    sK557: ( complex > complex ) > set_complex > ( complex > real ) > complex ).

thf(func_def_1492,type,
    sK558: produc9072475918466114483BT_nat > nat ).

thf(func_def_1493,type,
    sK559: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_1494,type,
    sK560: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_1495,type,
    sK561: produc9072475918466114483BT_nat > nat ).

thf(func_def_1496,type,
    sK562: produc9072475918466114483BT_nat > nat ).

thf(func_def_1497,type,
    sK563: produc9072475918466114483BT_nat > $o ).

thf(func_def_1498,type,
    sK564: produc9072475918466114483BT_nat > $o ).

thf(func_def_1499,type,
    sK565: produc9072475918466114483BT_nat > nat ).

thf(func_def_1500,type,
    sK566: produc9072475918466114483BT_nat > $o ).

thf(func_def_1501,type,
    sK567: produc9072475918466114483BT_nat > $o ).

thf(func_def_1502,type,
    sK568: produc9072475918466114483BT_nat > nat ).

thf(func_def_1503,type,
    sK569: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_1504,type,
    sK570: produc9072475918466114483BT_nat > nat ).

thf(func_def_1505,type,
    sK571: produc9072475918466114483BT_nat > nat ).

thf(func_def_1506,type,
    sK572: produc9072475918466114483BT_nat > nat ).

thf(func_def_1507,type,
    sK573: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_1508,type,
    sK574: produc9072475918466114483BT_nat > nat ).

thf(func_def_1509,type,
    sK575: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_1510,type,
    sK576: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_1511,type,
    sK577: produc9072475918466114483BT_nat > nat ).

thf(func_def_1512,type,
    sK578: produc9072475918466114483BT_nat > $o ).

thf(func_def_1513,type,
    sK579: produc9072475918466114483BT_nat > $o ).

thf(func_def_1514,type,
    sK580: produc9072475918466114483BT_nat > nat ).

thf(func_def_1515,type,
    sK581: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_1516,type,
    sK582: produc9072475918466114483BT_nat > nat ).

thf(func_def_1517,type,
    sK583: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_1518,type,
    sK584: produc9072475918466114483BT_nat > nat ).

thf(func_def_1519,type,
    sK585: set_int > int > ( int > $o ) > int ).

thf(func_def_1520,type,
    sK586: int > set_int > int > int ).

thf(func_def_1521,type,
    sK587: int > set_int > int > int ).

thf(func_def_1522,type,
    sK588: set_int > ( int > $o ) > int > int ).

thf(func_def_1523,type,
    sK589: ( nat > rat ) > ( set_nat > $o ) > set_nat ).

thf(func_def_1524,type,
    sK590: ( nat > rat ) > ( set_nat > $o ) > nat ).

thf(func_def_1525,type,
    sK591: product_prod_int_int > int ).

thf(func_def_1526,type,
    sK592: product_prod_int_int > int ).

thf(func_def_1527,type,
    sK593: ( real > complex ) > ( real > complex ) > set_real > real ).

thf(func_def_1528,type,
    sK594: ( real > complex ) > set_real > set_real > real ).

thf(func_def_1529,type,
    sK595: vEBT_VEBT > $o ).

thf(func_def_1530,type,
    sK596: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1531,type,
    sK597: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1532,type,
    sK598: vEBT_VEBT > nat ).

thf(func_def_1533,type,
    sK599: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1534,type,
    sK600: vEBT_VEBT > nat ).

thf(func_def_1535,type,
    sK601: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1536,type,
    sK602: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1537,type,
    sK603: vEBT_VEBT > $o ).

thf(func_def_1538,type,
    sK604: nat > nat > nat ).

thf(func_def_1539,type,
    sK605: ( rat > real ) > rat ).

thf(func_def_1540,type,
    sK606: ( rat > real ) > rat ).

thf(func_def_1541,type,
    sK607: int > nat ).

thf(func_def_1542,type,
    sK608: ( num > rat ) > num ).

thf(func_def_1543,type,
    sK609: ( num > rat ) > num ).

thf(func_def_1544,type,
    sK610: ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1545,type,
    sK611: ( int > $o ) > int > set_int > int ).

thf(func_def_1546,type,
    sK612: int > int > set_int > int ).

thf(func_def_1547,type,
    sK613: int > int > set_int > int ).

thf(func_def_1548,type,
    sK614: int > set_int > ( int > $o ) > int ).

thf(func_def_1549,type,
    sK615: rat > int ).

thf(func_def_1550,type,
    sK616: ( nat > real ) > nat ).

thf(func_def_1551,type,
    sK617: real > ( nat > real ) > real ).

thf(func_def_1552,type,
    sK618: real > ( nat > real ) > nat ).

thf(func_def_1553,type,
    sK619: set_nat > set_nat > nat ).

thf(func_def_1554,type,
    sK620: rat > rat ).

thf(func_def_1555,type,
    sK621: ( num > real ) > num ).

thf(func_def_1556,type,
    sK622: ( num > real ) > num ).

thf(func_def_1557,type,
    sK623: ( int > int > $o ) > product_prod_int_int > int ).

thf(func_def_1558,type,
    sK624: ( int > int > $o ) > product_prod_int_int > int ).

thf(func_def_1559,type,
    sK625: ( real > real ) > set_real > real ).

thf(func_def_1560,type,
    sK626: ( int > real ) > ( int > real ) > set_int > int ).

thf(func_def_1561,type,
    sK627: set_complex > ( complex > real ) > ( complex > real ) > complex ).

thf(func_def_1562,type,
    sK628: real > real ).

thf(func_def_1563,type,
    sK629: ( int > $o ) > list_int > nat ).

thf(func_def_1564,type,
    sK630: ( int > $o ) > list_int > int ).

thf(func_def_1565,type,
    sK631: ( rat > rat > $o ) > rat ).

thf(func_def_1566,type,
    sK632: ( rat > rat > $o ) > rat ).

thf(func_def_1567,type,
    sK633: ( rat > rat > $o ) > rat ).

thf(func_def_1568,type,
    sK634: ( rat > rat > $o ) > rat ).

thf(func_def_1569,type,
    sK635: ( rat > rat > $o ) > rat ).

thf(func_def_1570,type,
    sK636: list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1571,type,
    sK637: ( real > real ) > real > real > real ).

thf(func_def_1572,type,
    sK638: ( real > real ) > real > real > real ).

thf(func_def_1573,type,
    sK639: real > real > ( real > real ) > real ).

thf(func_def_1574,type,
    sK640: set_int > ( int > nat ) > int ).

thf(func_def_1575,type,
    sK641: set_complex > ( complex > nat ) > complex ).

thf(func_def_1576,type,
    sK642: set_nat > ( set_nat > $o ) > nat ).

thf(func_def_1577,type,
    sK643: set_nat > ( set_nat > $o ) > set_nat ).

thf(func_def_1578,type,
    sK644: ( rat > int ) > rat ).

thf(func_def_1579,type,
    sK645: ( rat > int ) > rat ).

thf(func_def_1580,type,
    sK646: ( set_real > $o ) > set_real > set_real ).

thf(func_def_1581,type,
    sK647: ( int > real ) > set_int > int ).

thf(func_def_1582,type,
    sK648: ( int > real ) > set_int > int ).

thf(func_def_1583,type,
    sK649: ( option_num > option_num > $o ) > option_num > option_num > num ).

thf(func_def_1584,type,
    sK650: ( option_num > option_num > $o ) > option_num > option_num > num ).

thf(func_def_1585,type,
    sK651: ( rat > nat ) > rat ).

thf(func_def_1586,type,
    sK652: ( rat > nat ) > rat ).

thf(func_def_1587,type,
    sK653: ( real > $o ) > real > real ).

thf(func_def_1588,type,
    sK654: ( real > $o ) > real > real ).

thf(func_def_1589,type,
    sK655: real > ( real > $o ) > real ).

thf(func_def_1590,type,
    sK656: real > ( real > $o ) > real ).

thf(func_def_1591,type,
    sK657: nat > vEBT_VEBT > nat ).

thf(func_def_1592,type,
    sK658: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1593,type,
    sK659: nat > vEBT_VEBT > nat ).

thf(func_def_1594,type,
    sK660: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1595,type,
    sK661: nat > vEBT_VEBT > nat ).

thf(func_def_1596,type,
    sK662: nat > vEBT_VEBT > nat ).

thf(func_def_1597,type,
    sK663: nat > vEBT_VEBT > nat ).

thf(func_def_1598,type,
    sK664: nat > vEBT_VEBT > nat ).

thf(func_def_1599,type,
    sK665: nat > vEBT_VEBT > nat ).

thf(func_def_1600,type,
    sK666: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1601,type,
    sK667: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1602,type,
    sK668: nat > vEBT_VEBT > nat ).

thf(func_def_1603,type,
    sK669: vEBT_VEBT > nat > nat ).

thf(func_def_1604,type,
    sK670: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1605,type,
    sK671: vEBT_VEBT > nat > nat ).

thf(func_def_1606,type,
    sK672: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1607,type,
    sK673: vEBT_VEBT > nat > nat ).

thf(func_def_1608,type,
    sK674: vEBT_VEBT > nat > nat ).

thf(func_def_1609,type,
    sK675: vEBT_VEBT > nat > nat ).

thf(func_def_1610,type,
    sK676: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1611,type,
    sK677: vEBT_VEBT > nat > nat ).

thf(func_def_1612,type,
    sK678: vEBT_VEBT > nat > nat ).

thf(func_def_1613,type,
    sK679: vEBT_VEBT > nat > nat ).

thf(func_def_1614,type,
    sK680: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1615,type,
    sK681: nat > list_VEBT_VEBT > nat ).

thf(func_def_1616,type,
    sK682: nat > list_VEBT_VEBT > nat ).

thf(func_def_1617,type,
    sK683: vEBT_VEBT > $o ).

thf(func_def_1618,type,
    sK684: vEBT_VEBT > $o ).

thf(func_def_1619,type,
    sK685: ( int > int > set_set_nat ) > set_nat > product_prod_int_int > int ).

thf(func_def_1620,type,
    sK686: ( int > int > set_set_nat ) > set_nat > product_prod_int_int > int ).

thf(func_def_1621,type,
    sK687: ( set_nat > $o ) > ( nat > nat ) > set_nat ).

thf(func_def_1622,type,
    sK688: ( set_nat > $o ) > ( nat > nat ) > nat ).

thf(func_def_1623,type,
    sK689: ( int > rat ) > ( int > rat ) > set_int > ( rat > rat > $o ) > int ).

thf(func_def_1624,type,
    sK690: ( rat > rat > $o ) > rat ).

thf(func_def_1625,type,
    sK691: ( rat > rat > $o ) > rat ).

thf(func_def_1626,type,
    sK692: ( rat > rat > $o ) > rat ).

thf(func_def_1627,type,
    sK693: ( rat > rat > $o ) > rat ).

thf(func_def_1628,type,
    sK694: ( nat > num ) > nat ).

thf(func_def_1629,type,
    sK695: ( nat > num ) > nat ).

thf(func_def_1630,type,
    sK696: nat > vEBT_VEBT > $o ).

thf(func_def_1631,type,
    sK697: nat > vEBT_VEBT > $o ).

thf(func_def_1632,type,
    sK698: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1633,type,
    sK699: vEBT_VEBT > nat > nat ).

thf(func_def_1634,type,
    sK700: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1635,type,
    sK701: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_1636,type,
    sK702: ( nat > rat ) > nat ).

thf(func_def_1637,type,
    sK703: ( nat > real ) > nat ).

thf(func_def_1638,type,
    sK704: ( nat > real ) > nat ).

thf(func_def_1639,type,
    sK705: nat > ( nat > $o ) > nat ).

thf(func_def_1640,type,
    sK706: nat > ( nat > $o ) > nat ).

thf(func_def_1641,type,
    sK707: ( rat > rat > $o ) > set_complex > ( complex > rat ) > ( complex > rat ) > complex ).

thf(func_def_1642,type,
    sK708: ( rat > rat > $o ) > rat ).

thf(func_def_1643,type,
    sK709: ( rat > rat > $o ) > rat ).

thf(func_def_1644,type,
    sK710: ( rat > rat > $o ) > rat ).

thf(func_def_1645,type,
    sK711: ( rat > rat > $o ) > rat ).

thf(func_def_1646,type,
    sK712: real > int ).

thf(func_def_1647,type,
    sK713: produc7036089656553540234on_num > num ).

thf(func_def_1648,type,
    sK714: produc7036089656553540234on_num > num > num > $o ).

thf(func_def_1649,type,
    sK715: produc7036089656553540234on_num > num > num > $o ).

thf(func_def_1650,type,
    sK716: produc7036089656553540234on_num > num ).

thf(func_def_1651,type,
    sK717: produc7036089656553540234on_num > num ).

thf(func_def_1652,type,
    sK718: produc7036089656553540234on_num > num > num > $o ).

thf(func_def_1653,type,
    sK719: produc7036089656553540234on_num > option_num ).

thf(func_def_1654,type,
    sK720: set_set_nat > ( set_set_nat > $o ) > set_nat ).

thf(func_def_1655,type,
    sK721: set_set_nat > ( set_set_nat > $o ) > set_set_nat ).

thf(func_def_1656,type,
    sK722: set_nat > set_nat > ( nat > rat ) > nat ).

thf(func_def_1657,type,
    sK723: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1658,type,
    sK724: vEBT_VEBT > nat ).

thf(func_def_1659,type,
    sK725: vEBT_VEBT > nat ).

thf(func_def_1660,type,
    sK726: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1661,type,
    sK727: vEBT_VEBT > nat ).

thf(func_def_1662,type,
    sK728: vEBT_VEBT > nat ).

thf(func_def_1663,type,
    sK729: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1664,type,
    sK730: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1665,type,
    sK731: vEBT_VEBT > $o ).

thf(func_def_1666,type,
    sK732: vEBT_VEBT > $o ).

thf(func_def_1667,type,
    sK733: set_nat > ( set_nat > $o ) > nat ).

thf(func_def_1668,type,
    sK734: set_nat > ( set_nat > $o ) > set_nat ).

thf(func_def_1669,type,
    sK735: vEBT_VEBT > nat > nat ).

thf(func_def_1670,type,
    sK736: vEBT_VEBT > nat > nat ).

thf(func_def_1671,type,
    sK737: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1672,type,
    sK738: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1673,type,
    sK739: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1674,type,
    sK740: vEBT_VEBT > nat > nat ).

thf(func_def_1675,type,
    sK741: vEBT_VEBT > nat > nat ).

thf(func_def_1676,type,
    sK742: vEBT_VEBT > nat > nat ).

thf(func_def_1677,type,
    sK743: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1678,type,
    sK744: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1679,type,
    sK745: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1680,type,
    sK746: vEBT_VEBT > nat > nat ).

thf(func_def_1681,type,
    sK747: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1682,type,
    sK748: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1683,type,
    sK749: vEBT_VEBT > $o ).

thf(func_def_1684,type,
    sK750: vEBT_VEBT > $o ).

thf(func_def_1685,type,
    sK751: int > int > int ).

thf(func_def_1686,type,
    sK752: int > int > int ).

thf(func_def_1687,type,
    sK753: set_set_int > set_int ).

thf(func_def_1688,type,
    sK754: nat > nat > nat ).

thf(func_def_1689,type,
    sK755: set_rat > rat ).

thf(func_def_1690,type,
    sK756: ( int > rat ) > set_int > int ).

thf(func_def_1691,type,
    sK757: real > real > ( real > real ) > real ).

thf(func_def_1692,type,
    sK758: real > ( real > real ) > ( real > real ) > real > real ).

thf(func_def_1693,type,
    sK759: ( real > real ) > ( real > real ) > ( real > real ) > real > ( real > real ) > real > real ).

thf(func_def_1694,type,
    sK760: real > real > ( real > real ) > real ).

thf(func_def_1695,type,
    sK761: real > real > ( real > real ) > ( real > real ) > real ).

thf(func_def_1696,type,
    sK762: set_nat > ( nat > rat ) > nat ).

thf(func_def_1697,type,
    sK763: set_nat > rat > rat > ( nat > rat ) > nat ).

thf(func_def_1698,type,
    sK764: ( complex > real ) > set_complex > complex ).

thf(func_def_1699,type,
    sK765: ( set_num > $o ) > num ).

thf(func_def_1700,type,
    sK766: ( set_num > $o ) > set_num ).

thf(func_def_1701,type,
    sK767: rat > int ).

thf(func_def_1702,type,
    sK768: produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > int > produc8923325533196201883nteger ).

thf(func_def_1703,type,
    sK769: produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > int > code_integer > option6357759511663192854e_term ).

thf(func_def_1704,type,
    sK770: ( num > rat ) > num ).

thf(func_def_1705,type,
    sK771: ( num > rat ) > num ).

thf(func_def_1706,type,
    sK772: ( rat > int ) > rat ).

thf(func_def_1707,type,
    sK773: ( rat > int ) > rat ).

thf(func_def_1708,type,
    sK774: rat > int ).

thf(func_def_1709,type,
    sK775: ( nat > real ) > nat ).

thf(func_def_1710,type,
    sK776: ( nat > real ) > nat ).

thf(func_def_1711,type,
    sK777: ( num > rat ) > num ).

thf(func_def_1712,type,
    sK778: ( num > rat ) > num ).

thf(func_def_1713,type,
    sK779: ( real > $o ) > real ).

thf(func_def_1714,type,
    sK780: ( real > $o ) > real ).

thf(func_def_1715,type,
    sK781: ( real > $o ) > nat ).

thf(func_def_1716,type,
    sK782: ( $o > $o ) > list_o > nat ).

thf(func_def_1717,type,
    sK783: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_1718,type,
    sK784: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_1719,type,
    sK785: list_VEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_1720,type,
    sK786: set_nat > nat ).

thf(func_def_1721,type,
    sK787: product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).

thf(func_def_1722,type,
    sK788: product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > nat ).

thf(func_def_1723,type,
    sK789: ( int > nat ) > ( int > nat ) > set_int > int ).

thf(func_def_1724,type,
    sK790: ( complex > int ) > set_complex > complex ).

thf(func_def_1725,type,
    sK791: set_rat > rat ).

thf(func_def_1726,type,
    sK792: ( complex > int ) > ( complex > int ) > set_complex > complex ).

thf(func_def_1727,type,
    sK793: ( rat > rat > $o ) > ( nat > rat ) > set_nat > ( nat > rat ) > nat ).

thf(func_def_1728,type,
    sK794: ( rat > rat > $o ) > rat ).

thf(func_def_1729,type,
    sK795: ( rat > rat > $o ) > rat ).

thf(func_def_1730,type,
    sK796: ( rat > rat > $o ) > rat ).

thf(func_def_1731,type,
    sK797: ( rat > rat > $o ) > rat ).

thf(func_def_1732,type,
    sK798: option_nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1733,type,
    sK799: option_nat > vEBT_VEBT > nat ).

thf(func_def_1734,type,
    sK800: option_nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1735,type,
    sK801: vEBT_VEBT > option_nat > $o ).

thf(func_def_1736,type,
    sK802: vEBT_VEBT > option_nat > $o ).

thf(func_def_1737,type,
    sK803: option_nat > vEBT_VEBT > nat ).

thf(func_def_1738,type,
    sK804: option_nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1739,type,
    sK805: option_nat > vEBT_VEBT > nat ).

thf(func_def_1740,type,
    sK806: option_nat > vEBT_VEBT > nat ).

thf(func_def_1741,type,
    sK807: option_nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1742,type,
    sK808: set_nat > ( set_nat > $o ) > set_nat ).

thf(func_def_1743,type,
    sK809: int > nat ).

thf(func_def_1744,type,
    sK810: int > nat ).

thf(func_def_1745,type,
    sK811: ( complex > real ) > ( complex > real ) > ( real > real > $o ) > set_complex > complex ).

thf(func_def_1746,type,
    sK812: ( real > real > $o ) > real ).

thf(func_def_1747,type,
    sK813: ( real > real > $o ) > real ).

thf(func_def_1748,type,
    sK814: ( real > real > $o ) > real ).

thf(func_def_1749,type,
    sK815: ( real > real > $o ) > real ).

thf(func_def_1750,type,
    sK816: ( set_complex > $o ) > ( complex > rat ) > set_complex ).

thf(func_def_1751,type,
    sK817: ( set_complex > $o ) > ( complex > rat ) > complex ).

thf(func_def_1752,type,
    sK818: int > nat ).

thf(func_def_1753,type,
    sK819: ( list_int > $o ) > list_int ).

thf(func_def_1754,type,
    sK820: ( complex > nat ) > set_complex > complex ).

thf(func_def_1755,type,
    sK821: nat > nat > nat ).

thf(func_def_1756,type,
    sK822: nat > nat > nat ).

thf(func_def_1757,type,
    sK823: nat > nat > nat ).

thf(func_def_1758,type,
    sK824: ( int > rat ) > set_int > ( int > rat ) > int ).

thf(func_def_1759,type,
    sK825: ( nat > real ) > real > nat ).

thf(func_def_1760,type,
    sK826: produc7773217078559923341nt_int > int ).

thf(func_def_1761,type,
    sK827: produc7773217078559923341nt_int > int ).

thf(func_def_1762,type,
    sK828: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_1763,type,
    sK829: ( set_num > $o ) > num ).

thf(func_def_1764,type,
    sK830: ( set_num > $o ) > set_num ).

thf(func_def_1765,type,
    sK831: ( rat > real ) > rat ).

thf(func_def_1766,type,
    sK832: ( rat > real ) > rat ).

thf(func_def_1767,type,
    sK833: ( set_nat > $o ) > set_nat > set_nat ).

thf(func_def_1768,type,
    sK834: ( rat > num ) > rat ).

thf(func_def_1769,type,
    sK835: ( rat > num ) > rat ).

thf(func_def_1770,type,
    sK836: ( rat > int ) > rat ).

thf(func_def_1771,type,
    sK837: ( rat > int ) > rat ).

thf(func_def_1772,type,
    sK838: real > ( real > real ) > real ).

thf(func_def_1773,type,
    sK839: ( complex > nat ) > ( complex > nat ) > set_complex > complex ).

thf(func_def_1774,type,
    sK840: ( complex > nat ) > set_complex > set_complex > complex ).

thf(func_def_1775,type,
    sK841: ( int > rat ) > set_int > int ).

thf(func_def_1776,type,
    sK842: ( int > rat ) > ( int > rat ) > set_int > set_int > ( int > int ) > int ).

thf(func_def_1777,type,
    sK843: int > ( int > $o ) > int ).

thf(func_def_1778,type,
    sK844: int > ( int > $o ) > int ).

thf(func_def_1779,type,
    sK845: int > ( int > $o ) > int ).

thf(func_def_1780,type,
    sK846: int > ( int > $o ) > int ).

thf(func_def_1781,type,
    sK847: int > int > int > int ).

thf(func_def_1782,type,
    sK848: code_integer > code_integer > ( real > code_integer ) > set_real > real ).

thf(func_def_1783,type,
    sK849: ( real > code_integer ) > set_real > real ).

thf(func_def_1784,type,
    sK850: ( num > num ) > num ).

thf(func_def_1785,type,
    sK851: ( num > num ) > num ).

thf(func_def_1786,type,
    sK852: list_o > $o > $o ).

thf(func_def_1787,type,
    sK853: ( nat > $o ) > nat ).

thf(func_def_1788,type,
    sK854: ( nat > rat ) > nat ).

thf(func_def_1789,type,
    sK855: nat > nat ).

thf(func_def_1790,type,
    sK856: ( real > nat ) > set_real > real ).

thf(func_def_1791,type,
    sK857: ( real > nat ) > set_real > real ).

thf(func_def_1792,type,
    sK858: ( int > rat ) > int ).

thf(func_def_1793,type,
    sK859: ( int > rat ) > int ).

thf(func_def_1794,type,
    sK860: list_VEBT_VEBT > set_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1795,type,
    sK861: set_rat > rat ).

thf(func_def_1796,type,
    sK862: int > int ).

thf(func_def_1797,type,
    sK863: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_1798,type,
    sK864: filter_nat > nat ).

thf(func_def_1799,type,
    sK865: set_real > set_real > ( real > int ) > real ).

thf(func_def_1800,type,
    sK866: set_real > ( real > int ) > set_real > real ).

thf(func_def_1801,type,
    sK867: int > list_int > int ).

thf(func_def_1802,type,
    sK868: ( nat > rat ) > set_nat > nat ).

thf(func_def_1803,type,
    sK869: ( nat > rat ) > set_nat > nat ).

thf(func_def_1804,type,
    sK870: nat > nat > ( nat > $o ) > nat ).

thf(func_def_1805,type,
    sK871: nat > nat > ( nat > $o ) > nat ).

thf(func_def_1806,type,
    sK872: set_nat > ( nat > rat ) > ( nat > nat ) > ( nat > rat ) > set_nat > nat ).

thf(func_def_1807,type,
    sK873: ( nat > rat ) > set_nat > nat ).

thf(func_def_1808,type,
    sK874: ( complex > num ) > ( set_complex > $o ) > complex ).

thf(func_def_1809,type,
    sK875: ( complex > num ) > ( set_complex > $o ) > set_complex ).

thf(func_def_1810,type,
    sK876: int > int ).

thf(func_def_1811,type,
    sK877: ( rat > int ) > rat ).

thf(func_def_1812,type,
    sK878: ( rat > int ) > rat ).

thf(func_def_1813,type,
    sK879: vEBT_VEBT > nat > nat ).

thf(func_def_1814,type,
    sK880: vEBT_VEBT > nat > nat ).

thf(func_def_1815,type,
    sK881: vEBT_VEBT > nat > nat ).

thf(func_def_1816,type,
    sK882: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1817,type,
    sK883: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1818,type,
    sK884: nat > vEBT_VEBT > $o ).

thf(func_def_1819,type,
    sK885: nat > vEBT_VEBT > $o ).

thf(func_def_1820,type,
    sK886: code_integer > code_integer ).

thf(func_def_1821,type,
    sK887: set_int > set_int > int ).

thf(func_def_1822,type,
    sK888: ( rat > nat ) > rat ).

thf(func_def_1823,type,
    sK889: ( rat > nat ) > rat ).

thf(func_def_1824,type,
    sK890: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1825,type,
    sK891: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_1826,type,
    sK892: vEBT_VEBT > nat > nat ).

thf(func_def_1827,type,
    sK893: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1828,type,
    sK894: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1829,type,
    sK895: vEBT_VEBT > $o ).

thf(func_def_1830,type,
    sK896: vEBT_VEBT > $o ).

thf(func_def_1831,type,
    sK897: list_int > set_int > int ).

thf(func_def_1832,type,
    sK898: rat > rat > nat ).

thf(func_def_1833,type,
    sK899: ( nat > complex ) > set_nat > set_nat > nat ).

thf(func_def_1834,type,
    sK900: set_int > ( int > complex ) > ( int > complex ) > ( complex > complex > $o ) > int ).

thf(func_def_1835,type,
    sK901: ( complex > complex > $o ) > complex ).

thf(func_def_1836,type,
    sK902: ( complex > complex > $o ) > complex ).

thf(func_def_1837,type,
    sK903: ( complex > complex > $o ) > complex ).

thf(func_def_1838,type,
    sK904: ( complex > complex > $o ) > complex ).

thf(func_def_1839,type,
    sK905: nat > nat ).

thf(func_def_1840,type,
    sK906: nat > nat > nat ).

thf(func_def_1841,type,
    sK907: ( rat > rat ) > rat ).

thf(func_def_1842,type,
    sK908: ( rat > rat ) > rat ).

thf(func_def_1843,type,
    sK909: vEBT_VEBT > nat > $o ).

thf(func_def_1844,type,
    sK910: vEBT_VEBT > nat > $o ).

thf(func_def_1845,type,
    sK911: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1846,type,
    sK912: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1847,type,
    sK913: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1848,type,
    sK914: nat > vEBT_VEBT > nat ).

thf(func_def_1849,type,
    sK915: nat > vEBT_VEBT > nat ).

thf(func_def_1850,type,
    sK916: nat > vEBT_VEBT > nat ).

thf(func_def_1851,type,
    sK917: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1852,type,
    sK918: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1853,type,
    sK919: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1854,type,
    sK920: vEBT_VEBT > nat ).

thf(func_def_1855,type,
    sK921: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1856,type,
    sK922: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1857,type,
    sK923: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1858,type,
    sK924: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1859,type,
    sK925: nat > list_int ).

thf(func_def_1860,type,
    sK926: nat > ( nat > $o ) > nat ).

thf(func_def_1861,type,
    sK927: nat > nat > nat > nat ).

thf(func_def_1862,type,
    sK928: nat > nat > nat > nat ).

thf(func_def_1863,type,
    sK929: set_real > ( real > nat ) > real ).

thf(func_def_1864,type,
    sK930: set_complex > ( complex > complex ) > complex ).

thf(func_def_1865,type,
    sK931: ( rat > rat ) > rat ).

thf(func_def_1866,type,
    sK932: ( rat > rat ) > rat ).

thf(func_def_1867,type,
    sK933: set_nat > ( nat > int ) > nat ).

thf(func_def_1868,type,
    sK934: ( nat > set_int ) > nat ).

thf(func_def_1869,type,
    sK935: ( nat > $o ) > nat > nat ).

thf(func_def_1870,type,
    sK936: ( nat > $o ) > nat > nat ).

thf(func_def_1871,type,
    sK937: set_complex > complex > ( complex > rat ) > complex ).

thf(func_def_1872,type,
    sK938: real > nat ).

thf(func_def_1873,type,
    sK939: real > nat ).

thf(func_def_1874,type,
    sK940: nat > nat ).

thf(func_def_1875,type,
    sK941: vEBT_VEBT > $o ).

thf(func_def_1876,type,
    sK942: vEBT_VEBT > $o ).

thf(func_def_1877,type,
    sK943: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_1878,type,
    sK944: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_1879,type,
    sK945: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).

thf(func_def_1880,type,
    sK946: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_1881,type,
    sK947: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).

thf(func_def_1882,type,
    sK948: nat > option_nat > vEBT_VEBT > $o ).

thf(func_def_1883,type,
    sK949: nat > option_nat > vEBT_VEBT > $o ).

thf(func_def_1884,type,
    sK950: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1885,type,
    sK951: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1886,type,
    sK952: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1887,type,
    sK953: vEBT_VEBT > nat ).

thf(func_def_1888,type,
    sK954: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1889,type,
    sK955: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1890,type,
    sK956: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1891,type,
    sK957: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_1892,type,
    sK958: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1893,type,
    sK959: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_1894,type,
    sK960: rat > rat > rat ).

thf(func_def_1895,type,
    sK961: set_real > ( real > rat ) > real ).

thf(func_def_1896,type,
    sK962: set_real > ( real > rat ) > real ).

thf(func_def_1897,type,
    sK963: ( nat > nat ) > set_nat > nat ).

thf(func_def_1898,type,
    sK964: ( set_int > $o ) > set_int > int ).

thf(func_def_1899,type,
    sK965: ( set_int > $o ) > set_int > set_int ).

thf(func_def_1900,type,
    sK966: ( int > int > $o ) > int ).

thf(func_def_1901,type,
    sK967: ( int > int > $o ) > int ).

thf(func_def_1902,type,
    sK968: ( int > int > $o ) > int ).

thf(func_def_1903,type,
    sK969: ( int > int > $o ) > int ).

thf(func_def_1904,type,
    sK970: ( nat > rat ) > set_nat > nat ).

thf(func_def_1905,type,
    sK971: ( nat > $o ) > nat ).

thf(func_def_1906,type,
    sK972: ( nat > rat ) > set_nat > nat ).

thf(func_def_1907,type,
    sK973: list_o > ( $o > $o ) > nat ).

thf(func_def_1908,type,
    sK974: list_o > ( $o > $o ) > $o ).

thf(func_def_1909,type,
    sK975: ( set_real > $o ) > set_real ).

thf(func_def_1910,type,
    sK976: ( nat > real ) > nat ).

thf(func_def_1911,type,
    sK977: ( nat > real ) > nat ).

thf(func_def_1912,type,
    sK978: real > real > nat ).

thf(func_def_1913,type,
    sK979: nat > list_nat ).

thf(func_def_1914,type,
    sK980: nat > nat ).

thf(func_def_1915,type,
    sK981: set_int > ( int > real ) > int ).

thf(func_def_1916,type,
    sK982: ( nat > real ) > nat ).

thf(func_def_1917,type,
    sK983: ( nat > real ) > nat ).

thf(func_def_1918,type,
    sK984: nat > ( nat > int > $o ) > list_int ).

thf(func_def_1919,type,
    sK985: nat > ( nat > int > $o ) > nat ).

thf(func_def_1920,type,
    sK986: nat > ( nat > int > $o ) > int ).

thf(func_def_1921,type,
    sK987: list_int > nat > ( nat > int > $o ) > nat ).

thf(func_def_1922,type,
    sK988: ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1923,type,
    sK989: rat > rat > rat > rat ).

thf(func_def_1924,type,
    sK990: ( nat > $o ) > nat > nat ).

thf(func_def_1925,type,
    sK991: ( nat > $o ) > nat > nat ).

thf(func_def_1926,type,
    sK992: ( nat > num ) > nat ).

thf(func_def_1927,type,
    sK993: real > ( real > real ) > real ).

thf(func_def_1928,type,
    sK994: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_1929,type,
    sK995: ( int > int > $o ) > product_prod_int_int > int ).

thf(func_def_1930,type,
    sK996: ( int > int > $o ) > product_prod_int_int > int ).

thf(func_def_1931,type,
    sK997: real > ( nat > real ) > real ).

thf(func_def_1932,type,
    sK998: ( int > $o ) > ( int > $o ) > int ).

thf(func_def_1933,type,
    sK999: code_integer > code_integer > code_integer ).

thf(func_def_1934,type,
    sK1000: rat > rat ).

thf(func_def_1935,type,
    sK1001: code_integer > code_integer > code_integer ).

thf(func_def_1936,type,
    sK1002: option_nat > nat ).

thf(func_def_1937,type,
    sK1003: nat > nat > nat ).

thf(func_def_1938,type,
    sK1004: nat > vEBT_VEBT > $o ).

thf(func_def_1939,type,
    sK1005: nat > vEBT_VEBT > $o ).

thf(func_def_1940,type,
    sK1006: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1941,type,
    sK1007: vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_1942,type,
    sK1008: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1943,type,
    sK1009: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1944,type,
    sK1010: nat > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_1945,type,
    sK1011: nat > vEBT_VEBT > nat ).

thf(func_def_1946,type,
    sK1012: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1947,type,
    sK1013: ( nat > real ) > nat ).

thf(func_def_1948,type,
    sK1014: ( nat > real ) > nat ).

thf(func_def_1949,type,
    sK1015: ( rat > rat ) > rat ).

thf(func_def_1950,type,
    sK1016: ( rat > rat ) > rat ).

thf(func_def_1951,type,
    sK1017: complex > real ).

thf(func_def_1952,type,
    sK1018: complex > real ).

thf(func_def_1953,type,
    sK1019: list_set_nat > set_nat > nat ).

thf(func_def_1954,type,
    sK1020: ( nat > num ) > nat ).

thf(func_def_1955,type,
    sK1021: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1956,type,
    sK1022: vEBT_VEBT > nat > nat ).

thf(func_def_1957,type,
    sK1023: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1958,type,
    sK1024: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1959,type,
    sK1025: vEBT_VEBT > nat > nat ).

thf(func_def_1960,type,
    sK1026: vEBT_VEBT > nat > nat ).

thf(func_def_1961,type,
    sK1027: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1962,type,
    sK1028: vEBT_VEBT > nat > nat ).

thf(func_def_1963,type,
    sK1029: vEBT_VEBT > nat > nat ).

thf(func_def_1964,type,
    sK1030: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_1965,type,
    sK1031: vEBT_VEBT > nat > nat ).

thf(func_def_1966,type,
    sK1032: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_1967,type,
    sK1033: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1968,type,
    sK1034: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_1969,type,
    sK1035: nat > vEBT_VEBT > $o ).

thf(func_def_1970,type,
    sK1036: nat > vEBT_VEBT > $o ).

thf(func_def_1971,type,
    sK1037: set_nat > ( nat > nat ) > nat ).

thf(func_def_1972,type,
    sK1038: int > set_int > int > int ).

thf(func_def_1973,type,
    sK1039: int > set_int > int > int ).

thf(func_def_1974,type,
    sK1040: set_real > ( real > int ) > set_real > real ).

thf(func_def_1975,type,
    sK1041: ( real > int ) > set_real > set_real > real ).

thf(func_def_1976,type,
    sK1042: ( real > int ) > real ).

thf(func_def_1977,type,
    sK1043: ( real > int ) > real ).

thf(func_def_1978,type,
    sK1044: rat > rat ).

thf(func_def_1979,type,
    sK1045: set_real > ( real > rat ) > set_real > real ).

thf(func_def_1980,type,
    sK1046: set_real > set_real > ( real > rat ) > real ).

thf(func_def_1981,type,
    sK1047: nat > nat > nat ).

thf(func_def_1982,type,
    sK1048: ( int > $o ) > set_int > int > int ).

thf(func_def_1983,type,
    sK1049: int > set_int > int > int ).

thf(func_def_1984,type,
    sK1050: int > set_int > int > int ).

thf(func_def_1985,type,
    sK1051: int > ( int > $o ) > set_int > int ).

thf(func_def_1986,type,
    sK1052: int > int > int > int ).

thf(func_def_1987,type,
    sK1053: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1988,type,
    sK1054: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1989,type,
    sK1055: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_1990,type,
    sK1056: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1991,type,
    sK1057: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1992,type,
    sK1058: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_1993,type,
    sK1059: set_real > ( real > real ) > set_real > real ).

thf(func_def_1994,type,
    sK1060: set_rat > rat > rat ).

thf(func_def_1995,type,
    sK1061: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_1996,type,
    sK1062: produc2285326912895808259nt_int > product_prod_int_int ).

thf(func_def_1997,type,
    sK1063: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_1998,type,
    sK1064: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_1999,type,
    sK1065: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2000,type,
    sK1066: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_2001,type,
    sK1067: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_2002,type,
    sK1068: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_2003,type,
    sK1069: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_2004,type,
    sK1070: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_2005,type,
    sK1071: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2006,type,
    sK1072: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2007,type,
    sK1073: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_2008,type,
    sK1074: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2009,type,
    sK1075: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2010,type,
    sK1076: nat > vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_2011,type,
    sK1077: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2012,type,
    sK1078: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2013,type,
    sK1079: ( rat > rat ) > rat ).

thf(func_def_2014,type,
    sK1080: ( rat > rat ) > rat ).

thf(func_def_2015,type,
    sK1081: real > ( real > real ) > ( real > real ) > real > real ).

thf(func_def_2016,type,
    sK1082: real > ( real > real ) > real > real ).

thf(func_def_2017,type,
    sK1083: complex > set_complex > ( complex > nat ) > complex ).

thf(func_def_2018,type,
    sK1084: set_complex > ( complex > nat ) > complex ).

thf(func_def_2019,type,
    sK1085: ( nat > real ) > nat ).

thf(func_def_2020,type,
    sK1086: ( nat > real ) > nat ).

thf(func_def_2021,type,
    sK1087: ( real > int ) > real ).

thf(func_def_2022,type,
    sK1088: ( real > int ) > real ).

thf(func_def_2023,type,
    sK1089: set_complex > ( complex > nat ) > ( complex > nat ) > complex ).

thf(func_def_2024,type,
    sK1090: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_2025,type,
    sK1091: ( num > num ) > num ).

thf(func_def_2026,type,
    sK1092: ( num > num ) > num ).

thf(func_def_2027,type,
    sK1093: nat > nat ).

thf(func_def_2028,type,
    sK1094: int > list_int > nat ).

thf(func_def_2029,type,
    sK1095: set_int > ( int > int ) > int ).

thf(func_def_2030,type,
    sK1096: produc2285326912895808259nt_int > product_prod_int_int ).

thf(func_def_2031,type,
    sK1097: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_2032,type,
    sK1098: $o > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2033,type,
    sK1099: $o > vEBT_VEBT > nat ).

thf(func_def_2034,type,
    sK1100: $o > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2035,type,
    sK1101: $o > vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_2036,type,
    sK1102: $o > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2037,type,
    sK1103: $o > vEBT_VEBT > nat ).

thf(func_def_2038,type,
    sK1104: $o > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2039,type,
    sK1105: $o > vEBT_VEBT > $o ).

thf(func_def_2040,type,
    sK1106: vEBT_VEBT > $o > $o ).

thf(func_def_2041,type,
    sK1107: int > nat ).

thf(func_def_2042,type,
    sK1108: int > nat ).

thf(func_def_2043,type,
    sK1109: real > nat ).

thf(func_def_2044,type,
    sK1110: set_complex > set_complex > complex ).

thf(func_def_2045,type,
    sK1111: int > nat ).

thf(func_def_2046,type,
    sK1112: set_int > int > ( int > $o ) > int ).

thf(func_def_2047,type,
    sK1113: int > set_int > int > int ).

thf(func_def_2048,type,
    sK1114: int > set_int > int > int ).

thf(func_def_2049,type,
    sK1115: ( int > $o ) > set_int > int > int ).

thf(func_def_2050,type,
    sK1116: ( num > num ) > num ).

thf(func_def_2051,type,
    sK1117: ( num > num ) > num ).

thf(func_def_2052,type,
    sK1118: product_prod_int_int > int ).

thf(func_def_2053,type,
    sK1119: product_prod_int_int > int ).

thf(func_def_2054,type,
    sK1120: ( real > real ) > set_real > set_real > real ).

thf(func_def_2055,type,
    sK1121: ( real > real ) > set_real > set_real > real ).

thf(func_def_2056,type,
    sK1122: $o > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2057,type,
    sK1123: $o > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2058,type,
    sK1124: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2059,type,
    sK1125: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_2060,type,
    sK1126: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_2061,type,
    sK1127: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2062,type,
    sK1128: $o > vEBT_VEBT > nat > nat ).

thf(func_def_2063,type,
    sK1129: $o > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2064,type,
    sK1130: $o > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2065,type,
    sK1131: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_2066,type,
    sK1132: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2067,type,
    sK1133: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2068,type,
    sK1134: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2069,type,
    sK1135: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_2070,type,
    sK1136: $o > nat > vEBT_VEBT > $o ).

thf(func_def_2071,type,
    sK1137: $o > nat > vEBT_VEBT > $o ).

thf(func_def_2072,type,
    sK1138: rat > rat ).

thf(func_def_2073,type,
    sK1139: rat > nat ).

thf(func_def_2074,type,
    sK1140: rat > rat ).

thf(func_def_2075,type,
    sK1141: produc7773217078559923341nt_int > product_prod_int_int ).

thf(func_def_2076,type,
    sK1142: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_2077,type,
    sK1143: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_2078,type,
    sK1144: product_prod_int_int > ( int > int > set_int ) > int > int ).

thf(func_def_2079,type,
    sK1145: product_prod_int_int > ( int > int > set_int ) > int > int ).

thf(func_def_2080,type,
    sK1146: set_int > ( int > nat ) > int ).

thf(func_def_2081,type,
    sK1147: set_int > ( int > nat ) > int ).

thf(func_def_2082,type,
    sK1148: real > real ).

thf(func_def_2083,type,
    sK1149: ( int > $o ) > int ).

thf(func_def_2084,type,
    sK1150: int > set_int > ( int > $o ) > int ).

thf(func_def_2085,type,
    sK1151: int > set_int > ( int > $o ) > int ).

thf(func_def_2086,type,
    sK1152: ( int > $o ) > int > int ).

thf(func_def_2087,type,
    sK1153: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2088,type,
    sK1154: ( int > $o ) > int > int ).

thf(func_def_2089,type,
    sK1155: ( int > $o ) > int > int ).

thf(func_def_2090,type,
    sK1156: ( int > $o ) > set_int > int > int ).

thf(func_def_2091,type,
    sK1157: set_complex > set_complex > ( complex > rat ) > complex ).

thf(func_def_2092,type,
    sK1158: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).

thf(func_def_2093,type,
    sK1159: int > int > ( int > int > $o ) > int ).

thf(func_def_2094,type,
    sK1160: int > int > ( int > int > $o ) > int ).

thf(func_def_2095,type,
    sK1161: real > real ).

thf(func_def_2096,type,
    sK1162: real > ( real > $o ) > real ).

thf(func_def_2097,type,
    sK1163: real > ( real > $o ) > real ).

thf(func_def_2098,type,
    sK1164: set_int > set_int > ( int > complex ) > int ).

thf(func_def_2099,type,
    sK1165: ( real > real ) > real ).

thf(func_def_2100,type,
    sK1166: ( real > real ) > real ).

thf(func_def_2101,type,
    sK1167: real > ( real > real ) > real > real ).

thf(func_def_2102,type,
    sK1168: real > ( real > real ) > real > real ).

thf(func_def_2103,type,
    sK1169: int > int > int > int ).

thf(func_def_2104,type,
    sK1170: int > int > int > int ).

thf(func_def_2105,type,
    sK1171: produc8763457246119570046nteger > code_integer ).

thf(func_def_2106,type,
    sK1172: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_2107,type,
    sK1173: produc8763457246119570046nteger > code_integer ).

thf(func_def_2108,type,
    sK1174: real > ( real > real ) > real ).

thf(func_def_2109,type,
    sK1175: int > set_int > ( int > rat ) > int ).

thf(func_def_2110,type,
    sK1176: ( real > real ) > real ).

thf(func_def_2111,type,
    sK1177: ( real > real ) > real ).

thf(func_def_2112,type,
    sK1178: set_real > set_real > real ).

thf(func_def_2113,type,
    sK1179: product_prod_num_num > num ).

thf(func_def_2114,type,
    sK1180: product_prod_num_num > num ).

thf(func_def_2115,type,
    sK1181: product_prod_num_num > num ).

thf(func_def_2116,type,
    sK1182: product_prod_num_num > num ).

thf(func_def_2117,type,
    sK1183: product_prod_num_num > num ).

thf(func_def_2118,type,
    sK1184: product_prod_num_num > num ).

thf(func_def_2119,type,
    sK1185: product_prod_num_num > num ).

thf(func_def_2120,type,
    sK1186: product_prod_num_num > num ).

thf(func_def_2121,type,
    sK1187: product_prod_num_num > num ).

thf(func_def_2122,type,
    sK1188: product_prod_num_num > num ).

thf(func_def_2123,type,
    sK1189: product_prod_num_num > num ).

thf(func_def_2124,type,
    sK1190: product_prod_num_num > num ).

thf(func_def_2125,type,
    sK1191: ( set_real > $o ) > real ).

thf(func_def_2126,type,
    sK1192: ( set_real > $o ) > set_real ).

thf(func_def_2127,type,
    sK1193: nat > nat > nat > nat ).

thf(func_def_2128,type,
    sK1194: ( nat > rat ) > nat ).

thf(func_def_2129,type,
    sK1195: ( nat > rat ) > nat ).

thf(func_def_2130,type,
    sK1196: list_nat > ( nat > $o ) > nat ).

thf(func_def_2131,type,
    sK1197: list_nat > ( nat > $o ) > nat ).

thf(func_def_2132,type,
    sK1198: real > real ).

thf(func_def_2133,type,
    sK1199: rat > rat ).

thf(func_def_2134,type,
    sK1200: ( set_int > $o ) > set_int ).

thf(func_def_2135,type,
    sK1201: ( set_int > $o ) > int ).

thf(func_def_2136,type,
    sK1202: ( nat > rat ) > nat ).

thf(func_def_2137,type,
    sK1203: ( nat > nat > $o ) > nat ).

thf(func_def_2138,type,
    sK1204: ( nat > nat > $o ) > nat ).

thf(func_def_2139,type,
    sK1205: ( nat > nat > $o ) > nat ).

thf(func_def_2140,type,
    sK1206: ( nat > nat > $o ) > nat ).

thf(func_def_2141,type,
    sK1207: ( nat > int ) > int > nat > nat ).

thf(func_def_2142,type,
    sK1208: ( nat > int ) > nat > nat ).

thf(func_def_2143,type,
    sK1209: set_complex > ( complex > real ) > complex ).

thf(func_def_2144,type,
    sK1210: set_complex > ( complex > real ) > complex ).

thf(func_def_2145,type,
    sK1211: real > nat > real > ( nat > real > real ) > real ).

thf(func_def_2146,type,
    sK1212: real > nat > real > ( nat > real > real ) > nat ).

thf(func_def_2147,type,
    sK1213: real > real > ( real > real ) > ( nat > real > real ) > nat > real ).

thf(func_def_2148,type,
    sK1214: real > real ).

thf(func_def_2149,type,
    sK1215: set_complex > ( set_complex > $o ) > set_complex ).

thf(func_def_2150,type,
    sK1216: set_complex > ( set_complex > $o ) > complex ).

thf(func_def_2151,type,
    sK1217: vEBT_VEBT > $o ).

thf(func_def_2152,type,
    sK1218: vEBT_VEBT > $o ).

thf(func_def_2153,type,
    sK1219: nat > nat ).

thf(func_def_2154,type,
    sK1220: int > int ).

thf(func_def_2155,type,
    sK1221: rat > rat > rat ).

thf(func_def_2156,type,
    sK1222: produc7773217078559923341nt_int > complex > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > int > option6357759511663192854e_term ).

thf(func_def_2157,type,
    sK1223: produc7773217078559923341nt_int > complex > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > product_prod_int_int ).

thf(func_def_2158,type,
    sK1224: int > ( int > $o ) > int ).

thf(func_def_2159,type,
    sK1225: ( nat > rat ) > nat ).

thf(func_def_2160,type,
    sK1226: ( nat > rat ) > nat ).

thf(func_def_2161,type,
    sK1227: real > real ).

thf(func_def_2162,type,
    sK1228: real > real > ( real > real ) > real ).

thf(func_def_2163,type,
    sK1229: ( nat > rat ) > set_complex > ( complex > rat ) > ( complex > nat ) > set_nat > nat ).

thf(func_def_2164,type,
    sK1230: set_complex > ( complex > rat ) > complex ).

thf(func_def_2165,type,
    sK1231: ( nat > num ) > nat ).

thf(func_def_2166,type,
    sK1232: ( real > real ) > real > set_real > real ).

thf(func_def_2167,type,
    sK1233: ( nat > set_int ) > nat ).

thf(func_def_2168,type,
    sK1234: complex > int ).

thf(func_def_2169,type,
    sK1235: ( real > real ) > set_real > set_real > real ).

thf(func_def_2170,type,
    sK1236: ( real > real ) > ( real > real ) > set_real > real ).

thf(func_def_2171,type,
    sK1237: ( int > rat ) > int ).

thf(func_def_2172,type,
    sK1238: ( int > rat ) > int ).

thf(func_def_2173,type,
    sK1239: int > int ).

thf(func_def_2174,type,
    sK1240: nat > ( nat > vEBT_VEBT > $o ) > vEBT_VEBT ).

thf(func_def_2175,type,
    sK1241: list_VEBT_VEBT > nat > ( nat > vEBT_VEBT > $o ) > nat ).

thf(func_def_2176,type,
    sK1242: nat > ( nat > vEBT_VEBT > $o ) > list_VEBT_VEBT ).

thf(func_def_2177,type,
    sK1243: nat > ( nat > vEBT_VEBT > $o ) > nat ).

thf(func_def_2178,type,
    sK1244: set_real > ( real > real ) > ( real > real ) > ( real > real ) > real ).

thf(func_def_2179,type,
    sK1245: ( real > real ) > set_real > set_real > set_real > set_real > real ).

thf(func_def_2180,type,
    sK1246: ( real > real ) > ( real > real ) > set_real > set_real > real ).

thf(func_def_2181,type,
    sK1247: ( real > real ) > ( real > real ) > set_real > set_real > real ).

thf(func_def_2182,type,
    sK1248: ( real > real ) > set_real > real ).

thf(func_def_2183,type,
    sK1249: ( real > real ) > set_real > real ).

thf(func_def_2184,type,
    sK1250: set_real > set_real > set_real > ( real > real ) > set_real > real ).

thf(func_def_2185,type,
    sK1251: ( real > real > $o ) > real ).

thf(func_def_2186,type,
    sK1252: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_2187,type,
    sK1253: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_2188,type,
    sK1254: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_2189,type,
    sK1255: nat > ( nat > nat > $o ) > nat ).

thf(func_def_2190,type,
    sK1256: list_nat > nat > ( nat > nat > $o ) > nat ).

thf(func_def_2191,type,
    sK1257: nat > ( nat > nat > $o ) > list_nat ).

thf(func_def_2192,type,
    sK1258: nat > ( nat > nat > $o ) > nat ).

thf(func_def_2193,type,
    sK1259: ( int > $o ) > int ).

thf(func_def_2194,type,
    sK1260: ( int > $o ) > int ).

thf(func_def_2195,type,
    sK1261: nat > nat > nat ).

thf(func_def_2196,type,
    sK1262: nat > nat > nat ).

thf(func_def_2197,type,
    sK1263: ( rat > rat > $o ) > rat ).

thf(func_def_2198,type,
    sK1264: ( rat > rat > $o ) > rat ).

thf(func_def_2199,type,
    sK1265: ( rat > rat > $o ) > rat ).

thf(func_def_2200,type,
    sK1266: ( rat > rat > $o ) > rat ).

thf(func_def_2201,type,
    sK1267: num > num > num ).

thf(func_def_2202,type,
    sK1268: num > num > num > num ).

thf(func_def_2203,type,
    sK1269: num > num > num > num ).

thf(func_def_2204,type,
    sK1270: num > num > num > num ).

thf(func_def_2205,type,
    sK1271: num > num > num > num ).

thf(func_def_2206,type,
    sK1272: num > num > num > num ).

thf(func_def_2207,type,
    sK1273: num > num > num > num ).

thf(func_def_2208,type,
    sK1274: num > num > num > num ).

thf(func_def_2209,type,
    sK1275: num > num > num ).

thf(func_def_2210,type,
    sK1276: num > num > num > num ).

thf(func_def_2211,type,
    sK1277: num > num > num > num ).

thf(func_def_2212,type,
    sK1278: num > num > num > num ).

thf(func_def_2213,type,
    sK1279: ( nat > $o ) > nat > nat ).

thf(func_def_2214,type,
    sK1280: ( nat > $o ) > nat > nat ).

thf(func_def_2215,type,
    sK1281: real > real ).

thf(func_def_2216,type,
    sK1282: vEBT_VEBT > nat ).

thf(func_def_2217,type,
    sK1283: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2218,type,
    sK1284: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2219,type,
    sK1285: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).

thf(func_def_2220,type,
    sK1286: product_prod_nat_nat > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > $o ) > nat ).

thf(func_def_2221,type,
    sK1287: set_int > set_int > ( real > int ) > ( int > real ) > int ).

thf(func_def_2222,type,
    sK1288: ( int > real ) > set_real > set_real > set_int > set_int > int ).

thf(func_def_2223,type,
    sK1289: set_real > set_real > ( real > int ) > set_int > set_int > real ).

thf(func_def_2224,type,
    sK1290: ( int > real ) > ( real > int ) > set_real > set_real > real ).

thf(func_def_2225,type,
    sK1291: ( int > complex ) > set_int > int ).

thf(func_def_2226,type,
    sK1292: ( real > complex ) > set_real > real ).

thf(func_def_2227,type,
    sK1293: ( int > complex ) > ( real > int ) > set_real > ( real > complex ) > real ).

thf(func_def_2228,type,
    sK1294: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_2229,type,
    sK1295: produc5542196010084753463at_nat > product_prod_nat_nat ).

thf(func_def_2230,type,
    sK1296: produc5542196010084753463at_nat > product_prod_nat_nat ).

thf(func_def_2231,type,
    sK1297: produc5542196010084753463at_nat > product_prod_nat_nat ).

thf(func_def_2232,type,
    sK1298: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_2233,type,
    sK1299: produc5542196010084753463at_nat > option4927543243414619207at_nat ).

thf(func_def_2234,type,
    sK1300: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_2235,type,
    sK1301: set_real > ( real > real ) > real > real ).

thf(func_def_2236,type,
    sK1302: ( complex > rat ) > set_complex > complex ).

thf(func_def_2237,type,
    sK1303: ( complex > rat ) > set_complex > complex ).

thf(func_def_2238,type,
    sK1304: ( rat > nat ) > rat ).

thf(func_def_2239,type,
    sK1305: ( rat > nat ) > rat ).

thf(func_def_2240,type,
    sK1306: vEBT_VEBT > nat > $o ).

thf(func_def_2241,type,
    sK1307: vEBT_VEBT > nat > $o ).

thf(func_def_2242,type,
    sK1308: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2243,type,
    sK1309: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2244,type,
    sK1310: nat > vEBT_VEBT > nat ).

thf(func_def_2245,type,
    sK1311: nat > vEBT_VEBT > nat ).

thf(func_def_2246,type,
    sK1312: nat > vEBT_VEBT > nat ).

thf(func_def_2247,type,
    sK1313: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2248,type,
    sK1314: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2249,type,
    sK1315: vEBT_VEBT > nat > nat ).

thf(func_def_2250,type,
    sK1316: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2251,type,
    sK1317: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2252,type,
    sK1318: vEBT_VEBT > nat > product_prod_nat_nat ).

thf(func_def_2253,type,
    sK1319: vEBT_VEBT > nat > product_prod_nat_nat ).

thf(func_def_2254,type,
    sK1320: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2255,type,
    sK1321: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2256,type,
    sK1322: ( rat > rat ) > rat ).

thf(func_def_2257,type,
    sK1323: ( rat > rat ) > rat ).

thf(func_def_2258,type,
    sK1324: real > real > ( real > real ) > real ).

thf(func_def_2259,type,
    sK1325: real > real > ( real > real ) > real ).

thf(func_def_2260,type,
    sK1326: set_real > list_real > real ).

thf(func_def_2261,type,
    sK1327: set_real > set_real > ( real > rat ) > real ).

thf(func_def_2262,type,
    sK1328: ( real > rat ) > set_real > ( real > rat ) > real ).

thf(func_def_2263,type,
    sK1329: ( int > nat ) > set_int > int ).

thf(func_def_2264,type,
    sK1330: set_nat > nat ).

thf(func_def_2265,type,
    sK1331: nat > set_nat > nat ).

thf(func_def_2266,type,
    sK1332: set_int > set_int > ( int > complex ) > set_complex > set_complex > int ).

thf(func_def_2267,type,
    sK1333: set_complex > set_complex > ( int > complex ) > ( complex > int ) > complex ).

thf(func_def_2268,type,
    sK1334: set_int > ( int > real ) > ( complex > real ) > ( int > complex ) > int ).

thf(func_def_2269,type,
    sK1335: ( complex > real ) > set_complex > complex ).

thf(func_def_2270,type,
    sK1336: set_int > ( complex > int ) > set_int > ( int > complex ) > int ).

thf(func_def_2271,type,
    sK1337: ( int > real ) > set_int > int ).

thf(func_def_2272,type,
    sK1338: set_int > set_complex > ( complex > int ) > set_int > set_complex > complex ).

thf(func_def_2273,type,
    sK1339: nat > nat > nat ).

thf(func_def_2274,type,
    sK1340: ( real > real ) > real ).

thf(func_def_2275,type,
    sK1341: ( real > real ) > real ).

thf(func_def_2276,type,
    sK1342: real > real > real > real ).

thf(func_def_2277,type,
    sK1343: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_2278,type,
    sK1344: ( nat > $o ) > nat > nat ).

thf(func_def_2279,type,
    sK1345: ( nat > $o ) > nat > nat ).

thf(func_def_2280,type,
    sK1346: real > real ).

thf(func_def_2281,type,
    sK1347: complex > complex ).

thf(func_def_2282,type,
    sK1348: complex > real ).

thf(func_def_2283,type,
    sK1349: real > real ).

thf(func_def_2284,type,
    sK1350: ( nat > rat ) > ( nat > rat ) > set_nat > nat ).

thf(func_def_2285,type,
    sK1351: nat > list_o ).

thf(func_def_2286,type,
    sK1352: ( nat > $o ) > list_nat > nat ).

thf(func_def_2287,type,
    sK1353: num > set_num > num ).

thf(func_def_2288,type,
    sK1354: ( rat > int ) > rat ).

thf(func_def_2289,type,
    sK1355: ( rat > int ) > rat ).

thf(func_def_2290,type,
    sK1356: set_int > ( set_int > $o ) > set_int ).

thf(func_def_2291,type,
    sK1357: set_int > ( set_int > $o ) > int ).

thf(func_def_2292,type,
    sK1358: option_nat > vEBT_VEBT > $o ).

thf(func_def_2293,type,
    sK1359: option_nat > vEBT_VEBT > $o ).

thf(func_def_2294,type,
    sK1360: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2295,type,
    sK1361: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2296,type,
    sK1362: vEBT_VEBT > nat ).

thf(func_def_2297,type,
    sK1363: vEBT_VEBT > option_nat > nat ).

thf(func_def_2298,type,
    sK1364: vEBT_VEBT > option_nat > nat ).

thf(func_def_2299,type,
    sK1365: vEBT_VEBT > option_nat > list_VEBT_VEBT ).

thf(func_def_2300,type,
    sK1366: vEBT_VEBT > option_nat > nat ).

thf(func_def_2301,type,
    sK1367: vEBT_VEBT > option_nat > vEBT_VEBT ).

thf(func_def_2302,type,
    sK1368: produc1908205239877642774nteger > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8923325533196201883nteger ).

thf(func_def_2303,type,
    sK1369: produc1908205239877642774nteger > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_2304,type,
    sK1370: nat > nat ).

thf(func_def_2305,type,
    sK1371: ( set_int > $o ) > set_int > set_int ).

thf(func_def_2306,type,
    sK1372: complex > ( int > int > set_complex ) > product_prod_int_int > int ).

thf(func_def_2307,type,
    sK1373: complex > ( int > int > set_complex ) > product_prod_int_int > int ).

thf(func_def_2308,type,
    sK1374: num > num ).

thf(func_def_2309,type,
    sK1375: ( nat > real ) > real > nat ).

thf(func_def_2310,type,
    sK1376: ( nat > real ) > real ).

thf(func_def_2311,type,
    sK1377: set_num > num ).

thf(func_def_2312,type,
    sK1378: nat > produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8923325533196201883nteger ).

thf(func_def_2313,type,
    sK1379: nat > produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > code_integer > option6357759511663192854e_term ).

thf(func_def_2314,type,
    sK1380: set_real > ( real > nat ) > real ).

thf(func_def_2315,type,
    sK1381: ( complex > complex > $o ) > ( nat > complex ) > set_nat > ( nat > complex ) > nat ).

thf(func_def_2316,type,
    sK1382: ( complex > complex > $o ) > complex ).

thf(func_def_2317,type,
    sK1383: ( complex > complex > $o ) > complex ).

thf(func_def_2318,type,
    sK1384: ( complex > complex > $o ) > complex ).

thf(func_def_2319,type,
    sK1385: ( complex > complex > $o ) > complex ).

thf(func_def_2320,type,
    sK1386: num > num ).

thf(func_def_2321,type,
    sK1387: ( rat > real ) > rat ).

thf(func_def_2322,type,
    sK1388: ( rat > real ) > rat ).

thf(func_def_2323,type,
    sK1389: nat > ( nat > $o ) > nat ).

thf(func_def_2324,type,
    sK1390: rat > int ).

thf(func_def_2325,type,
    sK1391: int > int ).

thf(func_def_2326,type,
    sK1392: set_int > int > int ).

thf(func_def_2327,type,
    sK1393: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2328,type,
    sK1394: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2329,type,
    sK1395: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2330,type,
    sK1396: rat > rat > rat ).

thf(func_def_2331,type,
    sK1397: ( int > real ) > set_int > set_int > int ).

thf(func_def_2332,type,
    sK1398: option_num > num ).

thf(func_def_2333,type,
    sK1399: set_complex > ( complex > int ) > ( complex > int ) > complex ).

thf(func_def_2334,type,
    sK1400: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_2335,type,
    sK1401: ( nat > real > real ) > nat > real > nat ).

thf(func_def_2336,type,
    sK1402: ( nat > real > real ) > nat > real > real ).

thf(func_def_2337,type,
    sK1403: ( real > real ) > ( nat > real > real ) > nat > real > real ).

thf(func_def_2338,type,
    sK1404: set_int > set_int > ( int > int ) > ( int > int ) > int ).

thf(func_def_2339,type,
    sK1405: set_int > set_int > ( int > int ) > ( int > int ) > int ).

thf(func_def_2340,type,
    sK1406: set_int > ( int > real ) > ( int > real ) > ( int > int ) > int ).

thf(func_def_2341,type,
    sK1407: ( int > real ) > set_int > int ).

thf(func_def_2342,type,
    sK1408: ( int > int ) > set_int > set_int > set_int > set_int > int ).

thf(func_def_2343,type,
    sK1409: set_int > ( int > real ) > int ).

thf(func_def_2344,type,
    sK1410: ( int > int ) > set_int > set_int > set_int > set_int > int ).

thf(func_def_2345,type,
    sK1411: ( real > real ) > set_real > real ).

thf(func_def_2346,type,
    sK1412: ( real > real ) > set_real > real ).

thf(func_def_2347,type,
    sK1413: ( complex > int ) > ( complex > int ) > set_complex > complex ).

thf(func_def_2348,type,
    sK1414: nat > vEBT_VEBT > nat ).

thf(func_def_2349,type,
    sK1415: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2350,type,
    sK1416: nat > vEBT_VEBT > nat ).

thf(func_def_2351,type,
    sK1417: nat > vEBT_VEBT > nat ).

thf(func_def_2352,type,
    sK1418: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2353,type,
    sK1419: nat > vEBT_VEBT > nat ).

thf(func_def_2354,type,
    sK1420: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2355,type,
    sK1421: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2356,type,
    sK1422: nat > vEBT_VEBT > nat ).

thf(func_def_2357,type,
    sK1423: nat > vEBT_VEBT > nat ).

thf(func_def_2358,type,
    sK1424: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2359,type,
    sK1425: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2360,type,
    sK1426: ( nat > nat > $o ) > nat ).

thf(func_def_2361,type,
    sK1427: ( nat > nat > $o ) > nat ).

thf(func_def_2362,type,
    sK1428: ( nat > nat > $o ) > nat ).

thf(func_def_2363,type,
    sK1429: ( nat > nat > $o ) > nat ).

thf(func_def_2364,type,
    sK1430: ( complex > real ) > set_complex > complex ).

thf(func_def_2365,type,
    sK1431: set_real > ( real > nat ) > real ).

thf(func_def_2366,type,
    sK1432: int > int ).

thf(func_def_2367,type,
    sK1433: int > nat ).

thf(func_def_2368,type,
    sK1434: ( int > real ) > set_int > set_int > int ).

thf(func_def_2369,type,
    sK1435: produc1908205239877642774nteger > code_integer ).

thf(func_def_2370,type,
    sK1436: produc1908205239877642774nteger > code_integer ).

thf(func_def_2371,type,
    sK1437: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_2372,type,
    sK1438: nat > ( nat > $o ) > nat ).

thf(func_def_2373,type,
    sK1439: nat > vEBT_VEBT > nat ).

thf(func_def_2374,type,
    sK1440: real > real > real ).

thf(func_def_2375,type,
    sK1441: set_complex > ( complex > nat ) > complex ).

thf(func_def_2376,type,
    sK1442: ( real > num ) > real ).

thf(func_def_2377,type,
    sK1443: ( real > num ) > real ).

thf(func_def_2378,type,
    sK1444: nat > real > real ).

thf(func_def_2379,type,
    sK1445: ( nat > complex ) > set_nat > set_nat > nat ).

thf(func_def_2380,type,
    sK1446: ( nat > complex ) > set_nat > ( nat > complex ) > nat ).

thf(func_def_2381,type,
    sK1447: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_2382,type,
    sK1448: produc7773217078559923341nt_int > product_prod_int_int ).

thf(func_def_2383,type,
    sK1449: ( complex > rat ) > ( complex > int ) > ( int > rat ) > set_int > set_complex > int ).

thf(func_def_2384,type,
    sK1450: ( complex > rat ) > set_complex > complex ).

thf(func_def_2385,type,
    sK1451: ( complex > real ) > set_complex > ( complex > real ) > complex ).

thf(func_def_2386,type,
    sK1452: ( complex > real ) > set_complex > set_complex > complex ).

thf(func_def_2387,type,
    sK1453: nat > nat > nat ).

thf(func_def_2388,type,
    sK1454: nat > nat > nat ).

thf(func_def_2389,type,
    sK1455: nat > nat > nat ).

thf(func_def_2390,type,
    sK1456: ( num > int ) > num ).

thf(func_def_2391,type,
    sK1457: ( num > int ) > num ).

thf(func_def_2392,type,
    sK1458: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2393,type,
    sK1459: produc9072475918466114483BT_nat > nat ).

thf(func_def_2394,type,
    sK1460: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2395,type,
    sK1461: produc9072475918466114483BT_nat > nat ).

thf(func_def_2396,type,
    sK1462: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).

thf(func_def_2397,type,
    sK1463: produc9072475918466114483BT_nat > nat ).

thf(func_def_2398,type,
    sK1464: produc9072475918466114483BT_nat > $o ).

thf(func_def_2399,type,
    sK1465: produc9072475918466114483BT_nat > $o ).

thf(func_def_2400,type,
    sK1466: ( set_complex > $o ) > set_complex > complex ).

thf(func_def_2401,type,
    sK1467: ( set_complex > $o ) > set_complex > set_complex ).

thf(func_def_2402,type,
    sK1468: option_num > num ).

thf(func_def_2403,type,
    sK1469: option_num > option_num > option_num > ( num > num > num ) > num ).

thf(func_def_2404,type,
    sK1470: option_num > option_num > option_num > ( num > num > num ) > num ).

thf(func_def_2405,type,
    sK1471: set_nat > ( nat > rat ) > nat ).

thf(func_def_2406,type,
    sK1472: int > int > int ).

thf(func_def_2407,type,
    sK1473: set_complex > ( complex > nat ) > ( complex > nat ) > complex ).

thf(func_def_2408,type,
    sK1474: int > int ).

thf(func_def_2409,type,
    sK1475: ( real > real ) > set_real > real ).

thf(func_def_2410,type,
    sK1476: set_int > set_int > ( int > real ) > set_real > set_real > int ).

thf(func_def_2411,type,
    sK1477: ( int > real ) > set_int > int ).

thf(func_def_2412,type,
    sK1478: set_int > ( int > real ) > ( real > real ) > ( int > real ) > int ).

thf(func_def_2413,type,
    sK1479: ( real > int ) > set_int > ( int > real ) > set_int > int ).

thf(func_def_2414,type,
    sK1480: set_real > ( real > int ) > set_real > set_int > set_int > real ).

thf(func_def_2415,type,
    sK1481: set_real > ( real > int ) > set_real > ( int > real ) > real ).

thf(func_def_2416,type,
    sK1482: ( real > nat ) > ( real > nat ) > real ).

thf(func_def_2417,type,
    sK1483: ( real > nat ) > real ).

thf(func_def_2418,type,
    sK1484: ( real > nat ) > real ).

thf(func_def_2419,type,
    sK1485: rat > rat > rat ).

thf(func_def_2420,type,
    sK1486: ( rat > num ) > rat ).

thf(func_def_2421,type,
    sK1487: ( rat > num ) > rat ).

thf(func_def_2422,type,
    sK1488: ( real > rat ) > set_real > real ).

thf(func_def_2423,type,
    sK1489: ( int > int > $o ) > int > int > int ).

thf(func_def_2424,type,
    sK1490: ( int > int > $o ) > int > int > int ).

thf(func_def_2425,type,
    sK1491: nat > nat > nat ).

thf(func_def_2426,type,
    sK1492: complex > set_complex > ( complex > nat ) > complex ).

thf(func_def_2427,type,
    sK1493: set_complex > ( complex > real ) > set_complex > complex ).

thf(func_def_2428,type,
    sK1494: real > int ).

thf(func_def_2429,type,
    sK1495: nat > nat > ( nat > $o ) > nat ).

thf(func_def_2430,type,
    sK1496: real > real ).

thf(func_def_2431,type,
    sK1497: set_real > ( real > rat ) > real ).

thf(func_def_2432,type,
    sK1498: rat > ( real > rat ) > set_real > rat > real ).

thf(func_def_2433,type,
    sK1499: option_nat > nat ).

thf(func_def_2434,type,
    sK1500: set_real > real > ( real > real ) > real ).

thf(func_def_2435,type,
    sK1501: ( rat > int ) > rat ).

thf(func_def_2436,type,
    sK1502: ( rat > int ) > rat ).

thf(func_def_2437,type,
    sK1503: ( code_integer > $o ) > code_integer > code_integer ).

thf(func_def_2438,type,
    sK1504: ( code_integer > $o ) > code_integer > code_integer ).

thf(func_def_2439,type,
    sK1505: ( num > rat ) > num ).

thf(func_def_2440,type,
    sK1506: ( num > rat ) > num ).

thf(func_def_2441,type,
    sK1507: ( num > rat ) > num ).

thf(func_def_2442,type,
    sK1508: ( num > rat ) > num ).

thf(func_def_2443,type,
    sK1509: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2444,type,
    sK1510: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2445,type,
    sK1511: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2446,type,
    sK1512: nat > ( nat > real ) > nat ).

thf(func_def_2447,type,
    sK1513: product_prod_int_int > ( int > int > set_real ) > real > int ).

thf(func_def_2448,type,
    sK1514: product_prod_int_int > ( int > int > set_real ) > real > int ).

thf(func_def_2449,type,
    sK1515: nat > nat ).

thf(func_def_2450,type,
    sK1516: rat > rat > rat ).

thf(func_def_2451,type,
    sK1517: num > num ).

thf(func_def_2452,type,
    sK1518: set_nat > ( nat > complex ) > nat ).

thf(func_def_2453,type,
    sK1519: ( int > complex ) > set_int > int ).

thf(func_def_2454,type,
    sK1520: set_real > set_real > ( real > int ) > set_int > set_int > real ).

thf(func_def_2455,type,
    sK1521: set_int > ( real > complex ) > ( int > real ) > ( int > complex ) > int ).

thf(func_def_2456,type,
    sK1522: ( real > complex ) > set_real > real ).

thf(func_def_2457,type,
    sK1523: set_int > set_int > set_real > ( int > real ) > set_real > int ).

thf(func_def_2458,type,
    sK1524: ( real > int ) > set_int > set_int > ( int > real ) > int ).

thf(func_def_2459,type,
    sK1525: ( real > int ) > set_real > ( int > real ) > set_real > real ).

thf(func_def_2460,type,
    sK1526: real > real > ( real > real > real ) > real ).

thf(func_def_2461,type,
    sK1527: ( real > real ) > real > real > ( real > real > real ) > real ).

thf(func_def_2462,type,
    sK1528: set_int > ( int > nat ) > int ).

thf(func_def_2463,type,
    sK1529: int > int ).

thf(func_def_2464,type,
    sK1530: ( product_prod_nat_nat > $o ) > nat ).

thf(func_def_2465,type,
    sK1531: nat > ( product_prod_nat_nat > $o ) > nat ).

thf(func_def_2466,type,
    sK1532: nat > ( product_prod_nat_nat > $o ) > nat ).

thf(func_def_2467,type,
    sK1533: ( complex > int ) > set_complex > set_complex > complex ).

thf(func_def_2468,type,
    sK1534: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_2469,type,
    sK1535: real > ( real > real ) > real > ( real > real ) > real ).

thf(func_def_2470,type,
    sK1536: real > real > ( real > real ) > real ).

thf(func_def_2471,type,
    sK1537: rat > rat ).

thf(func_def_2472,type,
    sK1538: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).

thf(func_def_2473,type,
    sK1539: ( real > real ) > set_real > real ).

thf(func_def_2474,type,
    sK1540: set_set_nat > set_set_nat > set_nat ).

thf(func_def_2475,type,
    sK1541: ( nat > num ) > ( set_nat > $o ) > nat ).

thf(func_def_2476,type,
    sK1542: ( nat > num ) > ( set_nat > $o ) > set_nat ).

thf(func_def_2477,type,
    sK1543: ( nat > int ) > set_nat > ( nat > int ) > nat ).

thf(func_def_2478,type,
    sK1544: set_nat > ( nat > int ) > ( nat > int ) > nat ).

thf(func_def_2479,type,
    sK1545: set_num > num ).

thf(func_def_2480,type,
    sK1546: set_real > set_real > ( real > int ) > real ).

thf(func_def_2481,type,
    sK1547: real > int ).

thf(func_def_2482,type,
    sK1548: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_2483,type,
    sK1549: produc8763457246119570046nteger > code_integer ).

thf(func_def_2484,type,
    sK1550: produc8763457246119570046nteger > code_integer ).

thf(func_def_2485,type,
    sK1551: nat > nat ).

thf(func_def_2486,type,
    sK1552: ( nat > $o ) > nat > nat ).

thf(func_def_2487,type,
    sK1553: set_list_o > nat ).

thf(func_def_2488,type,
    sK1554: real > real ).

thf(func_def_2489,type,
    sK1555: ( real > $o ) > real > real ).

thf(func_def_2490,type,
    sK1556: ( real > $o ) > real > real ).

thf(func_def_2491,type,
    sK1557: ( real > $o ) > real > real ).

thf(func_def_2492,type,
    sK1558: ( real > $o ) > real > real ).

thf(func_def_2493,type,
    sK1559: ( real > nat ) > ( real > nat ) > set_real > real ).

thf(func_def_2494,type,
    sK1560: set_real > ( real > nat ) > real ).

thf(func_def_2495,type,
    sK1561: ( int > $o ) > int > int ).

thf(func_def_2496,type,
    sK1562: ( set_nat > $o ) > ( set_nat > $o ) > set_nat ).

thf(func_def_2497,type,
    sK1563: ( num > nat ) > num ).

thf(func_def_2498,type,
    sK1564: ( num > nat ) > num ).

thf(func_def_2499,type,
    sK1565: ( real > $o ) > real ).

thf(func_def_2500,type,
    sK1566: int > int > set_int > int ).

thf(func_def_2501,type,
    sK1567: int > int > set_int > int ).

thf(func_def_2502,type,
    sK1568: ( real > rat ) > set_real > real ).

thf(func_def_2503,type,
    sK1569: ( nat > int ) > ( nat > int ) > set_nat > nat ).

thf(func_def_2504,type,
    sK1570: set_complex > ( complex > rat ) > complex ).

thf(func_def_2505,type,
    sK1571: ( complex > real ) > set_complex > complex ).

thf(func_def_2506,type,
    sK1572: set_num > num ).

thf(func_def_2507,type,
    sK1573: real > int ).

thf(func_def_2508,type,
    sK1574: real > ( real > real ) > real > real ).

thf(func_def_2509,type,
    sK1575: ( real > real ) > real > real > real ).

thf(func_def_2510,type,
    sK1576: real > real > ( real > real ) > real ).

thf(func_def_2511,type,
    sK1577: ( real > real ) > real > ( real > real ) > real > real ).

thf(func_def_2512,type,
    sK1578: ( real > real ) > real > ( real > real ) > real > real ).

thf(func_def_2513,type,
    sK1579: ( real > real ) > real > ( real > real ) > real > real ).

thf(func_def_2514,type,
    sK1580: real > real > ( real > real ) > real ).

thf(func_def_2515,type,
    sK1581: ( int > real ) > set_int > int ).

thf(func_def_2516,type,
    sK1582: nat > ( nat > real ) > ( nat > real ) > nat ).

thf(func_def_2517,type,
    sK1583: ( real > $o ) > list_real > real ).

thf(func_def_2518,type,
    sK1584: ( set_int > $o ) > set_int ).

thf(func_def_2519,type,
    sK1585: ( set_int > $o ) > int ).

thf(func_def_2520,type,
    sK1586: rat > rat ).

thf(func_def_2521,type,
    sK1587: rat > rat ).

thf(func_def_2522,type,
    sK1588: set_real > ( real > real ) > real ).

thf(func_def_2523,type,
    sK1589: ( nat > $o ) > nat ).

thf(func_def_2524,type,
    sK1590: set_real > ( real > rat ) > real ).

thf(func_def_2525,type,
    sK1591: rat > rat > rat ).

thf(func_def_2526,type,
    sK1592: nat > nat > nat > nat ).

thf(func_def_2527,type,
    sK1593: nat > nat > nat > nat ).

thf(func_def_2528,type,
    sK1594: rat > rat ).

thf(func_def_2529,type,
    sK1595: nat > set_nat > nat ).

thf(func_def_2530,type,
    sK1596: $o > nat > vEBT_VEBT > nat ).

thf(func_def_2531,type,
    sK1597: $o > nat > vEBT_VEBT > nat ).

thf(func_def_2532,type,
    sK1598: $o > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2533,type,
    sK1599: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2534,type,
    sK1600: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).

thf(func_def_2535,type,
    sK1601: vEBT_VEBT > $o > nat > nat ).

thf(func_def_2536,type,
    sK1602: vEBT_VEBT > $o > nat > vEBT_VEBT ).

thf(func_def_2537,type,
    sK1603: vEBT_VEBT > nat > $o > nat ).

thf(func_def_2538,type,
    sK1604: vEBT_VEBT > nat > $o > nat ).

thf(func_def_2539,type,
    sK1605: vEBT_VEBT > nat > $o > nat ).

thf(func_def_2540,type,
    sK1606: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).

thf(func_def_2541,type,
    sK1607: vEBT_VEBT > nat > $o > vEBT_VEBT ).

thf(func_def_2542,type,
    sK1608: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2543,type,
    sK1609: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2544,type,
    sK1610: vEBT_VEBT > $o ).

thf(func_def_2545,type,
    sK1611: vEBT_VEBT > $o ).

thf(func_def_2546,type,
    sK1612: int > int > set_int > int ).

thf(func_def_2547,type,
    sK1613: int > int > set_int > int ).

thf(func_def_2548,type,
    sK1614: product_prod_int_int > int ).

thf(func_def_2549,type,
    sK1615: product_prod_int_int > int ).

thf(func_def_2550,type,
    sK1616: real > real > real ).

thf(func_def_2551,type,
    sK1617: num > num ).

thf(func_def_2552,type,
    sK1618: rat > rat > rat ).

thf(func_def_2553,type,
    sK1619: real > nat > real ).

thf(func_def_2554,type,
    sK1620: ( set_complex > $o ) > ( complex > nat ) > complex ).

thf(func_def_2555,type,
    sK1621: ( set_complex > $o ) > ( complex > nat ) > set_complex ).

thf(func_def_2556,type,
    sK1622: ( rat > nat ) > rat ).

thf(func_def_2557,type,
    sK1623: ( rat > nat ) > rat ).

thf(func_def_2558,type,
    sK1624: ( nat > int ) > nat > nat ).

thf(func_def_2559,type,
    sK1625: ( nat > int ) > int > nat > nat ).

thf(func_def_2560,type,
    sK1626: ( int > rat ) > set_int > int ).

thf(func_def_2561,type,
    sK1627: ( int > rat ) > set_int > int ).

thf(func_def_2562,type,
    sK1628: int > ( int > $o ) > int ).

thf(func_def_2563,type,
    sK1629: int > ( int > $o ) > int ).

thf(func_def_2564,type,
    sK1630: ( int > $o ) > int > int ).

thf(func_def_2565,type,
    sK1631: ( int > $o ) > int > int ).

thf(func_def_2566,type,
    sK1632: ( nat > $o ) > nat > nat ).

thf(func_def_2567,type,
    sK1633: ( nat > $o ) > nat > nat ).

thf(func_def_2568,type,
    sK1634: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > complex > produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_2569,type,
    sK1635: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > complex > produc7773217078559923341nt_int > product_prod_int_int ).

thf(func_def_2570,type,
    sK1636: ( nat > $o ) > nat > nat ).

thf(func_def_2571,type,
    sK1637: ( nat > $o ) > nat > nat ).

thf(func_def_2572,type,
    sK1638: produc9072475918466114483BT_nat > nat ).

thf(func_def_2573,type,
    sK1639: produc9072475918466114483BT_nat > $o ).

thf(func_def_2574,type,
    sK1640: produc9072475918466114483BT_nat > $o ).

thf(func_def_2575,type,
    sK1641: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2576,type,
    sK1642: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2577,type,
    sK1643: produc9072475918466114483BT_nat > nat ).

thf(func_def_2578,type,
    sK1644: produc9072475918466114483BT_nat > nat ).

thf(func_def_2579,type,
    sK1645: produc9072475918466114483BT_nat > nat ).

thf(func_def_2580,type,
    sK1646: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2581,type,
    sK1647: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2582,type,
    sK1648: produc9072475918466114483BT_nat > nat ).

thf(func_def_2583,type,
    sK1649: produc9072475918466114483BT_nat > nat ).

thf(func_def_2584,type,
    sK1650: produc9072475918466114483BT_nat > nat ).

thf(func_def_2585,type,
    sK1651: produc9072475918466114483BT_nat > nat ).

thf(func_def_2586,type,
    sK1652: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2587,type,
    sK1653: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2588,type,
    sK1654: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2589,type,
    sK1655: produc9072475918466114483BT_nat > nat ).

thf(func_def_2590,type,
    sK1656: produc9072475918466114483BT_nat > nat ).

thf(func_def_2591,type,
    sK1657: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2592,type,
    sK1658: produc9072475918466114483BT_nat > nat ).

thf(func_def_2593,type,
    sK1659: real > int ).

thf(func_def_2594,type,
    sK1660: ( real > real ) > real > real > real ).

thf(func_def_2595,type,
    sK1661: ( real > real ) > real > real > real ).

thf(func_def_2596,type,
    sK1662: real > ( real > real ) > real > real > real ).

thf(func_def_2597,type,
    sK1663: real > real > ( real > real ) > real ).

thf(func_def_2598,type,
    sK1664: ( num > real ) > num ).

thf(func_def_2599,type,
    sK1665: ( num > real ) > num ).

thf(func_def_2600,type,
    sK1666: ( int > num ) > ( set_int > $o ) > set_int ).

thf(func_def_2601,type,
    sK1667: ( int > num ) > ( set_int > $o ) > int ).

thf(func_def_2602,type,
    sK1668: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_2603,type,
    sK1669: list_real > ( real > $o ) > nat ).

thf(func_def_2604,type,
    sK1670: set_nat > ( nat > rat ) > nat ).

thf(func_def_2605,type,
    sK1671: real > ( real > real ) > real ).

thf(func_def_2606,type,
    sK1672: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2607,type,
    sK1673: vEBT_VEBT > nat > nat ).

thf(func_def_2608,type,
    sK1674: vEBT_VEBT > nat > nat ).

thf(func_def_2609,type,
    sK1675: vEBT_VEBT > nat > nat ).

thf(func_def_2610,type,
    sK1676: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2611,type,
    sK1677: nat > vEBT_VEBT > $o ).

thf(func_def_2612,type,
    sK1678: nat > vEBT_VEBT > $o ).

thf(func_def_2613,type,
    sK1679: ( set_nat > $o ) > ( set_nat > $o ) > set_nat ).

thf(func_def_2614,type,
    sK1680: ( complex > rat ) > set_complex > complex ).

thf(func_def_2615,type,
    sK1681: ( list_nat > $o ) > list_nat ).

thf(func_def_2616,type,
    sK1682: ( int > complex ) > set_int > int ).

thf(func_def_2617,type,
    sK1683: ( int > int ) > ( int > int ) > set_int > set_int > int ).

thf(func_def_2618,type,
    sK1684: set_int > set_int > ( int > int ) > set_int > set_int > int ).

thf(func_def_2619,type,
    sK1685: ( int > complex ) > set_int > int ).

thf(func_def_2620,type,
    sK1686: set_int > set_int > set_int > ( int > int ) > set_int > int ).

thf(func_def_2621,type,
    sK1687: ( int > int ) > set_int > set_int > ( int > int ) > int ).

thf(func_def_2622,type,
    sK1688: ( int > complex ) > ( int > complex ) > ( int > int ) > set_int > int ).

thf(func_def_2623,type,
    sK1689: set_complex > ( complex > nat ) > complex ).

thf(func_def_2624,type,
    sK1690: set_complex > ( complex > nat ) > complex ).

thf(func_def_2625,type,
    sK1691: ( nat > real > real ) > nat > real > real ).

thf(func_def_2626,type,
    sK1692: ( nat > real > real ) > nat > real > nat ).

thf(func_def_2627,type,
    sK1693: ( nat > int ) > nat ).

thf(func_def_2628,type,
    sK1694: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_2629,type,
    sK1695: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2630,type,
    sK1696: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2631,type,
    sK1697: vEBT_VEBT > nat ).

thf(func_def_2632,type,
    sK1698: vEBT_VEBT > $o ).

thf(func_def_2633,type,
    sK1699: vEBT_VEBT > $o ).

thf(func_def_2634,type,
    sK1700: nat > $o > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2635,type,
    sK1701: nat > $o > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2636,type,
    sK1702: nat > $o > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_2637,type,
    sK1703: vEBT_VEBT > nat > $o > nat ).

thf(func_def_2638,type,
    sK1704: vEBT_VEBT > nat > $o > vEBT_VEBT ).

thf(func_def_2639,type,
    sK1705: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).

thf(func_def_2640,type,
    sK1706: vEBT_VEBT > nat > $o > option4927543243414619207at_nat ).

thf(func_def_2641,type,
    sK1707: $o > nat > vEBT_VEBT > $o ).

thf(func_def_2642,type,
    sK1708: $o > nat > vEBT_VEBT > $o ).

thf(func_def_2643,type,
    sK1709: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2644,type,
    sK1710: vEBT_VEBT > option_nat > nat ).

thf(func_def_2645,type,
    sK1711: vEBT_VEBT > option_nat > nat ).

thf(func_def_2646,type,
    sK1712: vEBT_VEBT > option_nat > vEBT_VEBT ).

thf(func_def_2647,type,
    sK1713: vEBT_VEBT > option_nat > list_VEBT_VEBT ).

thf(func_def_2648,type,
    sK1714: vEBT_VEBT > option_nat > nat ).

thf(func_def_2649,type,
    sK1715: vEBT_VEBT > option_nat > $o ).

thf(func_def_2650,type,
    sK1716: vEBT_VEBT > option_nat > $o ).

thf(func_def_2651,type,
    sK1717: option_nat > vEBT_VEBT > nat ).

thf(func_def_2652,type,
    sK1718: option_nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2653,type,
    sK1719: option_nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2654,type,
    sK1720: code_integer > code_integer > code_integer > code_integer ).

thf(func_def_2655,type,
    sK1721: real > real > real ).

thf(func_def_2656,type,
    sK1722: int > int ).

thf(func_def_2657,type,
    sK1723: real > real > real ).

thf(func_def_2658,type,
    sK1724: ( rat > int ) > rat ).

thf(func_def_2659,type,
    sK1725: ( rat > int ) > rat ).

thf(func_def_2660,type,
    sK1726: nat > nat > vEBT_VEBT > nat ).

thf(func_def_2661,type,
    sK1727: ( real > nat ) > set_real > set_real > real ).

thf(func_def_2662,type,
    sK1728: ( real > nat ) > set_real > ( real > nat ) > real ).

thf(func_def_2663,type,
    sK1729: real > real ).

thf(func_def_2664,type,
    sK1730: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_2665,type,
    sK1731: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2666,type,
    sK1732: nat > vEBT_VEBT > nat ).

thf(func_def_2667,type,
    sK1733: nat > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_2668,type,
    sK1734: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2669,type,
    sK1735: vEBT_VEBT > nat > $o ).

thf(func_def_2670,type,
    sK1736: vEBT_VEBT > nat > $o ).

thf(func_def_2671,type,
    sK1737: ( nat > real ) > real ).

thf(func_def_2672,type,
    sK1738: real > ( nat > real ) > nat ).

thf(func_def_2673,type,
    sK1739: set_rat > rat > rat ).

thf(func_def_2674,type,
    sK1740: ( nat > nat > $o ) > nat ).

thf(func_def_2675,type,
    sK1741: ( nat > nat > $o ) > nat ).

thf(func_def_2676,type,
    sK1742: ( nat > nat > $o ) > nat ).

thf(func_def_2677,type,
    sK1743: ( nat > nat > $o ) > nat ).

thf(func_def_2678,type,
    sK1744: ( nat > nat > $o ) > nat ).

thf(func_def_2679,type,
    sK1745: ( rat > num ) > rat ).

thf(func_def_2680,type,
    sK1746: ( rat > num ) > rat ).

thf(func_def_2681,type,
    sK1747: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2682,type,
    sK1748: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2683,type,
    sK1749: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2684,type,
    sK1750: nat > ( nat > $o ) > nat ).

thf(func_def_2685,type,
    sK1751: ( real > rat ) > real ).

thf(func_def_2686,type,
    sK1752: ( real > rat ) > real ).

thf(func_def_2687,type,
    sK1753: int > set_int > int ).

thf(func_def_2688,type,
    sK1754: set_int > int ).

thf(func_def_2689,type,
    sK1755: produc9072475918466114483BT_nat > $o ).

thf(func_def_2690,type,
    sK1756: produc9072475918466114483BT_nat > $o ).

thf(func_def_2691,type,
    sK1757: produc9072475918466114483BT_nat > nat ).

thf(func_def_2692,type,
    sK1758: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2693,type,
    sK1759: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2694,type,
    sK1760: produc9072475918466114483BT_nat > nat ).

thf(func_def_2695,type,
    sK1761: produc9072475918466114483BT_nat > nat ).

thf(func_def_2696,type,
    sK1762: produc9072475918466114483BT_nat > nat ).

thf(func_def_2697,type,
    sK1763: produc9072475918466114483BT_nat > nat ).

thf(func_def_2698,type,
    sK1764: produc9072475918466114483BT_nat > $o ).

thf(func_def_2699,type,
    sK1765: produc9072475918466114483BT_nat > $o ).

thf(func_def_2700,type,
    sK1766: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2701,type,
    sK1767: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_2702,type,
    sK1768: produc9072475918466114483BT_nat > nat ).

thf(func_def_2703,type,
    sK1769: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2704,type,
    sK1770: produc9072475918466114483BT_nat > nat ).

thf(func_def_2705,type,
    sK1771: produc9072475918466114483BT_nat > nat ).

thf(func_def_2706,type,
    sK1772: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2707,type,
    sK1773: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2708,type,
    sK1774: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_2709,type,
    sK1775: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2710,type,
    sK1776: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2711,type,
    sK1777: produc9072475918466114483BT_nat > nat ).

thf(func_def_2712,type,
    sK1778: list_int > ( int > $o ) > nat ).

thf(func_def_2713,type,
    sK1779: set_nat > ( nat > rat ) > nat ).

thf(func_def_2714,type,
    sK1780: set_real > ( real > nat ) > real ).

thf(func_def_2715,type,
    sK1781: ( complex > real ) > set_complex > complex ).

thf(func_def_2716,type,
    sK1782: ( nat > nat ) > nat ).

thf(func_def_2717,type,
    sK1783: ( nat > nat ) > nat ).

thf(func_def_2718,type,
    sK1784: ( set_nat > $o ) > set_nat ).

thf(func_def_2719,type,
    sK1785: num > num ).

thf(func_def_2720,type,
    sK1786: ( option_nat > option_nat > $o ) > option_nat > option_nat > nat ).

thf(func_def_2721,type,
    sK1787: ( option_nat > option_nat > $o ) > option_nat > option_nat > nat ).

thf(func_def_2722,type,
    sK1788: ( complex > rat ) > set_complex > set_complex > complex ).

thf(func_def_2723,type,
    sK1789: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2724,type,
    sK1790: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2725,type,
    sK1791: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2726,type,
    sK1792: option_nat > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2727,type,
    sK1793: option_nat > nat > vEBT_VEBT > nat ).

thf(func_def_2728,type,
    sK1794: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2729,type,
    sK1795: vEBT_VEBT > nat > option_nat > list_VEBT_VEBT ).

thf(func_def_2730,type,
    sK1796: vEBT_VEBT > nat > option_nat > product_prod_nat_nat ).

thf(func_def_2731,type,
    sK1797: vEBT_VEBT > nat > option_nat > vEBT_VEBT ).

thf(func_def_2732,type,
    sK1798: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_2733,type,
    sK1799: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_2734,type,
    sK1800: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_2735,type,
    sK1801: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_2736,type,
    sK1802: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_2737,type,
    sK1803: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).

thf(func_def_2738,type,
    sK1804: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).

thf(func_def_2739,type,
    sK1805: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_2740,type,
    sK1806: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_2741,type,
    sK1807: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_2742,type,
    sK1808: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_2743,type,
    sK1809: vEBT_VEBT > nat > option_nat > nat ).

thf(func_def_2744,type,
    sK1810: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2745,type,
    sK1811: nat > option_nat > vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_2746,type,
    sK1812: nat > option_nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2747,type,
    sK1813: real > real > ( complex > real ) > set_complex > complex ).

thf(func_def_2748,type,
    sK1814: set_complex > ( complex > real ) > complex ).

thf(func_def_2749,type,
    sK1815: set_real > set_real > ( real > int ) > real ).

thf(func_def_2750,type,
    sK1816: set_real > ( real > int ) > ( real > int ) > real ).

thf(func_def_2751,type,
    sK1817: ( real > real ) > set_real > real ).

thf(func_def_2752,type,
    sK1818: set_int > set_complex > ( int > real ) > ( complex > real ) > ( complex > int ) > int ).

thf(func_def_2753,type,
    sK1819: set_complex > ( complex > real ) > complex ).

thf(func_def_2754,type,
    sK1820: ( nat > real ) > nat > int ).

thf(func_def_2755,type,
    sK1821: nat > nat > nat ).

thf(func_def_2756,type,
    sK1822: ( complex > rat ) > set_complex > complex ).

thf(func_def_2757,type,
    sK1823: set_int > ( int > real ) > int ).

thf(func_def_2758,type,
    sK1824: int > int > int > int ).

thf(func_def_2759,type,
    sK1825: int > int > int > int ).

thf(func_def_2760,type,
    sK1826: vEBT_VEBT > option_nat > $o ).

thf(func_def_2761,type,
    sK1827: vEBT_VEBT > option_nat > $o ).

thf(func_def_2762,type,
    sK1828: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2763,type,
    sK1829: vEBT_VEBT > nat ).

thf(func_def_2764,type,
    sK1830: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2765,type,
    sK1831: vEBT_VEBT > option_nat > nat ).

thf(func_def_2766,type,
    sK1832: vEBT_VEBT > option_nat > nat ).

thf(func_def_2767,type,
    sK1833: vEBT_VEBT > option_nat > nat ).

thf(func_def_2768,type,
    sK1834: vEBT_VEBT > option_nat > list_VEBT_VEBT ).

thf(func_def_2769,type,
    sK1835: vEBT_VEBT > option_nat > vEBT_VEBT ).

thf(func_def_2770,type,
    sK1836: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2771,type,
    sK1837: code_integer > code_integer ).

thf(func_def_2772,type,
    sK1838: ( produc7773217078559923341nt_int > $o ) > int > option6357759511663192854e_term ).

thf(func_def_2773,type,
    sK1839: ( produc7773217078559923341nt_int > $o ) > int ).

thf(func_def_2774,type,
    sK1840: ( produc7773217078559923341nt_int > $o ) > int ).

thf(func_def_2775,type,
    sK1841: set_nat > list_nat ).

thf(func_def_2776,type,
    sK1842: int > set_int > int > int ).

thf(func_def_2777,type,
    sK1843: int > set_int > int > int ).

thf(func_def_2778,type,
    sK1844: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2779,type,
    sK1845: num > num ).

thf(func_def_2780,type,
    sK1846: ( int > real ) > int ).

thf(func_def_2781,type,
    sK1847: ( int > real ) > int ).

thf(func_def_2782,type,
    sK1848: ( int > $o ) > int ).

thf(func_def_2783,type,
    sK1849: ( int > $o ) > int ).

thf(func_def_2784,type,
    sK1850: ( int > $o ) > $o ).

thf(func_def_2785,type,
    sK1851: real > ( real > real ) > nat > ( nat > real > real ) > real ).

thf(func_def_2786,type,
    sK1852: ( nat > real > real ) > real ).

thf(func_def_2787,type,
    sK1853: ( nat > real > real ) > nat ).

thf(func_def_2788,type,
    sK1854: ( real > rat ) > real ).

thf(func_def_2789,type,
    sK1855: ( real > rat ) > real ).

thf(func_def_2790,type,
    sK1856: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2791,type,
    sK1857: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2792,type,
    sK1858: vEBT_VEBT > nat > nat ).

thf(func_def_2793,type,
    sK1859: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2794,type,
    sK1860: vEBT_VEBT > nat > nat ).

thf(func_def_2795,type,
    sK1861: vEBT_VEBT > nat > nat ).

thf(func_def_2796,type,
    sK1862: vEBT_VEBT > nat > nat ).

thf(func_def_2797,type,
    sK1863: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2798,type,
    sK1864: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2799,type,
    sK1865: nat > vEBT_VEBT > nat ).

thf(func_def_2800,type,
    sK1866: nat > vEBT_VEBT > nat ).

thf(func_def_2801,type,
    sK1867: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2802,type,
    sK1868: ( set_set_nat > $o ) > set_set_nat > set_set_nat ).

thf(func_def_2803,type,
    sK1869: ( real > real ) > set_real > real ).

thf(func_def_2804,type,
    sK1870: real > int ).

thf(func_def_2805,type,
    sK1871: ( $o > $o ) > product_prod_int_int > ( int > int > $o ) > int ).

thf(func_def_2806,type,
    sK1872: ( $o > $o ) > product_prod_int_int > ( int > int > $o ) > int ).

thf(func_def_2807,type,
    sK1873: set_real > ( real > int ) > ( real > int ) > real ).

thf(func_def_2808,type,
    sK1874: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2809,type,
    sK1875: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2810,type,
    sK1876: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_2811,type,
    sK1877: code_integer > code_integer > code_integer ).

thf(func_def_2812,type,
    sK1878: ( real > real ) > real > real ).

thf(func_def_2813,type,
    sK1879: real > real ).

thf(func_def_2814,type,
    sK1880: nat > nat ).

thf(func_def_2815,type,
    sK1881: nat > nat ).

thf(func_def_2816,type,
    sK1882: ( real > real ) > ( real > real ) > real > real > real ).

thf(func_def_2817,type,
    sK1883: ( real > real ) > real > real > ( real > real ) > real ).

thf(func_def_2818,type,
    sK1884: set_list_nat > nat ).

thf(func_def_2819,type,
    sK1885: ( real > nat ) > set_real > real ).

thf(func_def_2820,type,
    sK1886: nat > nat ).

thf(func_def_2821,type,
    sK1887: ( int > real ) > set_int > ( int > real ) > int ).

thf(func_def_2822,type,
    sK1888: real > real > ( real > real ) > real ).

thf(func_def_2823,type,
    sK1889: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > int > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_2824,type,
    sK1890: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > int > produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_2825,type,
    sK1891: ( num > int ) > num ).

thf(func_def_2826,type,
    sK1892: ( num > int ) > num ).

thf(func_def_2827,type,
    sK1893: ( num > rat ) > num ).

thf(func_def_2828,type,
    sK1894: ( num > rat ) > num ).

thf(func_def_2829,type,
    sK1895: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2830,type,
    sK1896: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2831,type,
    sK1897: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_2832,type,
    sK1898: ( int > nat ) > set_int > ( int > nat ) > int ).

thf(func_def_2833,type,
    sK1899: ( nat > $o ) > nat ).

thf(func_def_2834,type,
    sK1900: nat > ( nat > $o ) > nat ).

thf(func_def_2835,type,
    sK1901: real > ( real > $o ) > nat > real ).

thf(func_def_2836,type,
    sK1902: set_real > real > ( real > real ) > real ).

thf(func_def_2837,type,
    sK1903: ( real > rat ) > real ).

thf(func_def_2838,type,
    sK1904: ( real > rat ) > real ).

thf(func_def_2839,type,
    sK1905: real > real > ( real > real ) > real ).

thf(func_def_2840,type,
    sK1906: set_nat > nat ).

thf(func_def_2841,type,
    sK1907: ( int > $o ) > int > int ).

thf(func_def_2842,type,
    sK1908: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_2843,type,
    sK1909: produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_2844,type,
    sK1910: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_2845,type,
    sK1911: nat > ( vEBT_VEBT > $o ) > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2846,type,
    sK1912: ( nat > $o ) > nat ).

thf(func_def_2847,type,
    sK1913: ( nat > $o ) > nat ).

thf(func_def_2848,type,
    sK1914: ( real > real ) > real ).

thf(func_def_2849,type,
    sK1915: ( product_prod_int_int > $o ) > int ).

thf(func_def_2850,type,
    sK1916: ( product_prod_int_int > $o ) > int ).

thf(func_def_2851,type,
    sK1917: ( set_complex > $o ) > set_complex > set_complex ).

thf(func_def_2852,type,
    sK1918: ( complex > real ) > set_complex > complex > complex ).

thf(func_def_2853,type,
    sK1919: ( nat > real ) > set_nat > nat ).

thf(func_def_2854,type,
    sK1920: set_nat > list_set_nat > set_nat ).

thf(func_def_2855,type,
    sK1921: int > int > int ).

thf(func_def_2856,type,
    sK1922: int > int > int ).

thf(func_def_2857,type,
    sK1923: set_nat > nat > nat ).

thf(func_def_2858,type,
    sK1924: produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > code_integer > option6357759511663192854e_term ).

thf(func_def_2859,type,
    sK1925: produc8763457246119570046nteger > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8923325533196201883nteger ).

thf(func_def_2860,type,
    sK1926: ( nat > nat ) > nat > nat > nat ).

thf(func_def_2861,type,
    sK1927: set_set_nat > set_nat > set_nat ).

thf(func_def_2862,type,
    sK1928: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2863,type,
    sK1929: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_2864,type,
    sK1930: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2865,type,
    sK1931: ( nat > real ) > nat ).

thf(func_def_2866,type,
    sK1932: int > ( nat > $o ) > nat ).

thf(func_def_2867,type,
    sK1933: ( int > $o ) > int > int ).

thf(func_def_2868,type,
    sK1934: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_2869,type,
    sK1935: list_VEBT_VEBT > nat ).

thf(func_def_2870,type,
    sK1936: vEBT_VEBT > nat ).

thf(func_def_2871,type,
    sK1937: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_2872,type,
    sK1938: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_2873,type,
    sK1939: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_2874,type,
    sK1940: set_real > ( real > complex ) > real ).

thf(func_def_2875,type,
    sK1941: rat > rat ).

thf(func_def_2876,type,
    sK1942: product_prod_int_int > int > int > int ).

thf(func_def_2877,type,
    sK1943: product_prod_int_int > int > int > int ).

thf(func_def_2878,type,
    sK1944: int > int > product_prod_int_int > int ).

thf(func_def_2879,type,
    sK1945: produc9072475918466114483BT_nat > nat ).

thf(func_def_2880,type,
    sK1946: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_2881,type,
    sK1947: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2882,type,
    sK1948: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2883,type,
    sK1949: produc9072475918466114483BT_nat > $o ).

thf(func_def_2884,type,
    sK1950: produc9072475918466114483BT_nat > nat ).

thf(func_def_2885,type,
    sK1951: produc9072475918466114483BT_nat > $o ).

thf(func_def_2886,type,
    sK1952: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2887,type,
    sK1953: produc9072475918466114483BT_nat > nat ).

thf(func_def_2888,type,
    sK1954: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_2889,type,
    sK1955: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2890,type,
    sK1956: produc9072475918466114483BT_nat > nat ).

thf(func_def_2891,type,
    sK1957: produc9072475918466114483BT_nat > nat ).

thf(func_def_2892,type,
    sK1958: produc9072475918466114483BT_nat > nat ).

thf(func_def_2893,type,
    sK1959: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2894,type,
    sK1960: produc9072475918466114483BT_nat > nat ).

thf(func_def_2895,type,
    sK1961: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2896,type,
    sK1962: produc9072475918466114483BT_nat > $o ).

thf(func_def_2897,type,
    sK1963: produc9072475918466114483BT_nat > $o ).

thf(func_def_2898,type,
    sK1964: produc9072475918466114483BT_nat > nat ).

thf(func_def_2899,type,
    sK1965: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_2900,type,
    sK1966: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_2901,type,
    sK1967: produc9072475918466114483BT_nat > nat ).

thf(func_def_2902,type,
    sK1968: produc9072475918466114483BT_nat > $o ).

thf(func_def_2903,type,
    sK1969: produc9072475918466114483BT_nat > $o ).

thf(func_def_2904,type,
    sK1970: set_real > ( real > rat ) > ( real > rat ) > real ).

thf(func_def_2905,type,
    sK1971: set_real > set_real > ( real > int ) > real ).

thf(func_def_2906,type,
    sK1972: set_real > ( real > int ) > ( real > int ) > real ).

thf(func_def_2907,type,
    sK1973: ( nat > nat ) > nat ).

thf(func_def_2908,type,
    sK1974: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2909,type,
    sK1975: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2910,type,
    sK1976: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_2911,type,
    sK1977: real > nat > real ).

thf(func_def_2912,type,
    sK1978: ( int > int > $o ) > int ).

thf(func_def_2913,type,
    sK1979: ( rat > real ) > rat ).

thf(func_def_2914,type,
    sK1980: ( rat > real ) > rat ).

thf(func_def_2915,type,
    sK1981: ( nat > real ) > nat ).

thf(func_def_2916,type,
    sK1982: set_complex > ( complex > int ) > ( complex > int ) > complex ).

thf(func_def_2917,type,
    sK1983: ( real > real ) > set_real > ( real > complex ) > real ).

thf(func_def_2918,type,
    sK1984: rat > rat ).

thf(func_def_2919,type,
    sK1985: ( rat > rat ) > rat ).

thf(func_def_2920,type,
    sK1986: ( rat > rat ) > rat ).

thf(func_def_2921,type,
    sK1987: set_set_int > set_int ).

thf(func_def_2922,type,
    sK1988: rat > nat ).

thf(func_def_2923,type,
    sK1989: nat > nat > nat ).

thf(func_def_2924,type,
    sK1990: ( int > int ) > ( int > int ) > set_int > int ).

thf(func_def_2925,type,
    sK1991: vEBT_VEBT > $o > nat > $o ).

thf(func_def_2926,type,
    sK1992: vEBT_VEBT > $o > nat > $o ).

thf(func_def_2927,type,
    sK1993: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2928,type,
    sK1994: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_2929,type,
    sK1995: $o > nat > vEBT_VEBT > nat ).

thf(func_def_2930,type,
    sK1996: $o > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2931,type,
    sK1997: $o > nat > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_2932,type,
    sK1998: ( int > int > set_int ) > int > product_prod_int_int > int ).

thf(func_def_2933,type,
    sK1999: ( int > int > set_int ) > int > product_prod_int_int > int ).

thf(func_def_2934,type,
    sK2000: ( int > real ) > int ).

thf(func_def_2935,type,
    sK2001: ( int > real ) > int ).

thf(func_def_2936,type,
    sK2002: ( num > rat ) > num ).

thf(func_def_2937,type,
    sK2003: ( num > rat ) > num ).

thf(func_def_2938,type,
    sK2004: ( set_complex > $o ) > complex ).

thf(func_def_2939,type,
    sK2005: ( set_complex > $o ) > set_complex ).

thf(func_def_2940,type,
    sK2006: real > ( real > real ) > real ).

thf(func_def_2941,type,
    sK2007: produc1908205239877642774nteger > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_2942,type,
    sK2008: produc1908205239877642774nteger > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8923325533196201883nteger ).

thf(func_def_2943,type,
    sK2009: ( nat > int ) > set_nat > set_nat > nat ).

thf(func_def_2944,type,
    sK2010: int > int > int ).

thf(func_def_2945,type,
    sK2011: ( num > real ) > num ).

thf(func_def_2946,type,
    sK2012: ( num > real ) > num ).

thf(func_def_2947,type,
    sK2013: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_2948,type,
    sK2014: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_2949,type,
    sK2015: ( real > real ) > real > set_real > real ).

thf(func_def_2950,type,
    sK2016: ( rat > $o ) > int ).

thf(func_def_2951,type,
    sK2017: ( rat > $o ) > int ).

thf(func_def_2952,type,
    sK2018: nat > vEBT_VEBT > $o ).

thf(func_def_2953,type,
    sK2019: nat > vEBT_VEBT > $o ).

thf(func_def_2954,type,
    sK2020: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_2955,type,
    sK2021: vEBT_VEBT > nat > nat ).

thf(func_def_2956,type,
    sK2022: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_2957,type,
    sK2023: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_2958,type,
    sK2024: ( num > num ) > num ).

thf(func_def_2959,type,
    sK2025: ( num > num ) > num ).

thf(func_def_2960,type,
    sK2026: ( nat > real > real ) > nat > real > real > real ).

thf(func_def_2961,type,
    sK2027: ( nat > real > real ) > nat > real > real > nat ).

thf(func_def_2962,type,
    sK2028: real > nat > real > ( real > real ) > ( nat > real > real ) > real ).

thf(func_def_2963,type,
    sK2029: ( int > rat ) > set_int > ( int > rat ) > int ).

thf(func_def_2964,type,
    sK2030: ( produc1908205239877642774nteger > $o ) > produc8923325533196201883nteger ).

thf(func_def_2965,type,
    sK2031: ( produc1908205239877642774nteger > $o ) > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_2966,type,
    sK2032: nat > ( nat > $o ) > nat ).

thf(func_def_2967,type,
    sK2033: nat > ( nat > $o ) > nat ).

thf(func_def_2968,type,
    sK2034: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_2969,type,
    sK2035: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > nat ).

thf(func_def_2970,type,
    sK2036: ( nat > rat ) > nat ).

thf(func_def_2971,type,
    sK2037: ( nat > rat ) > nat ).

thf(func_def_2972,type,
    sK2038: nat > nat > ( nat > $o ) > nat ).

thf(func_def_2973,type,
    sK2039: ( real > $o ) > nat ).

thf(func_def_2974,type,
    sK2040: ( real > $o ) > real ).

thf(func_def_2975,type,
    sK2041: ( real > $o ) > real ).

thf(func_def_2976,type,
    sK2042: ( num > rat ) > num ).

thf(func_def_2977,type,
    sK2043: ( num > rat ) > num ).

thf(func_def_2978,type,
    sK2044: nat > ( nat > nat ) > nat ).

thf(func_def_2979,type,
    sK2045: nat > ( nat > nat ) > nat ).

thf(func_def_2980,type,
    sK2046: ( set_int > $o ) > set_int ).

thf(func_def_2981,type,
    sK2047: ( rat > real ) > rat ).

thf(func_def_2982,type,
    sK2048: ( rat > real ) > rat ).

thf(func_def_2983,type,
    sK2049: ( nat > real ) > real > nat > int ).

thf(func_def_2984,type,
    sK2050: ( nat > nat ) > nat ).

thf(func_def_2985,type,
    sK2051: set_real > real ).

thf(func_def_2986,type,
    sK2052: real > set_real > real ).

thf(func_def_2987,type,
    sK2053: real > set_real > real ).

thf(func_def_2988,type,
    sK2054: ( real > real ) > real ).

thf(func_def_2989,type,
    sK2055: ( real > real ) > real ).

thf(func_def_2990,type,
    sK2056: list_nat > ( nat > $o ) > nat ).

thf(func_def_2991,type,
    sK2057: ( nat > rat ) > nat ).

thf(func_def_2992,type,
    sK2058: ( nat > rat ) > nat ).

thf(func_def_2993,type,
    sK2059: set_nat > nat ).

thf(func_def_2994,type,
    sK2060: nat > set_nat > nat ).

thf(func_def_2995,type,
    sK2061: ( nat > rat ) > set_nat > nat ).

thf(func_def_2996,type,
    sK2062: set_real > ( real > rat ) > real ).

thf(func_def_2997,type,
    sK2063: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_2998,type,
    sK2064: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_2999,type,
    sK2065: vEBT_VEBT > nat ).

thf(func_def_3000,type,
    sK2066: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3001,type,
    sK2067: vEBT_VEBT > $o ).

thf(func_def_3002,type,
    sK2068: vEBT_VEBT > nat ).

thf(func_def_3003,type,
    sK2069: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3004,type,
    sK2070: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3005,type,
    sK2071: vEBT_VEBT > $o ).

thf(func_def_3006,type,
    sK2072: ( nat > $o ) > nat ).

thf(func_def_3007,type,
    sK2073: ( nat > $o ) > nat ).

thf(func_def_3008,type,
    sK2074: ( nat > $o ) > $o ).

thf(func_def_3009,type,
    sK2075: ( nat > rat ) > nat ).

thf(func_def_3010,type,
    sK2076: ( nat > rat ) > nat ).

thf(func_def_3011,type,
    sK2077: ( rat > num ) > rat ).

thf(func_def_3012,type,
    sK2078: ( rat > num ) > rat ).

thf(func_def_3013,type,
    sK2079: real > real > nat ).

thf(func_def_3014,type,
    sK2080: set_real > real > ( real > rat ) > real ).

thf(func_def_3015,type,
    sK2081: set_real > ( real > rat ) > real ).

thf(func_def_3016,type,
    sK2082: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).

thf(func_def_3017,type,
    sK2083: ( real > complex ) > set_real > ( real > complex ) > real ).

thf(func_def_3018,type,
    sK2084: set_real > set_real > ( real > complex ) > real ).

thf(func_def_3019,type,
    sK2085: set_int > set_set_int > set_int ).

thf(func_def_3020,type,
    sK2086: set_real > real ).

thf(func_def_3021,type,
    sK2087: ( nat > nat > $o ) > nat ).

thf(func_def_3022,type,
    sK2088: ( nat > nat > $o ) > nat ).

thf(func_def_3023,type,
    sK2089: ( nat > nat > $o ) > nat ).

thf(func_def_3024,type,
    sK2090: ( nat > nat > $o ) > nat ).

thf(func_def_3025,type,
    sK2091: ( nat > nat > $o ) > nat ).

thf(func_def_3026,type,
    sK2092: nat > nat > nat ).

thf(func_def_3027,type,
    sK2093: nat > nat > nat ).

thf(func_def_3028,type,
    sK2094: nat > nat > nat ).

thf(func_def_3029,type,
    sK2095: set_int > ( int > rat ) > ( int > rat ) > int ).

thf(func_def_3030,type,
    sK2096: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3031,type,
    sK2097: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3032,type,
    sK2098: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3033,type,
    sK2099: set_real > real ).

thf(func_def_3034,type,
    sK2100: ( set_nat > $o ) > nat ).

thf(func_def_3035,type,
    sK2101: ( set_nat > $o ) > set_nat ).

thf(func_def_3036,type,
    sK2102: produc1193250871479095198on_num > num > num > num ).

thf(func_def_3037,type,
    sK2103: produc1193250871479095198on_num > num ).

thf(func_def_3038,type,
    sK2104: produc1193250871479095198on_num > num ).

thf(func_def_3039,type,
    sK2105: produc1193250871479095198on_num > num > num > num ).

thf(func_def_3040,type,
    sK2106: produc1193250871479095198on_num > num ).

thf(func_def_3041,type,
    sK2107: produc1193250871479095198on_num > num > num > num ).

thf(func_def_3042,type,
    sK2108: produc1193250871479095198on_num > option_num ).

thf(func_def_3043,type,
    sK2109: real > ( nat > real ) > nat ).

thf(func_def_3044,type,
    sK2110: ( num > real ) > num ).

thf(func_def_3045,type,
    sK2111: ( num > real ) > num ).

thf(func_def_3046,type,
    sK2112: ( nat > real > real ) > real > nat > real ).

thf(func_def_3047,type,
    sK2113: ( nat > real > real ) > real > nat > nat ).

thf(func_def_3048,type,
    sK2114: ( real > real ) > nat > real > ( nat > real > real ) > real ).

thf(func_def_3049,type,
    sK2115: set_nat > ( nat > complex ) > set_nat > nat ).

thf(func_def_3050,type,
    sK2116: set_nat > set_nat > ( nat > complex ) > nat ).

thf(func_def_3051,type,
    sK2117: complex > real ).

thf(func_def_3052,type,
    sK2118: vEBT_VEBT > nat ).

thf(func_def_3053,type,
    sK2119: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3054,type,
    sK2120: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3055,type,
    sK2121: nat > vEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_3056,type,
    sK2122: nat > vEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_3057,type,
    sK2123: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_3058,type,
    sK2124: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_3059,type,
    sK2125: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3060,type,
    sK2126: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_3061,type,
    sK2127: list_VEBT_VEBT > nat ).

thf(func_def_3062,type,
    sK2128: nat > nat > nat ).

thf(func_def_3063,type,
    sK2129: set_real > set_real > ( real > real ) > real ).

thf(func_def_3064,type,
    sK2130: ( real > real ) > set_real > set_real > real ).

thf(func_def_3065,type,
    sK2131: ( complex > nat ) > set_complex > complex ).

thf(func_def_3066,type,
    sK2132: set_set_nat > set_nat > set_nat ).

thf(func_def_3067,type,
    sK2133: real > real > real ).

thf(func_def_3068,type,
    sK2134: set_complex > ( complex > nat ) > ( complex > nat ) > complex ).

thf(func_def_3069,type,
    sK2135: ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).

thf(func_def_3070,type,
    sK2136: ( ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > product_prod_nat_nat > ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).

thf(func_def_3071,type,
    sK2137: ( complex > rat ) > set_complex > complex ).

thf(func_def_3072,type,
    sK2138: rat > ( complex > rat ) > set_complex > rat > complex ).

thf(func_def_3073,type,
    sK2139: real > int ).

thf(func_def_3074,type,
    sK2140: list_nat > nat > nat ).

thf(func_def_3075,type,
    sK2141: list_nat > nat > list_nat ).

thf(func_def_3076,type,
    sK2142: list_int > int > int ).

thf(func_def_3077,type,
    sK2143: real > nat ).

thf(func_def_3078,type,
    sK2144: ( complex > rat ) > set_complex > set_complex > complex ).

thf(func_def_3079,type,
    sK2145: rat > nat ).

thf(func_def_3080,type,
    sK2146: set_nat > nat ).

thf(func_def_3081,type,
    sK2147: ( $o > $o ) > list_o > $o ).

thf(func_def_3082,type,
    sK2148: ( set_nat > $o ) > set_nat ).

thf(func_def_3083,type,
    sK2149: ( set_nat > $o ) > nat ).

thf(func_def_3084,type,
    sK2150: ( int > nat ) > set_int > int ).

thf(func_def_3085,type,
    sK2151: real > nat > real ).

thf(func_def_3086,type,
    sK2152: ( num > int ) > num ).

thf(func_def_3087,type,
    sK2153: ( num > int ) > num ).

thf(func_def_3088,type,
    sK2154: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).

thf(func_def_3089,type,
    sK2155: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > nat ).

thf(func_def_3090,type,
    sK2156: real > real > real ).

thf(func_def_3091,type,
    sK2157: real > real > real ).

thf(func_def_3092,type,
    sK2158: set_complex > ( set_complex > $o ) > set_complex ).

thf(func_def_3093,type,
    sK2159: real > real > real ).

thf(func_def_3094,type,
    sK2160: ( int > $o ) > int > int ).

thf(func_def_3095,type,
    sK2161: ( int > $o ) > int > int ).

thf(func_def_3096,type,
    sK2162: int > int > set_int > int ).

thf(func_def_3097,type,
    sK2163: int > int > set_int > int ).

thf(func_def_3098,type,
    sK2164: int > int ).

thf(func_def_3099,type,
    sK2165: ( num > nat ) > num ).

thf(func_def_3100,type,
    sK2166: ( num > nat ) > num ).

thf(func_def_3101,type,
    sK2167: nat ).

thf(func_def_3102,type,
    sK2168: set_int > int ).

thf(func_def_3103,type,
    sK2169: ( nat > rat ) > nat ).

thf(func_def_3104,type,
    sK2170: ( nat > rat ) > nat ).

thf(func_def_3105,type,
    sK2171: set_complex > ( complex > real ) > complex ).

thf(func_def_3106,type,
    sK2172: int > set_int > int > int ).

thf(func_def_3107,type,
    sK2173: int > set_int > int > int ).

thf(func_def_3108,type,
    sK2174: ( complex > real ) > set_complex > complex ).

thf(func_def_3109,type,
    sK2175: int > nat > ( nat > int ) > nat ).

thf(func_def_3110,type,
    sK2176: int > int > int ).

thf(func_def_3111,type,
    sK2177: set_nat > set_nat > ( nat > int ) > nat ).

thf(func_def_3112,type,
    sK2178: real > nat ).

thf(func_def_3113,type,
    sK2179: ( nat > $o ) > nat > nat ).

thf(func_def_3114,type,
    sK2180: int > int > ( int > $o ) > int ).

thf(func_def_3115,type,
    sK2181: int > int > ( int > $o ) > int ).

thf(func_def_3116,type,
    sK2182: ( int > $o ) > int > int > int ).

thf(func_def_3117,type,
    sK2183: ( int > $o ) > int > int > int ).

thf(func_def_3118,type,
    sK2184: nat > real > real ).

thf(func_def_3119,type,
    sK2185: set_int > ( int > rat ) > set_int > int ).

thf(func_def_3120,type,
    sK2186: ( int > int > set_nat ) > nat > product_prod_int_int > int ).

thf(func_def_3121,type,
    sK2187: ( int > int > set_nat ) > nat > product_prod_int_int > int ).

thf(func_def_3122,type,
    sK2188: ( nat > $o ) > nat ).

thf(func_def_3123,type,
    sK2189: ( real > real ) > ( nat > real > real ) > nat > real > real > real ).

thf(func_def_3124,type,
    sK2190: real > real > nat > ( nat > real > real ) > nat ).

thf(func_def_3125,type,
    sK2191: real > real > nat > ( nat > real > real ) > real ).

thf(func_def_3126,type,
    sK2192: set_complex > ( complex > nat ) > complex ).

thf(func_def_3127,type,
    sK2193: ( real > real ) > ( real > real ) > set_real > real ).

thf(func_def_3128,type,
    sK2194: set_real > ( real > real ) > set_real > real ).

thf(func_def_3129,type,
    sK2195: ( int > int > int ) > ( product_prod_int_int > int ) > int ).

thf(func_def_3130,type,
    sK2196: ( int > int > int ) > ( product_prod_int_int > int ) > int ).

thf(func_def_3131,type,
    sK2197: set_real > ( real > rat ) > set_real > real ).

thf(func_def_3132,type,
    sK2198: set_real > ( real > rat ) > set_real > real ).

thf(func_def_3133,type,
    sK2199: ( real > rat ) > set_real > real ).

thf(func_def_3134,type,
    sK2200: nat > nat ).

thf(func_def_3135,type,
    sK2201: int > nat ).

thf(func_def_3136,type,
    sK2202: int > nat ).

thf(func_def_3137,type,
    sK2203: real > ( nat > real ) > real > ( real > nat > real ) > nat ).

thf(func_def_3138,type,
    sK2204: real > ( nat > real ) > real > ( real > nat > real ) > real ).

thf(func_def_3139,type,
    sK2205: real > ( nat > real ) > real > ( real > nat > real ) > real ).

thf(func_def_3140,type,
    sK2206: real > real > ( real > nat > real ) > real ).

thf(func_def_3141,type,
    sK2207: real > ( real > nat > real ) > ( real > nat > real ) > nat ).

thf(func_def_3142,type,
    sK2208: ( real > nat ) > real ).

thf(func_def_3143,type,
    sK2209: ( real > nat ) > real ).

thf(func_def_3144,type,
    sK2210: set_real > real ).

thf(func_def_3145,type,
    sK2211: int > nat ).

thf(func_def_3146,type,
    sK2212: ( nat > num ) > nat ).

thf(func_def_3147,type,
    sK2213: ( rat > $o ) > rat > rat ).

thf(func_def_3148,type,
    sK2214: ( rat > $o ) > rat > rat ).

thf(func_def_3149,type,
    sK2215: rat > ( rat > $o ) > rat ).

thf(func_def_3150,type,
    sK2216: rat > ( rat > $o ) > rat ).

thf(func_def_3151,type,
    sK2217: real > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_3152,type,
    sK2218: real > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_3153,type,
    sK2219: nat > ( nat > rat ) > rat > nat ).

thf(func_def_3154,type,
    sK2220: vEBT_VEBT > nat ).

thf(func_def_3155,type,
    sK2221: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_3156,type,
    sK2222: list_VEBT_VEBT > nat ).

thf(func_def_3157,type,
    sK2223: nat > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_3158,type,
    sK2224: ( complex > rat ) > set_complex > set_complex > complex ).

thf(func_def_3159,type,
    sK2225: set_complex > set_complex > ( complex > rat ) > complex ).

thf(func_def_3160,type,
    sK2226: code_integer > code_integer > code_integer ).

thf(func_def_3161,type,
    sK2227: int > ( int > $o ) > int ).

thf(func_def_3162,type,
    sK2228: int > ( int > $o ) > int ).

thf(func_def_3163,type,
    sK2229: ( int > $o ) > int ).

thf(func_def_3164,type,
    sK2230: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3165,type,
    sK2231: set_rat > rat ).

thf(func_def_3166,type,
    sK2232: ( real > real ) > set_real > real ).

thf(func_def_3167,type,
    sK2233: list_nat > set_nat > nat ).

thf(func_def_3168,type,
    sK2234: ( nat > real ) > nat ).

thf(func_def_3169,type,
    sK2235: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3170,type,
    sK2236: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3171,type,
    sK2237: nat > vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_3172,type,
    sK2238: nat > vEBT_VEBT > vEBT_VEBT > $o ).

thf(func_def_3173,type,
    sK2239: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3174,type,
    sK2240: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3175,type,
    sK2241: nat > nat ).

thf(func_def_3176,type,
    sK2242: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3177,type,
    sK2243: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3178,type,
    sK2244: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3179,type,
    sK2245: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3180,type,
    sK2246: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3181,type,
    sK2247: vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3182,type,
    sK2248: vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3183,type,
    sK2249: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3184,type,
    sK2250: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3185,type,
    sK2251: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3186,type,
    sK2252: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3187,type,
    sK2253: vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3188,type,
    sK2254: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3189,type,
    sK2255: vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3190,type,
    sK2256: vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3191,type,
    sK2257: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3192,type,
    sK2258: ( num > num > $o ) > num ).

thf(func_def_3193,type,
    sK2259: ( num > num > $o ) > num ).

thf(func_def_3194,type,
    sK2260: ( num > num > $o ) > num ).

thf(func_def_3195,type,
    sK2261: ( num > num > $o ) > num ).

thf(func_def_3196,type,
    sK2262: nat > ( nat > $o ) > nat ).

thf(func_def_3197,type,
    sK2263: nat > ( nat > $o ) > nat ).

thf(func_def_3198,type,
    sK2264: ( real > nat ) > ( real > nat ) > set_real > real ).

thf(func_def_3199,type,
    sK2265: ( nat > real ) > real ).

thf(func_def_3200,type,
    sK2266: ( nat > real ) > nat ).

thf(func_def_3201,type,
    sK2267: ( nat > real ) > nat ).

thf(func_def_3202,type,
    sK2268: set_real > ( real > int ) > real ).

thf(func_def_3203,type,
    sK2269: real > real ).

thf(func_def_3204,type,
    sK2270: ( nat > rat ) > set_nat > set_nat > nat ).

thf(func_def_3205,type,
    sK2271: int > set_int > int > int ).

thf(func_def_3206,type,
    sK2272: int > set_int > int > int ).

thf(func_def_3207,type,
    sK2273: ( int > real ) > int ).

thf(func_def_3208,type,
    sK2274: ( int > real ) > int ).

thf(func_def_3209,type,
    sK2275: nat > nat > nat ).

thf(func_def_3210,type,
    sK2276: set_real > ( real > rat ) > real ).

thf(func_def_3211,type,
    sK2277: ( num > num ) > num ).

thf(func_def_3212,type,
    sK2278: ( num > num ) > num ).

thf(func_def_3213,type,
    sK2279: ( option4927543243414619207at_nat > option_num > $o ) > option_num > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_3214,type,
    sK2280: ( option4927543243414619207at_nat > option_num > $o ) > option_num > option4927543243414619207at_nat > num ).

thf(func_def_3215,type,
    sK2281: int > nat ).

thf(func_def_3216,type,
    sK2282: int > ( int > nat ) > set_int > int ).

thf(func_def_3217,type,
    sK2283: ( int > nat ) > set_int > int ).

thf(func_def_3218,type,
    sK2284: ( nat > rat ) > nat ).

thf(func_def_3219,type,
    sK2285: vEBT_VEBT > nat > $o ).

thf(func_def_3220,type,
    sK2286: vEBT_VEBT > nat > $o ).

thf(func_def_3221,type,
    sK2287: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3222,type,
    sK2288: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3223,type,
    sK2289: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_3224,type,
    sK2290: vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_3225,type,
    sK2291: vEBT_VEBT > nat > nat ).

thf(func_def_3226,type,
    sK2292: vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3227,type,
    sK2293: vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3228,type,
    sK2294: set_set_nat > ( set_set_nat > $o ) > set_nat ).

thf(func_def_3229,type,
    sK2295: set_set_nat > ( set_set_nat > $o ) > set_set_nat ).

thf(func_def_3230,type,
    sK2296: ( nat > nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat ).

thf(func_def_3231,type,
    sK2297: ( nat > nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > nat ).

thf(func_def_3232,type,
    sK2298: real > list_real > real ).

thf(func_def_3233,type,
    sK2299: set_real > ( real > real ) > real ).

thf(func_def_3234,type,
    sK2300: set_nat > ( nat > code_integer ) > nat ).

thf(func_def_3235,type,
    sK2301: set_nat > code_integer > code_integer > ( nat > code_integer ) > nat ).

thf(func_def_3236,type,
    sK2302: nat > nat > nat > nat ).

thf(func_def_3237,type,
    sK2303: num > num ).

thf(func_def_3238,type,
    sK2304: ( int > nat ) > ( int > nat ) > set_int > int ).

thf(func_def_3239,type,
    sK2305: set_int > int ).

thf(func_def_3240,type,
    sK2306: produc9072475918466114483BT_nat > nat ).

thf(func_def_3241,type,
    sK2307: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3242,type,
    sK2308: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).

thf(func_def_3243,type,
    sK2309: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3244,type,
    sK2310: produc9072475918466114483BT_nat > nat ).

thf(func_def_3245,type,
    sK2311: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3246,type,
    sK2312: produc9072475918466114483BT_nat > nat ).

thf(func_def_3247,type,
    sK2313: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3248,type,
    sK2314: produc9072475918466114483BT_nat > nat ).

thf(func_def_3249,type,
    sK2315: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3250,type,
    sK2316: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3251,type,
    sK2317: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).

thf(func_def_3252,type,
    sK2318: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3253,type,
    sK2319: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3254,type,
    sK2320: produc9072475918466114483BT_nat > nat ).

thf(func_def_3255,type,
    sK2321: produc9072475918466114483BT_nat > nat ).

thf(func_def_3256,type,
    sK2322: produc9072475918466114483BT_nat > nat ).

thf(func_def_3257,type,
    sK2323: produc9072475918466114483BT_nat > nat ).

thf(func_def_3258,type,
    sK2324: produc9072475918466114483BT_nat > $o ).

thf(func_def_3259,type,
    sK2325: produc9072475918466114483BT_nat > $o ).

thf(func_def_3260,type,
    sK2326: produc9072475918466114483BT_nat > nat ).

thf(func_def_3261,type,
    sK2327: ( int > int > $o ) > int ).

thf(func_def_3262,type,
    sK2328: ( int > int > $o ) > int ).

thf(func_def_3263,type,
    sK2329: ( int > int > $o ) > int ).

thf(func_def_3264,type,
    sK2330: ( int > int > $o ) > int ).

thf(func_def_3265,type,
    sK2331: ( int > int > $o ) > int ).

thf(func_def_3266,type,
    sK2332: ( nat > nat ) > nat ).

thf(func_def_3267,type,
    sK2333: real > real > ( real > real ) > real ).

thf(func_def_3268,type,
    sK2334: ( set_real > $o ) > set_real > set_real ).

thf(func_def_3269,type,
    sK2335: ( set_real > $o ) > set_real > real ).

thf(func_def_3270,type,
    sK2336: option_num > num ).

thf(func_def_3271,type,
    sK2337: ( real > real ) > real ).

thf(func_def_3272,type,
    sK2338: ( real > real ) > real ).

thf(func_def_3273,type,
    sK2339: nat > set_nat > ( nat > nat ) > nat ).

thf(func_def_3274,type,
    sK2340: set_nat > ( nat > nat ) > nat ).

thf(func_def_3275,type,
    sK2341: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).

thf(func_def_3276,type,
    sK2342: set_nat > nat > nat ).

thf(func_def_3277,type,
    sK2343: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_3278,type,
    sK2344: ( nat > $o ) > nat ).

thf(func_def_3279,type,
    sK2345: produc8306885398267862888on_nat > nat > nat > nat ).

thf(func_def_3280,type,
    sK2346: produc8306885398267862888on_nat > nat ).

thf(func_def_3281,type,
    sK2347: produc8306885398267862888on_nat > nat > nat > nat ).

thf(func_def_3282,type,
    sK2348: produc8306885398267862888on_nat > option_nat ).

thf(func_def_3283,type,
    sK2349: produc8306885398267862888on_nat > nat ).

thf(func_def_3284,type,
    sK2350: produc8306885398267862888on_nat > nat > nat > nat ).

thf(func_def_3285,type,
    sK2351: produc8306885398267862888on_nat > nat ).

thf(func_def_3286,type,
    sK2352: produc2233624965454879586on_nat > option_nat ).

thf(func_def_3287,type,
    sK2353: produc2233624965454879586on_nat > nat > nat > $o ).

thf(func_def_3288,type,
    sK2354: produc2233624965454879586on_nat > nat ).

thf(func_def_3289,type,
    sK2355: produc2233624965454879586on_nat > nat ).

thf(func_def_3290,type,
    sK2356: produc2233624965454879586on_nat > nat > nat > $o ).

thf(func_def_3291,type,
    sK2357: produc2233624965454879586on_nat > nat > nat > $o ).

thf(func_def_3292,type,
    sK2358: produc2233624965454879586on_nat > nat ).

thf(func_def_3293,type,
    sK2359: ( int > nat ) > set_int > int ).

thf(func_def_3294,type,
    sK2360: ( set_real > $o ) > real ).

thf(func_def_3295,type,
    sK2361: ( set_real > $o ) > set_real ).

thf(func_def_3296,type,
    sK2362: int > int ).

thf(func_def_3297,type,
    sK2363: ( rat > real ) > rat ).

thf(func_def_3298,type,
    sK2364: ( rat > real ) > rat ).

thf(func_def_3299,type,
    sK2365: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).

thf(func_def_3300,type,
    sK2366: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3301,type,
    sK2367: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3302,type,
    sK2368: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3303,type,
    sK2369: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3304,type,
    sK2370: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3305,type,
    sK2371: vEBT_VEBT > vEBT_VEBT > nat > nat ).

thf(func_def_3306,type,
    sK2372: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3307,type,
    sK2373: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3308,type,
    sK2374: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3309,type,
    sK2375: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3310,type,
    sK2376: vEBT_VEBT > vEBT_VEBT > nat > option4927543243414619207at_nat ).

thf(func_def_3311,type,
    sK2377: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3312,type,
    sK2378: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3313,type,
    sK2379: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3314,type,
    sK2380: nat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_3315,type,
    sK2381: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3316,type,
    sK2382: list_complex > ( complex > $o ) > nat ).

thf(func_def_3317,type,
    sK2383: ( option_num > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option_num > product_prod_nat_nat ).

thf(func_def_3318,type,
    sK2384: ( option_num > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option_num > num ).

thf(func_def_3319,type,
    sK2385: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).

thf(func_def_3320,type,
    sK2386: nat > real > real ).

thf(func_def_3321,type,
    sK2387: ( complex > $o ) > list_complex > complex ).

thf(func_def_3322,type,
    sK2388: nat > ( nat > $o ) > nat > nat ).

thf(func_def_3323,type,
    sK2389: nat > nat ).

thf(func_def_3324,type,
    sK2390: list_nat > list_nat > nat ).

thf(func_def_3325,type,
    sK2391: ( rat > real ) > rat ).

thf(func_def_3326,type,
    sK2392: ( rat > real ) > rat ).

thf(func_def_3327,type,
    sK2393: ( option_num > option_nat > $o ) > option_nat > option_num > num ).

thf(func_def_3328,type,
    sK2394: ( option_num > option_nat > $o ) > option_nat > option_num > nat ).

thf(func_def_3329,type,
    sK2395: nat > nat ).

thf(func_def_3330,type,
    sK2396: ( list_VEBT_VEBT > $o ) > list_VEBT_VEBT ).

thf(func_def_3331,type,
    sK2397: ( real > real ) > set_real > real ).

thf(func_def_3332,type,
    sK2398: real > real > real > real ).

thf(func_def_3333,type,
    sK2399: ( int > $o ) > int > int ).

thf(func_def_3334,type,
    sK2400: ( int > $o ) > int > int ).

thf(func_def_3335,type,
    sK2401: num > num ).

thf(func_def_3336,type,
    sK2402: num > num ).

thf(func_def_3337,type,
    sK2403: nat > nat ).

thf(func_def_3338,type,
    sK2404: ( rat > num ) > rat ).

thf(func_def_3339,type,
    sK2405: ( rat > num ) > rat ).

thf(func_def_3340,type,
    sK2406: set_set_nat > set_set_nat > set_nat ).

thf(func_def_3341,type,
    sK2407: real > real > real ).

thf(func_def_3342,type,
    sK2408: set_nat > set_nat > ( nat > complex ) > nat ).

thf(func_def_3343,type,
    sK2409: set_nat > set_nat > ( nat > complex ) > nat ).

thf(func_def_3344,type,
    sK2410: set_num > num ).

thf(func_def_3345,type,
    sK2411: real > real > nat ).

thf(func_def_3346,type,
    sK2412: ( rat > nat ) > rat ).

thf(func_def_3347,type,
    sK2413: ( rat > nat ) > rat ).

thf(func_def_3348,type,
    sK2414: real > real ).

thf(func_def_3349,type,
    sK2415: set_int > ( int > rat ) > int ).

thf(func_def_3350,type,
    sK2416: set_int > set_int > ( int > complex ) > int ).

thf(func_def_3351,type,
    sK2417: real > real > real ).

thf(func_def_3352,type,
    sK2418: ( nat > $o ) > nat ).

thf(func_def_3353,type,
    sK2419: rat > rat > rat ).

thf(func_def_3354,type,
    sK2420: real > ( real > real ) > real ).

thf(func_def_3355,type,
    sK2421: ( nat > num ) > nat ).

thf(func_def_3356,type,
    sK2422: ( nat > num ) > nat ).

thf(func_def_3357,type,
    sK2423: ( set_rat > $o ) > set_rat ).

thf(func_def_3358,type,
    sK2424: ( set_rat > $o ) > rat ).

thf(func_def_3359,type,
    sK2425: code_integer > code_integer > code_integer ).

thf(func_def_3360,type,
    sK2426: real > real > real > real ).

thf(func_def_3361,type,
    sK2427: ( num > nat ) > num ).

thf(func_def_3362,type,
    sK2428: ( num > nat ) > num ).

thf(func_def_3363,type,
    sK2429: ( int > $o ) > int > int ).

thf(func_def_3364,type,
    sK2430: nat > nat ).

thf(func_def_3365,type,
    sK2431: num > num > num > num ).

thf(func_def_3366,type,
    sK2432: num > num > num > num ).

thf(func_def_3367,type,
    sK2433: num > num > num ).

thf(func_def_3368,type,
    sK2434: num > num ).

thf(func_def_3369,type,
    sK2435: num > num > num > num ).

thf(func_def_3370,type,
    sK2436: num > num > num > num ).

thf(func_def_3371,type,
    sK2437: num > num ).

thf(func_def_3372,type,
    sK2438: num > num > num > num ).

thf(func_def_3373,type,
    sK2439: num > num > num > num ).

thf(func_def_3374,type,
    sK2440: num > num > num ).

thf(func_def_3375,type,
    sK2441: num > num > num > num ).

thf(func_def_3376,type,
    sK2442: num > num > num > num ).

thf(func_def_3377,type,
    sK2443: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_3378,type,
    sK2444: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_3379,type,
    sK2445: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_3380,type,
    sK2446: real > real > real ).

thf(func_def_3381,type,
    sK2447: nat > list_nat > nat ).

thf(func_def_3382,type,
    sK2448: ( real > num ) > real ).

thf(func_def_3383,type,
    sK2449: ( real > num ) > real ).

thf(func_def_3384,type,
    sK2450: real > real > real ).

thf(func_def_3385,type,
    sK2451: int > nat ).

thf(func_def_3386,type,
    sK2452: nat > nat ).

thf(func_def_3387,type,
    sK2453: set_int > ( int > rat ) > int ).

thf(func_def_3388,type,
    sK2454: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3389,type,
    sK2455: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_3390,type,
    sK2456: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3391,type,
    sK2457: vEBT_VEBT > nat ).

thf(func_def_3392,type,
    sK2458: vEBT_VEBT > $o ).

thf(func_def_3393,type,
    sK2459: vEBT_VEBT > $o ).

thf(func_def_3394,type,
    sK2460: ( num > nat ) > num ).

thf(func_def_3395,type,
    sK2461: ( num > nat ) > num ).

thf(func_def_3396,type,
    sK2462: ( produc7773217078559923341nt_int > $o ) > product_prod_int_int ).

thf(func_def_3397,type,
    sK2463: ( produc7773217078559923341nt_int > $o ) > int > option6357759511663192854e_term ).

thf(func_def_3398,type,
    sK2464: nat > nat > ( nat > $o ) > nat ).

thf(func_def_3399,type,
    sK2465: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).

thf(func_def_3400,type,
    sK2466: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3401,type,
    sK2467: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).

thf(func_def_3402,type,
    sK2468: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3403,type,
    sK2469: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3404,type,
    sK2470: vEBT_VEBT > $o ).

thf(func_def_3405,type,
    sK2471: vEBT_VEBT > $o ).

thf(func_def_3406,type,
    sK2472: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_3407,type,
    sK2473: vEBT_VEBT > option_nat > nat > $o ).

thf(func_def_3408,type,
    sK2474: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_3409,type,
    sK2475: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_3410,type,
    sK2476: nat > nat ).

thf(func_def_3411,type,
    sK2477: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3412,type,
    sK2478: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3413,type,
    sK2479: vEBT_VEBT > nat ).

thf(func_def_3414,type,
    sK2480: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3415,type,
    sK2481: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_3416,type,
    sK2482: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3417,type,
    sK2483: vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_3418,type,
    sK2484: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3419,type,
    sK2485: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3420,type,
    sK2486: ( nat > nat > $o ) > nat ).

thf(func_def_3421,type,
    sK2487: ( nat > nat > $o ) > nat ).

thf(func_def_3422,type,
    sK2488: ( nat > nat > $o ) > nat ).

thf(func_def_3423,type,
    sK2489: ( int > nat ) > ( int > nat ) > set_int > int ).

thf(func_def_3424,type,
    sK2490: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > nat > code_integer > option6357759511663192854e_term ).

thf(func_def_3425,type,
    sK2491: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > nat > produc8923325533196201883nteger ).

thf(func_def_3426,type,
    sK2492: nat > nat > nat ).

thf(func_def_3427,type,
    sK2493: real > ( real > real ) > real > real ).

thf(func_def_3428,type,
    sK2494: list_o > list_o > nat ).

thf(func_def_3429,type,
    sK2495: real > real ).

thf(func_def_3430,type,
    sK2496: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3431,type,
    sK2497: ( complex > nat ) > set_complex > set_complex > complex ).

thf(func_def_3432,type,
    sK2498: nat > list_VEBT_VEBT ).

thf(func_def_3433,type,
    sK2499: ( real > num ) > real ).

thf(func_def_3434,type,
    sK2500: ( real > num ) > real ).

thf(func_def_3435,type,
    sK2501: ( rat > num ) > rat ).

thf(func_def_3436,type,
    sK2502: ( rat > num ) > rat ).

thf(func_def_3437,type,
    sK2503: ( num > $o ) > ( num > $o ) > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3438,type,
    sK2504: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3439,type,
    sK2505: num > ( num > $o ) > ( num > $o ) > num ).

thf(func_def_3440,type,
    sK2506: ( complex > rat ) > set_complex > complex ).

thf(func_def_3441,type,
    sK2507: real > real ).

thf(func_def_3442,type,
    sK2508: ( nat > real ) > ( nat > real ) > real ).

thf(func_def_3443,type,
    sK2509: ( nat > real ) > ( nat > real ) > nat ).

thf(func_def_3444,type,
    sK2510: ( nat > real ) > nat ).

thf(func_def_3445,type,
    sK2511: ( nat > real ) > nat ).

thf(func_def_3446,type,
    sK2512: produc2285326912895808259nt_int > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_3447,type,
    sK2513: produc2285326912895808259nt_int > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_3448,type,
    sK2514: real > real > real ).

thf(func_def_3449,type,
    sK2515: ( complex > complex ) > set_complex > ( complex > real ) > set_complex > ( complex > real ) > complex ).

thf(func_def_3450,type,
    sK2516: set_complex > ( complex > real ) > complex ).

thf(func_def_3451,type,
    sK2517: nat > nat > nat ).

thf(func_def_3452,type,
    sK2518: list_set_nat > set_set_nat > set_nat ).

thf(func_def_3453,type,
    sK2519: real > real > real ).

thf(func_def_3454,type,
    sK2520: ( nat > int ) > nat ).

thf(func_def_3455,type,
    sK2521: ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_3456,type,
    sK2522: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_3457,type,
    sK2523: rat > ( rat > $o ) > ( rat > $o ) > rat ).

thf(func_def_3458,type,
    sK2524: real > real ).

thf(func_def_3459,type,
    sK2525: ( nat > $o ) > nat ).

thf(func_def_3460,type,
    sK2526: set_nat > ( nat > rat ) > nat ).

thf(func_def_3461,type,
    sK2527: ( nat > nat ) > nat ).

thf(func_def_3462,type,
    sK2528: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > product_prod_int_int ).

thf(func_def_3463,type,
    sK2529: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_3464,type,
    sK2530: ( rat > num ) > rat ).

thf(func_def_3465,type,
    sK2531: ( rat > num ) > rat ).

thf(func_def_3466,type,
    sK2532: ( nat > $o ) > nat ).

thf(func_def_3467,type,
    sK2533: option_nat > nat ).

thf(func_def_3468,type,
    sK2534: ( set_set_nat > $o ) > set_set_nat > set_set_nat ).

thf(func_def_3469,type,
    sK2535: ( complex > $o ) > ( complex > $o ) > complex ).

thf(func_def_3470,type,
    sK2536: ( nat > nat > $o ) > nat ).

thf(func_def_3471,type,
    sK2537: ( nat > nat > $o ) > nat ).

thf(func_def_3472,type,
    sK2538: ( nat > nat > $o ) > nat ).

thf(func_def_3473,type,
    sK2539: ( nat > nat > $o ) > nat ).

thf(func_def_3474,type,
    sK2540: ( complex > nat ) > set_complex > ( complex > nat ) > ( nat > nat > $o ) > complex ).

thf(func_def_3475,type,
    sK2541: set_real > ( set_real > $o ) > set_real ).

thf(func_def_3476,type,
    sK2542: set_real > ( set_real > $o ) > real ).

thf(func_def_3477,type,
    sK2543: ( nat > real > real ) > real ).

thf(func_def_3478,type,
    sK2544: ( nat > real > real ) > nat ).

thf(func_def_3479,type,
    sK2545: nat > ( nat > real > real ) > real > ( real > real ) > real ).

thf(func_def_3480,type,
    sK2546: ( int > int > set_nat ) > product_prod_int_int > nat > int ).

thf(func_def_3481,type,
    sK2547: ( int > int > set_nat ) > product_prod_int_int > nat > int ).

thf(func_def_3482,type,
    sK2548: list_complex > complex > complex ).

thf(func_def_3483,type,
    sK2549: nat > nat > nat ).

thf(func_def_3484,type,
    sK2550: real > nat ).

thf(func_def_3485,type,
    sK2551: real > real > real ).

thf(func_def_3486,type,
    sK2552: int > int > int ).

thf(func_def_3487,type,
    sK2553: int > int ).

thf(func_def_3488,type,
    sK2554: ( int > rat ) > set_int > int ).

thf(func_def_3489,type,
    sK2555: num > num ).

thf(func_def_3490,type,
    sK2556: real > nat > real ).

thf(func_def_3491,type,
    sK2557: nat > nat > nat ).

thf(func_def_3492,type,
    sK2558: real > real ).

thf(func_def_3493,type,
    sK2559: nat > ( nat > $o ) > nat > nat ).

thf(func_def_3494,type,
    sK2560: ( int > $o ) > int ).

thf(func_def_3495,type,
    sK2561: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3496,type,
    sK2562: ( int > $o ) > int > int ).

thf(func_def_3497,type,
    sK2563: ( int > $o ) > int > int ).

thf(func_def_3498,type,
    sK2564: vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_3499,type,
    sK2565: set_real > ( real > rat ) > ( real > rat ) > real ).

thf(func_def_3500,type,
    sK2566: vEBT_VEBT > nat ).

thf(func_def_3501,type,
    sK2567: nat > real > real ).

thf(func_def_3502,type,
    sK2568: ( rat > $o ) > rat > rat ).

thf(func_def_3503,type,
    sK2569: ( rat > $o ) > rat > rat ).

thf(func_def_3504,type,
    sK2570: ( rat > $o ) > rat > rat ).

thf(func_def_3505,type,
    sK2571: ( rat > $o ) > rat > rat ).

thf(func_def_3506,type,
    sK2572: list_real > real > nat ).

thf(func_def_3507,type,
    sK2573: ( real > real ) > ( real > real ) > set_real > set_real > real ).

thf(func_def_3508,type,
    sK2574: ( real > complex ) > ( real > real ) > ( real > complex ) > set_real > real ).

thf(func_def_3509,type,
    sK2575: set_real > ( real > complex ) > real ).

thf(func_def_3510,type,
    sK2576: set_real > set_real > ( real > real ) > set_real > set_real > real ).

thf(func_def_3511,type,
    sK2577: ( real > complex ) > set_real > real ).

thf(func_def_3512,type,
    sK2578: set_real > set_real > set_real > ( real > real ) > set_real > real ).

thf(func_def_3513,type,
    sK2579: ( real > real ) > set_real > ( real > real ) > set_real > real ).

thf(func_def_3514,type,
    sK2580: ( real > nat ) > real ).

thf(func_def_3515,type,
    sK2581: ( real > nat ) > real ).

thf(func_def_3516,type,
    sK2582: ( complex > nat ) > set_complex > complex ).

thf(func_def_3517,type,
    sK2583: produc9072475918466114483BT_nat > $o ).

thf(func_def_3518,type,
    sK2584: produc9072475918466114483BT_nat > $o ).

thf(func_def_3519,type,
    sK2585: produc9072475918466114483BT_nat > nat ).

thf(func_def_3520,type,
    sK2586: produc9072475918466114483BT_nat > nat ).

thf(func_def_3521,type,
    sK2587: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3522,type,
    sK2588: produc9072475918466114483BT_nat > nat ).

thf(func_def_3523,type,
    sK2589: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3524,type,
    sK2590: produc9072475918466114483BT_nat > nat ).

thf(func_def_3525,type,
    sK2591: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3526,type,
    sK2592: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3527,type,
    sK2593: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_3528,type,
    sK2594: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3529,type,
    sK2595: produc9072475918466114483BT_nat > nat ).

thf(func_def_3530,type,
    sK2596: produc9072475918466114483BT_nat > nat ).

thf(func_def_3531,type,
    sK2597: produc9072475918466114483BT_nat > nat ).

thf(func_def_3532,type,
    sK2598: produc9072475918466114483BT_nat > nat ).

thf(func_def_3533,type,
    sK2599: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3534,type,
    sK2600: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3535,type,
    sK2601: produc9072475918466114483BT_nat > product_prod_nat_nat ).

thf(func_def_3536,type,
    sK2602: produc9072475918466114483BT_nat > nat ).

thf(func_def_3537,type,
    sK2603: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3538,type,
    sK2604: rat > rat ).

thf(func_def_3539,type,
    sK2605: int > int > int ).

thf(func_def_3540,type,
    sK2606: ( real > int ) > set_real > ( real > int ) > real ).

thf(func_def_3541,type,
    sK2607: ( nat > real ) > set_nat > ( nat > complex ) > nat ).

thf(func_def_3542,type,
    sK2608: ( num > nat ) > num ).

thf(func_def_3543,type,
    sK2609: ( num > nat ) > num ).

thf(func_def_3544,type,
    sK2610: ( code_integer > $o ) > $o ).

thf(func_def_3545,type,
    sK2611: ( code_integer > $o ) > code_integer ).

thf(func_def_3546,type,
    sK2612: ( code_integer > $o ) > code_integer ).

thf(func_def_3547,type,
    sK2613: ( num > num > $o ) > num ).

thf(func_def_3548,type,
    sK2614: ( num > num > $o ) > num ).

thf(func_def_3549,type,
    sK2615: ( num > num > $o ) > num ).

thf(func_def_3550,type,
    sK2616: ( num > num > $o ) > num ).

thf(func_def_3551,type,
    sK2617: ( num > num > $o ) > num ).

thf(func_def_3552,type,
    sK2618: nat > set_nat > nat ).

thf(func_def_3553,type,
    sK2619: nat > nat > nat ).

thf(func_def_3554,type,
    sK2620: produc7773217078559923341nt_int > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_3555,type,
    sK2621: produc7773217078559923341nt_int > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > int > option6357759511663192854e_term ).

thf(func_def_3556,type,
    sK2622: ( complex > $o ) > ( complex > $o ) > complex ).

thf(func_def_3557,type,
    sK2623: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > product_prod_int_int ).

thf(func_def_3558,type,
    sK2624: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > int > option6357759511663192854e_term ).

thf(func_def_3559,type,
    sK2625: ( rat > real ) > rat ).

thf(func_def_3560,type,
    sK2626: ( rat > real ) > rat ).

thf(func_def_3561,type,
    sK2627: nat > ( nat > $o ) > nat ).

thf(func_def_3562,type,
    sK2628: set_int > set_int > int ).

thf(func_def_3563,type,
    sK2629: ( complex > $o ) > ( complex > $o ) > complex ).

thf(func_def_3564,type,
    sK2630: ( set_nat > $o ) > ( set_nat > $o ) > set_nat ).

thf(func_def_3565,type,
    sK2631: set_int > int ).

thf(func_def_3566,type,
    sK2632: nat > set_nat > ( nat > rat ) > nat ).

thf(func_def_3567,type,
    sK2633: real > ( real > real ) > real > real ).

thf(func_def_3568,type,
    sK2634: real > ( real > real ) > real > real ).

thf(func_def_3569,type,
    sK2635: int > int ).

thf(func_def_3570,type,
    sK2636: ( nat > nat ) > nat ).

thf(func_def_3571,type,
    sK2637: nat > nat > nat ).

thf(func_def_3572,type,
    sK2638: ( nat > complex ) > set_nat > set_nat > nat ).

thf(func_def_3573,type,
    sK2639: ( rat > int ) > rat ).

thf(func_def_3574,type,
    sK2640: ( rat > int ) > rat ).

thf(func_def_3575,type,
    sK2641: nat > ( nat > $o ) > nat ).

thf(func_def_3576,type,
    sK2642: ( num > nat ) > num ).

thf(func_def_3577,type,
    sK2643: ( num > nat ) > num ).

thf(func_def_3578,type,
    sK2644: ( nat > real ) > nat ).

thf(func_def_3579,type,
    sK2645: ( nat > real ) > nat ).

thf(func_def_3580,type,
    sK2646: ( nat > nat > $o ) > nat ).

thf(func_def_3581,type,
    sK2647: ( nat > nat > $o ) > nat ).

thf(func_def_3582,type,
    sK2648: ( nat > nat > $o ) > nat ).

thf(func_def_3583,type,
    sK2649: ( nat > nat > $o ) > nat ).

thf(func_def_3584,type,
    sK2650: product_prod_nat_nat > nat ).

thf(func_def_3585,type,
    sK2651: product_prod_nat_nat > nat ).

thf(func_def_3586,type,
    sK2652: ( nat > nat ) > nat ).

thf(func_def_3587,type,
    sK2653: ( nat > nat ) > nat ).

thf(func_def_3588,type,
    sK2654: real > int ).

thf(func_def_3589,type,
    sK2655: set_int > ( int > rat ) > int ).

thf(func_def_3590,type,
    sK2656: set_int > ( nat > rat ) > ( int > nat ) > ( int > rat ) > set_nat > nat ).

thf(func_def_3591,type,
    sK2657: real > ( real > real ) > real ).

thf(func_def_3592,type,
    sK2658: real > ( real > real ) > ( real > real > real ) > real > real ).

thf(func_def_3593,type,
    sK2659: real > ( real > real ) > ( real > real > real ) > real > real ).

thf(func_def_3594,type,
    sK2660: list_VEBT_VEBT > list_VEBT_VEBT > nat ).

thf(func_def_3595,type,
    sK2661: set_list_VEBT_VEBT > nat ).

thf(func_def_3596,type,
    sK2662: list_complex > set_complex > complex ).

thf(func_def_3597,type,
    sK2663: ( real > rat ) > real ).

thf(func_def_3598,type,
    sK2664: ( real > rat ) > real ).

thf(func_def_3599,type,
    sK2665: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_3600,type,
    sK2666: set_complex > set_complex > ( complex > int ) > complex ).

thf(func_def_3601,type,
    sK2667: real > real > real > real ).

thf(func_def_3602,type,
    sK2668: ( int > real ) > set_int > int ).

thf(func_def_3603,type,
    sK2669: ( set_int > $o ) > int ).

thf(func_def_3604,type,
    sK2670: ( set_int > $o ) > set_int ).

thf(func_def_3605,type,
    sK2671: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term ).

thf(func_def_3606,type,
    sK2672: produc1908205239877642774nteger > produc8923325533196201883nteger ).

thf(func_def_3607,type,
    sK2673: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > nat ).

thf(func_def_3608,type,
    sK2674: ( set_nat > $o ) > list_set_nat > set_nat ).

thf(func_def_3609,type,
    sK2675: ( num > real ) > num ).

thf(func_def_3610,type,
    sK2676: ( num > real ) > num ).

thf(func_def_3611,type,
    sK2677: ( nat > real ) > real ).

thf(func_def_3612,type,
    sK2678: nat > ( nat > real ) > nat ).

thf(func_def_3613,type,
    sK2679: set_int > ( int > rat ) > ( int > rat ) > int ).

thf(func_def_3614,type,
    sK2680: real > real ).

thf(func_def_3615,type,
    sK2681: real > nat ).

thf(func_def_3616,type,
    sK2682: int > set_int > int > int ).

thf(func_def_3617,type,
    sK2683: int > set_int > int > int ).

thf(func_def_3618,type,
    sK2684: ( nat > real ) > nat ).

thf(func_def_3619,type,
    sK2685: ( nat > real ) > nat ).

thf(func_def_3620,type,
    sK2686: ( int > real ) > set_int > int ).

thf(func_def_3621,type,
    sK2687: real > real > set_int > ( int > real ) > int ).

thf(func_def_3622,type,
    sK2688: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3623,type,
    sK2689: real > real > ( real > real ) > real ).

thf(func_def_3624,type,
    sK2690: ( complex > rat ) > set_complex > ( complex > rat ) > complex ).

thf(func_def_3625,type,
    sK2691: ( real > rat ) > real ).

thf(func_def_3626,type,
    sK2692: ( real > rat ) > real ).

thf(func_def_3627,type,
    sK2693: ( product_prod_int_int > $o ) > product_prod_int_int > ( int > int > product_prod_int_int ) > int ).

thf(func_def_3628,type,
    sK2694: ( product_prod_int_int > $o ) > product_prod_int_int > ( int > int > product_prod_int_int ) > int ).

thf(func_def_3629,type,
    sK2695: ( set_real > $o ) > set_real > set_real ).

thf(func_def_3630,type,
    sK2696: rat > rat > rat > rat ).

thf(func_def_3631,type,
    sK2697: ( nat > $o ) > nat ).

thf(func_def_3632,type,
    sK2698: ( int > real ) > set_int > int ).

thf(func_def_3633,type,
    sK2699: ( int > int ) > ( int > real ) > ( int > real ) > set_int > set_int > int ).

thf(func_def_3634,type,
    sK2700: ( rat > rat ) > rat ).

thf(func_def_3635,type,
    sK2701: ( rat > rat ) > rat ).

thf(func_def_3636,type,
    sK2702: num > num ).

thf(func_def_3637,type,
    sK2703: ( nat > complex ) > set_nat > set_nat > nat ).

thf(func_def_3638,type,
    sK2704: ( nat > complex ) > ( nat > complex ) > set_nat > nat ).

thf(func_def_3639,type,
    sK2705: int > set_int > int > int ).

thf(func_def_3640,type,
    sK2706: int > set_int > int > int ).

thf(func_def_3641,type,
    sK2707: set_nat > nat > nat ).

thf(func_def_3642,type,
    sK2708: ( nat > rat ) > ( nat > int ) > set_nat > ( int > rat ) > set_int > int ).

thf(func_def_3643,type,
    sK2709: ( nat > rat ) > set_nat > nat ).

thf(func_def_3644,type,
    sK2710: set_real > set_real > ( real > rat ) > real ).

thf(func_def_3645,type,
    sK2711: set_real > ( real > rat ) > ( real > rat ) > real ).

thf(func_def_3646,type,
    sK2712: set_complex > set_complex > complex ).

thf(func_def_3647,type,
    sK2713: set_real > set_real > ( real > rat ) > real ).

thf(func_def_3648,type,
    sK2714: ( vEBT_VEBT > $o ) > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3649,type,
    sK2715: set_int > ( set_int > $o ) > set_int ).

thf(func_def_3650,type,
    sK2716: ( real > complex ) > set_real > set_real > real ).

thf(func_def_3651,type,
    sK2717: set_real > ( real > complex ) > set_real > real ).

thf(func_def_3652,type,
    sK2718: $o > nat > vEBT_VEBT > nat ).

thf(func_def_3653,type,
    sK2719: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3654,type,
    sK2720: $o > nat > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_3655,type,
    sK2721: $o > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3656,type,
    sK2722: vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_3657,type,
    sK2723: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3658,type,
    sK2724: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3659,type,
    sK2725: nat > vEBT_VEBT > $o > $o ).

thf(func_def_3660,type,
    sK2726: nat > vEBT_VEBT > $o > $o ).

thf(func_def_3661,type,
    sK2727: ( real > nat ) > ( real > nat ) > set_real > real ).

thf(func_def_3662,type,
    sK2728: ( set_complex > $o ) > set_complex ).

thf(func_def_3663,type,
    sK2729: real > ( nat > real ) > nat ).

thf(func_def_3664,type,
    sK2730: ( nat > real ) > real ).

thf(func_def_3665,type,
    sK2731: ( set_nat > $o ) > set_nat ).

thf(func_def_3666,type,
    sK2732: ( set_nat > $o ) > nat ).

thf(func_def_3667,type,
    sK2733: set_list_int > nat ).

thf(func_def_3668,type,
    sK2734: ( list_o > $o ) > list_o ).

thf(func_def_3669,type,
    sK2735: ( real > real ) > set_real > ( real > real ) > real ).

thf(func_def_3670,type,
    sK2736: ( extended_enat > $o ) > extended_enat ).

thf(func_def_3671,type,
    sK2737: code_integer > code_integer > code_integer ).

thf(func_def_3672,type,
    sK2738: vEBT_VEBT > list_VEBT_VEBT > nat > nat ).

thf(func_def_3673,type,
    sK2739: vEBT_VEBT > list_VEBT_VEBT > nat > nat ).

thf(func_def_3674,type,
    sK2740: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_3675,type,
    sK2741: list_VEBT_VEBT > nat > nat > nat > nat > nat ).

thf(func_def_3676,type,
    sK2742: list_VEBT_VEBT > vEBT_VEBT ).

thf(func_def_3677,type,
    sK2743: list_VEBT_VEBT > nat ).

thf(func_def_3678,type,
    sK2744: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3679,type,
    sK2745: set_complex > list_complex ).

thf(func_def_3680,type,
    sK2746: int > int ).

thf(func_def_3681,type,
    sK2747: real > ( real > real ) > real > ( real > real ) > real ).

thf(func_def_3682,type,
    sK2748: ( nat > nat ) > set_nat > nat ).

thf(func_def_3683,type,
    sK2749: vEBT_VEBT > $o ).

thf(func_def_3684,type,
    sK2750: vEBT_VEBT > $o ).

thf(func_def_3685,type,
    sK2751: set_int > ( int > complex ) > int ).

thf(func_def_3686,type,
    sK2752: ( int > num ) > int ).

thf(func_def_3687,type,
    sK2753: ( int > num ) > int ).

thf(func_def_3688,type,
    sK2754: ( nat > $o ) > nat ).

thf(func_def_3689,type,
    sK2755: real > nat ).

thf(func_def_3690,type,
    sK2756: real > nat ).

thf(func_def_3691,type,
    sK2757: set_nat > ( nat > rat ) > set_nat > nat ).

thf(func_def_3692,type,
    sK2758: set_int > ( set_int > $o ) > set_int ).

thf(func_def_3693,type,
    sK2759: ( int > $o ) > int ).

thf(func_def_3694,type,
    sK2760: int > ( int > $o ) > int ).

thf(func_def_3695,type,
    sK2761: int > ( int > $o ) > int ).

thf(func_def_3696,type,
    sK2762: int > ( int > $o ) > int ).

thf(func_def_3697,type,
    sK2763: int > set_int > ( int > $o ) > int ).

thf(func_def_3698,type,
    sK2764: int > set_int > ( int > $o ) > int ).

thf(func_def_3699,type,
    sK2765: ( int > $o ) > int > int ).

thf(func_def_3700,type,
    sK2766: ( int > $o ) > int ).

thf(func_def_3701,type,
    sK2767: set_int > ( int > $o ) > int > int ).

thf(func_def_3702,type,
    sK2768: int > ( int > $o ) > int ).

thf(func_def_3703,type,
    sK2769: int > ( int > $o ) > int ).

thf(func_def_3704,type,
    sK2770: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3705,type,
    sK2771: real > real > ( real > real > $o ) > real ).

thf(func_def_3706,type,
    sK2772: real > real > real > ( real > real > $o ) > real ).

thf(func_def_3707,type,
    sK2773: real > real > real > ( real > real > $o ) > real ).

thf(func_def_3708,type,
    sK2774: ( real > real > $o ) > real ).

thf(func_def_3709,type,
    sK2775: ( real > real > $o ) > real ).

thf(func_def_3710,type,
    sK2776: ( real > real > $o ) > real ).

thf(func_def_3711,type,
    sK2777: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).

thf(func_def_3712,type,
    sK2778: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3713,type,
    sK2779: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3714,type,
    sK2780: int > ( int > $o ) > ( int > $o ) > int ).

thf(func_def_3715,type,
    sK2781: ( real > real ) > real > real > real ).

thf(func_def_3716,type,
    sK2782: real > real > ( real > real ) > ( real > real ) > real ).

thf(func_def_3717,type,
    sK2783: ( num > int ) > num ).

thf(func_def_3718,type,
    sK2784: ( num > int ) > num ).

thf(func_def_3719,type,
    sK2785: ( product_prod_int_int > $o ) > ( int > int > $o ) > int ).

thf(func_def_3720,type,
    sK2786: ( product_prod_int_int > $o ) > ( int > int > $o ) > int ).

thf(func_def_3721,type,
    sK2787: set_real > ( real > real ) > real ).

thf(func_def_3722,type,
    sK2788: set_real > ( real > real ) > real > real > real ).

thf(func_def_3723,type,
    sK2789: ( set_real > $o ) > ( real > num ) > real ).

thf(func_def_3724,type,
    sK2790: ( set_real > $o ) > ( real > num ) > set_real ).

thf(func_def_3725,type,
    sK2791: ( int > $o ) > int > int ).

thf(func_def_3726,type,
    sK2792: complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3727,type,
    sK2793: ( complex > nat ) > set_complex > complex ).

thf(func_def_3728,type,
    sK2794: ( code_integer > code_integer > $o ) > code_integer ).

thf(func_def_3729,type,
    sK2795: ( real > nat ) > real > set_real > real ).

thf(func_def_3730,type,
    sK2796: produc9072475918466114483BT_nat > nat ).

thf(func_def_3731,type,
    sK2797: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).

thf(func_def_3732,type,
    sK2798: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3733,type,
    sK2799: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3734,type,
    sK2800: produc9072475918466114483BT_nat > $o ).

thf(func_def_3735,type,
    sK2801: produc9072475918466114483BT_nat > $o ).

thf(func_def_3736,type,
    sK2802: produc9072475918466114483BT_nat > nat ).

thf(func_def_3737,type,
    sK2803: produc9072475918466114483BT_nat > nat ).

thf(func_def_3738,type,
    sK2804: produc9072475918466114483BT_nat > vEBT_VEBT ).

thf(func_def_3739,type,
    sK2805: produc9072475918466114483BT_nat > list_VEBT_VEBT ).

thf(func_def_3740,type,
    sK2806: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).

thf(func_def_3741,type,
    sK2807: produc9072475918466114483BT_nat > nat ).

thf(func_def_3742,type,
    sK2808: set_complex > ( complex > rat ) > complex ).

thf(func_def_3743,type,
    sK2809: complex > ( complex > $o ) > complex ).

thf(func_def_3744,type,
    sK2810: complex > ( complex > $o ) > complex ).

thf(func_def_3745,type,
    sK2811: int > nat ).

thf(func_def_3746,type,
    sK2812: int > nat ).

thf(func_def_3747,type,
    sK2813: nat > nat > nat ).

thf(func_def_3748,type,
    sK2814: nat > ( nat > $o ) > nat > nat ).

thf(func_def_3749,type,
    sK2815: option_num > num ).

thf(func_def_3750,type,
    sK2816: ( produc2285326912895808259nt_int > $o ) > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_3751,type,
    sK2817: ( produc2285326912895808259nt_int > $o ) > product_prod_int_int ).

thf(func_def_3752,type,
    sK2818: produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_3753,type,
    sK2819: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_3754,type,
    sK2820: ( real > real ) > real ).

thf(func_def_3755,type,
    sK2821: ( real > real ) > real ).

thf(func_def_3756,type,
    sK2822: set_complex > ( complex > real ) > ( complex > real ) > complex ).

thf(func_def_3757,type,
    sK2823: set_complex > set_complex > ( complex > real ) > complex ).

thf(func_def_3758,type,
    sK2824: real > real > nat ).

thf(func_def_3759,type,
    sK2825: int > set_int > int > int ).

thf(func_def_3760,type,
    sK2826: int > set_int > int > int ).

thf(func_def_3761,type,
    sK2827: ( nat > $o ) > list_nat > nat ).

thf(func_def_3762,type,
    sK2828: nat > nat > nat ).

thf(func_def_3763,type,
    sK2829: set_complex > ( complex > nat ) > complex ).

thf(func_def_3764,type,
    sK2830: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3765,type,
    sK2831: nat > vEBT_VEBT > nat ).

thf(func_def_3766,type,
    sK2832: nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3767,type,
    sK2833: nat > vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_3768,type,
    sK2834: vEBT_VEBT > $o ).

thf(func_def_3769,type,
    sK2835: vEBT_VEBT > $o ).

thf(func_def_3770,type,
    sK2836: set_nat > set_nat > nat ).

thf(func_def_3771,type,
    sK2837: rat > rat > rat ).

thf(func_def_3772,type,
    sK2838: ( real > real ) > real > real ).

thf(func_def_3773,type,
    sK2839: nat > vEBT_VEBT > nat ).

thf(func_def_3774,type,
    sK2840: ( nat > real > real ) > real > nat > real ).

thf(func_def_3775,type,
    sK2841: ( nat > real > real ) > real > nat > nat ).

thf(func_def_3776,type,
    sK2842: ( real > real ) > nat > ( nat > real > real ) > real > real ).

thf(func_def_3777,type,
    sK2843: real > real ).

thf(func_def_3778,type,
    sK2844: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3779,type,
    sK2845: ( nat > nat > $o ) > nat ).

thf(func_def_3780,type,
    sK2846: ( nat > nat > $o ) > nat ).

thf(func_def_3781,type,
    sK2847: ( nat > nat > $o ) > nat ).

thf(func_def_3782,type,
    sK2848: ( nat > nat > $o ) > nat ).

thf(func_def_3783,type,
    sK2849: ( nat > nat > $o ) > nat ).

thf(func_def_3784,type,
    sK2850: nat > vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3785,type,
    sK2851: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3786,type,
    sK2852: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3787,type,
    sK2853: vEBT_VEBT > vEBT_VEBT > nat > nat ).

thf(func_def_3788,type,
    sK2854: vEBT_VEBT > vEBT_VEBT > nat > nat ).

thf(func_def_3789,type,
    sK2855: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3790,type,
    sK2856: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3791,type,
    sK2857: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3792,type,
    sK2858: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3793,type,
    sK2859: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3794,type,
    sK2860: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_3795,type,
    sK2861: vEBT_VEBT > vEBT_VEBT > nat > $o ).

thf(func_def_3796,type,
    sK2862: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3797,type,
    sK2863: vEBT_VEBT > nat > vEBT_VEBT > $o ).

thf(func_def_3798,type,
    sK2864: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3799,type,
    sK2865: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3800,type,
    sK2866: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3801,type,
    sK2867: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3802,type,
    sK2868: vEBT_VEBT > nat > vEBT_VEBT > nat ).

thf(func_def_3803,type,
    sK2869: nat > vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3804,type,
    sK2870: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3805,type,
    sK2871: nat > vEBT_VEBT > vEBT_VEBT > nat ).

thf(func_def_3806,type,
    sK2872: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3807,type,
    sK2873: set_complex > set_complex > ( complex > real ) > complex ).

thf(func_def_3808,type,
    sK2874: set_complex > ( complex > real ) > set_complex > complex ).

thf(func_def_3809,type,
    sK2875: set_int > int > ( int > nat ) > int ).

thf(func_def_3810,type,
    sK2876: set_nat > nat ).

thf(func_def_3811,type,
    sK2877: vEBT_VEBT > $o ).

thf(func_def_3812,type,
    sK2878: vEBT_VEBT > $o ).

thf(func_def_3813,type,
    sK2879: vEBT_VEBT > option4927543243414619207at_nat ).

thf(func_def_3814,type,
    sK2880: vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3815,type,
    sK2881: vEBT_VEBT > nat ).

thf(func_def_3816,type,
    sK2882: vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3817,type,
    sK2883: nat > nat ).

thf(func_def_3818,type,
    sK2884: nat > nat ).

thf(func_def_3819,type,
    sK2885: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_3820,type,
    sK2886: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_3821,type,
    sK2887: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_3822,type,
    sK2888: ( set_nat > $o ) > list_set_nat > nat ).

thf(func_def_3823,type,
    sK2889: real > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > produc8923325533196201883nteger ).

thf(func_def_3824,type,
    sK2890: real > ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term ).

thf(func_def_3825,type,
    sK2891: nat > nat ).

thf(func_def_3826,type,
    sK2892: set_complex > ( set_complex > $o ) > set_complex ).

thf(func_def_3827,type,
    sK2893: ( rat > rat ) > rat ).

thf(func_def_3828,type,
    sK2894: ( rat > rat ) > rat ).

thf(func_def_3829,type,
    sK2895: ( nat > $o ) > nat > nat ).

thf(func_def_3830,type,
    sK2896: ( nat > $o ) > nat > nat ).

thf(func_def_3831,type,
    sK2897: ( int > nat ) > ( nat > nat > $o ) > ( int > nat ) > set_int > int ).

thf(func_def_3832,type,
    sK2898: ( nat > nat > $o ) > nat ).

thf(func_def_3833,type,
    sK2899: ( nat > nat > $o ) > nat ).

thf(func_def_3834,type,
    sK2900: ( nat > nat > $o ) > nat ).

thf(func_def_3835,type,
    sK2901: ( nat > nat > $o ) > nat ).

thf(func_def_3836,type,
    sK2902: set_real > real ).

thf(func_def_3837,type,
    sK2903: vEBT_VEBT > nat > $o > vEBT_VEBT ).

thf(func_def_3838,type,
    sK2904: vEBT_VEBT > nat > $o > nat ).

thf(func_def_3839,type,
    sK2905: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).

thf(func_def_3840,type,
    sK2906: vEBT_VEBT > nat > $o > option4927543243414619207at_nat ).

thf(func_def_3841,type,
    sK2907: vEBT_VEBT > nat > $o > vEBT_VEBT ).

thf(func_def_3842,type,
    sK2908: vEBT_VEBT > $o ).

thf(func_def_3843,type,
    sK2909: vEBT_VEBT > $o ).

thf(func_def_3844,type,
    sK2910: ( real > int ) > real ).

thf(func_def_3845,type,
    sK2911: ( real > int ) > real ).

thf(func_def_3846,type,
    sK2912: set_nat > nat > nat ).

thf(func_def_3847,type,
    sK2913: ( real > real ) > ( nat > real ) > real > nat > real ).

thf(func_def_3848,type,
    sK2914: set_int > set_set_int > set_int ).

thf(func_def_3849,type,
    sK2915: set_int > ( int > nat ) > int ).

thf(func_def_3850,type,
    sK2916: int > int > int ).

thf(func_def_3851,type,
    sK2917: nat > nat > nat ).

thf(func_def_3852,type,
    sK2918: nat > nat > nat ).

thf(func_def_3853,type,
    sK2919: set_complex > ( complex > real ) > set_complex > complex ).

thf(func_def_3854,type,
    sK2920: set_nat > nat ).

thf(func_def_3855,type,
    sK2921: real > real > real ).

thf(func_def_3856,type,
    sK2922: list_nat > nat > nat ).

thf(func_def_3857,type,
    sK2923: set_complex > ( complex > code_integer ) > complex ).

thf(func_def_3858,type,
    sK2924: set_complex > code_integer > code_integer > ( complex > code_integer ) > complex ).

thf(func_def_3859,type,
    sK2925: rat > rat ).

thf(func_def_3860,type,
    sK2926: vEBT_VEBT > $o ).

thf(func_def_3861,type,
    sK2927: vEBT_VEBT > $o ).

thf(func_def_3862,type,
    sK2928: int > int > int ).

thf(func_def_3863,type,
    sK2929: real > real ).

thf(func_def_3864,type,
    sK2930: ( nat > real ) > set_nat > ( nat > real ) > nat ).

thf(func_def_3865,type,
    sK2931: rat > rat ).

thf(func_def_3866,type,
    sK2932: nat > nat ).

thf(func_def_3867,type,
    sK2933: ( nat > $o ) > nat > nat > nat ).

thf(func_def_3868,type,
    sK2934: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_3869,type,
    sK2935: produc5491161045314408544at_nat > option4927543243414619207at_nat ).

thf(func_def_3870,type,
    sK2936: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_3871,type,
    sK2937: produc5491161045314408544at_nat > product_prod_nat_nat ).

thf(func_def_3872,type,
    sK2938: produc5491161045314408544at_nat > product_prod_nat_nat ).

thf(func_def_3873,type,
    sK2939: produc5491161045314408544at_nat > product_prod_nat_nat ).

thf(func_def_3874,type,
    sK2940: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_3875,type,
    sK2941: int > set_int > ( int > nat ) > int ).

thf(func_def_3876,type,
    sK2942: set_int > ( int > nat ) > int ).

thf(func_def_3877,type,
    sK2943: set_complex > ( complex > real ) > complex ).

thf(func_def_3878,type,
    sK2944: nat > nat ).

thf(func_def_3879,type,
    sK2945: nat > set_nat > nat ).

thf(func_def_3880,type,
    sK2946: real > int ).

thf(func_def_3881,type,
    sK2947: ( rat > rat ) > rat ).

thf(func_def_3882,type,
    sK2948: ( rat > rat ) > rat ).

thf(func_def_3883,type,
    sK2949: ( int > $o ) > int > int > int ).

thf(func_def_3884,type,
    sK2950: ( int > $o ) > int > int > int ).

thf(func_def_3885,type,
    sK2951: int > ( int > $o ) > int > int ).

thf(func_def_3886,type,
    sK2952: int > ( int > $o ) > int > int ).

thf(func_def_3887,type,
    sK2953: ( produc8763457246119570046nteger > $o ) > produc8923325533196201883nteger ).

thf(func_def_3888,type,
    sK2954: ( produc8763457246119570046nteger > $o ) > code_integer > option6357759511663192854e_term ).

thf(func_def_3889,type,
    sK2955: rat > rat ).

thf(func_def_3890,type,
    sK2956: ( complex > real ) > set_complex > set_complex > complex ).

thf(func_def_3891,type,
    sK2957: ( complex > rat ) > set_complex > set_complex > complex ).

thf(func_def_3892,type,
    sK2958: complex > product_prod_int_int > ( int > int > set_complex ) > int ).

thf(func_def_3893,type,
    sK2959: complex > product_prod_int_int > ( int > int > set_complex ) > int ).

thf(func_def_3894,type,
    sK2960: real > real ).

thf(func_def_3895,type,
    sK2961: ( rat > nat ) > rat ).

thf(func_def_3896,type,
    sK2962: ( rat > nat ) > rat ).

thf(func_def_3897,type,
    sK2963: ( rat > rat > $o ) > rat ).

thf(func_def_3898,type,
    sK2964: ( option4927543243414619207at_nat > option_nat > $o ) > option_nat > option4927543243414619207at_nat > nat ).

thf(func_def_3899,type,
    sK2965: ( option4927543243414619207at_nat > option_nat > $o ) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_3900,type,
    sK2966: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat ).

thf(func_def_3901,type,
    sK2967: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > nat ).

thf(func_def_3902,type,
    sK2968: set_int > ( int > real ) > int ).

thf(func_def_3903,type,
    sK2969: ( int > complex ) > set_int > ( int > real ) > ( complex > real ) > set_complex > complex ).

thf(func_def_3904,type,
    sK2970: int > int > set_int > int ).

thf(func_def_3905,type,
    sK2971: int > int > set_int > int ).

thf(func_def_3906,type,
    sK2972: real > nat ).

thf(func_def_3907,type,
    sK2973: real > nat ).

thf(func_def_3908,type,
    sK2974: ( num > num ) > num ).

thf(func_def_3909,type,
    sK2975: ( num > num ) > num ).

thf(func_def_3910,type,
    sK2976: nat > nat ).

thf(func_def_3911,type,
    sK2977: nat > nat > nat > nat ).

thf(func_def_3912,type,
    sK2978: nat > nat > nat > nat ).

thf(func_def_3913,type,
    sK2979: ( rat > rat ) > rat ).

thf(func_def_3914,type,
    sK2980: ( rat > rat ) > rat ).

thf(func_def_3915,type,
    sK2981: set_int > ( int > real ) > int ).

thf(func_def_3916,type,
    sK2982: set_complex > ( complex > int ) > set_complex > complex ).

thf(func_def_3917,type,
    sK2983: ( complex > int ) > set_complex > ( complex > int ) > complex ).

thf(func_def_3918,type,
    sK2984: real > set_real > real ).

thf(func_def_3919,type,
    sK2985: produc2285326912895808259nt_int > int ).

thf(func_def_3920,type,
    sK2986: produc2285326912895808259nt_int > int ).

thf(func_def_3921,type,
    sK2987: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_3922,type,
    sK2988: ( int > rat ) > int ).

thf(func_def_3923,type,
    sK2989: ( int > rat ) > int ).

thf(func_def_3924,type,
    sK2990: list_int > list_int > nat ).

thf(func_def_3925,type,
    sK2991: real > ( real > real ) > real ).

thf(func_def_3926,type,
    sK2992: ( nat > num ) > nat ).

thf(func_def_3927,type,
    sK2993: ( nat > num ) > nat ).

thf(func_def_3928,type,
    sK2994: set_VEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3929,type,
    sK2995: ( real > real > $o ) > real ).

thf(func_def_3930,type,
    sK2996: ( real > real > $o ) > real ).

thf(func_def_3931,type,
    sK2997: ( real > real > $o ) > real ).

thf(func_def_3932,type,
    sK2998: ( real > real > $o ) > real ).

thf(func_def_3933,type,
    sK2999: ( real > real > $o ) > real ).

thf(func_def_3934,type,
    sK3000: set_nat > ( set_nat > $o ) > set_nat ).

thf(func_def_3935,type,
    sK3001: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3936,type,
    sK3002: set_complex > ( complex > nat ) > set_complex > complex ).

thf(func_def_3937,type,
    sK3003: rat > rat > rat ).

thf(func_def_3938,type,
    sK3004: ( rat > num ) > rat ).

thf(func_def_3939,type,
    sK3005: ( rat > num ) > rat ).

thf(func_def_3940,type,
    sK3006: real > set_real > real ).

thf(func_def_3941,type,
    sK3007: ( int > rat ) > int ).

thf(func_def_3942,type,
    sK3008: ( int > rat ) > int ).

thf(func_def_3943,type,
    sK3009: int > set_int > int ).

thf(func_def_3944,type,
    sK3010: nat > set_nat > nat ).

thf(func_def_3945,type,
    sK3011: ( int > real ) > set_int > int ).

thf(func_def_3946,type,
    sK3012: ( real > rat ) > real ).

thf(func_def_3947,type,
    sK3013: ( real > rat ) > real ).

thf(func_def_3948,type,
    sK3014: ( nat > nat ) > ( nat > nat ) > nat ).

thf(func_def_3949,type,
    sK3015: real > real > real ).

thf(func_def_3950,type,
    sK3016: nat > ( int > $o ) > int > int ).

thf(func_def_3951,type,
    sK3017: ( produc2285326912895808259nt_int > $o ) > int ).

thf(func_def_3952,type,
    sK3018: ( produc2285326912895808259nt_int > $o ) > produc8551481072490612790e_term > option6357759511663192854e_term ).

thf(func_def_3953,type,
    sK3019: ( produc2285326912895808259nt_int > $o ) > int ).

thf(func_def_3954,type,
    sK3020: ( rat > num ) > rat ).

thf(func_def_3955,type,
    sK3021: ( rat > num ) > rat ).

thf(func_def_3956,type,
    sK3022: nat > ( nat > $o ) > nat > nat ).

thf(func_def_3957,type,
    sK3023: nat > ( nat > $o ) > nat > nat ).

thf(func_def_3958,type,
    sK3024: num > num ).

thf(func_def_3959,type,
    sK3025: ( complex > rat ) > ( complex > rat ) > set_complex > complex ).

thf(func_def_3960,type,
    sK3026: set_complex > ( complex > rat ) > set_complex > complex ).

thf(func_def_3961,type,
    sK3027: set_complex > ( complex > rat ) > set_complex > complex ).

thf(func_def_3962,type,
    sK3028: set_complex > ( complex > rat ) > set_complex > complex ).

thf(func_def_3963,type,
    sK3029: option_nat > vEBT_VEBT > nat > vEBT_VEBT ).

thf(func_def_3964,type,
    sK3030: option_nat > vEBT_VEBT > nat > product_prod_nat_nat ).

thf(func_def_3965,type,
    sK3031: option_nat > vEBT_VEBT > nat > list_VEBT_VEBT ).

thf(func_def_3966,type,
    sK3032: option_nat > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3967,type,
    sK3033: option_nat > nat > vEBT_VEBT > product_prod_nat_nat ).

thf(func_def_3968,type,
    sK3034: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3969,type,
    sK3035: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3970,type,
    sK3036: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3971,type,
    sK3037: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).

thf(func_def_3972,type,
    sK3038: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).

thf(func_def_3973,type,
    sK3039: vEBT_VEBT > option_nat > nat > nat ).

thf(func_def_3974,type,
    sK3040: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_3975,type,
    sK3041: vEBT_VEBT > nat > option_nat > $o ).

thf(func_def_3976,type,
    sK3042: vEBT_VEBT > nat > option_nat > nat ).

thf(func_def_3977,type,
    sK3043: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_3978,type,
    sK3044: nat > vEBT_VEBT > option_nat > $o ).

thf(func_def_3979,type,
    sK3045: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(func_def_3980,type,
    sK3046: option_nat > nat > vEBT_VEBT > vEBT_VEBT ).

thf(func_def_3981,type,
    sK3047: option_nat > nat > vEBT_VEBT > nat ).

thf(func_def_3982,type,
    sK3048: ( rat > nat ) > rat ).

thf(func_def_3983,type,
    sK3049: ( rat > nat ) > rat ).

thf(func_def_3984,type,
    sK3050: list_o > ( $o > $o ) > $o ).

thf(func_def_3985,type,
    sK3051: rat > rat > rat ).

thf(func_def_3986,type,
    sK3052: ( nat > int ) > nat ).

thf(func_def_3987,type,
    sK3053: ( produc8763457246119570046nteger > $o ) > code_integer > option6357759511663192854e_term ).

thf(func_def_3988,type,
    sK3054: ( produc8763457246119570046nteger > $o ) > code_integer ).

thf(func_def_3989,type,
    sK3055: ( produc8763457246119570046nteger > $o ) > code_integer ).

thf(func_def_3990,type,
    sK3056: set_complex > ( complex > rat ) > complex ).

thf(func_def_3991,type,
    sK3057: ( int > nat ) > set_int > ( int > nat ) > int ).

thf(func_def_3992,type,
    sK3058: int > set_int > int > int ).

thf(func_def_3993,type,
    sK3059: int > set_int > int > int ).

thf(func_def_3994,type,
    sK3060: set_real > set_real > real ).

thf(func_def_3995,type,
    sK3061: set_complex > ( complex > rat ) > complex ).

thf(func_def_3996,type,
    sK3062: ( nat > rat ) > nat ).

thf(func_def_3997,type,
    sK3063: ( nat > rat ) > nat ).

thf(func_def_3998,type,
    sK3064: real > real ).

thf(func_def_3999,type,
    sK3065: ( nat > real ) > nat ).

thf(func_def_4000,type,
    sK3066: ( nat > real ) > nat ).

thf(func_def_4001,type,
    sK3067: ( set_real > $o ) > set_real > set_real ).

thf(func_def_4002,type,
    sK3068: rat > ( rat > $o ) > rat ).

thf(func_def_4003,type,
    sK3069: rat > ( rat > $o ) > rat ).

thf(func_def_4004,type,
    sK3070: ( nat > int ) > nat ).

thf(func_def_4005,type,
    sK3071: real ).

thf(func_def_4006,type,
    sK3072: ( nat > $o ) > nat ).

thf(func_def_4007,type,
    sK3073: ( int > int > $o ) > ( nat > int ) > set_nat > ( nat > int ) > nat ).

thf(func_def_4008,type,
    sK3074: ( int > int > $o ) > int ).

thf(func_def_4009,type,
    sK3075: ( int > int > $o ) > int ).

thf(func_def_4010,type,
    sK3076: ( int > int > $o ) > int ).

thf(func_def_4011,type,
    sK3077: ( int > int > $o ) > int ).

thf(func_def_4012,type,
    sK3078: ( rat > nat ) > rat ).

thf(func_def_4013,type,
    sK3079: ( rat > nat ) > rat ).

thf(func_def_4014,type,
    sK3080: nat > ( nat > nat ) > nat ).

thf(func_def_4015,type,
    sK3081: nat > ( nat > nat ) > nat ).

thf(func_def_4016,type,
    sK3082: ( nat > nat ) > nat > nat ).

thf(func_def_4017,type,
    sK3083: ( nat > nat ) > nat > nat ).

thf(func_def_4018,type,
    sK3084: ( option_nat > option_num > $o ) > option_nat > option_num > num ).

thf(func_def_4019,type,
    sK3085: ( option_nat > option_num > $o ) > option_nat > option_num > nat ).

thf(func_def_4020,type,
    sK3086: set_int > list_int ).

thf(func_def_4021,type,
    sK3087: real > real > ( real > real ) > real ).

thf(func_def_4022,type,
    sK3088: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_4023,type,
    sK3089: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_4024,type,
    sK3090: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_4026,type,
    ph3092: 
      !>[X0: $tType] : X0 ).

thf(f63226,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f62941,f62971,f63225]) ).

thf(f63225,plain,
    ~ spl3091_4,
    inference(avatar_contradiction_clause,[status(thm)],[f63224]) ).

thf(f63224,plain,
    ( $false
    | ~ spl3091_4 ),
    inference(subsumption_resolution,[status(thm)],[f63223,f63116]) ).

thf(f63116,plain,
    ( ! [X0: nat] :
        ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X0 )
       != $true )
    | ~ spl3091_4 ),
    inference(subsumption_resolution,[status(thm)],[f63115,f63051]) ).

thf(f63051,plain,
    ( ( maxs
     != ( vEBT_VEBT_high @ ma @ m ) )
    | ~ spl3091_4 ),
    inference(forward_demodulation,[status(thm)],[f63050,f54758]) ).

thf(f54758,plain,
    m = na,
    inference(cnf_transformation,[status(thm)],[f3]) ).

thf(f3,axiom,
    m = na,
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_2__C8_C) ).

thf(f63050,plain,
    ( ( maxs
     != ( vEBT_VEBT_high @ ma @ na ) )
    | ~ spl3091_4 ),
    inference(forward_demodulation,[status(thm)],[f44468,f62690]) ).

thf(f62690,plain,
    ( ( xa = ma )
    | ~ spl3091_4 ),
    inference(avatar_component_clause,[status(thm)],[f62689]) ).

thf(f62689,definition,
    ( spl3091_4
  <=> ( xa = ma ) ),
    introduced(definition,[new_symbols(naming,[spl3091_4])],[avatar_definition]) ).

thf(f44468,plain,
    ( maxs
   != ( vEBT_VEBT_high @ xa @ na ) ),
    inference(cnf_transformation,[status(thm)],[f18090]) ).

thf(f18090,plain,
    ( ( ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
      = $true )
    & ( maxs
     != ( vEBT_VEBT_high @ xa @ na ) ) ),
    inference(fool_elimination,[status(thm)],[f18089]) ).

thf(f18089,plain,
    ( ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
    & ( maxs
     != ( vEBT_VEBT_high @ xa @ na ) ) ),
    inference(rectify,[status(thm)],[f11]) ).

thf(f11,axiom,
    ( ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
    & ( maxs
     != ( vEBT_VEBT_high @ xa @ na ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_10_bb) ).

thf(f63115,plain,
    ( ! [X0: nat] :
        ( ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X0 )
         != $true )
        | ( maxs
          = ( vEBT_VEBT_high @ ma @ m ) ) )
    | ~ spl3091_4 ),
    inference(superposition,[status(thm)],[f63041,f48921]) ).

thf(f48921,plain,
    ! [X2: nat,X3: vEBT_VEBT,X0: nat,X1: list_VEBT_VEBT] :
      ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3 ) @ X0 )
        = ( nth_VEBT_VEBT @ X1 @ X0 ) )
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[status(thm)],[f30243]) ).

thf(f30243,plain,
    ! [X0: nat,X1: list_VEBT_VEBT,X2: nat,X3: vEBT_VEBT] :
      ( ( X0 = X2 )
      | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3 ) @ X0 )
        = ( nth_VEBT_VEBT @ X1 @ X0 ) ) ),
    inference(ennf_transformation,[status(thm)],[f25941]) ).

thf(f25941,plain,
    ! [X0: nat,X1: list_VEBT_VEBT,X2: nat,X3: vEBT_VEBT] :
      ( ( X0 != X2 )
     => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3 ) @ X0 )
        = ( nth_VEBT_VEBT @ X1 @ X0 ) ) ),
    inference(rectify,[status(thm)],[f23]) ).

thf(f23,axiom,
    ! [X14: nat,X13: list_VEBT_VEBT,X5: nat,X0: vEBT_VEBT] :
      ( ( X5 != X14 )
     => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X13 @ X5 @ X0 ) @ X14 )
        = ( nth_VEBT_VEBT @ X13 @ X14 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_22_nth__list__update__neq) ).

thf(f63041,plain,
    ( ! [X0: nat] :
        ( $true
       != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ m ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ m ) ) @ ( vEBT_VEBT_low @ ma @ m ) ) ) @ maxs ) @ X0 ) )
    | ~ spl3091_4 ),
    inference(backward_demodulation,[status(thm)],[f63039,f62690]) ).

thf(f63039,plain,
    ! [X0: nat] :
      ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ m ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ m ) ) @ ( vEBT_VEBT_low @ xa @ m ) ) ) @ maxs ) @ X0 )
     != $true ),
    inference(forward_demodulation,[status(thm)],[f48048,f54758]) ).

thf(f48048,plain,
    ! [X0: nat] :
      ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X0 )
     != $true ),
    inference(cnf_transformation,[status(thm)],[f28053]) ).

thf(f28053,plain,
    ! [X0: nat] :
      ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X0 )
     != $true ),
    inference(ennf_transformation,[status(thm)],[f14452]) ).

thf(f14452,plain,
    ~ ? [X0: nat] :
        ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X0 )
        = $true ),
    inference(fool_elimination,[status(thm)],[f14451]) ).

thf(f14451,plain,
    ~ ? [X0: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X0 ),
    inference(rectify,[status(thm)],[f10250]) ).

thf(f10250,negated_conjecture,
    ~ ? [X17: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X17 ),
    inference(negated_conjecture,[status(cth)],[f10249]) ).

thf(f10249,conjecture,
    ? [X17: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X17 ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',conj_0) ).

thf(f63223,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ ( sK2200 @ maxs ) )
    = $true ),
    inference(subsumption_resolution,[status(thm)],[f63202,f47822]) ).

thf(f47822,plain,
    ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f11713]) ).

thf(f11713,plain,
    ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
    = $true ),
    inference(fool_elimination,[status(thm)],[f11712]) ).

thf(f11712,plain,
    vEBT_V8194947554948674370ptions @ summary @ maxs,
    inference(rectify,[status(thm)],[f2]) ).

thf(f2,axiom,
    vEBT_V8194947554948674370ptions @ summary @ maxs,
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062) ).

thf(f63202,plain,
    ( ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
     != $true )
    | ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ ( sK2200 @ maxs ) )
      = $true ) ),
    inference(trivial_inequality_removal,[status(thm)],[f63197]) ).

thf(f63197,plain,
    ( ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
     != $true )
    | ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ ( sK2200 @ maxs ) )
      = $true )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f63195,f63070]) ).

thf(f63070,plain,
    ( $true
    = ( ord_less_nat @ maxs @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ),
    inference(forward_demodulation,[status(thm)],[f44469,f52161]) ).

thf(f52161,plain,
    ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m )
    = ( size_s6755466524823107622T_VEBT @ treeList ) ),
    inference(cnf_transformation,[status(thm)],[f37]) ).

thf(f37,axiom,
    ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m )
    = ( size_s6755466524823107622T_VEBT @ treeList ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_36__C2_C) ).

thf(f44469,plain,
    ( ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f18090]) ).

thf(f63195,plain,
    ! [X0: nat] :
      ( ( ( ord_less_nat @ X0 @ ( size_s6755466524823107622T_VEBT @ treeList ) )
       != $true )
      | ( $true
       != ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
      | ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ ( sK2200 @ X0 ) )
        = $true ) ),
    inference(forward_demodulation,[status(thm)],[f52451,f52161]) ).

thf(f52451,plain,
    ! [X0: nat] :
      ( ( $true
       != ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
      | ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ ( sK2200 @ X0 ) )
        = $true )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f39256]) ).

thf(f39256,plain,
    ! [X0: nat] :
      ( ( ( ( $true
            = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
          | ! [X1: nat] :
              ( $true
             != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) ) )
        & ( ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ ( sK2200 @ X0 ) )
            = $true )
          | ( $true
           != ( vEBT_V8194947554948674370ptions @ summary @ X0 ) ) ) )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2200])],[f39254,f39255]) ).

thf(f39255,plain,
    ! [X0: nat] :
      ( ? [X2: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X2 )
          = $true )
     => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ ( sK2200 @ X0 ) )
        = $true ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f39254,plain,
    ! [X0: nat] :
      ( ( ( ( $true
            = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
          | ! [X1: nat] :
              ( $true
             != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) ) )
        & ( ? [X2: nat] :
              ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X2 )
              = $true )
          | ( $true
           != ( vEBT_V8194947554948674370ptions @ summary @ X0 ) ) ) )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
    inference(rectify,[status(thm)],[f39253]) ).

thf(f39253,plain,
    ! [X0: nat] :
      ( ( ( ( $true
            = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
          | ! [X1: nat] :
              ( $true
             != ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) ) )
        & ( ? [X1: nat] :
              ( $true
              = ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) )
          | ( $true
           != ( vEBT_V8194947554948674370ptions @ summary @ X0 ) ) ) )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
    inference(nnf_transformation,[status(thm)],[f29955]) ).

thf(f29955,plain,
    ! [X0: nat] :
      ( ( ( $true
          = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
      <=> ? [X1: nat] :
            ( $true
            = ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) ) )
      | ( $true
       != ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
    inference(ennf_transformation,[status(thm)],[f17320]) ).

thf(f17320,plain,
    ! [X0: nat] :
      ( ( $true
        = ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
     => ( ( $true
          = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) )
      <=> ? [X1: nat] :
            ( $true
            = ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f17319]) ).

thf(f17319,plain,
    ! [X0: nat] :
      ( ( ord_less_nat @ X0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
     => ? [X1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X0 ) @ X1 )
          = ( vEBT_V8194947554948674370ptions @ summary @ X0 ) ) ),
    inference(rectify,[status(thm)],[f14]) ).

thf(f14,axiom,
    ! [X6: nat] :
      ( ( ord_less_nat @ X6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
     => ? [X7: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X6 ) @ X7 )
          = ( vEBT_V8194947554948674370ptions @ summary @ X6 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_13__C4_C) ).

thf(f62971,plain,
    ~ spl3091_2,
    inference(avatar_split_clause,[status(thm)],[f56192,f62680]) ).

thf(f62680,definition,
    ( spl3091_2
  <=> ( mi = ma ) ),
    introduced(definition,[new_symbols(naming,[spl3091_2])],[avatar_definition]) ).

thf(f56192,plain,
    mi != ma,
    inference(cnf_transformation,[status(thm)],[f13476]) ).

thf(f13476,plain,
    ( ( ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
      = $true )
    & ( mi != ma ) ),
    inference(fool_elimination,[status(thm)],[f13475]) ).

thf(f13475,plain,
    ( ( mi != ma )
    & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
    inference(rectify,[status(thm)],[f45]) ).

thf(f45,axiom,
    ( ( mi != ma )
    & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_44__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062) ).

thf(f62941,plain,
    ( spl3091_2
    | spl3091_4 ),
    inference(avatar_split_clause,[status(thm)],[f47546,f62689,f62680]) ).

thf(f47546,plain,
    ( ( xa = ma )
    | ( mi = ma ) ),
    inference(cnf_transformation,[status(thm)],[f28522]) ).

thf(f28522,plain,
    ( ( ( mi
        = ( if_nat
          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
            = none_nat )
          @ mi
          @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) ) )
      | ( xa != ma ) )
    & ( ( mi = ma )
      | ( xa = ma ) ) ),
    inference(ennf_transformation,[status(thm)],[f23540]) ).

thf(f23540,plain,
    ( ( ( xa != ma )
     => ( mi = ma ) )
    & ( ( xa = ma )
     => ( mi
        = ( if_nat
          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
            = none_nat )
          @ mi
          @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f2752]) ).

thf(f2752,axiom,
    ( ( ( xa != ma )
     => ( mi = ma ) )
    & ( ( xa = ma )
     => ( ( if_nat
          @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
            = none_nat )
          @ mi
          @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) )
        = mi ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_2751_aampt) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP262^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34  % Computer : n029.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Fri Feb 27 06:07:44 EST 2026
% 0.17/0.34  % CPUTime  : 
% 0.17/0.34  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47  ---- Original DTF file ---
% 0.28/0.47  thf(spec,logic,$$dhol).
% 0.28/0.47  %------------------------------------------------------------------------------
% 0.28/0.47  % File     : ITP262^1 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.28/0.47  % Domain   : Interactive Theorem Proving
% 0.28/0.47  % Problem  : Sledgehammer problem VEBT_DeleteCorrectness 00209_010241
% 0.28/0.47  % Version  : [Des22] axioms.
% 0.28/0.47  % English  :
% 0.28/0.47  
% 0.28/0.47  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.47  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.28/0.47  % Source   : [Des22]
% 0.28/0.47  % Names    : 0073_VEBT_DeleteCorrectness_00209_010241 [Des22]
% 0.28/0.47  
% 0.28/0.47  % Status   : Theorem
% 0.28/0.47  % Rating   : ? v9.2.1
% 0.28/0.47  % Syntax   : Number of formulae    : 11165 (5808 unt; 916 typ;   0 def)
% 0.28/0.47  %            Number of atoms       : 28393 (12566 equ;   0 cnn)
% 0.28/0.47  %            Maximal formula atoms :   71 (   2 avg)
% 0.28/0.47  %            Number of connectives : 116376 (2919   ~; 529   |;1869   &;100321   @)
% 0.28/0.47  %                                         (   0 <=>;10738  =>;   0  <=;   0 <~>)
% 0.28/0.47  %            Maximal formula depth :   39 (   6 avg)
% 0.28/0.47  %            Number of types       :   95 (  94 usr)
% 0.28/0.47  %            Number of type conns  : 3561 (3561   >;   0   *;   0   +;   0  <<)
% 0.28/0.47  %            Number of symbols     :  825 ( 822 usr;  59 con; 0-8 aty)
% 0.28/0.47  %            Number of variables   : 25514 (1740   ^;23048   !; 726   ?;25514   :)
% 0.28/0.47  % SPC      : TH0_THM_EQU_NAR
% 0.28/0.47  
% 0.28/0.47  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.28/0.47  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.28/0.47  %            proofs - 
% 0.28/0.47  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.28/0.47  %            2022-02-18 07:48:59.771
% 0.28/0.47  % Bugfixes : Added ()s around negated sides of equations.
% 0.28/0.47  %------------------------------------------------------------------------------
% 0.28/0.47  % Could-be-implicit typings (94)
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.28/0.47      produc5542196010084753463at_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.28/0.47      produc1908205239877642774nteger: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.28/0.47      produc5491161045314408544at_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.28/0.47      produc2285326912895808259nt_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 0.28/0.47      produc8763457246119570046nteger: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.28/0.47      produc7773217078559923341nt_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.28/0.47      produc1193250871479095198on_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 0.28/0.47      produc8306885398267862888on_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.28/0.47      produc6121120109295599847at_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.28/0.47      produc7036089656553540234on_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 0.28/0.47      produc2233624965454879586on_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J,type,
% 0.28/0.47      produc6241069584506657477e_term: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 0.28/0.47      set_fi4554929511873752355omplex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      list_P7413028617227757229T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J,type,
% 0.28/0.47      produc8551481072490612790e_term: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
% 0.28/0.47      option6357759511663192854e_term: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 0.28/0.47      produc3447558737645232053on_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 0.28/0.47      produc4953844613479565601on_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 0.28/0.47      set_fi7789364187291644575l_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.28/0.47      filter6041513312241820739omplex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      list_P7037539587688870467BT_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 0.28/0.47      list_P4547456442757143711BT_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      list_P5647936690300460905T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      produc8243902056947475879T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.28/0.47      set_Pr5085853215250843933omplex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.28/0.47      produc8923325533196201883nteger: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 0.28/0.47      list_P3126845725202233233VEBT_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      list_P7495141550334521929T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.28/0.47      filter2146258269922977983l_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      option4927543243414619207at_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      filter1242075044329608583at_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.28/0.47      set_Pr6218003697084177305l_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.28/0.47      produc9072475918466114483BT_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.28/0.47      produc4894624898956917775BT_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      produc8025551001238799321T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.28/0.47      set_Pr958786334691620121nt_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 0.28/0.47      produc4411394909380815293omplex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 0.28/0.47      list_P7333126701944960589_nat_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      list_P6285523579766656935_o_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 0.28/0.47      list_P3795440434834930179_o_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      set_list_VEBT_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.28/0.47      produc334124729049499915VEBT_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      produc2504756804600209347T_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.28/0.47      produc6271795597528267376eger_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.28/0.47      produc2422161461964618553l_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.28/0.47      product_prod_num_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 0.28/0.47      product_prod_nat_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      product_prod_nat_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.47      product_prod_int_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 0.28/0.47      list_P4002435161011370285od_o_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__List__Olist_It__Complex__Ocomplex_J_J,type,
% 0.28/0.47      set_list_complex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Complex__Ocomplex_J_J,type,
% 0.28/0.47      set_set_complex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      list_VEBT_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.28/0.47      set_list_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
% 0.28/0.47      set_list_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 0.28/0.47      product_prod_nat_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 0.28/0.47      product_prod_o_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.28/0.47      product_prod_o_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.47      list_set_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      set_VEBT_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.47      set_set_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.28/0.47      set_set_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 0.28/0.47      set_Code_integer: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.28/0.47      set_Product_unit: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Extended____Nat__Oenat_J,type,
% 0.28/0.47      set_Extended_enat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.28/0.47      list_complex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
% 0.28/0.47      set_list_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.28/0.47      product_prod_o_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.47      set_complex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
% 0.28/0.47      filter_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.47      option_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
% 0.28/0.47      option_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
% 0.28/0.47      filter_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.28/0.47      set_char: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
% 0.28/0.47      list_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.47      set_real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47      list_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.47      list_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      vEBT_VEBT: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 0.28/0.47      set_rat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
% 0.28/0.47      set_num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      set_nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      set_int: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Code____Numeral__Ointeger,type,
% 0.28/0.47      code_integer: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Extended____Nat__Oenat,type,
% 0.28/0.47      extended_enat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__List__Olist_I_Eo_J,type,
% 0.28/0.47      list_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Complex__Ocomplex,type,
% 0.28/0.47      complex: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 0.28/0.47      set_o: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__String__Ochar,type,
% 0.28/0.47      char: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Real__Oreal,type,
% 0.28/0.47      real: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Rat__Orat,type,
% 0.28/0.47      rat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Num__Onum,type,
% 0.28/0.47      num: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Nat__Onat,type,
% 0.28/0.47      nat: $tType ).
% 0.28/0.47  
% 0.28/0.47  thf(ty_n_t__Int__Oint,type,
% 0.28/0.47      int: $tType ).
% 0.28/0.47  
% 0.28/0.47  % Explicit typings (822)
% 0.28/0.47  thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 0.28/0.47      archim7802044766580827645g_real: real > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 0.28/0.47      archim3151403230148437115or_rat: rat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 0.28/0.47      archim6058952711729229775r_real: real > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 0.28/0.47      archim7778729529865785530nd_rat: rat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 0.28/0.47      archim8280529875227126926d_real: real > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Binomial_Obinomial,type,
% 0.28/0.47      binomial: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 0.28/0.47      bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oand__not__num,type,
% 0.28/0.47      bit_and_not_num: num > num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 0.28/0.47      bit_concat_bit: nat > int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 0.28/0.47      bit_or_not_num_neg: num > num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 0.28/0.47      bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 0.28/0.47      bit_ri7919022796975470100ot_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_ri631733984087533419it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 0.28/0.47      bit_se725231765392027082nd_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 0.28/0.47      bit_se727722235901077358nd_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se8568078237143864401it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se8570568707652914677it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se2159334234014336723it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se2161824704523386999it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se2119862282449309892nteger: nat > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 0.28/0.47      bit_se2000444600071755411sk_int: nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 0.28/0.47      bit_se2002935070580805687sk_nat: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 0.28/0.47      bit_se1409905431419307370or_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 0.28/0.47      bit_se1412395901928357646or_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se545348938243370406it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se547839408752420682it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se7879613467334960850it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se7882103937844011126it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se2923211474154528505it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se2925701944663578781it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      bit_se8260200283734997820nteger: nat > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
% 0.28/0.47      bit_se4203085406695923979it_int: nat > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se4205575877204974255it_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
% 0.28/0.47      bit_se6526347334894502574or_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
% 0.28/0.47      bit_se6528837805403552850or_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
% 0.28/0.47      bit_se1146084159140164899it_int: int > nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
% 0.28/0.47      bit_se1148574629649215175it_nat: nat > nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 0.28/0.47      bit_take_bit_num: nat > num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 0.28/0.47      code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Odivmod__abs,type,
% 0.28/0.47      code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 0.28/0.47      code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
% 0.28/0.47      code_int_of_integer: code_integer > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 0.28/0.47      code_integer_of_int: int > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 0.28/0.47      code_integer_of_num: num > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 0.28/0.47      code_nat_of_integer: code_integer > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Onegative,type,
% 0.28/0.47      code_negative: num > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Onum__of__integer,type,
% 0.28/0.47      code_num_of_integer: code_integer > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Numeral_Opositive,type,
% 0.28/0.47      code_positive: num > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Target__Int_Onegative,type,
% 0.28/0.47      code_Target_negative: num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Code__Target__Int_Opositive,type,
% 0.28/0.47      code_Target_positive: num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.28/0.47      comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.28/0.47      comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Real__Oreal,type,
% 0.28/0.47      comple4887499456419720421f_real: set_real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 0.28/0.47      complete_Sup_Sup_int: set_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
% 0.28/0.47      complete_Sup_Sup_nat: set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
% 0.28/0.47      comple1385675409528146559p_real: set_real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      comple7399068483239264473et_nat: set_set_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_OArg,type,
% 0.28/0.47      arg: complex > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocis,type,
% 0.28/0.47      cis: real > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocnj,type,
% 0.28/0.47      cnj: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocomplex_OComplex,type,
% 0.28/0.47      complex2: real > real > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocomplex_OIm,type,
% 0.28/0.47      im: complex > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocomplex_ORe,type,
% 0.28/0.47      re: complex > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Ocsqrt,type,
% 0.28/0.47      csqrt: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Complex_Oimaginary__unit,type,
% 0.28/0.47      imaginary_unit: complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Deriv_Odifferentiable_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Deriv_Ohas__derivative_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Deriv_Ohas__field__derivative_001t__Real__Oreal,type,
% 0.28/0.47      has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Oadjust__div,type,
% 0.28/0.47      adjust_div: product_prod_int_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Oadjust__mod,type,
% 0.28/0.47      adjust_mod: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Odivmod__nat,type,
% 0.28/0.47      divmod_nat: nat > nat > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Oeucl__rel__int,type,
% 0.28/0.47      eucl_rel_int: int > int > product_prod_int_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 0.28/0.47      unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 0.28/0.47      unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 0.28/0.47      unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 0.28/0.47      unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 0.28/0.47      unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 0.28/0.47      unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 0.28/0.47      semiri5044797733671781792omplex: nat > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 0.28/0.47      semiri1408675320244567234ct_nat: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 0.28/0.47      semiri2265585572941072030t_real: nat > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 0.28/0.47      invers8013647133539491842omplex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 0.28/0.47      inverse_inverse_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 0.28/0.47      inverse_inverse_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 0.28/0.47      at_bot_real: filter_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 0.28/0.47      at_top_nat: filter_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 0.28/0.47      at_top_real: filter_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 0.28/0.47      eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 0.28/0.47      eventually_real: ( real > $o ) > filter_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.47      filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 0.28/0.47      princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.28/0.47      princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 0.28/0.47      finite_card_o: set_o > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 0.28/0.47      finite_card_complex: set_complex > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 0.28/0.47      finite_card_int: set_int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 0.28/0.47      finite_card_nat: set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 0.28/0.47      finite410649719033368117t_unit: set_Product_unit > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      finite_card_set_nat: set_set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 0.28/0.47      finite_card_char: set_char > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 0.28/0.47      finite_finite_o: set_o > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 0.28/0.47      finite3207457112153483333omplex: set_complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 0.28/0.47      finite_finite_int: set_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 0.28/0.47      finite_finite_list_o: set_list_o > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.28/0.47      finite8712137658972009173omplex: set_list_complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.47      finite3922522038869484883st_int: set_list_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47      finite8100373058378681591st_nat: set_list_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 0.28/0.47      finite_finite_nat: set_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 0.28/0.47      finite_finite_num: set_num > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 0.28/0.47      finite_finite_rat: set_rat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 0.28/0.47      finite_finite_real: set_real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.47      finite6551019134538273531omplex: set_set_complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      finite6197958912794628473et_int: set_set_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      finite1152437895449049373et_nat: set_set_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.28/0.47      bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 0.28/0.47      bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.28/0.47      comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 0.28/0.47      comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Oid_001_Eo,type,
% 0.28/0.47      id_o: $o > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 0.28/0.47      id_nat: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.28/0.47      map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.47      map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.28/0.47      map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.28/0.47      map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 0.28/0.47      gcd_Gcd_int: set_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 0.28/0.47      gcd_Gcd_nat: set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Obezw,type,
% 0.28/0.47      bezw: nat > nat > product_prod_int_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Obezw__rel,type,
% 0.28/0.47      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 0.28/0.47      gcd_gcd_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 0.28/0.47      gcd_gcd_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 0.28/0.47      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      abs_abs_Code_integer: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 0.28/0.47      abs_abs_complex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 0.28/0.47      abs_abs_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 0.28/0.47      abs_abs_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 0.28/0.47      abs_abs_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 0.28/0.47      minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 0.28/0.47      minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.28/0.47      minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 0.28/0.47      minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
% 0.28/0.47      minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 0.28/0.47      minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 0.28/0.47      minus_minus_complex: complex > complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 0.28/0.47      minus_minus_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.28/0.47      minus_minus_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 0.28/0.47      minus_minus_rat: rat > rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 0.28/0.47      minus_minus_real: real > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.47      minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      minus_minus_set_int: set_int > set_int > set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.28/0.47      minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.47      minus_minus_set_real: set_real > set_real > set_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.47      minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      one_one_Code_integer: code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 0.28/0.47      one_one_complex: complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      one_on7984719198319812577d_enat: extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.28/0.47      one_one_int: int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.28/0.47      one_one_nat: nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 0.28/0.47      one_one_rat: rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 0.28/0.47      one_one_real: real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 0.28/0.47      plus_plus_complex: complex > complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 0.28/0.47      plus_plus_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.28/0.47      plus_plus_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 0.28/0.47      plus_plus_num: num > num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 0.28/0.47      plus_plus_rat: rat > rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.28/0.47      plus_plus_real: real > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      sgn_sgn_Code_integer: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Osgn__class_Osgn_001t__Complex__Ocomplex,type,
% 0.28/0.47      sgn_sgn_complex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 0.28/0.47      sgn_sgn_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 0.28/0.47      sgn_sgn_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 0.28/0.47      sgn_sgn_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 0.28/0.47      times_times_complex: complex > complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 0.28/0.47      times_times_int: int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.28/0.47      times_times_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 0.28/0.47      times_times_num: num > num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 0.28/0.47      times_times_rat: rat > rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 0.28/0.47      times_times_real: real > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      uminus1351360451143612070nteger: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 0.28/0.47      uminus1482373934393186551omplex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 0.28/0.47      uminus_uminus_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 0.28/0.47      uminus_uminus_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 0.28/0.47      uminus_uminus_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.47      uminus8566677241136511917omplex: set_complex > set_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      uminus1532241313380277803et_int: set_int > set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      uminus5710092332889474511et_nat: set_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.47      uminus612125837232591019t_real: set_real > set_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.47      uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      zero_z3403309356797280102nteger: code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 0.28/0.47      zero_zero_complex: complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      zero_z5237406670263579293d_enat: extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.28/0.47      zero_zero_int: int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.28/0.47      zero_zero_nat: nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 0.28/0.47      zero_zero_rat: rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.28/0.47      zero_zero_real: real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.28/0.47      groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 0.28/0.47      groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 0.28/0.47      groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Rat__Orat,type,
% 0.28/0.47      groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 0.28/0.47      groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 0.28/0.47      groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.47      groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Nat__Onat,type,
% 0.28/0.47      groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Rat__Orat,type,
% 0.28/0.47      groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Real__Oreal,type,
% 0.28/0.47      groups8778361861064173332t_real: ( int > real ) > set_int > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 0.28/0.47      groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Int__Oint,type,
% 0.28/0.47      groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.28/0.47      groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.47      groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.28/0.47      groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 0.28/0.47      groups1932886352136224148al_int: ( real > int ) > set_real > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Nat__Onat,type,
% 0.28/0.47      groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Rat__Orat,type,
% 0.28/0.47      groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.47      groups8097168146408367636l_real: ( real > real ) > set_real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Complex__Ocomplex,type,
% 0.28/0.47      groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 0.28/0.47      groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Real__Oreal,type,
% 0.28/0.47      groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.47      groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
% 0.28/0.47      groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__List_Ocomm__semiring__0__class_Ohorner__sum_001_Eo_001t__Int__Oint,type,
% 0.28/0.47      groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Nat__Onat,type,
% 0.28/0.47      groups4561878855575611511st_nat: list_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_HOL_OThe_001t__Int__Oint,type,
% 0.28/0.47      the_int: ( int > $o ) > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
% 0.28/0.47      the_real: ( real > $o ) > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.47      if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Complex__Ocomplex,type,
% 0.28/0.47      if_complex: $o > complex > complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Int__Oint,type,
% 0.28/0.47      if_int: $o > int > int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.47      if_list_int: $o > list_int > list_int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47      if_list_nat: $o > list_nat > list_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Nat__Onat,type,
% 0.28/0.47      if_nat: $o > nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Num__Onum,type,
% 0.28/0.47      if_num: $o > num > num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.28/0.47      if_option_nat: $o > option_nat > option_nat > option_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.47      if_option_num: $o > option_num > option_num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 0.28/0.47      if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.28/0.47      if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.47      if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Rat__Orat,type,
% 0.28/0.47      if_rat: $o > rat > rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Real__Oreal,type,
% 0.28/0.47      if_real: $o > real > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      if_set_int: $o > set_int > set_int > set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_OAbs__Integ,type,
% 0.28/0.47      abs_Integ: product_prod_nat_nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_ORep__Integ,type,
% 0.28/0.47      rep_Integ: int > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oint__ge__less__than,type,
% 0.28/0.47      int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oint__ge__less__than2,type,
% 0.28/0.47      int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Onat,type,
% 0.28/0.47      nat2: int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 0.28/0.47      ring_1_Ints_complex: set_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 0.28/0.47      ring_1_Ints_real: set_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      ring_18347121197199848620nteger: int > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 0.28/0.47      ring_17405671764205052669omplex: int > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 0.28/0.47      ring_1_of_int_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 0.28/0.47      ring_1_of_int_rat: int > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 0.28/0.47      ring_1_of_int_real: int > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 0.28/0.47      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.28/0.47      sup_sup_nat: nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 0.28/0.47      lattic8263393255366662781ax_int: set_int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 0.28/0.47      lattic8265883725875713057ax_nat: set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.47      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 0.28/0.47      at_infinity_real: filter_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 0.28/0.47      append_int: list_int > list_int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.28/0.47      append_nat: list_nat > list_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 0.28/0.47      distinct_int: list_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 0.28/0.47      distinct_nat: list_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 0.28/0.47      linord2614967742042102400et_nat: set_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 0.28/0.47      cons_int: int > list_int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.28/0.47      cons_nat: nat > list_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 0.28/0.47      nil_int: list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.28/0.47      nil_nat: list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.47      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 0.28/0.47      set_o2: list_o > set_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 0.28/0.47      set_complex2: list_complex > set_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 0.28/0.47      set_int2: list_int > set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.28/0.47      set_nat2: list_nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 0.28/0.47      set_real2: list_real > set_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      set_set_nat2: list_set_nat > set_set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001_Eo,type,
% 0.28/0.47      list_update_o: list_o > nat > $o > list_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 0.28/0.47      list_update_complex: list_complex > nat > complex > list_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 0.28/0.47      list_update_int: list_int > nat > int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 0.28/0.47      list_update_nat: list_nat > nat > nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 0.28/0.47      list_update_real: list_real > nat > real > list_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001_Eo,type,
% 0.28/0.47      nth_o: list_o > nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 0.28/0.47      nth_complex: list_complex > nat > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 0.28/0.47      nth_int: list_int > nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.28/0.47      nth_nat: list_nat > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.28/0.47      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.28/0.47      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 0.28/0.47      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 0.28/0.47      nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.28/0.47      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.28/0.47      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.28/0.47      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.28/0.47      nth_real: list_real > nat > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      nth_set_nat: list_set_nat > nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 0.28/0.47      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 0.28/0.47      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 0.28/0.47      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 0.28/0.47      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.28/0.47      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.28/0.47      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.28/0.47      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 0.28/0.47      remdups_nat: list_nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001_Eo,type,
% 0.28/0.47      replicate_o: nat > $o > list_o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 0.28/0.47      replicate_complex: nat > complex > list_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 0.28/0.47      replicate_int: nat > int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 0.28/0.47      replicate_nat: nat > nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 0.28/0.47      replicate_real: nat > real > list_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      replicate_set_nat: nat > set_nat > list_set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oupt,type,
% 0.28/0.47      upt: nat > nat > list_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oupto,type,
% 0.28/0.47      upto: int > int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oupto__aux,type,
% 0.28/0.47      upto_aux: int > int > list_int > list_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_List_Oupto__rel,type,
% 0.28/0.47      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_OSuc,type,
% 0.28/0.47      suc: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.28/0.47      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.28/0.47      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.47      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Onat_Opred,type,
% 0.28/0.47      pred: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      semiri4939895301339042750nteger: nat > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 0.28/0.47      semiri8010041392384452111omplex: nat > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      semiri4216267220026989637d_enat: nat > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.28/0.47      semiri1314217659103216013at_int: nat > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.28/0.47      semiri1316708129612266289at_nat: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 0.28/0.47      semiri681578069525770553at_rat: nat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.28/0.47      semiri5074537144036343181t_real: nat > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 0.28/0.47      size_size_list_o: list_o > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.28/0.47      size_s3451745648224563538omplex: list_complex > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.47      size_size_list_int: list_int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.47      size_size_list_nat: list_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 0.28/0.47      size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 0.28/0.47      size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 0.28/0.47      size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.28/0.47      size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 0.28/0.47      size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 0.28/0.47      size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  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,
% 0.28/0.47      size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 0.28/0.47      size_size_list_real: list_real > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.47      size_s3254054031482475050et_nat: list_set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.47      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 0.28/0.47      size_size_num: num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.28/0.47      size_size_option_nat: option_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.47      size_size_option_num: option_num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.28/0.47      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 0.28/0.47      size_size_char: char > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.47      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 0.28/0.47      nat_list_encode: list_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 0.28/0.47      nat_list_encode_rel: list_nat > list_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 0.28/0.47      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 0.28/0.47      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 0.28/0.47      nat_prod_encode: product_prod_nat_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 0.28/0.47      nat_set_decode: nat > set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 0.28/0.47      nat_set_encode: set_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.28/0.47      nat_triangle: nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_NthRoot_Oroot,type,
% 0.28/0.47      root: nat > real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_NthRoot_Osqrt,type,
% 0.28/0.47      sqrt: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_OBitM,type,
% 0.28/0.47      bitM: num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oinc,type,
% 0.28/0.47      inc: num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 0.28/0.47      neg_nu7009210354673126013omplex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 0.28/0.47      neg_numeral_dbl_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 0.28/0.47      neg_numeral_dbl_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 0.28/0.47      neg_numeral_dbl_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 0.28/0.47      neg_nu6511756317524482435omplex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 0.28/0.47      neg_nu3811975205180677377ec_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 0.28/0.47      neg_nu3179335615603231917ec_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 0.28/0.47      neg_nu6075765906172075777c_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 0.28/0.47      neg_nu8557863876264182079omplex: complex > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 0.28/0.47      neg_nu5851722552734809277nc_int: int > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 0.28/0.47      neg_nu5219082963157363817nc_rat: rat > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 0.28/0.47      neg_nu8295874005876285629c_real: real > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 0.28/0.47      neg_numeral_sub_int: num > num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum_OBit0,type,
% 0.28/0.47      bit0: num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum_OBit1,type,
% 0.28/0.47      bit1: num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum_OOne,type,
% 0.28/0.47      one: num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.47      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum_Osize__num,type,
% 0.28/0.47      size_num: num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onum__of__nat,type,
% 0.28/0.47      num_of_nat: nat > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 0.28/0.47      numera6620942414471956472nteger: num > code_integer ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 0.28/0.47      numera6690914467698888265omplex: num > complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      numera1916890842035813515d_enat: num > extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 0.28/0.47      numeral_numeral_int: num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 0.28/0.47      numeral_numeral_nat: num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 0.28/0.47      numeral_numeral_rat: num > rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 0.28/0.47      numeral_numeral_real: num > real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Opow,type,
% 0.28/0.47      pow: num > num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Opred__numeral,type,
% 0.28/0.47      pred_numeral: num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Num_Osqr,type,
% 0.28/0.47      sqr: num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 0.28/0.47      none_nat: option_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 0.28/0.47      none_num: option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 0.28/0.47      some_nat: nat > option_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 0.28/0.47      some_num: num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 0.28/0.47      case_option_int_num: int > ( num > int ) > option_num > int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 0.28/0.47      case_option_num_num: num > ( num > num ) > option_num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 0.28/0.47      case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
% 0.28/0.47      size_option_nat: ( nat > nat ) > option_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 0.28/0.47      size_option_num: ( num > nat ) > option_num > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 0.28/0.47      the_nat: option_nat > nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 0.28/0.47      the_num: option_num > num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.47      the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 0.28/0.47      bot_bo4199563552545308370d_enat: extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.28/0.47      bot_bot_nat: nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.47      bot_bot_set_complex: set_complex ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
% 0.28/0.47      bot_bo7653980558646680370d_enat: set_Extended_enat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.47      bot_bot_set_int: set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.47      bot_bot_set_nat: set_nat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
% 0.28/0.47      bot_bot_set_num: set_num ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.28/0.47      bot_bot_set_rat: set_rat ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.47      bot_bot_set_real: set_real ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.28/0.47      bot_bot_set_set_int: set_set_int ).
% 0.28/0.47  
% 0.28/0.47  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.48      bot_bot_set_set_nat: set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.48      bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 0.28/0.48      ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.28/0.48      ord_less_int: int > int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.28/0.48      ord_less_nat: nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 0.28/0.48      ord_less_num: num > num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 0.28/0.48      ord_less_rat: rat > rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.28/0.48      ord_less_real: real > real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 0.28/0.48      ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      ord_less_set_complex: set_complex > set_complex > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      ord_less_set_int: set_int > set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      ord_less_set_nat: set_nat > set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
% 0.28/0.48      ord_less_set_num: set_num > set_num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.28/0.48      ord_less_set_rat: set_rat > set_rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.48      ord_less_set_real: set_real > set_real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.28/0.48      ord_less_set_set_int: set_set_int > set_set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.48      ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 0.28/0.48      ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.28/0.48      ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_Eo_J,type,
% 0.28/0.48      ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.28/0.48      ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 0.28/0.48      ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 0.28/0.48      ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 0.28/0.48      ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 0.28/0.48      ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Real__Oreal_J,type,
% 0.28/0.48      ord_le4104064031414453916r_real: filter_real > filter_real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.28/0.48      ord_less_eq_int: int > int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.28/0.48      ord_less_eq_nat: nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 0.28/0.48      ord_less_eq_num: num > num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 0.28/0.48      ord_less_eq_rat: rat > rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.28/0.48      ord_less_eq_real: real > real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.48      ord_less_eq_set_o: set_o > set_o > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 0.28/0.48      ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      ord_less_eq_set_int: set_int > set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
% 0.28/0.48      ord_less_eq_set_num: set_num > set_num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.28/0.48      ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.28/0.48      ord_less_eq_set_rat: set_rat > set_rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.48      ord_less_eq_set_real: set_real > set_real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.28/0.48      ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.48      ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.48      ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 0.28/0.48      ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 0.28/0.48      ord_max_int: int > int > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 0.28/0.48      ord_max_nat: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 0.28/0.48      ord_max_num: num > num > num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 0.28/0.48      ord_max_rat: rat > rat > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 0.28/0.48      ord_max_real: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      ord_max_set_int: set_int > set_int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 0.28/0.48      order_Greatest_nat: ( nat > $o ) > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.48      order_9091379641038594480t_real: ( nat > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      order_mono_nat_nat: ( nat > nat ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.48      order_mono_nat_real: ( nat > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 0.28/0.48      top_top_set_o: set_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      top_top_set_nat: set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 0.28/0.48      top_to1996260823553986621t_unit: set_Product_unit ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.48      top_top_set_real: set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 0.28/0.48      top_top_set_char: set_char ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 0.28/0.48      power_power_complex: complex > nat > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 0.28/0.48      power_power_int: int > nat > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 0.28/0.48      power_power_nat: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 0.28/0.48      power_power_rat: rat > nat > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 0.28/0.48      power_power_real: real > nat > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.28/0.48      produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.48      produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 0.28/0.48      produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 0.28/0.48      produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 0.28/0.48      produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 0.28/0.48      produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.28/0.48      produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.48      produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.28/0.48      produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.28/0.48      produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 0.28/0.48      product_Pair_o_o: $o > $o > product_prod_o_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 0.28/0.48      product_Pair_o_int: $o > int > product_prod_o_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 0.28/0.48      product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 0.28/0.48      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.48      product_Pair_int_int: int > int > product_prod_int_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 0.28/0.48      product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 0.28/0.48      product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 0.28/0.48      product_Pair_num_num: num > num > product_prod_num_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.28/0.48      produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.48      produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.28/0.48      produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.28/0.48      produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.28/0.48      produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.28/0.48      produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 0.28/0.48      produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.48      produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 0.28/0.48      produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      produc7959293469001253456omplex: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > produc7773217078559923341nt_int > set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 0.28/0.48      produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 0.28/0.48      produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.28/0.48      produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 0.28/0.48      produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.28/0.48      produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 0.28/0.48      produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 0.28/0.48      produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.48      produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.48      produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.28/0.48      produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 0.28/0.48      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 0.28/0.48      produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 0.28/0.48      produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 0.28/0.48  
% 0.28/0.48  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,
% 0.28/0.48      produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 0.28/0.48      produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.48      produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.28/0.48      produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 0.28/0.48      produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.48      product_fst_int_int: product_prod_int_int > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      product_fst_nat_nat: product_prod_nat_nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.48      product_snd_int_int: product_prod_int_int > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rat_OFract,type,
% 0.28/0.48      fract: int > int > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rat_OFrct,type,
% 0.28/0.48      frct: product_prod_int_int > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rat_Onormalize,type,
% 0.28/0.48      normalize: product_prod_int_int > product_prod_int_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rat_Oof__int,type,
% 0.28/0.48      of_int: int > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rat_Oquotient__of,type,
% 0.28/0.48      quotient_of: rat > product_prod_int_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 0.28/0.48      real_V2521375963428798218omplex: set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.48      real_V5970128139526366754l_real: ( real > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 0.28/0.48      real_V3694042436643373181omplex: complex > complex > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 0.28/0.48      real_V975177566351809787t_real: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 0.28/0.48      real_V1022390504157884413omplex: complex > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 0.28/0.48      real_V7735802525324610683m_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 0.28/0.48      real_V4546457046886955230omplex: real > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 0.28/0.48      real_V2046097035970521341omplex: real > complex > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 0.28/0.48      real_V1485227260804924795R_real: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 0.28/0.48      divide1717551699836669952omplex: complex > complex > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 0.28/0.48      divide_divide_int: int > int > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 0.28/0.48      divide_divide_nat: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 0.28/0.48      divide_divide_rat: rat > rat > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 0.28/0.48      divide_divide_real: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 0.28/0.48      dvd_dvd_complex: complex > complex > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 0.28/0.48      dvd_dvd_int: int > int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 0.28/0.48      dvd_dvd_nat: nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 0.28/0.48      dvd_dvd_rat: rat > rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 0.28/0.48      dvd_dvd_real: real > real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 0.28/0.48      modulo_modulo_int: int > int > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 0.28/0.48      modulo_modulo_nat: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      zero_n356916108424825756nteger: $o > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 0.28/0.48      zero_n1201886186963655149omplex: $o > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 0.28/0.48      zero_n2684676970156552555ol_int: $o > int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 0.28/0.48      zero_n2687167440665602831ol_nat: $o > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 0.28/0.48      zero_n2052037380579107095ol_rat: $o > rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 0.28/0.48      zero_n3304061248610475627l_real: $o > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 0.28/0.48      suminf_complex: ( nat > complex ) > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 0.28/0.48      suminf_real: ( nat > real ) > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 0.28/0.48      summable_real: ( nat > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 0.28/0.48      sums_real: ( nat > real ) > real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 0.28/0.48      collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 0.28/0.48      collect_complex: ( complex > $o ) > set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 0.28/0.48      collect_int: ( int > $o ) > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 0.28/0.48      collect_list_o: ( list_o > $o ) > set_list_o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.28/0.48      collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.48      collect_list_int: ( list_int > $o ) > set_list_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.48      collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.48      collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.28/0.48      collect_nat: ( nat > $o ) > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 0.28/0.48      collect_num: ( num > $o ) > set_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 0.28/0.48      collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.48      collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 0.28/0.48      collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 0.28/0.48      collect_rat: ( rat > $o ) > set_rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.28/0.48      collect_real: ( real > $o ) > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 0.28/0.48      collect_set_complex: ( set_complex > $o ) > set_set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      collect_set_int: ( set_int > $o ) > set_set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 0.28/0.48      pow_nat: set_nat > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 0.28/0.48      image_int_int: ( int > int ) > set_int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 0.28/0.48      image_nat_int: ( nat > int ) > set_nat > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.28/0.48      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.28/0.48      image_nat_real: ( nat > real ) > set_nat > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 0.28/0.48      image_nat_char: ( nat > char ) > set_nat > set_char ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 0.28/0.48      image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.28/0.48      image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.48      image_real_real: ( real > real ) > set_real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 0.28/0.48      image_char_nat: ( char > nat ) > set_char > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 0.28/0.48      insert_complex: complex > set_complex > set_complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 0.28/0.48      insert_int: int > set_int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.28/0.48      insert_nat: nat > set_nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 0.28/0.48      insert_num: num > set_num > set_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 0.28/0.48      insert_rat: rat > set_rat > set_rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 0.28/0.48      insert_real: real > set_real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 0.28/0.48      set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 0.28/0.48      set_or1266510415728281911st_int: int > int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 0.28/0.48      set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 0.28/0.48      set_or7049704709247886629st_num: num > num > set_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 0.28/0.48      set_or633870826150836451st_rat: rat > rat > set_rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 0.28/0.48      set_or1222579329274155063t_real: real > real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 0.28/0.48      set_or4662586982721622107an_int: int > int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 0.28/0.48      set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 0.28/0.48      set_ord_atLeast_nat: nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 0.28/0.48      set_ord_atLeast_real: real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 0.28/0.48      set_ord_atMost_int: int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 0.28/0.48      set_ord_atMost_nat: nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 0.28/0.48      set_or6656581121297822940st_int: int > int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 0.28/0.48      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 0.28/0.48      set_or5832277885323065728an_int: int > int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 0.28/0.48      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 0.28/0.48      set_or1633881224788618240n_real: real > real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 0.28/0.48      set_or1210151606488870762an_nat: nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 0.28/0.48      set_or5849166863359141190n_real: real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
% 0.28/0.48      set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 0.28/0.48      set_ord_lessThan_int: int > set_int ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 0.28/0.48      set_ord_lessThan_nat: nat > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 0.28/0.48      set_ord_lessThan_num: num > set_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 0.28/0.48      set_ord_lessThan_rat: rat > set_rat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 0.28/0.48      set_or5984915006950818249n_real: real > set_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Oascii__of,type,
% 0.28/0.48      ascii_of: char > char ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Ochar_OChar,type,
% 0.28/0.48      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Ochar_Osize__char,type,
% 0.28/0.48      size_char: char > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 0.28/0.48      comm_s629917340098488124ar_nat: char > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Ointeger__of__char,type,
% 0.28/0.48      integer_of_char: char > code_integer ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 0.28/0.48      unique3096191561947761185of_nat: nat > char ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.48      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.28/0.48      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 0.28/0.48      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 0.28/0.48      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 0.28/0.48      topolo2815343760600316023s_real: real > filter_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 0.28/0.48      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 0.28/0.48      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 0.28/0.48      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oarccos,type,
% 0.28/0.48      arccos: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 0.28/0.48      arcosh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oarcsin,type,
% 0.28/0.48      arcsin: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oarctan,type,
% 0.28/0.48      arctan: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 0.28/0.48      arsinh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 0.28/0.48      artanh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 0.28/0.48      cos_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Ocos__coeff,type,
% 0.28/0.48      cos_coeff: nat > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 0.28/0.48      cosh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 0.28/0.48      cot_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 0.28/0.48      exp_complex: complex > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 0.28/0.48      exp_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 0.28/0.48      ln_ln_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Olog,type,
% 0.28/0.48      log: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Opi,type,
% 0.28/0.48      pi: real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 0.28/0.48      powr_real: real > real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 0.28/0.48      sin_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Osin__coeff,type,
% 0.28/0.48      sin_coeff: nat > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 0.28/0.48      sinh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 0.28/0.48      tan_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 0.28/0.48      tanh_complex: complex > complex ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 0.28/0.48      tanh_real: real > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.28/0.48      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.28/0.48      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.28/0.48      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.28/0.48      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.28/0.48      vEBT_VEBT_high: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.28/0.48      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.28/0.48      vEBT_VEBT_low: nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.28/0.48      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.28/0.48      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.28/0.48      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.28/0.48      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.28/0.48      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.28/0.48      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.28/0.48      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.28/0.48      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.28/0.48      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.28/0.48      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 0.28/0.48      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 0.28/0.48      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 0.28/0.48      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 0.28/0.48      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 0.28/0.48      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 0.28/0.48      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 0.28/0.48      vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 0.28/0.48      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 0.28/0.48      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 0.28/0.48      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 0.28/0.48      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 0.28/0.48      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 0.28/0.48      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 0.28/0.48      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 0.28/0.48      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 0.28/0.48      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 0.28/0.48      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 0.28/0.48      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 0.28/0.48      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.48      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 0.28/0.48      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 0.28/0.48      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 0.28/0.48      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 0.28/0.48      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 0.28/0.48      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 0.28/0.48      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 0.28/0.48      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 0.28/0.48      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 0.28/0.48      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 0.28/0.48      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 0.28/0.48      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.48      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 0.28/0.48      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.48      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.28/0.48      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 0.28/0.48      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.28/0.48      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 0.28/0.48      fChoice_real: ( real > $o ) > real ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001_Eo,type,
% 0.28/0.48      member_o: $o > set_o > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 0.28/0.48      member_complex: complex > set_complex > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Int__Oint,type,
% 0.28/0.48      member_int: int > set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 0.28/0.48      member_list_o: list_o > set_list_o > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 0.28/0.48      member_list_int: list_int > set_list_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.28/0.48      member_list_nat: list_nat > set_list_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.28/0.48      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Nat__Onat,type,
% 0.28/0.48      member_nat: nat > set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Num__Onum,type,
% 0.28/0.48      member_num: num > set_num > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.28/0.48      member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Rat__Orat,type,
% 0.28/0.48      member_rat: rat > set_rat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Real__Oreal,type,
% 0.28/0.48      member_real: real > set_real > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.48      member_set_int: set_int > set_set_int > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.28/0.48      member_set_nat: set_nat > set_set_nat > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.28/0.48      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_deg____,type,
% 0.28/0.48      deg: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_m____,type,
% 0.28/0.48      m: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_ma____,type,
% 0.28/0.48      ma: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_maxs____,type,
% 0.28/0.48      maxs: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_mi____,type,
% 0.28/0.48      mi: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_na____,type,
% 0.28/0.48      na: nat ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_summary____,type,
% 0.28/0.48      summary: vEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_treeList____,type,
% 0.28/0.48      treeList: list_VEBT_VEBT ).
% 0.28/0.48  
% 0.28/0.48  thf(sy_v_xa____,type,
% 0.28/0.48      xa: nat ).
% 0.28/0.48  
% 0.28/0.48  % Relevant facts (10208)
% 0.28/0.48  thf(fact_0__C1_C,axiom,
% 0.28/0.48      vEBT_invar_vebt @ summary @ m ).
% 0.28/0.48  
% 0.28/0.48  % "1"
% 0.28/0.48  thf(fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062,axiom,
% 0.28/0.48      vEBT_V8194947554948674370ptions @ summary @ maxs ).
% 0.28/0.48  
% 0.28/0.48  % \<open>both_member_options summary maxs\<close>
% 0.28/0.48  thf(fact_2__C8_C,axiom,
% 0.28/0.48      na = m ).
% 0.28/0.48  
% 0.28/0.48  % "8"
% 0.28/0.48  thf(fact_3_bit__split__inv,axiom,
% 0.28/0.48      ! [X: nat,D: nat] :
% 0.28/0.48        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 0.28/0.48        = X ) ).
% 0.28/0.48  
% 0.28/0.48  % bit_split_inv
% 0.28/0.48  thf(fact_4_dele__bmo__cont__corr,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 0.28/0.48          = ( ( X != Y )
% 0.28/0.48            & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % dele_bmo_cont_corr
% 0.28/0.48  thf(fact_5__092_060open_062invar__vebt_A_ItreeList_091high_Ax_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_Ax_An_J_A_Ilow_Ax_An_J_093_A_B_Amaxs_J_An_092_060close_062,axiom,
% 0.28/0.48      vEBT_invar_vebt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ na ).
% 0.28/0.48  
% 0.28/0.48  % \<open>invar_vebt (treeList[high x n := vebt_delete (treeList ! high x n) (low x n)] ! maxs) n\<close>
% 0.28/0.48  thf(fact_6_xnotmi,axiom,
% 0.28/0.48      xa != mi ).
% 0.28/0.48  
% 0.28/0.48  % xnotmi
% 0.28/0.48  thf(fact_7_hlist,axiom,
% 0.28/0.48      ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( vEBT_VEBT_high @ xa @ na ) )
% 0.28/0.48      = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % hlist
% 0.28/0.48  thf(fact_8_nnvalid,axiom,
% 0.28/0.48      vEBT_invar_vebt @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na ).
% 0.28/0.48  
% 0.28/0.48  % nnvalid
% 0.28/0.48  thf(fact_9_ninNullc,axiom,
% 0.28/0.48      vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ).
% 0.28/0.48  
% 0.28/0.48  % ninNullc
% 0.28/0.48  thf(fact_10_bb,axiom,
% 0.28/0.48      ( ( maxs
% 0.28/0.48       != ( vEBT_VEBT_high @ xa @ na ) )
% 0.28/0.48      & ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % bb
% 0.28/0.48  thf(fact_11_True,axiom,
% 0.28/0.48      xa = ma ).
% 0.28/0.48  
% 0.28/0.48  % True
% 0.28/0.48  thf(fact_12_nothlist,axiom,
% 0.28/0.48      ! [I: nat] :
% 0.28/0.48        ( ( I
% 0.28/0.48         != ( vEBT_VEBT_high @ xa @ na ) )
% 0.28/0.48       => ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48         => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I )
% 0.28/0.48            = ( nth_VEBT_VEBT @ treeList @ I ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nothlist
% 0.28/0.48  thf(fact_13__C4_C,axiom,
% 0.28/0.48      ! [I2: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X2 ) )
% 0.28/0.48          = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "4"
% 0.28/0.48  thf(fact_14_in__children__def,axiom,
% 0.28/0.48      ( vEBT_V5917875025757280293ildren
% 0.28/0.48      = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ N2 ) ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_children_def
% 0.28/0.48  thf(fact_15_newsummvalid,axiom,
% 0.28/0.48      vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ m ).
% 0.28/0.48  
% 0.28/0.48  % newsummvalid
% 0.28/0.48  thf(fact_16__C4_OIH_C_I1_J,axiom,
% 0.28/0.48      ! [X4: vEBT_VEBT] :
% 0.28/0.48        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.28/0.48       => ( ( vEBT_invar_vebt @ X4 @ na )
% 0.28/0.48          & ! [Xa: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ X4 @ Xa ) @ na ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "4.IH"(1)
% 0.28/0.48  thf(fact_17_list__update__id,axiom,
% 0.28/0.48      ! [Xs: list_nat,I: nat] :
% 0.28/0.48        ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 0.28/0.48        = Xs ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_id
% 0.28/0.48  thf(fact_18_list__update__id,axiom,
% 0.28/0.48      ! [Xs: list_int,I: nat] :
% 0.28/0.48        ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 0.28/0.48        = Xs ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_id
% 0.28/0.48  thf(fact_19_list__update__id,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,I: nat] :
% 0.28/0.48        ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 0.28/0.48        = Xs ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_id
% 0.28/0.48  thf(fact_20_nth__list__update__neq,axiom,
% 0.28/0.48      ! [I: nat,J: nat,Xs: list_nat,X: nat] :
% 0.28/0.48        ( ( I != J )
% 0.28/0.48       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 0.28/0.48          = ( nth_nat @ Xs @ J ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_neq
% 0.28/0.48  thf(fact_21_nth__list__update__neq,axiom,
% 0.28/0.48      ! [I: nat,J: nat,Xs: list_int,X: int] :
% 0.28/0.48        ( ( I != J )
% 0.28/0.48       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 0.28/0.48          = ( nth_int @ Xs @ J ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_neq
% 0.28/0.48  thf(fact_22_nth__list__update__neq,axiom,
% 0.28/0.48      ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.28/0.48        ( ( I != J )
% 0.28/0.48       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 0.28/0.48          = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_neq
% 0.28/0.48  thf(fact_23__092_060open_062treeList_A_B_Ahigh_Ax_An_A_092_060in_062_Aset_AtreeList_092_060close_062,axiom,
% 0.28/0.48      member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ).
% 0.28/0.48  
% 0.28/0.48  % \<open>treeList ! high x n \<in> set treeList\<close>
% 0.28/0.48  thf(fact_24_allvalidinlist,axiom,
% 0.28/0.48      ! [X4: vEBT_VEBT] :
% 0.28/0.48        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ) )
% 0.28/0.48       => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 0.28/0.48  
% 0.28/0.48  % allvalidinlist
% 0.28/0.48  thf(fact_25__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062,axiom,
% 0.28/0.48      vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( vEBT_VEBT_low @ ma @ na ) ).
% 0.28/0.48  
% 0.28/0.48  % \<open>both_member_options (treeList ! high ma n) (low ma n)\<close>
% 0.28/0.48  thf(fact_26__C111_C,axiom,
% 0.28/0.48      ! [I2: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I2 ) @ X2 ) )
% 0.28/0.48          = ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ I2 ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "111"
% 0.28/0.48  thf(fact_27__C4_OIH_C_I2_J,axiom,
% 0.28/0.48      ! [X: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ X ) @ m ) ).
% 0.28/0.48  
% 0.28/0.48  % "4.IH"(2)
% 0.28/0.48  thf(fact_28_list__update__overwrite,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.28/0.48        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
% 0.28/0.48        = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_overwrite
% 0.28/0.48  thf(fact_29_not__min__Null__member,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT] :
% 0.28/0.48        ( ~ ( vEBT_VEBT_minNull @ T )
% 0.28/0.48       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 0.28/0.48  
% 0.28/0.48  % not_min_Null_member
% 0.28/0.48  thf(fact_30__C5_C,axiom,
% 0.28/0.48      ( ( mi = ma )
% 0.28/0.48     => ! [X4: vEBT_VEBT] :
% 0.28/0.48          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.28/0.48         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "5"
% 0.28/0.48  thf(fact_31__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 0.28/0.48      ( ( xa != mi )
% 0.28/0.48      | ( xa != ma ) ) ).
% 0.28/0.48  
% 0.28/0.48  % \<open>x \<noteq> mi \<or> x \<noteq> ma\<close>
% 0.28/0.48  thf(fact_32__C0_C,axiom,
% 0.28/0.48      ! [X4: vEBT_VEBT] :
% 0.28/0.48        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.28/0.48       => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "0"
% 0.28/0.48  thf(fact_33_hlbound,axiom,
% 0.28/0.48      ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48      & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % hlbound
% 0.28/0.48  thf(fact_34__C4_Ohyps_C_I7_J,axiom,
% 0.28/0.48      ord_less_eq_nat @ mi @ ma ).
% 0.28/0.48  
% 0.28/0.48  % "4.hyps"(7)
% 0.28/0.48  thf(fact_35__C4_Ohyps_C_I8_J,axiom,
% 0.28/0.48      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.28/0.48  
% 0.28/0.48  % "4.hyps"(8)
% 0.28/0.48  thf(fact_36__C2_C,axiom,
% 0.28/0.48      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.28/0.48      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "2"
% 0.28/0.48  thf(fact_37__C7_C,axiom,
% 0.28/0.48      ( ( mi != ma )
% 0.28/0.48     => ! [I2: nat] :
% 0.28/0.48          ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.28/0.48                = I2 )
% 0.28/0.48             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.28/0.48            & ! [Y2: nat] :
% 0.28/0.48                ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 0.28/0.48                    = I2 )
% 0.28/0.48                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 0.28/0.48               => ( ( ord_less_nat @ mi @ Y2 )
% 0.28/0.48                  & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "7"
% 0.28/0.48  thf(fact_38_list__update__swap,axiom,
% 0.28/0.48      ! [I: nat,I3: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X5: vEBT_VEBT] :
% 0.28/0.48        ( ( I != I3 )
% 0.28/0.48       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I3 @ X5 )
% 0.28/0.48          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X5 ) @ I @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_swap
% 0.28/0.48  thf(fact_39_yhelper,axiom,
% 0.28/0.48      ! [Y: nat] :
% 0.28/0.48        ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ Y @ na ) ) @ ( vEBT_VEBT_low @ Y @ na ) )
% 0.28/0.48       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48         => ( ( ord_less_nat @ mi @ Y )
% 0.28/0.48            & ( ord_less_eq_nat @ Y @ ma )
% 0.28/0.48            & ( ord_less_nat @ ( vEBT_VEBT_low @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % yhelper
% 0.28/0.48  thf(fact_40__C7b_C,axiom,
% 0.28/0.48      ! [I2: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.28/0.48       => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.28/0.48              = I2 )
% 0.28/0.48           => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.28/0.48          & ! [Y2: nat] :
% 0.28/0.48              ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 0.28/0.48                  = I2 )
% 0.28/0.48                & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 0.28/0.48             => ( ( ord_less_nat @ mi @ Y2 )
% 0.28/0.48                & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "7b"
% 0.28/0.48  thf(fact_41_valid__insert__both__member__options__pres,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48           => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.28/0.48             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % valid_insert_both_member_options_pres
% 0.28/0.48  thf(fact_42_valid__insert__both__member__options__add,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % valid_insert_both_member_options_add
% 0.28/0.48  thf(fact_43_newlistlength,axiom,
% 0.28/0.48      ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) )
% 0.28/0.48      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.28/0.48  
% 0.28/0.48  % newlistlength
% 0.28/0.48  thf(fact_44__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 0.28/0.48      ( ( mi != ma )
% 0.28/0.48      & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % \<open>mi \<noteq> ma \<and> x < 2 ^ deg\<close>
% 0.28/0.48  thf(fact_45_member__bound,axiom,
% 0.28/0.48      ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 0.28/0.48        ( ( vEBT_vebt_member @ Tree @ X )
% 0.28/0.48       => ( ( vEBT_invar_vebt @ Tree @ N )
% 0.28/0.48         => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % member_bound
% 0.28/0.48  thf(fact_46_less__exp,axiom,
% 0.28/0.48      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % less_exp
% 0.28/0.48  thf(fact_47_semiring__norm_I85_J,axiom,
% 0.28/0.48      ! [M: num] :
% 0.28/0.48        ( ( bit0 @ M )
% 0.28/0.48       != one ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(85)
% 0.28/0.48  thf(fact_48_semiring__norm_I83_J,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( one
% 0.28/0.48       != ( bit0 @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(83)
% 0.28/0.48  thf(fact_49_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: real,P: real > $o] :
% 0.28/0.48        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_50_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 0.28/0.48        ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_51_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: complex,P: complex > $o] :
% 0.28/0.48        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_52_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: set_nat,P: set_nat > $o] :
% 0.28/0.48        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_53_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: nat,P: nat > $o] :
% 0.28/0.48        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_54_mem__Collect__eq,axiom,
% 0.28/0.48      ! [A: int,P: int > $o] :
% 0.28/0.48        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.28/0.48        = ( P @ A ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mem_Collect_eq
% 0.28/0.48  thf(fact_55_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_real] :
% 0.28/0.48        ( ( collect_real
% 0.28/0.48          @ ^ [X3: real] : ( member_real @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_56_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_Pr958786334691620121nt_int] :
% 0.28/0.48        ( ( collec213857154873943460nt_int
% 0.28/0.48          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_57_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_complex] :
% 0.28/0.48        ( ( collect_complex
% 0.28/0.48          @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_58_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_set_nat] :
% 0.28/0.48        ( ( collect_set_nat
% 0.28/0.48          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_59_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_nat] :
% 0.28/0.48        ( ( collect_nat
% 0.28/0.48          @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_60_Collect__mem__eq,axiom,
% 0.28/0.48      ! [A2: set_int] :
% 0.28/0.48        ( ( collect_int
% 0.28/0.48          @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 0.28/0.48        = A2 ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_mem_eq
% 0.28/0.48  thf(fact_61_Collect__cong,axiom,
% 0.28/0.48      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 0.28/0.48        ( ! [X6: product_prod_int_int] :
% 0.28/0.48            ( ( P @ X6 )
% 0.28/0.48            = ( Q @ X6 ) )
% 0.28/0.48       => ( ( collec213857154873943460nt_int @ P )
% 0.28/0.48          = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_cong
% 0.28/0.48  thf(fact_62_Collect__cong,axiom,
% 0.28/0.48      ! [P: complex > $o,Q: complex > $o] :
% 0.28/0.48        ( ! [X6: complex] :
% 0.28/0.48            ( ( P @ X6 )
% 0.28/0.48            = ( Q @ X6 ) )
% 0.28/0.48       => ( ( collect_complex @ P )
% 0.28/0.48          = ( collect_complex @ Q ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_cong
% 0.28/0.48  thf(fact_63_Collect__cong,axiom,
% 0.28/0.48      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.28/0.48        ( ! [X6: set_nat] :
% 0.28/0.48            ( ( P @ X6 )
% 0.28/0.48            = ( Q @ X6 ) )
% 0.28/0.48       => ( ( collect_set_nat @ P )
% 0.28/0.48          = ( collect_set_nat @ Q ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_cong
% 0.28/0.48  thf(fact_64_Collect__cong,axiom,
% 0.28/0.48      ! [P: nat > $o,Q: nat > $o] :
% 0.28/0.48        ( ! [X6: nat] :
% 0.28/0.48            ( ( P @ X6 )
% 0.28/0.48            = ( Q @ X6 ) )
% 0.28/0.48       => ( ( collect_nat @ P )
% 0.28/0.48          = ( collect_nat @ Q ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_cong
% 0.28/0.48  thf(fact_65_Collect__cong,axiom,
% 0.28/0.48      ! [P: int > $o,Q: int > $o] :
% 0.28/0.48        ( ! [X6: int] :
% 0.28/0.48            ( ( P @ X6 )
% 0.28/0.48            = ( Q @ X6 ) )
% 0.28/0.48       => ( ( collect_int @ P )
% 0.28/0.48          = ( collect_int @ Q ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Collect_cong
% 0.28/0.48  thf(fact_66_numeral__less__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.28/0.48        = ( ord_less_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_less_iff
% 0.28/0.48  thf(fact_67_numeral__less__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.28/0.48        = ( ord_less_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_less_iff
% 0.28/0.48  thf(fact_68_numeral__less__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.48        = ( ord_less_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_less_iff
% 0.28/0.48  thf(fact_69_numeral__less__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.28/0.48        = ( ord_less_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_less_iff
% 0.28/0.48  thf(fact_70_high__bound__aux,axiom,
% 0.28/0.48      ! [Ma: nat,N: nat,M: nat] :
% 0.28/0.48        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.28/0.48       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % high_bound_aux
% 0.28/0.48  thf(fact_71_min__Null__member,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,X: nat] :
% 0.28/0.48        ( ( vEBT_VEBT_minNull @ T )
% 0.28/0.48       => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % min_Null_member
% 0.28/0.48  thf(fact_72__C3_C,axiom,
% 0.28/0.48      ( deg
% 0.28/0.48      = ( plus_plus_nat @ na @ m ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "3"
% 0.28/0.48  thf(fact_73_both__member__options__equiv__member,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.28/0.48          = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % both_member_options_equiv_member
% 0.28/0.48  thf(fact_74_valid__member__both__member__options,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.28/0.48         => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % valid_member_both_member_options
% 0.28/0.48  thf(fact_75_min__in__set__def,axiom,
% 0.28/0.48      ( vEBT_VEBT_min_in_set
% 0.28/0.48      = ( ^ [Xs2: set_nat,X3: nat] :
% 0.28/0.48            ( ( member_nat @ X3 @ Xs2 )
% 0.28/0.48            & ! [Y3: nat] :
% 0.28/0.48                ( ( member_nat @ Y3 @ Xs2 )
% 0.28/0.48               => ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % min_in_set_def
% 0.28/0.48  thf(fact_76_max__in__set__def,axiom,
% 0.28/0.48      ( vEBT_VEBT_max_in_set
% 0.28/0.48      = ( ^ [Xs2: set_nat,X3: nat] :
% 0.28/0.48            ( ( member_nat @ X3 @ Xs2 )
% 0.28/0.48            & ! [Y3: nat] :
% 0.28/0.48                ( ( member_nat @ Y3 @ Xs2 )
% 0.28/0.48               => ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % max_in_set_def
% 0.28/0.48  thf(fact_77_inthall,axiom,
% 0.28/0.48      ! [Xs: list_complex,P: complex > $o,N: nat] :
% 0.28/0.48        ( ! [X6: complex] :
% 0.28/0.48            ( ( member_complex @ X6 @ ( set_complex2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_78_inthall,axiom,
% 0.28/0.48      ! [Xs: list_real,P: real > $o,N: nat] :
% 0.28/0.48        ( ! [X6: real] :
% 0.28/0.48            ( ( member_real @ X6 @ ( set_real2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_79_inthall,axiom,
% 0.28/0.48      ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 0.28/0.48        ( ! [X6: set_nat] :
% 0.28/0.48            ( ( member_set_nat @ X6 @ ( set_set_nat2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_80_inthall,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 0.28/0.48        ( ! [X6: vEBT_VEBT] :
% 0.28/0.48            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_81_inthall,axiom,
% 0.28/0.48      ! [Xs: list_o,P: $o > $o,N: nat] :
% 0.28/0.48        ( ! [X6: $o] :
% 0.28/0.48            ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_82_inthall,axiom,
% 0.28/0.48      ! [Xs: list_nat,P: nat > $o,N: nat] :
% 0.28/0.48        ( ! [X6: nat] :
% 0.28/0.48            ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_83_inthall,axiom,
% 0.28/0.48      ! [Xs: list_int,P: int > $o,N: nat] :
% 0.28/0.48        ( ! [X6: int] :
% 0.28/0.48            ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 0.28/0.48           => ( P @ X6 ) )
% 0.28/0.48       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.28/0.48         => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inthall
% 0.28/0.48  thf(fact_84_numeral__eq__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( numera6690914467698888265omplex @ M )
% 0.28/0.48          = ( numera6690914467698888265omplex @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_eq_iff
% 0.28/0.48  thf(fact_85_numeral__eq__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( numeral_numeral_real @ M )
% 0.28/0.48          = ( numeral_numeral_real @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_eq_iff
% 0.28/0.48  thf(fact_86_numeral__eq__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( numeral_numeral_rat @ M )
% 0.28/0.48          = ( numeral_numeral_rat @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_eq_iff
% 0.28/0.48  thf(fact_87_numeral__eq__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( numeral_numeral_nat @ M )
% 0.28/0.48          = ( numeral_numeral_nat @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_eq_iff
% 0.28/0.48  thf(fact_88_numeral__eq__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( numeral_numeral_int @ M )
% 0.28/0.48          = ( numeral_numeral_int @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_eq_iff
% 0.28/0.48  thf(fact_89_semiring__norm_I87_J,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ( bit0 @ M )
% 0.28/0.48          = ( bit0 @ N ) )
% 0.28/0.48        = ( M = N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(87)
% 0.28/0.48  thf(fact_90__C12_C,axiom,
% 0.28/0.48      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 0.28/0.48  
% 0.28/0.48  % "12"
% 0.28/0.48  thf(fact_91_inrg,axiom,
% 0.28/0.48      ( ( ord_less_eq_nat @ mi @ xa )
% 0.28/0.48      & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 0.28/0.48  
% 0.28/0.48  % inrg
% 0.28/0.48  thf(fact_92_numeral__le__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.28/0.48        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_le_iff
% 0.28/0.48  thf(fact_93_numeral__le__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.28/0.48        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_le_iff
% 0.28/0.48  thf(fact_94_numeral__le__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.48        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_le_iff
% 0.28/0.48  thf(fact_95_numeral__le__iff,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.28/0.48        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_le_iff
% 0.28/0.48  thf(fact_96_numeral__plus__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.28/0.48        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_plus_numeral
% 0.28/0.48  thf(fact_97_numeral__plus__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.28/0.48        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_plus_numeral
% 0.28/0.48  thf(fact_98_numeral__plus__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.28/0.48        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_plus_numeral
% 0.28/0.48  thf(fact_99_numeral__plus__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.48        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_plus_numeral
% 0.28/0.48  thf(fact_100_numeral__plus__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.28/0.48        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_plus_numeral
% 0.28/0.48  thf(fact_101_add__numeral__left,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: complex] :
% 0.28/0.48        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.28/0.48        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_numeral_left
% 0.28/0.48  thf(fact_102_add__numeral__left,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: real] :
% 0.28/0.48        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.28/0.48        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_numeral_left
% 0.28/0.48  thf(fact_103_add__numeral__left,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: rat] :
% 0.28/0.48        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.28/0.48        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_numeral_left
% 0.28/0.48  thf(fact_104_add__numeral__left,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: nat] :
% 0.28/0.48        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.28/0.48        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_numeral_left
% 0.28/0.48  thf(fact_105_add__numeral__left,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: int] :
% 0.28/0.48        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.28/0.48        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_numeral_left
% 0.28/0.48  thf(fact_106_post__member__pre__member,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 0.28/0.48             => ( ( vEBT_vebt_member @ T @ Y )
% 0.28/0.48                | ( X = Y ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % post_member_pre_member
% 0.28/0.48  thf(fact_107_member__correct,axiom,
% 0.28/0.48      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.48        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.48       => ( ( vEBT_vebt_member @ T @ X )
% 0.28/0.48          = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % member_correct
% 0.28/0.48  thf(fact_108_length__list__update,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 0.28/0.48        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
% 0.28/0.48        = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_list_update
% 0.28/0.48  thf(fact_109_length__list__update,axiom,
% 0.28/0.48      ! [Xs: list_o,I: nat,X: $o] :
% 0.28/0.48        ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X ) )
% 0.28/0.48        = ( size_size_list_o @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_list_update
% 0.28/0.48  thf(fact_110_length__list__update,axiom,
% 0.28/0.48      ! [Xs: list_nat,I: nat,X: nat] :
% 0.28/0.48        ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X ) )
% 0.28/0.48        = ( size_size_list_nat @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_list_update
% 0.28/0.48  thf(fact_111_length__list__update,axiom,
% 0.28/0.48      ! [Xs: list_int,I: nat,X: int] :
% 0.28/0.48        ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X ) )
% 0.28/0.48        = ( size_size_list_int @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_list_update
% 0.28/0.48  thf(fact_112_semiring__norm_I78_J,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.28/0.48        = ( ord_less_num @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(78)
% 0.28/0.48  thf(fact_113_semiring__norm_I75_J,axiom,
% 0.28/0.48      ! [M: num] :
% 0.28/0.48        ~ ( ord_less_num @ M @ one ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(75)
% 0.28/0.48  thf(fact_114__C6_C,axiom,
% 0.28/0.48      ( ( ord_less_eq_nat @ mi @ ma )
% 0.28/0.48      & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % "6"
% 0.28/0.48  thf(fact_115_list__update__beyond,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 0.28/0.48       => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 0.28/0.48          = Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_beyond
% 0.28/0.48  thf(fact_116_list__update__beyond,axiom,
% 0.28/0.48      ! [Xs: list_o,I: nat,X: $o] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 0.28/0.48       => ( ( list_update_o @ Xs @ I @ X )
% 0.28/0.48          = Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_beyond
% 0.28/0.48  thf(fact_117_list__update__beyond,axiom,
% 0.28/0.48      ! [Xs: list_nat,I: nat,X: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 0.28/0.48       => ( ( list_update_nat @ Xs @ I @ X )
% 0.28/0.48          = Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_beyond
% 0.28/0.48  thf(fact_118_list__update__beyond,axiom,
% 0.28/0.48      ! [Xs: list_int,I: nat,X: int] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 0.28/0.48       => ( ( list_update_int @ Xs @ I @ X )
% 0.28/0.48          = Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_beyond
% 0.28/0.48  thf(fact_119_semiring__norm_I76_J,axiom,
% 0.28/0.48      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % semiring_norm(76)
% 0.28/0.48  thf(fact_120_nth__list__update__eq,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 0.28/0.48          = X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_eq
% 0.28/0.48  thf(fact_121_nth__list__update__eq,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_o,X: $o] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ I )
% 0.28/0.48          = X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_eq
% 0.28/0.48  thf(fact_122_nth__list__update__eq,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_nat,X: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 0.28/0.48          = X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_eq
% 0.28/0.48  thf(fact_123_nth__list__update__eq,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_int,X: int] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 0.28/0.48          = X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update_eq
% 0.28/0.48  thf(fact_124_set__swap,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 0.28/0.48            = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_swap
% 0.28/0.48  thf(fact_125_set__swap,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_o,J: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.28/0.48         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 0.28/0.48            = ( set_o2 @ Xs ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_swap
% 0.28/0.48  thf(fact_126_set__swap,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_nat,J: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 0.28/0.48            = ( set_nat2 @ Xs ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_swap
% 0.28/0.48  thf(fact_127_set__swap,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_int,J: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.28/0.48         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 0.28/0.48            = ( set_int2 @ Xs ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_swap
% 0.28/0.48  thf(fact_128_Ex__list__of__length,axiom,
% 0.28/0.48      ! [N: nat] :
% 0.28/0.48      ? [Xs3: list_VEBT_VEBT] :
% 0.28/0.48        ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.28/0.48        = N ) ).
% 0.28/0.48  
% 0.28/0.48  % Ex_list_of_length
% 0.28/0.48  thf(fact_129_Ex__list__of__length,axiom,
% 0.28/0.48      ! [N: nat] :
% 0.28/0.48      ? [Xs3: list_o] :
% 0.28/0.48        ( ( size_size_list_o @ Xs3 )
% 0.28/0.48        = N ) ).
% 0.28/0.48  
% 0.28/0.48  % Ex_list_of_length
% 0.28/0.48  thf(fact_130_Ex__list__of__length,axiom,
% 0.28/0.48      ! [N: nat] :
% 0.28/0.48      ? [Xs3: list_nat] :
% 0.28/0.48        ( ( size_size_list_nat @ Xs3 )
% 0.28/0.48        = N ) ).
% 0.28/0.48  
% 0.28/0.48  % Ex_list_of_length
% 0.28/0.48  thf(fact_131_Ex__list__of__length,axiom,
% 0.28/0.48      ! [N: nat] :
% 0.28/0.48      ? [Xs3: list_int] :
% 0.28/0.48        ( ( size_size_list_int @ Xs3 )
% 0.28/0.48        = N ) ).
% 0.28/0.48  
% 0.28/0.48  % Ex_list_of_length
% 0.28/0.48  thf(fact_132_neq__if__length__neq,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.28/0.48        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.28/0.48         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.28/0.48       => ( Xs != Ys ) ) ).
% 0.28/0.48  
% 0.28/0.48  % neq_if_length_neq
% 0.28/0.48  thf(fact_133_neq__if__length__neq,axiom,
% 0.28/0.48      ! [Xs: list_o,Ys: list_o] :
% 0.28/0.48        ( ( ( size_size_list_o @ Xs )
% 0.28/0.48         != ( size_size_list_o @ Ys ) )
% 0.28/0.48       => ( Xs != Ys ) ) ).
% 0.28/0.48  
% 0.28/0.48  % neq_if_length_neq
% 0.28/0.48  thf(fact_134_neq__if__length__neq,axiom,
% 0.28/0.48      ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.48        ( ( ( size_size_list_nat @ Xs )
% 0.28/0.48         != ( size_size_list_nat @ Ys ) )
% 0.28/0.48       => ( Xs != Ys ) ) ).
% 0.28/0.48  
% 0.28/0.48  % neq_if_length_neq
% 0.28/0.48  thf(fact_135_neq__if__length__neq,axiom,
% 0.28/0.48      ! [Xs: list_int,Ys: list_int] :
% 0.28/0.48        ( ( ( size_size_list_int @ Xs )
% 0.28/0.48         != ( size_size_list_int @ Ys ) )
% 0.28/0.48       => ( Xs != Ys ) ) ).
% 0.28/0.48  
% 0.28/0.48  % neq_if_length_neq
% 0.28/0.48  thf(fact_136_is__num__normalize_I1_J,axiom,
% 0.28/0.48      ! [A: real,B: real,C: real] :
% 0.28/0.48        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.48        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % is_num_normalize(1)
% 0.28/0.48  thf(fact_137_is__num__normalize_I1_J,axiom,
% 0.28/0.48      ! [A: rat,B: rat,C: rat] :
% 0.28/0.48        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.48        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % is_num_normalize(1)
% 0.28/0.48  thf(fact_138_is__num__normalize_I1_J,axiom,
% 0.28/0.48      ! [A: int,B: int,C: int] :
% 0.28/0.48        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.48        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % is_num_normalize(1)
% 0.28/0.48  thf(fact_139_length__induct,axiom,
% 0.28/0.48      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 0.28/0.48        ( ! [Xs3: list_VEBT_VEBT] :
% 0.28/0.48            ( ! [Ys2: list_VEBT_VEBT] :
% 0.28/0.48                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.28/0.48               => ( P @ Ys2 ) )
% 0.28/0.48           => ( P @ Xs3 ) )
% 0.28/0.48       => ( P @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_induct
% 0.28/0.48  thf(fact_140_length__induct,axiom,
% 0.28/0.48      ! [P: list_o > $o,Xs: list_o] :
% 0.28/0.48        ( ! [Xs3: list_o] :
% 0.28/0.48            ( ! [Ys2: list_o] :
% 0.28/0.48                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 0.28/0.48               => ( P @ Ys2 ) )
% 0.28/0.48           => ( P @ Xs3 ) )
% 0.28/0.48       => ( P @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_induct
% 0.28/0.48  thf(fact_141_length__induct,axiom,
% 0.28/0.48      ! [P: list_nat > $o,Xs: list_nat] :
% 0.28/0.48        ( ! [Xs3: list_nat] :
% 0.28/0.48            ( ! [Ys2: list_nat] :
% 0.28/0.48                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.28/0.48               => ( P @ Ys2 ) )
% 0.28/0.48           => ( P @ Xs3 ) )
% 0.28/0.48       => ( P @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_induct
% 0.28/0.48  thf(fact_142_length__induct,axiom,
% 0.28/0.48      ! [P: list_int > $o,Xs: list_int] :
% 0.28/0.48        ( ! [Xs3: list_int] :
% 0.28/0.48            ( ! [Ys2: list_int] :
% 0.28/0.48                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 0.28/0.48               => ( P @ Ys2 ) )
% 0.28/0.48           => ( P @ Xs3 ) )
% 0.28/0.48       => ( P @ Xs ) ) ).
% 0.28/0.48  
% 0.28/0.48  % length_induct
% 0.28/0.48  thf(fact_143_numeral__Bit0,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.28/0.48        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_Bit0
% 0.28/0.48  thf(fact_144_numeral__Bit0,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.28/0.48        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_Bit0
% 0.28/0.48  thf(fact_145_numeral__Bit0,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.28/0.48        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_Bit0
% 0.28/0.48  thf(fact_146_numeral__Bit0,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.28/0.48        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_Bit0
% 0.28/0.48  thf(fact_147_numeral__Bit0,axiom,
% 0.28/0.48      ! [N: num] :
% 0.28/0.48        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.28/0.48        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_Bit0
% 0.28/0.48  thf(fact_148_nth__equalityI,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.28/0.48        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.28/0.48          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.28/0.48       => ( ! [I4: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48             => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 0.28/0.48                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 0.28/0.48         => ( Xs = Ys ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_equalityI
% 0.28/0.48  thf(fact_149_nth__equalityI,axiom,
% 0.28/0.48      ! [Xs: list_o,Ys: list_o] :
% 0.28/0.48        ( ( ( size_size_list_o @ Xs )
% 0.28/0.48          = ( size_size_list_o @ Ys ) )
% 0.28/0.48       => ( ! [I4: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 0.28/0.48             => ( ( nth_o @ Xs @ I4 )
% 0.28/0.48                = ( nth_o @ Ys @ I4 ) ) )
% 0.28/0.48         => ( Xs = Ys ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_equalityI
% 0.28/0.48  thf(fact_150_nth__equalityI,axiom,
% 0.28/0.48      ! [Xs: list_nat,Ys: list_nat] :
% 0.28/0.48        ( ( ( size_size_list_nat @ Xs )
% 0.28/0.48          = ( size_size_list_nat @ Ys ) )
% 0.28/0.48       => ( ! [I4: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48             => ( ( nth_nat @ Xs @ I4 )
% 0.28/0.48                = ( nth_nat @ Ys @ I4 ) ) )
% 0.28/0.48         => ( Xs = Ys ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_equalityI
% 0.28/0.48  thf(fact_151_nth__equalityI,axiom,
% 0.28/0.48      ! [Xs: list_int,Ys: list_int] :
% 0.28/0.48        ( ( ( size_size_list_int @ Xs )
% 0.28/0.48          = ( size_size_list_int @ Ys ) )
% 0.28/0.48       => ( ! [I4: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 0.28/0.48             => ( ( nth_int @ Xs @ I4 )
% 0.28/0.48                = ( nth_int @ Ys @ I4 ) ) )
% 0.28/0.48         => ( Xs = Ys ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_equalityI
% 0.28/0.48  thf(fact_152_Skolem__list__nth,axiom,
% 0.28/0.48      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 0.28/0.48        ( ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48             => ? [X2: vEBT_VEBT] : ( P @ I5 @ X2 ) ) )
% 0.28/0.48        = ( ? [Xs2: list_VEBT_VEBT] :
% 0.28/0.48              ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.28/0.48                = K )
% 0.28/0.48              & ! [I5: nat] :
% 0.28/0.48                  ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48                 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs2 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Skolem_list_nth
% 0.28/0.48  thf(fact_153_Skolem__list__nth,axiom,
% 0.28/0.48      ! [K: nat,P: nat > $o > $o] :
% 0.28/0.48        ( ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48             => ? [X2: $o] : ( P @ I5 @ X2 ) ) )
% 0.28/0.48        = ( ? [Xs2: list_o] :
% 0.28/0.48              ( ( ( size_size_list_o @ Xs2 )
% 0.28/0.48                = K )
% 0.28/0.48              & ! [I5: nat] :
% 0.28/0.48                  ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48                 => ( P @ I5 @ ( nth_o @ Xs2 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Skolem_list_nth
% 0.28/0.48  thf(fact_154_Skolem__list__nth,axiom,
% 0.28/0.48      ! [K: nat,P: nat > nat > $o] :
% 0.28/0.48        ( ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48             => ? [X2: nat] : ( P @ I5 @ X2 ) ) )
% 0.28/0.48        = ( ? [Xs2: list_nat] :
% 0.28/0.48              ( ( ( size_size_list_nat @ Xs2 )
% 0.28/0.48                = K )
% 0.28/0.48              & ! [I5: nat] :
% 0.28/0.48                  ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48                 => ( P @ I5 @ ( nth_nat @ Xs2 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Skolem_list_nth
% 0.28/0.48  thf(fact_155_Skolem__list__nth,axiom,
% 0.28/0.48      ! [K: nat,P: nat > int > $o] :
% 0.28/0.48        ( ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48             => ? [X2: int] : ( P @ I5 @ X2 ) ) )
% 0.28/0.48        = ( ? [Xs2: list_int] :
% 0.28/0.48              ( ( ( size_size_list_int @ Xs2 )
% 0.28/0.48                = K )
% 0.28/0.48              & ! [I5: nat] :
% 0.28/0.48                  ( ( ord_less_nat @ I5 @ K )
% 0.28/0.48                 => ( P @ I5 @ ( nth_int @ Xs2 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % Skolem_list_nth
% 0.28/0.48  thf(fact_156_list__eq__iff__nth__eq,axiom,
% 0.28/0.48      ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 0.28/0.48      = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.28/0.48            ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.28/0.48              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.28/0.48            & ! [I5: nat] :
% 0.28/0.48                ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.28/0.48               => ( ( nth_VEBT_VEBT @ Xs2 @ I5 )
% 0.28/0.48                  = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_eq_iff_nth_eq
% 0.28/0.48  thf(fact_157_list__eq__iff__nth__eq,axiom,
% 0.28/0.48      ( ( ^ [Y4: list_o,Z2: list_o] : ( Y4 = Z2 ) )
% 0.28/0.48      = ( ^ [Xs2: list_o,Ys3: list_o] :
% 0.28/0.48            ( ( ( size_size_list_o @ Xs2 )
% 0.28/0.48              = ( size_size_list_o @ Ys3 ) )
% 0.28/0.48            & ! [I5: nat] :
% 0.28/0.48                ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 0.28/0.48               => ( ( nth_o @ Xs2 @ I5 )
% 0.28/0.48                  = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_eq_iff_nth_eq
% 0.28/0.48  thf(fact_158_list__eq__iff__nth__eq,axiom,
% 0.28/0.48      ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 0.28/0.48      = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 0.28/0.48            ( ( ( size_size_list_nat @ Xs2 )
% 0.28/0.48              = ( size_size_list_nat @ Ys3 ) )
% 0.28/0.48            & ! [I5: nat] :
% 0.28/0.48                ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 0.28/0.48               => ( ( nth_nat @ Xs2 @ I5 )
% 0.28/0.48                  = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_eq_iff_nth_eq
% 0.28/0.48  thf(fact_159_list__eq__iff__nth__eq,axiom,
% 0.28/0.48      ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 0.28/0.48      = ( ^ [Xs2: list_int,Ys3: list_int] :
% 0.28/0.48            ( ( ( size_size_list_int @ Xs2 )
% 0.28/0.48              = ( size_size_list_int @ Ys3 ) )
% 0.28/0.48            & ! [I5: nat] :
% 0.28/0.48                ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 0.28/0.48               => ( ( nth_int @ Xs2 @ I5 )
% 0.28/0.48                  = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_eq_iff_nth_eq
% 0.28/0.48  thf(fact_160_power2__nat__le__imp__le,axiom,
% 0.28/0.48      ! [M: nat,N: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.28/0.48       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % power2_nat_le_imp_le
% 0.28/0.48  thf(fact_161_power2__nat__le__eq__le,axiom,
% 0.28/0.48      ! [M: nat,N: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.48        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % power2_nat_le_eq_le
% 0.28/0.48  thf(fact_162_self__le__ge2__pow,axiom,
% 0.28/0.48      ! [K: nat,M: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.28/0.48       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % self_le_ge2_pow
% 0.28/0.48  thf(fact_163_all__set__conv__all__nth,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.28/0.48        ( ( ! [X3: vEBT_VEBT] :
% 0.28/0.48              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.48             => ( P @ X3 ) ) )
% 0.28/0.48        = ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48             => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_set_conv_all_nth
% 0.28/0.48  thf(fact_164_all__set__conv__all__nth,axiom,
% 0.28/0.48      ! [Xs: list_o,P: $o > $o] :
% 0.28/0.48        ( ( ! [X3: $o] :
% 0.28/0.48              ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.28/0.48             => ( P @ X3 ) ) )
% 0.28/0.48        = ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 0.28/0.48             => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_set_conv_all_nth
% 0.28/0.48  thf(fact_165_all__set__conv__all__nth,axiom,
% 0.28/0.48      ! [Xs: list_nat,P: nat > $o] :
% 0.28/0.48        ( ( ! [X3: nat] :
% 0.28/0.48              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.28/0.48             => ( P @ X3 ) ) )
% 0.28/0.48        = ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48             => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_set_conv_all_nth
% 0.28/0.48  thf(fact_166_all__set__conv__all__nth,axiom,
% 0.28/0.48      ! [Xs: list_int,P: int > $o] :
% 0.28/0.48        ( ( ! [X3: int] :
% 0.28/0.48              ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.28/0.48             => ( P @ X3 ) ) )
% 0.28/0.48        = ( ! [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 0.28/0.48             => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_set_conv_all_nth
% 0.28/0.48  thf(fact_167_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_complex,P: complex > $o,X: complex] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_168_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_real,P: real > $o,X: real] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_169_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_set_nat @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_170_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_171_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_o,P: $o > $o,X: $o] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_172_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_nat,P: nat > $o,X: nat] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_173_all__nth__imp__all__set,axiom,
% 0.28/0.48      ! [Xs: list_int,P: int > $o,X: int] :
% 0.28/0.48        ( ! [I4: nat] :
% 0.28/0.48            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 0.28/0.48           => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 0.28/0.48       => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.28/0.48         => ( P @ X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % all_nth_imp_all_set
% 0.28/0.48  thf(fact_174_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: complex,Xs: list_complex] :
% 0.28/0.48        ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.28/0.48              & ( ( nth_complex @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_175_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: real,Xs: list_real] :
% 0.28/0.48        ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 0.28/0.48              & ( ( nth_real @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_176_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: set_nat,Xs: list_set_nat] :
% 0.28/0.48        ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.28/0.48              & ( ( nth_set_nat @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_177_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.28/0.48        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48              & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_178_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: $o,Xs: list_o] :
% 0.28/0.48        ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 0.28/0.48              & ( ( nth_o @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_179_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: nat,Xs: list_nat] :
% 0.28/0.48        ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48              & ( ( nth_nat @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_180_in__set__conv__nth,axiom,
% 0.28/0.48      ! [X: int,Xs: list_int] :
% 0.28/0.48        ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.28/0.48        = ( ? [I5: nat] :
% 0.28/0.48              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 0.28/0.48              & ( ( nth_int @ Xs @ I5 )
% 0.28/0.48                = X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % in_set_conv_nth
% 0.28/0.48  thf(fact_181_list__ball__nth,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( ! [X6: vEBT_VEBT] :
% 0.28/0.48              ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.48             => ( P @ X6 ) )
% 0.28/0.48         => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_ball_nth
% 0.28/0.48  thf(fact_182_list__ball__nth,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_o,P: $o > $o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( ! [X6: $o] :
% 0.28/0.48              ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 0.28/0.48             => ( P @ X6 ) )
% 0.28/0.48         => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_ball_nth
% 0.28/0.48  thf(fact_183_list__ball__nth,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_nat,P: nat > $o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( ! [X6: nat] :
% 0.28/0.48              ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 0.28/0.48             => ( P @ X6 ) )
% 0.28/0.48         => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_ball_nth
% 0.28/0.48  thf(fact_184_list__ball__nth,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_int,P: int > $o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( ! [X6: int] :
% 0.28/0.48              ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 0.28/0.48             => ( P @ X6 ) )
% 0.28/0.48         => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_ball_nth
% 0.28/0.48  thf(fact_185_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_complex] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.28/0.48       => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_186_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_real] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.28/0.48       => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_187_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_set_nat] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.28/0.48       => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_188_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_189_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_190_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_nat] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_191_nth__mem,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_int] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_mem
% 0.28/0.48  thf(fact_192_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_complex,X: complex] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 0.28/0.48       => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_193_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_real,X: real] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.28/0.48       => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_194_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.28/0.48       => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_195_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_196_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_o,X: $o] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_197_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_nat,X: nat] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_198_set__update__memI,axiom,
% 0.28/0.48      ! [N: nat,Xs: list_int,X: int] :
% 0.28/0.48        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_update_memI
% 0.28/0.48  thf(fact_199_nth__list__update,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( ( ( I = J )
% 0.28/0.48           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 0.28/0.48              = X ) )
% 0.28/0.48          & ( ( I != J )
% 0.28/0.48           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 0.28/0.48              = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update
% 0.28/0.48  thf(fact_200_nth__list__update,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_o,X: $o,J: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ J )
% 0.28/0.48          = ( ( ( I = J )
% 0.28/0.48             => X )
% 0.28/0.48            & ( ( I != J )
% 0.28/0.48             => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update
% 0.28/0.48  thf(fact_201_nth__list__update,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( ( ( I = J )
% 0.28/0.48           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 0.28/0.48              = X ) )
% 0.28/0.48          & ( ( I != J )
% 0.28/0.48           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 0.28/0.48              = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update
% 0.28/0.48  thf(fact_202_nth__list__update,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_int,J: nat,X: int] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( ( ( I = J )
% 0.28/0.48           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 0.28/0.48              = X ) )
% 0.28/0.48          & ( ( I != J )
% 0.28/0.48           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 0.28/0.48              = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nth_list_update
% 0.28/0.48  thf(fact_203_list__update__same__conv,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.28/0.48       => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 0.28/0.48            = Xs )
% 0.28/0.48          = ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.28/0.48            = X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_same_conv
% 0.28/0.48  thf(fact_204_list__update__same__conv,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_o,X: $o] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.28/0.48       => ( ( ( list_update_o @ Xs @ I @ X )
% 0.28/0.48            = Xs )
% 0.28/0.48          = ( ( nth_o @ Xs @ I )
% 0.28/0.48            = X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_same_conv
% 0.28/0.48  thf(fact_205_list__update__same__conv,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_nat,X: nat] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.28/0.48       => ( ( ( list_update_nat @ Xs @ I @ X )
% 0.28/0.48            = Xs )
% 0.28/0.48          = ( ( nth_nat @ Xs @ I )
% 0.28/0.48            = X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_same_conv
% 0.28/0.48  thf(fact_206_list__update__same__conv,axiom,
% 0.28/0.48      ! [I: nat,Xs: list_int,X: int] :
% 0.28/0.48        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.28/0.48       => ( ( ( list_update_int @ Xs @ I @ X )
% 0.28/0.48            = Xs )
% 0.28/0.48          = ( ( nth_int @ Xs @ I )
% 0.28/0.48            = X ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % list_update_same_conv
% 0.28/0.48  thf(fact_207_set__n__deg__not__0,axiom,
% 0.28/0.48      ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 0.28/0.48        ( ! [X6: vEBT_VEBT] :
% 0.28/0.48            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.48           => ( vEBT_invar_vebt @ X6 @ N ) )
% 0.28/0.48       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.28/0.48            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.48         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % set_n_deg_not_0
% 0.28/0.48  thf(fact_208_bit__concat__def,axiom,
% 0.28/0.48      ( vEBT_VEBT_bit_concat
% 0.28/0.48      = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % bit_concat_def
% 0.28/0.48  thf(fact_209_low__inv,axiom,
% 0.28/0.48      ! [X: nat,N: nat,Y: nat] :
% 0.28/0.48        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.28/0.48          = X ) ) ).
% 0.28/0.48  
% 0.28/0.48  % low_inv
% 0.28/0.48  thf(fact_210_high__inv,axiom,
% 0.28/0.48      ! [X: nat,N: nat,Y: nat] :
% 0.28/0.48        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.48       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.28/0.48          = Y ) ) ).
% 0.28/0.48  
% 0.28/0.48  % high_inv
% 0.28/0.48  thf(fact_211__C9_C,axiom,
% 0.28/0.48      ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.48      = na ) ).
% 0.28/0.48  
% 0.28/0.48  % "9"
% 0.28/0.48  thf(fact_212_nat__add__left__cancel__le,axiom,
% 0.28/0.48      ! [K: nat,M: nat,N: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.28/0.48        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nat_add_left_cancel_le
% 0.28/0.48  thf(fact_213_nat__add__left__cancel__less,axiom,
% 0.28/0.48      ! [K: nat,M: nat,N: nat] :
% 0.28/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.28/0.48        = ( ord_less_nat @ M @ N ) ) ).
% 0.28/0.48  
% 0.28/0.48  % nat_add_left_cancel_less
% 0.28/0.48  thf(fact_214_enat__ord__number_I2_J,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.28/0.48        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % enat_ord_number(2)
% 0.28/0.48  thf(fact_215_add__less__cancel__right,axiom,
% 0.28/0.48      ! [A: real,C: real,B: real] :
% 0.28/0.48        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48        = ( ord_less_real @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_right
% 0.28/0.48  thf(fact_216_add__less__cancel__right,axiom,
% 0.28/0.48      ! [A: rat,C: rat,B: rat] :
% 0.28/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.48        = ( ord_less_rat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_right
% 0.28/0.48  thf(fact_217_add__less__cancel__right,axiom,
% 0.28/0.48      ! [A: nat,C: nat,B: nat] :
% 0.28/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.48        = ( ord_less_nat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_right
% 0.28/0.48  thf(fact_218_add__less__cancel__right,axiom,
% 0.28/0.48      ! [A: int,C: int,B: int] :
% 0.28/0.48        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.48        = ( ord_less_int @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_right
% 0.28/0.48  thf(fact_219_add__less__cancel__left,axiom,
% 0.28/0.48      ! [C: real,A: real,B: real] :
% 0.28/0.48        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.48        = ( ord_less_real @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_left
% 0.28/0.48  thf(fact_220_add__less__cancel__left,axiom,
% 0.28/0.48      ! [C: rat,A: rat,B: rat] :
% 0.28/0.48        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.28/0.48        = ( ord_less_rat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_left
% 0.28/0.48  thf(fact_221_add__less__cancel__left,axiom,
% 0.28/0.48      ! [C: nat,A: nat,B: nat] :
% 0.28/0.48        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.28/0.48        = ( ord_less_nat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_left
% 0.28/0.48  thf(fact_222_add__less__cancel__left,axiom,
% 0.28/0.48      ! [C: int,A: int,B: int] :
% 0.28/0.48        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.28/0.48        = ( ord_less_int @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_less_cancel_left
% 0.28/0.48  thf(fact_223_add__le__cancel__right,axiom,
% 0.28/0.48      ! [A: real,C: real,B: real] :
% 0.28/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.48        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_right
% 0.28/0.48  thf(fact_224_add__le__cancel__right,axiom,
% 0.28/0.48      ! [A: rat,C: rat,B: rat] :
% 0.28/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.48        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_right
% 0.28/0.48  thf(fact_225_add__le__cancel__right,axiom,
% 0.28/0.48      ! [A: nat,C: nat,B: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.48        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_right
% 0.28/0.48  thf(fact_226_add__le__cancel__right,axiom,
% 0.28/0.48      ! [A: int,C: int,B: int] :
% 0.28/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.48        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_right
% 0.28/0.48  thf(fact_227_add__le__cancel__left,axiom,
% 0.28/0.48      ! [C: real,A: real,B: real] :
% 0.28/0.48        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.48        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_left
% 0.28/0.48  thf(fact_228_add__le__cancel__left,axiom,
% 0.28/0.48      ! [C: rat,A: rat,B: rat] :
% 0.28/0.48        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.28/0.48        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_left
% 0.28/0.48  thf(fact_229_add__le__cancel__left,axiom,
% 0.28/0.48      ! [C: nat,A: nat,B: nat] :
% 0.28/0.48        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.28/0.48        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_left
% 0.28/0.48  thf(fact_230_add__le__cancel__left,axiom,
% 0.28/0.48      ! [C: int,A: int,B: int] :
% 0.28/0.48        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.28/0.48        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_le_cancel_left
% 0.28/0.48  thf(fact_231__C11_C,axiom,
% 0.28/0.48      ord_less_eq_nat @ one_one_nat @ na ).
% 0.28/0.48  
% 0.28/0.48  % "11"
% 0.28/0.48  thf(fact_232_add__left__cancel,axiom,
% 0.28/0.48      ! [A: real,B: real,C: real] :
% 0.28/0.48        ( ( ( plus_plus_real @ A @ B )
% 0.28/0.48          = ( plus_plus_real @ A @ C ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_left_cancel
% 0.28/0.48  thf(fact_233_add__left__cancel,axiom,
% 0.28/0.48      ! [A: rat,B: rat,C: rat] :
% 0.28/0.48        ( ( ( plus_plus_rat @ A @ B )
% 0.28/0.48          = ( plus_plus_rat @ A @ C ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_left_cancel
% 0.28/0.48  thf(fact_234_add__left__cancel,axiom,
% 0.28/0.48      ! [A: nat,B: nat,C: nat] :
% 0.28/0.48        ( ( ( plus_plus_nat @ A @ B )
% 0.28/0.48          = ( plus_plus_nat @ A @ C ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_left_cancel
% 0.28/0.48  thf(fact_235_add__left__cancel,axiom,
% 0.28/0.48      ! [A: int,B: int,C: int] :
% 0.28/0.48        ( ( ( plus_plus_int @ A @ B )
% 0.28/0.48          = ( plus_plus_int @ A @ C ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_left_cancel
% 0.28/0.48  thf(fact_236_add__right__cancel,axiom,
% 0.28/0.48      ! [B: real,A: real,C: real] :
% 0.28/0.48        ( ( ( plus_plus_real @ B @ A )
% 0.28/0.48          = ( plus_plus_real @ C @ A ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_right_cancel
% 0.28/0.48  thf(fact_237_add__right__cancel,axiom,
% 0.28/0.48      ! [B: rat,A: rat,C: rat] :
% 0.28/0.48        ( ( ( plus_plus_rat @ B @ A )
% 0.28/0.48          = ( plus_plus_rat @ C @ A ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_right_cancel
% 0.28/0.48  thf(fact_238_add__right__cancel,axiom,
% 0.28/0.48      ! [B: nat,A: nat,C: nat] :
% 0.28/0.48        ( ( ( plus_plus_nat @ B @ A )
% 0.28/0.48          = ( plus_plus_nat @ C @ A ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_right_cancel
% 0.28/0.48  thf(fact_239_add__right__cancel,axiom,
% 0.28/0.48      ! [B: int,A: int,C: int] :
% 0.28/0.48        ( ( ( plus_plus_int @ B @ A )
% 0.28/0.48          = ( plus_plus_int @ C @ A ) )
% 0.28/0.48        = ( B = C ) ) ).
% 0.28/0.48  
% 0.28/0.48  % add_right_cancel
% 0.28/0.48  thf(fact_240_pow__sum,axiom,
% 0.28/0.48      ! [A: nat,B: nat] :
% 0.28/0.48        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.28/0.48        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.28/0.48  
% 0.28/0.48  % pow_sum
% 0.28/0.48  thf(fact_241_high__def,axiom,
% 0.28/0.48      ( vEBT_VEBT_high
% 0.28/0.48      = ( ^ [X3: nat,N2: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % high_def
% 0.28/0.48  thf(fact_242_mult__numeral__left__semiring__numeral,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: complex] :
% 0.28/0.48        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 0.28/0.48        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mult_numeral_left_semiring_numeral
% 0.28/0.48  thf(fact_243_mult__numeral__left__semiring__numeral,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: real] :
% 0.28/0.48        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.28/0.48        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mult_numeral_left_semiring_numeral
% 0.28/0.48  thf(fact_244_mult__numeral__left__semiring__numeral,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: rat] :
% 0.28/0.48        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.28/0.48        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mult_numeral_left_semiring_numeral
% 0.28/0.48  thf(fact_245_mult__numeral__left__semiring__numeral,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: nat] :
% 0.28/0.48        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.28/0.48        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mult_numeral_left_semiring_numeral
% 0.28/0.48  thf(fact_246_mult__numeral__left__semiring__numeral,axiom,
% 0.28/0.48      ! [V: num,W: num,Z: int] :
% 0.28/0.48        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.28/0.48        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.28/0.48  
% 0.28/0.48  % mult_numeral_left_semiring_numeral
% 0.28/0.48  thf(fact_247_numeral__times__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 0.28/0.48        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_times_numeral
% 0.28/0.48  thf(fact_248_numeral__times__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.28/0.48        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_times_numeral
% 0.28/0.48  thf(fact_249_numeral__times__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.28/0.48        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_times_numeral
% 0.28/0.48  thf(fact_250_numeral__times__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.48        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_times_numeral
% 0.28/0.48  thf(fact_251_numeral__times__numeral,axiom,
% 0.28/0.48      ! [M: num,N: num] :
% 0.28/0.48        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.28/0.48        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.28/0.48  
% 0.28/0.48  % numeral_times_numeral
% 0.28/0.48  thf(fact_252_mult_Oright__neutral,axiom,
% 0.28/0.48      ! [A: complex] :
% 0.28/0.48        ( ( times_times_complex @ A @ one_one_complex )
% 0.28/0.48        = A ) ).
% 0.28/0.48  
% 0.28/0.48  % mult.right_neutral
% 0.28/0.48  thf(fact_253_mult_Oright__neutral,axiom,
% 0.28/0.48      ! [A: real] :
% 0.28/0.48        ( ( times_times_real @ A @ one_one_real )
% 0.28/0.48        = A ) ).
% 0.28/0.48  
% 0.28/0.48  % mult.right_neutral
% 0.28/0.48  thf(fact_254_mult_Oright__neutral,axiom,
% 0.28/0.48      ! [A: rat] :
% 0.28/0.48        ( ( times_times_rat @ A @ one_one_rat )
% 0.28/0.48        = A ) ).
% 0.28/0.48  
% 0.28/0.48  % mult.right_neutral
% 0.28/0.48  thf(fact_255_mult_Oright__neutral,axiom,
% 0.28/0.48      ! [A: nat] :
% 0.28/0.48        ( ( times_times_nat @ A @ one_one_nat )
% 0.28/0.48        = A ) ).
% 0.28/0.48  
% 0.28/0.48  % mult.right_neutral
% 0.28/0.48  thf(fact_256_mult_Oright__neutral,axiom,
% 0.28/0.48      ! [A: int] :
% 0.28/0.48        ( ( times_times_int @ A @ one_one_int )
% 0.28/0.48        = A ) ).
% 0.28/0.48  
% 0.28/0.48  % mult.right_neutral
% 0.28/0.48  thf(fact_257_mult__1,axiom,
% 0.28/0.48      ! [A: complex] :
% 0.28/0.48        ( ( times_times_complex @ one_one_complex @ A )
% 0.28/0.48        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_1
% 0.28/0.49  thf(fact_258_mult__1,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( times_times_real @ one_one_real @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_1
% 0.28/0.49  thf(fact_259_mult__1,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( times_times_rat @ one_one_rat @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_1
% 0.28/0.49  thf(fact_260_mult__1,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( times_times_nat @ one_one_nat @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_1
% 0.28/0.49  thf(fact_261_mult__1,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( times_times_int @ one_one_int @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_1
% 0.28/0.49  thf(fact_262_power__one,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( power_power_rat @ one_one_rat @ N )
% 0.28/0.49        = one_one_rat ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one
% 0.28/0.49  thf(fact_263_power__one,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( power_power_nat @ one_one_nat @ N )
% 0.28/0.49        = one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one
% 0.28/0.49  thf(fact_264_power__one,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( power_power_real @ one_one_real @ N )
% 0.28/0.49        = one_one_real ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one
% 0.28/0.49  thf(fact_265_power__one,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( power_power_int @ one_one_int @ N )
% 0.28/0.49        = one_one_int ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one
% 0.28/0.49  thf(fact_266_power__one,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( power_power_complex @ one_one_complex @ N )
% 0.28/0.49        = one_one_complex ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one
% 0.28/0.49  thf(fact_267_power__one__right,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( power_power_nat @ A @ one_one_nat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_right
% 0.28/0.49  thf(fact_268_power__one__right,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( power_power_real @ A @ one_one_nat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_right
% 0.28/0.49  thf(fact_269_power__one__right,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( power_power_int @ A @ one_one_nat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_right
% 0.28/0.49  thf(fact_270_power__one__right,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( power_power_complex @ A @ one_one_nat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_right
% 0.28/0.49  thf(fact_271_nat__1__eq__mult__iff,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( one_one_nat
% 0.28/0.49          = ( times_times_nat @ M @ N ) )
% 0.28/0.49        = ( ( M = one_one_nat )
% 0.28/0.49          & ( N = one_one_nat ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_1_eq_mult_iff
% 0.28/0.49  thf(fact_272_nat__mult__eq__1__iff,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ( times_times_nat @ M @ N )
% 0.28/0.49          = one_one_nat )
% 0.28/0.49        = ( ( M = one_one_nat )
% 0.28/0.49          & ( N = one_one_nat ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_mult_eq_1_iff
% 0.28/0.49  thf(fact_273_semiring__norm_I6_J,axiom,
% 0.28/0.49      ! [M: num,N: num] :
% 0.28/0.49        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.28/0.49        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % semiring_norm(6)
% 0.28/0.49  thf(fact_274_semiring__norm_I71_J,axiom,
% 0.28/0.49      ! [M: num,N: num] :
% 0.28/0.49        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.28/0.49        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % semiring_norm(71)
% 0.28/0.49  thf(fact_275_semiring__norm_I68_J,axiom,
% 0.28/0.49      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 0.28/0.49  
% 0.28/0.49  % semiring_norm(68)
% 0.28/0.49  thf(fact_276_distrib__right__numeral,axiom,
% 0.28/0.49      ! [A: complex,B: complex,V: num] :
% 0.28/0.49        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.28/0.49        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_right_numeral
% 0.28/0.49  thf(fact_277_distrib__right__numeral,axiom,
% 0.28/0.49      ! [A: real,B: real,V: num] :
% 0.28/0.49        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.49        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_right_numeral
% 0.28/0.49  thf(fact_278_distrib__right__numeral,axiom,
% 0.28/0.49      ! [A: rat,B: rat,V: num] :
% 0.28/0.49        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.49        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_right_numeral
% 0.28/0.49  thf(fact_279_distrib__right__numeral,axiom,
% 0.28/0.49      ! [A: nat,B: nat,V: num] :
% 0.28/0.49        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_right_numeral
% 0.28/0.49  thf(fact_280_distrib__right__numeral,axiom,
% 0.28/0.49      ! [A: int,B: int,V: num] :
% 0.28/0.49        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.49        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_right_numeral
% 0.28/0.49  thf(fact_281_distrib__left__numeral,axiom,
% 0.28/0.49      ! [V: num,B: complex,C: complex] :
% 0.28/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 0.28/0.49        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_left_numeral
% 0.28/0.49  thf(fact_282_distrib__left__numeral,axiom,
% 0.28/0.49      ! [V: num,B: real,C: real] :
% 0.28/0.49        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.49        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_left_numeral
% 0.28/0.49  thf(fact_283_distrib__left__numeral,axiom,
% 0.28/0.49      ! [V: num,B: rat,C: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.49        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_left_numeral
% 0.28/0.49  thf(fact_284_distrib__left__numeral,axiom,
% 0.28/0.49      ! [V: num,B: nat,C: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_left_numeral
% 0.28/0.49  thf(fact_285_distrib__left__numeral,axiom,
% 0.28/0.49      ! [V: num,B: int,C: int] :
% 0.28/0.49        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.49        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % distrib_left_numeral
% 0.28/0.49  thf(fact_286_numeral__eq__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ( numera6690914467698888265omplex @ N )
% 0.28/0.49          = one_one_complex )
% 0.28/0.49        = ( N = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_eq_one_iff
% 0.28/0.49  thf(fact_287_numeral__eq__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ( numeral_numeral_real @ N )
% 0.28/0.49          = one_one_real )
% 0.28/0.49        = ( N = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_eq_one_iff
% 0.28/0.49  thf(fact_288_numeral__eq__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ( numeral_numeral_rat @ N )
% 0.28/0.49          = one_one_rat )
% 0.28/0.49        = ( N = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_eq_one_iff
% 0.28/0.49  thf(fact_289_numeral__eq__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ( numeral_numeral_nat @ N )
% 0.28/0.49          = one_one_nat )
% 0.28/0.49        = ( N = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_eq_one_iff
% 0.28/0.49  thf(fact_290_numeral__eq__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ( numeral_numeral_int @ N )
% 0.28/0.49          = one_one_int )
% 0.28/0.49        = ( N = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_eq_one_iff
% 0.28/0.49  thf(fact_291_one__eq__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( one_one_complex
% 0.28/0.49          = ( numera6690914467698888265omplex @ N ) )
% 0.28/0.49        = ( one = N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_eq_numeral_iff
% 0.28/0.49  thf(fact_292_one__eq__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( one_one_real
% 0.28/0.49          = ( numeral_numeral_real @ N ) )
% 0.28/0.49        = ( one = N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_eq_numeral_iff
% 0.28/0.49  thf(fact_293_one__eq__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( one_one_rat
% 0.28/0.49          = ( numeral_numeral_rat @ N ) )
% 0.28/0.49        = ( one = N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_eq_numeral_iff
% 0.28/0.49  thf(fact_294_one__eq__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( one_one_nat
% 0.28/0.49          = ( numeral_numeral_nat @ N ) )
% 0.28/0.49        = ( one = N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_eq_numeral_iff
% 0.28/0.49  thf(fact_295_one__eq__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( one_one_int
% 0.28/0.49          = ( numeral_numeral_int @ N ) )
% 0.28/0.49        = ( one = N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_eq_numeral_iff
% 0.28/0.49  thf(fact_296_power__inject__exp,axiom,
% 0.28/0.49      ! [A: real,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49       => ( ( ( power_power_real @ A @ M )
% 0.28/0.49            = ( power_power_real @ A @ N ) )
% 0.28/0.49          = ( M = N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_inject_exp
% 0.28/0.49  thf(fact_297_power__inject__exp,axiom,
% 0.28/0.49      ! [A: rat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ( ( power_power_rat @ A @ M )
% 0.28/0.49            = ( power_power_rat @ A @ N ) )
% 0.28/0.49          = ( M = N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_inject_exp
% 0.28/0.49  thf(fact_298_power__inject__exp,axiom,
% 0.28/0.49      ! [A: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ( ( power_power_nat @ A @ M )
% 0.28/0.49            = ( power_power_nat @ A @ N ) )
% 0.28/0.49          = ( M = N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_inject_exp
% 0.28/0.49  thf(fact_299_power__inject__exp,axiom,
% 0.28/0.49      ! [A: int,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49       => ( ( ( power_power_int @ A @ M )
% 0.28/0.49            = ( power_power_int @ A @ N ) )
% 0.28/0.49          = ( M = N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_inject_exp
% 0.28/0.49  thf(fact_300_semiring__norm_I2_J,axiom,
% 0.28/0.49      ( ( plus_plus_num @ one @ one )
% 0.28/0.49      = ( bit0 @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % semiring_norm(2)
% 0.28/0.49  thf(fact_301_semiring__norm_I69_J,axiom,
% 0.28/0.49      ! [M: num] :
% 0.28/0.49        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.28/0.49  
% 0.28/0.49  % semiring_norm(69)
% 0.28/0.49  thf(fact_302_enat__ord__number_I1_J,axiom,
% 0.28/0.49      ! [M: num,N: num] :
% 0.28/0.49        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.28/0.49        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % enat_ord_number(1)
% 0.28/0.49  thf(fact_303_le__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [A: real,B: real,W: num] :
% 0.28/0.49        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.28/0.49        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_divide_eq_numeral1(1)
% 0.28/0.49  thf(fact_304_le__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [A: rat,B: rat,W: num] :
% 0.28/0.49        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.28/0.49        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_divide_eq_numeral1(1)
% 0.28/0.49  thf(fact_305_divide__le__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [B: real,W: num,A: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.28/0.49        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_le_eq_numeral1(1)
% 0.28/0.49  thf(fact_306_divide__le__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [B: rat,W: num,A: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.28/0.49        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_le_eq_numeral1(1)
% 0.28/0.49  thf(fact_307_divide__less__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [B: real,W: num,A: real] :
% 0.28/0.49        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 0.28/0.49        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_less_eq_numeral1(1)
% 0.28/0.49  thf(fact_308_divide__less__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [B: rat,W: num,A: rat] :
% 0.28/0.49        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.28/0.49        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_less_eq_numeral1(1)
% 0.28/0.49  thf(fact_309_less__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [A: real,B: real,W: num] :
% 0.28/0.49        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.28/0.49        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_divide_eq_numeral1(1)
% 0.28/0.49  thf(fact_310_less__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.49      ! [A: rat,B: rat,W: num] :
% 0.28/0.49        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.28/0.49        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_divide_eq_numeral1(1)
% 0.28/0.49  thf(fact_311_power__strict__increasing__iff,axiom,
% 0.28/0.49      ! [B: real,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ B )
% 0.28/0.49       => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 0.28/0.49          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing_iff
% 0.28/0.49  thf(fact_312_power__strict__increasing__iff,axiom,
% 0.28/0.49      ! [B: rat,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ B )
% 0.28/0.49       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.28/0.49          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing_iff
% 0.28/0.49  thf(fact_313_power__strict__increasing__iff,axiom,
% 0.28/0.49      ! [B: nat,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ B )
% 0.28/0.49       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.28/0.49          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing_iff
% 0.28/0.49  thf(fact_314_power__strict__increasing__iff,axiom,
% 0.28/0.49      ! [B: int,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ B )
% 0.28/0.49       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.28/0.49          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing_iff
% 0.28/0.49  thf(fact_315_power__add__numeral,axiom,
% 0.28/0.49      ! [A: complex,M: num,N: num] :
% 0.28/0.49        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.28/0.49        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral
% 0.28/0.49  thf(fact_316_power__add__numeral,axiom,
% 0.28/0.49      ! [A: real,M: num,N: num] :
% 0.28/0.49        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.28/0.49        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral
% 0.28/0.49  thf(fact_317_power__add__numeral,axiom,
% 0.28/0.49      ! [A: rat,M: num,N: num] :
% 0.28/0.49        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.28/0.49        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral
% 0.28/0.49  thf(fact_318_power__add__numeral,axiom,
% 0.28/0.49      ! [A: nat,M: num,N: num] :
% 0.28/0.49        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.28/0.49        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral
% 0.28/0.49  thf(fact_319_power__add__numeral,axiom,
% 0.28/0.49      ! [A: int,M: num,N: num] :
% 0.28/0.49        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.28/0.49        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral
% 0.28/0.49  thf(fact_320_power__add__numeral2,axiom,
% 0.28/0.49      ! [A: complex,M: num,N: num,B: complex] :
% 0.28/0.49        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.28/0.49        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral2
% 0.28/0.49  thf(fact_321_power__add__numeral2,axiom,
% 0.28/0.49      ! [A: real,M: num,N: num,B: real] :
% 0.28/0.49        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.28/0.49        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral2
% 0.28/0.49  thf(fact_322_power__add__numeral2,axiom,
% 0.28/0.49      ! [A: rat,M: num,N: num,B: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.28/0.49        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral2
% 0.28/0.49  thf(fact_323_power__add__numeral2,axiom,
% 0.28/0.49      ! [A: nat,M: num,N: num,B: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.28/0.49        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral2
% 0.28/0.49  thf(fact_324_power__add__numeral2,axiom,
% 0.28/0.49      ! [A: int,M: num,N: num,B: int] :
% 0.28/0.49        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.28/0.49        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add_numeral2
% 0.28/0.49  thf(fact_325_one__add__one,axiom,
% 0.28/0.49      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.28/0.49      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_add_one
% 0.28/0.49  thf(fact_326_one__add__one,axiom,
% 0.28/0.49      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.28/0.49      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_add_one
% 0.28/0.49  thf(fact_327_one__add__one,axiom,
% 0.28/0.49      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.28/0.49      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_add_one
% 0.28/0.49  thf(fact_328_one__add__one,axiom,
% 0.28/0.49      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.28/0.49      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_add_one
% 0.28/0.49  thf(fact_329_one__add__one,axiom,
% 0.28/0.49      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.28/0.49      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_add_one
% 0.28/0.49  thf(fact_330_power__increasing__iff,axiom,
% 0.28/0.49      ! [B: real,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ B )
% 0.28/0.49       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 0.28/0.49          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing_iff
% 0.28/0.49  thf(fact_331_power__increasing__iff,axiom,
% 0.28/0.49      ! [B: rat,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ B )
% 0.28/0.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.28/0.49          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing_iff
% 0.28/0.49  thf(fact_332_power__increasing__iff,axiom,
% 0.28/0.49      ! [B: nat,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ B )
% 0.28/0.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.28/0.49          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing_iff
% 0.28/0.49  thf(fact_333_power__increasing__iff,axiom,
% 0.28/0.49      ! [B: int,X: nat,Y: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ B )
% 0.28/0.49       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.28/0.49          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing_iff
% 0.28/0.49  thf(fact_334_numeral__plus__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 0.28/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_plus_one
% 0.28/0.49  thf(fact_335_numeral__plus__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.28/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_plus_one
% 0.28/0.49  thf(fact_336_numeral__plus__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.28/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_plus_one
% 0.28/0.49  thf(fact_337_numeral__plus__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.28/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_plus_one
% 0.28/0.49  thf(fact_338_numeral__plus__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.28/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_plus_one
% 0.28/0.49  thf(fact_339_one__plus__numeral,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 0.28/0.49        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral
% 0.28/0.49  thf(fact_340_one__plus__numeral,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.28/0.49        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral
% 0.28/0.49  thf(fact_341_one__plus__numeral,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.28/0.49        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral
% 0.28/0.49  thf(fact_342_one__plus__numeral,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.28/0.49        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral
% 0.28/0.49  thf(fact_343_one__plus__numeral,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.28/0.49        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral
% 0.28/0.49  thf(fact_344_numeral__le__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.28/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_le_one_iff
% 0.28/0.49  thf(fact_345_numeral__le__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.28/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_le_one_iff
% 0.28/0.49  thf(fact_346_numeral__le__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.28/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_le_one_iff
% 0.28/0.49  thf(fact_347_numeral__le__one__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.28/0.49        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_le_one_iff
% 0.28/0.49  thf(fact_348_one__less__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.28/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_less_numeral_iff
% 0.28/0.49  thf(fact_349_one__less__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.28/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_less_numeral_iff
% 0.28/0.49  thf(fact_350_one__less__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.28/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_less_numeral_iff
% 0.28/0.49  thf(fact_351_one__less__numeral__iff,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.28/0.49        = ( ord_less_num @ one @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_less_numeral_iff
% 0.28/0.49  thf(fact_352_enat__less__induct,axiom,
% 0.28/0.49      ! [P: extended_enat > $o,N: extended_enat] :
% 0.28/0.49        ( ! [N3: extended_enat] :
% 0.28/0.49            ( ! [M2: extended_enat] :
% 0.28/0.49                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 0.28/0.49               => ( P @ M2 ) )
% 0.28/0.49           => ( P @ N3 ) )
% 0.28/0.49       => ( P @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % enat_less_induct
% 0.28/0.49  thf(fact_353_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.49  thf(fact_354_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.49  thf(fact_355_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.49  thf(fact_356_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_mult_class.mult_ac(1)
% 0.28/0.49  thf(fact_357_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( times_times_complex @ one_one_complex @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % comm_monoid_mult_class.mult_1
% 0.28/0.49  thf(fact_358_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( times_times_real @ one_one_real @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % comm_monoid_mult_class.mult_1
% 0.28/0.49  thf(fact_359_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( times_times_rat @ one_one_rat @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % comm_monoid_mult_class.mult_1
% 0.28/0.49  thf(fact_360_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( times_times_nat @ one_one_nat @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % comm_monoid_mult_class.mult_1
% 0.28/0.49  thf(fact_361_comm__monoid__mult__class_Omult__1,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( times_times_int @ one_one_int @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % comm_monoid_mult_class.mult_1
% 0.28/0.49  thf(fact_362_mult_Oassoc,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.assoc
% 0.28/0.49  thf(fact_363_mult_Oassoc,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.assoc
% 0.28/0.49  thf(fact_364_mult_Oassoc,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.assoc
% 0.28/0.49  thf(fact_365_mult_Oassoc,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.28/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.assoc
% 0.28/0.49  thf(fact_366_mult_Ocommute,axiom,
% 0.28/0.49      ( times_times_real
% 0.28/0.49      = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.commute
% 0.28/0.49  thf(fact_367_mult_Ocommute,axiom,
% 0.28/0.49      ( times_times_rat
% 0.28/0.49      = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.commute
% 0.28/0.49  thf(fact_368_mult_Ocommute,axiom,
% 0.28/0.49      ( times_times_nat
% 0.28/0.49      = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.commute
% 0.28/0.49  thf(fact_369_mult_Ocommute,axiom,
% 0.28/0.49      ( times_times_int
% 0.28/0.49      = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.commute
% 0.28/0.49  thf(fact_370_mult_Ocomm__neutral,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( times_times_complex @ A @ one_one_complex )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.comm_neutral
% 0.28/0.49  thf(fact_371_mult_Ocomm__neutral,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( times_times_real @ A @ one_one_real )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.comm_neutral
% 0.28/0.49  thf(fact_372_mult_Ocomm__neutral,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( times_times_rat @ A @ one_one_rat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.comm_neutral
% 0.28/0.49  thf(fact_373_mult_Ocomm__neutral,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( times_times_nat @ A @ one_one_nat )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.comm_neutral
% 0.28/0.49  thf(fact_374_mult_Ocomm__neutral,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( times_times_int @ A @ one_one_int )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.comm_neutral
% 0.28/0.49  thf(fact_375_mult_Oleft__commute,axiom,
% 0.28/0.49      ! [B: real,A: real,C: real] :
% 0.28/0.49        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.28/0.49        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.left_commute
% 0.28/0.49  thf(fact_376_mult_Oleft__commute,axiom,
% 0.28/0.49      ! [B: rat,A: rat,C: rat] :
% 0.28/0.49        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.28/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.left_commute
% 0.28/0.49  thf(fact_377_mult_Oleft__commute,axiom,
% 0.28/0.49      ! [B: nat,A: nat,C: nat] :
% 0.28/0.49        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.28/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.left_commute
% 0.28/0.49  thf(fact_378_mult_Oleft__commute,axiom,
% 0.28/0.49      ! [B: int,A: int,C: int] :
% 0.28/0.49        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.28/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult.left_commute
% 0.28/0.49  thf(fact_379_nat__mult__1,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( times_times_nat @ one_one_nat @ N )
% 0.28/0.49        = N ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_mult_1
% 0.28/0.49  thf(fact_380_one__reorient,axiom,
% 0.28/0.49      ! [X: complex] :
% 0.28/0.49        ( ( one_one_complex = X )
% 0.28/0.49        = ( X = one_one_complex ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_reorient
% 0.28/0.49  thf(fact_381_one__reorient,axiom,
% 0.28/0.49      ! [X: real] :
% 0.28/0.49        ( ( one_one_real = X )
% 0.28/0.49        = ( X = one_one_real ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_reorient
% 0.28/0.49  thf(fact_382_one__reorient,axiom,
% 0.28/0.49      ! [X: rat] :
% 0.28/0.49        ( ( one_one_rat = X )
% 0.28/0.49        = ( X = one_one_rat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_reorient
% 0.28/0.49  thf(fact_383_one__reorient,axiom,
% 0.28/0.49      ! [X: nat] :
% 0.28/0.49        ( ( one_one_nat = X )
% 0.28/0.49        = ( X = one_one_nat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_reorient
% 0.28/0.49  thf(fact_384_one__reorient,axiom,
% 0.28/0.49      ! [X: int] :
% 0.28/0.49        ( ( one_one_int = X )
% 0.28/0.49        = ( X = one_one_int ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_reorient
% 0.28/0.49  thf(fact_385_nat__mult__1__right,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ( ( times_times_nat @ N @ one_one_nat )
% 0.28/0.49        = N ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_mult_1_right
% 0.28/0.49  thf(fact_386_power__one__over,axiom,
% 0.28/0.49      ! [A: complex,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 0.28/0.49        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_over
% 0.28/0.49  thf(fact_387_power__one__over,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 0.28/0.49        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_over
% 0.28/0.49  thf(fact_388_power__one__over,axiom,
% 0.28/0.49      ! [A: rat,N: nat] :
% 0.28/0.49        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 0.28/0.49        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_one_over
% 0.28/0.49  thf(fact_389_left__right__inverse__power,axiom,
% 0.28/0.49      ! [X: complex,Y: complex,N: nat] :
% 0.28/0.49        ( ( ( times_times_complex @ X @ Y )
% 0.28/0.49          = one_one_complex )
% 0.28/0.49       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 0.28/0.49          = one_one_complex ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_right_inverse_power
% 0.28/0.49  thf(fact_390_left__right__inverse__power,axiom,
% 0.28/0.49      ! [X: real,Y: real,N: nat] :
% 0.28/0.49        ( ( ( times_times_real @ X @ Y )
% 0.28/0.49          = one_one_real )
% 0.28/0.49       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 0.28/0.49          = one_one_real ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_right_inverse_power
% 0.28/0.49  thf(fact_391_left__right__inverse__power,axiom,
% 0.28/0.49      ! [X: rat,Y: rat,N: nat] :
% 0.28/0.49        ( ( ( times_times_rat @ X @ Y )
% 0.28/0.49          = one_one_rat )
% 0.28/0.49       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.28/0.49          = one_one_rat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_right_inverse_power
% 0.28/0.49  thf(fact_392_left__right__inverse__power,axiom,
% 0.28/0.49      ! [X: nat,Y: nat,N: nat] :
% 0.28/0.49        ( ( ( times_times_nat @ X @ Y )
% 0.28/0.49          = one_one_nat )
% 0.28/0.49       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 0.28/0.49          = one_one_nat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_right_inverse_power
% 0.28/0.49  thf(fact_393_left__right__inverse__power,axiom,
% 0.28/0.49      ! [X: int,Y: int,N: nat] :
% 0.28/0.49        ( ( ( times_times_int @ X @ Y )
% 0.28/0.49          = one_one_int )
% 0.28/0.49       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.28/0.49          = one_one_int ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_right_inverse_power
% 0.28/0.49  thf(fact_394_le__cube,axiom,
% 0.28/0.49      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_cube
% 0.28/0.49  thf(fact_395_le__square,axiom,
% 0.28/0.49      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_square
% 0.28/0.49  thf(fact_396_mult__le__mono,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ( ord_less_eq_nat @ K @ L2 )
% 0.28/0.49         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_le_mono
% 0.28/0.49  thf(fact_397_mult__le__mono1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_le_mono1
% 0.28/0.49  thf(fact_398_mult__le__mono2,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_le_mono2
% 0.28/0.49  thf(fact_399_add__mult__distrib,axiom,
% 0.28/0.49      ! [M: nat,N: nat,K: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mult_distrib
% 0.28/0.49  thf(fact_400_add__mult__distrib2,axiom,
% 0.28/0.49      ! [K: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mult_distrib2
% 0.28/0.49  thf(fact_401_power__gt1__lemma,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_gt1_lemma
% 0.28/0.49  thf(fact_402_power__gt1__lemma,axiom,
% 0.28/0.49      ! [A: rat,N: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_gt1_lemma
% 0.28/0.49  thf(fact_403_power__gt1__lemma,axiom,
% 0.28/0.49      ! [A: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_gt1_lemma
% 0.28/0.49  thf(fact_404_power__gt1__lemma,axiom,
% 0.28/0.49      ! [A: int,N: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_gt1_lemma
% 0.28/0.49  thf(fact_405_power__less__power__Suc,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_power_Suc
% 0.28/0.49  thf(fact_406_power__less__power__Suc,axiom,
% 0.28/0.49      ! [A: rat,N: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_power_Suc
% 0.28/0.49  thf(fact_407_power__less__power__Suc,axiom,
% 0.28/0.49      ! [A: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_power_Suc
% 0.28/0.49  thf(fact_408_power__less__power__Suc,axiom,
% 0.28/0.49      ! [A: int,N: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_power_Suc
% 0.28/0.49  thf(fact_409_power__divide,axiom,
% 0.28/0.49      ! [A: complex,B: complex,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 0.28/0.49        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_divide
% 0.28/0.49  thf(fact_410_power__divide,axiom,
% 0.28/0.49      ! [A: real,B: real,N: nat] :
% 0.28/0.49        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 0.28/0.49        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_divide
% 0.28/0.49  thf(fact_411_power__divide,axiom,
% 0.28/0.49      ! [A: rat,B: rat,N: nat] :
% 0.28/0.49        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 0.28/0.49        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_divide
% 0.28/0.49  thf(fact_412_add__One__commute,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ( ( plus_plus_num @ one @ N )
% 0.28/0.49        = ( plus_plus_num @ N @ one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_One_commute
% 0.28/0.49  thf(fact_413_le__num__One__iff,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( ord_less_eq_num @ X @ one )
% 0.28/0.49        = ( X = one ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_num_One_iff
% 0.28/0.49  thf(fact_414_power__commutes,axiom,
% 0.28/0.49      ! [A: complex,N: nat] :
% 0.28/0.49        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 0.28/0.49        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commutes
% 0.28/0.49  thf(fact_415_power__commutes,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 0.28/0.49        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commutes
% 0.28/0.49  thf(fact_416_power__commutes,axiom,
% 0.28/0.49      ! [A: rat,N: nat] :
% 0.28/0.49        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 0.28/0.49        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commutes
% 0.28/0.49  thf(fact_417_power__commutes,axiom,
% 0.28/0.49      ! [A: nat,N: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.28/0.49        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commutes
% 0.28/0.49  thf(fact_418_power__commutes,axiom,
% 0.28/0.49      ! [A: int,N: nat] :
% 0.28/0.49        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.28/0.49        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commutes
% 0.28/0.49  thf(fact_419_power__mult__distrib,axiom,
% 0.28/0.49      ! [A: complex,B: complex,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 0.28/0.49        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult_distrib
% 0.28/0.49  thf(fact_420_power__mult__distrib,axiom,
% 0.28/0.49      ! [A: real,B: real,N: nat] :
% 0.28/0.49        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 0.28/0.49        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult_distrib
% 0.28/0.49  thf(fact_421_power__mult__distrib,axiom,
% 0.28/0.49      ! [A: rat,B: rat,N: nat] :
% 0.28/0.49        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 0.28/0.49        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult_distrib
% 0.28/0.49  thf(fact_422_power__mult__distrib,axiom,
% 0.28/0.49      ! [A: nat,B: nat,N: nat] :
% 0.28/0.49        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.28/0.49        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult_distrib
% 0.28/0.49  thf(fact_423_power__mult__distrib,axiom,
% 0.28/0.49      ! [A: int,B: int,N: nat] :
% 0.28/0.49        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.28/0.49        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult_distrib
% 0.28/0.49  thf(fact_424_power__commuting__commutes,axiom,
% 0.28/0.49      ! [X: complex,Y: complex,N: nat] :
% 0.28/0.49        ( ( ( times_times_complex @ X @ Y )
% 0.28/0.49          = ( times_times_complex @ Y @ X ) )
% 0.28/0.49       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 0.28/0.49          = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commuting_commutes
% 0.28/0.49  thf(fact_425_power__commuting__commutes,axiom,
% 0.28/0.49      ! [X: real,Y: real,N: nat] :
% 0.28/0.49        ( ( ( times_times_real @ X @ Y )
% 0.28/0.49          = ( times_times_real @ Y @ X ) )
% 0.28/0.49       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 0.28/0.49          = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commuting_commutes
% 0.28/0.49  thf(fact_426_power__commuting__commutes,axiom,
% 0.28/0.49      ! [X: rat,Y: rat,N: nat] :
% 0.28/0.49        ( ( ( times_times_rat @ X @ Y )
% 0.28/0.49          = ( times_times_rat @ Y @ X ) )
% 0.28/0.49       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 0.28/0.49          = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commuting_commutes
% 0.28/0.49  thf(fact_427_power__commuting__commutes,axiom,
% 0.28/0.49      ! [X: nat,Y: nat,N: nat] :
% 0.28/0.49        ( ( ( times_times_nat @ X @ Y )
% 0.28/0.49          = ( times_times_nat @ Y @ X ) )
% 0.28/0.49       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 0.28/0.49          = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commuting_commutes
% 0.28/0.49  thf(fact_428_power__commuting__commutes,axiom,
% 0.28/0.49      ! [X: int,Y: int,N: nat] :
% 0.28/0.49        ( ( ( times_times_int @ X @ Y )
% 0.28/0.49          = ( times_times_int @ Y @ X ) )
% 0.28/0.49       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 0.28/0.49          = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_commuting_commutes
% 0.28/0.49  thf(fact_429_power__mult,axiom,
% 0.28/0.49      ! [A: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 0.28/0.49        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult
% 0.28/0.49  thf(fact_430_power__mult,axiom,
% 0.28/0.49      ! [A: real,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 0.28/0.49        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult
% 0.28/0.49  thf(fact_431_power__mult,axiom,
% 0.28/0.49      ! [A: int,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 0.28/0.49        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult
% 0.28/0.49  thf(fact_432_power__mult,axiom,
% 0.28/0.49      ! [A: complex,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 0.28/0.49        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_mult
% 0.28/0.49  thf(fact_433_le__numeral__extra_I4_J,axiom,
% 0.28/0.49      ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.28/0.49  
% 0.28/0.49  % le_numeral_extra(4)
% 0.28/0.49  thf(fact_434_le__numeral__extra_I4_J,axiom,
% 0.28/0.49      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.28/0.49  
% 0.28/0.49  % le_numeral_extra(4)
% 0.28/0.49  thf(fact_435_le__numeral__extra_I4_J,axiom,
% 0.28/0.49      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.28/0.49  
% 0.28/0.49  % le_numeral_extra(4)
% 0.28/0.49  thf(fact_436_le__numeral__extra_I4_J,axiom,
% 0.28/0.49      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.28/0.49  
% 0.28/0.49  % le_numeral_extra(4)
% 0.28/0.49  thf(fact_437_less__numeral__extra_I4_J,axiom,
% 0.28/0.49      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.28/0.49  
% 0.28/0.49  % less_numeral_extra(4)
% 0.28/0.49  thf(fact_438_less__numeral__extra_I4_J,axiom,
% 0.28/0.49      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.28/0.49  
% 0.28/0.49  % less_numeral_extra(4)
% 0.28/0.49  thf(fact_439_less__numeral__extra_I4_J,axiom,
% 0.28/0.49      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % less_numeral_extra(4)
% 0.28/0.49  thf(fact_440_less__numeral__extra_I4_J,axiom,
% 0.28/0.49      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.28/0.49  
% 0.28/0.49  % less_numeral_extra(4)
% 0.28/0.49  thf(fact_441_left__add__mult__distrib,axiom,
% 0.28/0.49      ! [I: nat,U: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_mult_distrib
% 0.28/0.49  thf(fact_442_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_complex,B3: set_complex] :
% 0.28/0.49        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: complex] :
% 0.28/0.49              ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 0.28/0.49             => ( member_complex @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_443_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_real,B3: set_real] :
% 0.28/0.49        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: real] :
% 0.28/0.49              ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.28/0.49             => ( member_real @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_444_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_set_nat,B3: set_set_nat] :
% 0.28/0.49        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: set_nat] :
% 0.28/0.49              ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.28/0.49             => ( member_set_nat @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_445_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 0.28/0.49        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: vEBT_VEBT] :
% 0.28/0.49              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.49             => ( member_VEBT_VEBT @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_446_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_nat,B3: set_nat] :
% 0.28/0.49        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: nat] :
% 0.28/0.49              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.28/0.49             => ( member_nat @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_447_subset__code_I1_J,axiom,
% 0.28/0.49      ! [Xs: list_int,B3: set_int] :
% 0.28/0.49        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 0.28/0.49        = ( ! [X3: int] :
% 0.28/0.49              ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.28/0.49             => ( member_int @ X3 @ B3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % subset_code(1)
% 0.28/0.49  thf(fact_448_divide__numeral__1,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_numeral_1
% 0.28/0.49  thf(fact_449_divide__numeral__1,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_numeral_1
% 0.28/0.49  thf(fact_450_divide__numeral__1,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % divide_numeral_1
% 0.28/0.49  thf(fact_451_mult__numeral__1,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1
% 0.28/0.49  thf(fact_452_mult__numeral__1,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1
% 0.28/0.49  thf(fact_453_mult__numeral__1,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1
% 0.28/0.49  thf(fact_454_mult__numeral__1,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1
% 0.28/0.49  thf(fact_455_mult__numeral__1,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1
% 0.28/0.49  thf(fact_456_mult__numeral__1__right,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1_right
% 0.28/0.49  thf(fact_457_mult__numeral__1__right,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1_right
% 0.28/0.49  thf(fact_458_mult__numeral__1__right,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1_right
% 0.28/0.49  thf(fact_459_mult__numeral__1__right,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1_right
% 0.28/0.49  thf(fact_460_mult__numeral__1__right,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.28/0.49        = A ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_numeral_1_right
% 0.28/0.49  thf(fact_461_power__add,axiom,
% 0.28/0.49      ! [A: complex,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add
% 0.28/0.49  thf(fact_462_power__add,axiom,
% 0.28/0.49      ! [A: real,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add
% 0.28/0.49  thf(fact_463_power__add,axiom,
% 0.28/0.49      ! [A: rat,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add
% 0.28/0.49  thf(fact_464_power__add,axiom,
% 0.28/0.49      ! [A: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add
% 0.28/0.49  thf(fact_465_power__add,axiom,
% 0.28/0.49      ! [A: int,M: nat,N: nat] :
% 0.28/0.49        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.49        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_add
% 0.28/0.49  thf(fact_466_one__le__numeral,axiom,
% 0.28/0.49      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_numeral
% 0.28/0.49  thf(fact_467_one__le__numeral,axiom,
% 0.28/0.49      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_numeral
% 0.28/0.49  thf(fact_468_one__le__numeral,axiom,
% 0.28/0.49      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_numeral
% 0.28/0.49  thf(fact_469_one__le__numeral,axiom,
% 0.28/0.49      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_numeral
% 0.28/0.49  thf(fact_470_not__numeral__less__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 0.28/0.49  
% 0.28/0.49  % not_numeral_less_one
% 0.28/0.49  thf(fact_471_not__numeral__less__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.28/0.49  
% 0.28/0.49  % not_numeral_less_one
% 0.28/0.49  thf(fact_472_not__numeral__less__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % not_numeral_less_one
% 0.28/0.49  thf(fact_473_not__numeral__less__one,axiom,
% 0.28/0.49      ! [N: num] :
% 0.28/0.49        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.28/0.49  
% 0.28/0.49  % not_numeral_less_one
% 0.28/0.49  thf(fact_474_one__plus__numeral__commute,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 0.28/0.49        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral_commute
% 0.28/0.49  thf(fact_475_one__plus__numeral__commute,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.28/0.49        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral_commute
% 0.28/0.49  thf(fact_476_one__plus__numeral__commute,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.28/0.49        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral_commute
% 0.28/0.49  thf(fact_477_one__plus__numeral__commute,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.28/0.49        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral_commute
% 0.28/0.49  thf(fact_478_one__plus__numeral__commute,axiom,
% 0.28/0.49      ! [X: num] :
% 0.28/0.49        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.28/0.49        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_plus_numeral_commute
% 0.28/0.49  thf(fact_479_numeral__One,axiom,
% 0.28/0.49      ( ( numera6690914467698888265omplex @ one )
% 0.28/0.49      = one_one_complex ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_One
% 0.28/0.49  thf(fact_480_numeral__One,axiom,
% 0.28/0.49      ( ( numeral_numeral_real @ one )
% 0.28/0.49      = one_one_real ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_One
% 0.28/0.49  thf(fact_481_numeral__One,axiom,
% 0.28/0.49      ( ( numeral_numeral_rat @ one )
% 0.28/0.49      = one_one_rat ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_One
% 0.28/0.49  thf(fact_482_numeral__One,axiom,
% 0.28/0.49      ( ( numeral_numeral_nat @ one )
% 0.28/0.49      = one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_One
% 0.28/0.49  thf(fact_483_numeral__One,axiom,
% 0.28/0.49      ( ( numeral_numeral_int @ one )
% 0.28/0.49      = one_one_int ) ).
% 0.28/0.49  
% 0.28/0.49  % numeral_One
% 0.28/0.49  thf(fact_484_one__le__power,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.28/0.49       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_power
% 0.28/0.49  thf(fact_485_one__le__power,axiom,
% 0.28/0.49      ! [A: rat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_power
% 0.28/0.49  thf(fact_486_one__le__power,axiom,
% 0.28/0.49      ! [A: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_power
% 0.28/0.49  thf(fact_487_one__le__power,axiom,
% 0.28/0.49      ! [A: int,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.28/0.49       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % one_le_power
% 0.28/0.49  thf(fact_488_numerals_I1_J,axiom,
% 0.28/0.49      ( ( numeral_numeral_nat @ one )
% 0.28/0.49      = one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % numerals(1)
% 0.28/0.49  thf(fact_489_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_complex,A2: set_complex,X: complex,I: nat] :
% 0.28/0.49        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_complex @ X @ A2 )
% 0.28/0.49         => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_490_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_real,A2: set_real,X: real,I: nat] :
% 0.28/0.49        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_real @ X @ A2 )
% 0.28/0.49         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_491_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 0.28/0.49        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_set_nat @ X @ A2 )
% 0.28/0.49         => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_492_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_nat,A2: set_nat,X: nat,I: nat] :
% 0.28/0.49        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_nat @ X @ A2 )
% 0.28/0.49         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_493_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 0.28/0.49        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_VEBT_VEBT @ X @ A2 )
% 0.28/0.49         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_494_set__update__subsetI,axiom,
% 0.28/0.49      ! [Xs: list_int,A2: set_int,X: int,I: nat] :
% 0.28/0.49        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 0.28/0.49       => ( ( member_int @ X @ A2 )
% 0.28/0.49         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % set_update_subsetI
% 0.28/0.49  thf(fact_495_power__less__imp__less__exp,axiom,
% 0.28/0.49      ! [A: real,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_imp_less_exp
% 0.28/0.49  thf(fact_496_power__less__imp__less__exp,axiom,
% 0.28/0.49      ! [A: rat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_imp_less_exp
% 0.28/0.49  thf(fact_497_power__less__imp__less__exp,axiom,
% 0.28/0.49      ! [A: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_imp_less_exp
% 0.28/0.49  thf(fact_498_power__less__imp__less__exp,axiom,
% 0.28/0.49      ! [A: int,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_less_imp_less_exp
% 0.28/0.49  thf(fact_499_power__strict__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: real] :
% 0.28/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing
% 0.28/0.49  thf(fact_500_power__strict__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.28/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing
% 0.28/0.49  thf(fact_501_power__strict__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.28/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing
% 0.28/0.49  thf(fact_502_power__strict__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: int] :
% 0.28/0.49        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_strict_increasing
% 0.28/0.49  thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_add_class.add_ac(1)
% 0.28/0.49  thf(fact_504_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_add_class.add_ac(1)
% 0.28/0.49  thf(fact_505_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_add_class.add_ac(1)
% 0.28/0.49  thf(fact_506_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ab_semigroup_add_class.add_ac(1)
% 0.28/0.49  thf(fact_507_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ( plus_plus_real @ I @ K )
% 0.28/0.49          = ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(4)
% 0.28/0.49  thf(fact_508_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ( plus_plus_rat @ I @ K )
% 0.28/0.49          = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(4)
% 0.28/0.49  thf(fact_509_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ( plus_plus_nat @ I @ K )
% 0.28/0.49          = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(4)
% 0.28/0.49  thf(fact_510_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ( plus_plus_int @ I @ K )
% 0.28/0.49          = ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(4)
% 0.28/0.49  thf(fact_511_group__cancel_Oadd1,axiom,
% 0.28/0.49      ! [A2: real,K: real,A: real,B: real] :
% 0.28/0.49        ( ( A2
% 0.28/0.49          = ( plus_plus_real @ K @ A ) )
% 0.28/0.49       => ( ( plus_plus_real @ A2 @ B )
% 0.28/0.49          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add1
% 0.28/0.49  thf(fact_512_group__cancel_Oadd1,axiom,
% 0.28/0.49      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.28/0.49        ( ( A2
% 0.28/0.49          = ( plus_plus_rat @ K @ A ) )
% 0.28/0.49       => ( ( plus_plus_rat @ A2 @ B )
% 0.28/0.49          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add1
% 0.28/0.49  thf(fact_513_group__cancel_Oadd1,axiom,
% 0.28/0.49      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.28/0.49        ( ( A2
% 0.28/0.49          = ( plus_plus_nat @ K @ A ) )
% 0.28/0.49       => ( ( plus_plus_nat @ A2 @ B )
% 0.28/0.49          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add1
% 0.28/0.49  thf(fact_514_group__cancel_Oadd1,axiom,
% 0.28/0.49      ! [A2: int,K: int,A: int,B: int] :
% 0.28/0.49        ( ( A2
% 0.28/0.49          = ( plus_plus_int @ K @ A ) )
% 0.28/0.49       => ( ( plus_plus_int @ A2 @ B )
% 0.28/0.49          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add1
% 0.28/0.49  thf(fact_515_group__cancel_Oadd2,axiom,
% 0.28/0.49      ! [B3: real,K: real,B: real,A: real] :
% 0.28/0.49        ( ( B3
% 0.28/0.49          = ( plus_plus_real @ K @ B ) )
% 0.28/0.49       => ( ( plus_plus_real @ A @ B3 )
% 0.28/0.49          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add2
% 0.28/0.49  thf(fact_516_group__cancel_Oadd2,axiom,
% 0.28/0.49      ! [B3: rat,K: rat,B: rat,A: rat] :
% 0.28/0.49        ( ( B3
% 0.28/0.49          = ( plus_plus_rat @ K @ B ) )
% 0.28/0.49       => ( ( plus_plus_rat @ A @ B3 )
% 0.28/0.49          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add2
% 0.28/0.49  thf(fact_517_group__cancel_Oadd2,axiom,
% 0.28/0.49      ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.28/0.49        ( ( B3
% 0.28/0.49          = ( plus_plus_nat @ K @ B ) )
% 0.28/0.49       => ( ( plus_plus_nat @ A @ B3 )
% 0.28/0.49          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add2
% 0.28/0.49  thf(fact_518_group__cancel_Oadd2,axiom,
% 0.28/0.49      ! [B3: int,K: int,B: int,A: int] :
% 0.28/0.49        ( ( B3
% 0.28/0.49          = ( plus_plus_int @ K @ B ) )
% 0.28/0.49       => ( ( plus_plus_int @ A @ B3 )
% 0.28/0.49          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % group_cancel.add2
% 0.28/0.49  thf(fact_519_add_Oassoc,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.assoc
% 0.28/0.49  thf(fact_520_add_Oassoc,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.assoc
% 0.28/0.49  thf(fact_521_add_Oassoc,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.assoc
% 0.28/0.49  thf(fact_522_add_Oassoc,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.49        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.assoc
% 0.28/0.49  thf(fact_523_add_Oleft__cancel,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ( plus_plus_real @ A @ B )
% 0.28/0.49          = ( plus_plus_real @ A @ C ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_cancel
% 0.28/0.49  thf(fact_524_add_Oleft__cancel,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ( plus_plus_rat @ A @ B )
% 0.28/0.49          = ( plus_plus_rat @ A @ C ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_cancel
% 0.28/0.49  thf(fact_525_add_Oleft__cancel,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ( plus_plus_int @ A @ B )
% 0.28/0.49          = ( plus_plus_int @ A @ C ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_cancel
% 0.28/0.49  thf(fact_526_add_Oright__cancel,axiom,
% 0.28/0.49      ! [B: real,A: real,C: real] :
% 0.28/0.49        ( ( ( plus_plus_real @ B @ A )
% 0.28/0.49          = ( plus_plus_real @ C @ A ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.right_cancel
% 0.28/0.49  thf(fact_527_add_Oright__cancel,axiom,
% 0.28/0.49      ! [B: rat,A: rat,C: rat] :
% 0.28/0.49        ( ( ( plus_plus_rat @ B @ A )
% 0.28/0.49          = ( plus_plus_rat @ C @ A ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.right_cancel
% 0.28/0.49  thf(fact_528_add_Oright__cancel,axiom,
% 0.28/0.49      ! [B: int,A: int,C: int] :
% 0.28/0.49        ( ( ( plus_plus_int @ B @ A )
% 0.28/0.49          = ( plus_plus_int @ C @ A ) )
% 0.28/0.49        = ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.right_cancel
% 0.28/0.49  thf(fact_529_add_Ocommute,axiom,
% 0.28/0.49      ( plus_plus_real
% 0.28/0.49      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.commute
% 0.28/0.49  thf(fact_530_add_Ocommute,axiom,
% 0.28/0.49      ( plus_plus_rat
% 0.28/0.49      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.commute
% 0.28/0.49  thf(fact_531_add_Ocommute,axiom,
% 0.28/0.49      ( plus_plus_nat
% 0.28/0.49      = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.commute
% 0.28/0.49  thf(fact_532_add_Ocommute,axiom,
% 0.28/0.49      ( plus_plus_int
% 0.28/0.49      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.commute
% 0.28/0.49  thf(fact_533_add_Oleft__commute,axiom,
% 0.28/0.49      ! [B: real,A: real,C: real] :
% 0.28/0.49        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.28/0.49        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_commute
% 0.28/0.49  thf(fact_534_add_Oleft__commute,axiom,
% 0.28/0.49      ! [B: rat,A: rat,C: rat] :
% 0.28/0.49        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.28/0.49        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_commute
% 0.28/0.49  thf(fact_535_add_Oleft__commute,axiom,
% 0.28/0.49      ! [B: nat,A: nat,C: nat] :
% 0.28/0.49        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.28/0.49        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_commute
% 0.28/0.49  thf(fact_536_add_Oleft__commute,axiom,
% 0.28/0.49      ! [B: int,A: int,C: int] :
% 0.28/0.49        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.28/0.49        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add.left_commute
% 0.28/0.49  thf(fact_537_add__left__imp__eq,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ( plus_plus_real @ A @ B )
% 0.28/0.49          = ( plus_plus_real @ A @ C ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_imp_eq
% 0.28/0.49  thf(fact_538_add__left__imp__eq,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ( plus_plus_rat @ A @ B )
% 0.28/0.49          = ( plus_plus_rat @ A @ C ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_imp_eq
% 0.28/0.49  thf(fact_539_add__left__imp__eq,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( ( plus_plus_nat @ A @ B )
% 0.28/0.49          = ( plus_plus_nat @ A @ C ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_imp_eq
% 0.28/0.49  thf(fact_540_add__left__imp__eq,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ( plus_plus_int @ A @ B )
% 0.28/0.49          = ( plus_plus_int @ A @ C ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_imp_eq
% 0.28/0.49  thf(fact_541_add__right__imp__eq,axiom,
% 0.28/0.49      ! [B: real,A: real,C: real] :
% 0.28/0.49        ( ( ( plus_plus_real @ B @ A )
% 0.28/0.49          = ( plus_plus_real @ C @ A ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_imp_eq
% 0.28/0.49  thf(fact_542_add__right__imp__eq,axiom,
% 0.28/0.49      ! [B: rat,A: rat,C: rat] :
% 0.28/0.49        ( ( ( plus_plus_rat @ B @ A )
% 0.28/0.49          = ( plus_plus_rat @ C @ A ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_imp_eq
% 0.28/0.49  thf(fact_543_add__right__imp__eq,axiom,
% 0.28/0.49      ! [B: nat,A: nat,C: nat] :
% 0.28/0.49        ( ( ( plus_plus_nat @ B @ A )
% 0.28/0.49          = ( plus_plus_nat @ C @ A ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_imp_eq
% 0.28/0.49  thf(fact_544_add__right__imp__eq,axiom,
% 0.28/0.49      ! [B: int,A: int,C: int] :
% 0.28/0.49        ( ( ( plus_plus_int @ B @ A )
% 0.28/0.49          = ( plus_plus_int @ C @ A ) )
% 0.28/0.49       => ( B = C ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_imp_eq
% 0.28/0.49  thf(fact_545_power__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: real] :
% 0.28/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.28/0.49         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing
% 0.28/0.49  thf(fact_546_power__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: rat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.28/0.49         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing
% 0.28/0.49  thf(fact_547_power__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.28/0.49         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing
% 0.28/0.49  thf(fact_548_power__increasing,axiom,
% 0.28/0.49      ! [N: nat,N4: nat,A: int] :
% 0.28/0.49        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.49       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.28/0.49         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_increasing
% 0.28/0.49  thf(fact_549_nat__neq__iff,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( M != N )
% 0.28/0.49        = ( ( ord_less_nat @ M @ N )
% 0.28/0.49          | ( ord_less_nat @ N @ M ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_neq_iff
% 0.28/0.49  thf(fact_550_less__not__refl,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ~ ( ord_less_nat @ N @ N ) ).
% 0.28/0.49  
% 0.28/0.49  % less_not_refl
% 0.28/0.49  thf(fact_551_less__not__refl2,axiom,
% 0.28/0.49      ! [N: nat,M: nat] :
% 0.28/0.49        ( ( ord_less_nat @ N @ M )
% 0.28/0.49       => ( M != N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_not_refl2
% 0.28/0.49  thf(fact_552_less__not__refl3,axiom,
% 0.28/0.49      ! [S: nat,T: nat] :
% 0.28/0.49        ( ( ord_less_nat @ S @ T )
% 0.28/0.49       => ( S != T ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_not_refl3
% 0.28/0.49  thf(fact_553_less__irrefl__nat,axiom,
% 0.28/0.49      ! [N: nat] :
% 0.28/0.49        ~ ( ord_less_nat @ N @ N ) ).
% 0.28/0.49  
% 0.28/0.49  % less_irrefl_nat
% 0.28/0.49  thf(fact_554_nat__less__induct,axiom,
% 0.28/0.49      ! [P: nat > $o,N: nat] :
% 0.28/0.49        ( ! [N3: nat] :
% 0.28/0.49            ( ! [M2: nat] :
% 0.28/0.49                ( ( ord_less_nat @ M2 @ N3 )
% 0.28/0.49               => ( P @ M2 ) )
% 0.28/0.49           => ( P @ N3 ) )
% 0.28/0.49       => ( P @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_less_induct
% 0.28/0.49  thf(fact_555_infinite__descent,axiom,
% 0.28/0.49      ! [P: nat > $o,N: nat] :
% 0.28/0.49        ( ! [N3: nat] :
% 0.28/0.49            ( ~ ( P @ N3 )
% 0.28/0.49           => ? [M2: nat] :
% 0.28/0.49                ( ( ord_less_nat @ M2 @ N3 )
% 0.28/0.49                & ~ ( P @ M2 ) ) )
% 0.28/0.49       => ( P @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % infinite_descent
% 0.28/0.49  thf(fact_556_linorder__neqE__nat,axiom,
% 0.28/0.49      ! [X: nat,Y: nat] :
% 0.28/0.49        ( ( X != Y )
% 0.28/0.49       => ( ~ ( ord_less_nat @ X @ Y )
% 0.28/0.49         => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % linorder_neqE_nat
% 0.28/0.49  thf(fact_557_le__refl,axiom,
% 0.28/0.49      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.28/0.49  
% 0.28/0.49  % le_refl
% 0.28/0.49  thf(fact_558_le__trans,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ( ord_less_eq_nat @ J @ K )
% 0.28/0.49         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_trans
% 0.28/0.49  thf(fact_559_eq__imp__le,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( M = N )
% 0.28/0.49       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % eq_imp_le
% 0.28/0.49  thf(fact_560_le__antisym,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.49       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.49         => ( M = N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_antisym
% 0.28/0.49  thf(fact_561_nat__le__linear,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.49        | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_le_linear
% 0.28/0.49  thf(fact_562_Nat_Oex__has__greatest__nat,axiom,
% 0.28/0.49      ! [P: nat > $o,K: nat,B: nat] :
% 0.28/0.49        ( ( P @ K )
% 0.28/0.49       => ( ! [Y5: nat] :
% 0.28/0.49              ( ( P @ Y5 )
% 0.28/0.49             => ( ord_less_eq_nat @ Y5 @ B ) )
% 0.28/0.49         => ? [X6: nat] :
% 0.28/0.49              ( ( P @ X6 )
% 0.28/0.49              & ! [Y2: nat] :
% 0.28/0.49                  ( ( P @ Y2 )
% 0.28/0.49                 => ( ord_less_eq_nat @ Y2 @ X6 ) ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % Nat.ex_has_greatest_nat
% 0.28/0.49  thf(fact_563_size__neq__size__imp__neq,axiom,
% 0.28/0.49      ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 0.28/0.49        ( ( ( size_s6755466524823107622T_VEBT @ X )
% 0.28/0.49         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 0.28/0.49       => ( X != Y ) ) ).
% 0.28/0.49  
% 0.28/0.49  % size_neq_size_imp_neq
% 0.28/0.49  thf(fact_564_size__neq__size__imp__neq,axiom,
% 0.28/0.49      ! [X: list_o,Y: list_o] :
% 0.28/0.49        ( ( ( size_size_list_o @ X )
% 0.28/0.49         != ( size_size_list_o @ Y ) )
% 0.28/0.49       => ( X != Y ) ) ).
% 0.28/0.49  
% 0.28/0.49  % size_neq_size_imp_neq
% 0.28/0.49  thf(fact_565_size__neq__size__imp__neq,axiom,
% 0.28/0.49      ! [X: list_nat,Y: list_nat] :
% 0.28/0.49        ( ( ( size_size_list_nat @ X )
% 0.28/0.49         != ( size_size_list_nat @ Y ) )
% 0.28/0.49       => ( X != Y ) ) ).
% 0.28/0.49  
% 0.28/0.49  % size_neq_size_imp_neq
% 0.28/0.49  thf(fact_566_size__neq__size__imp__neq,axiom,
% 0.28/0.49      ! [X: list_int,Y: list_int] :
% 0.28/0.49        ( ( ( size_size_list_int @ X )
% 0.28/0.49         != ( size_size_list_int @ Y ) )
% 0.28/0.49       => ( X != Y ) ) ).
% 0.28/0.49  
% 0.28/0.49  % size_neq_size_imp_neq
% 0.28/0.49  thf(fact_567_size__neq__size__imp__neq,axiom,
% 0.28/0.49      ! [X: num,Y: num] :
% 0.28/0.49        ( ( ( size_size_num @ X )
% 0.28/0.49         != ( size_size_num @ Y ) )
% 0.28/0.49       => ( X != Y ) ) ).
% 0.28/0.49  
% 0.28/0.49  % size_neq_size_imp_neq
% 0.28/0.49  thf(fact_568_mult__2,axiom,
% 0.28/0.49      ! [Z: complex] :
% 0.28/0.49        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 0.28/0.49        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2
% 0.28/0.49  thf(fact_569_mult__2,axiom,
% 0.28/0.49      ! [Z: real] :
% 0.28/0.49        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 0.28/0.49        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2
% 0.28/0.49  thf(fact_570_mult__2,axiom,
% 0.28/0.49      ! [Z: rat] :
% 0.28/0.49        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.28/0.49        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2
% 0.28/0.49  thf(fact_571_mult__2,axiom,
% 0.28/0.49      ! [Z: nat] :
% 0.28/0.49        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.28/0.49        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2
% 0.28/0.49  thf(fact_572_mult__2,axiom,
% 0.28/0.49      ! [Z: int] :
% 0.28/0.49        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.28/0.49        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2
% 0.28/0.49  thf(fact_573_mult__2__right,axiom,
% 0.28/0.49      ! [Z: complex] :
% 0.28/0.49        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_complex @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2_right
% 0.28/0.49  thf(fact_574_mult__2__right,axiom,
% 0.28/0.49      ! [Z: real] :
% 0.28/0.49        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_real @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2_right
% 0.28/0.49  thf(fact_575_mult__2__right,axiom,
% 0.28/0.49      ! [Z: rat] :
% 0.28/0.49        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2_right
% 0.28/0.49  thf(fact_576_mult__2__right,axiom,
% 0.28/0.49      ! [Z: nat] :
% 0.28/0.49        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2_right
% 0.28/0.49  thf(fact_577_mult__2__right,axiom,
% 0.28/0.49      ! [Z: int] :
% 0.28/0.49        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.28/0.49  
% 0.28/0.49  % mult_2_right
% 0.28/0.49  thf(fact_578_left__add__twice,axiom,
% 0.28/0.49      ! [A: complex,B: complex] :
% 0.28/0.49        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.28/0.49        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_twice
% 0.28/0.49  thf(fact_579_left__add__twice,axiom,
% 0.28/0.49      ! [A: real,B: real] :
% 0.28/0.49        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.28/0.49        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_twice
% 0.28/0.49  thf(fact_580_left__add__twice,axiom,
% 0.28/0.49      ! [A: rat,B: rat] :
% 0.28/0.49        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.28/0.49        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_twice
% 0.28/0.49  thf(fact_581_left__add__twice,axiom,
% 0.28/0.49      ! [A: nat,B: nat] :
% 0.28/0.49        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.28/0.49        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_twice
% 0.28/0.49  thf(fact_582_left__add__twice,axiom,
% 0.28/0.49      ! [A: int,B: int] :
% 0.28/0.49        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.28/0.49        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % left_add_twice
% 0.28/0.49  thf(fact_583_power4__eq__xxxx,axiom,
% 0.28/0.49      ! [X: complex] :
% 0.28/0.49        ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.28/0.49        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power4_eq_xxxx
% 0.28/0.49  thf(fact_584_power4__eq__xxxx,axiom,
% 0.28/0.49      ! [X: real] :
% 0.28/0.49        ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.28/0.49        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power4_eq_xxxx
% 0.28/0.49  thf(fact_585_power4__eq__xxxx,axiom,
% 0.28/0.49      ! [X: rat] :
% 0.28/0.49        ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.28/0.49        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power4_eq_xxxx
% 0.28/0.49  thf(fact_586_power4__eq__xxxx,axiom,
% 0.28/0.49      ! [X: nat] :
% 0.28/0.49        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.28/0.49        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power4_eq_xxxx
% 0.28/0.49  thf(fact_587_power4__eq__xxxx,axiom,
% 0.28/0.49      ! [X: int] :
% 0.28/0.49        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.28/0.49        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power4_eq_xxxx
% 0.28/0.49  thf(fact_588_power2__eq__square,axiom,
% 0.28/0.49      ! [A: complex] :
% 0.28/0.49        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( times_times_complex @ A @ A ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_eq_square
% 0.28/0.49  thf(fact_589_power2__eq__square,axiom,
% 0.28/0.49      ! [A: real] :
% 0.28/0.49        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( times_times_real @ A @ A ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_eq_square
% 0.28/0.49  thf(fact_590_power2__eq__square,axiom,
% 0.28/0.49      ! [A: rat] :
% 0.28/0.49        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( times_times_rat @ A @ A ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_eq_square
% 0.28/0.49  thf(fact_591_power2__eq__square,axiom,
% 0.28/0.49      ! [A: nat] :
% 0.28/0.49        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( times_times_nat @ A @ A ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_eq_square
% 0.28/0.49  thf(fact_592_power2__eq__square,axiom,
% 0.28/0.49      ! [A: int] :
% 0.28/0.49        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( times_times_int @ A @ A ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_eq_square
% 0.28/0.49  thf(fact_593_power__even__eq,axiom,
% 0.28/0.49      ! [A: nat,N: nat] :
% 0.28/0.49        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.49        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_even_eq
% 0.28/0.49  thf(fact_594_power__even__eq,axiom,
% 0.28/0.49      ! [A: real,N: nat] :
% 0.28/0.49        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.49        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_even_eq
% 0.28/0.49  thf(fact_595_power__even__eq,axiom,
% 0.28/0.49      ! [A: int,N: nat] :
% 0.28/0.49        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.49        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_even_eq
% 0.28/0.49  thf(fact_596_power__even__eq,axiom,
% 0.28/0.49      ! [A: complex,N: nat] :
% 0.28/0.49        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.49        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_even_eq
% 0.28/0.49  thf(fact_597_power__le__imp__le__exp,axiom,
% 0.28/0.49      ! [A: real,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.49       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.28/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_le_imp_le_exp
% 0.28/0.49  thf(fact_598_power__le__imp__le__exp,axiom,
% 0.28/0.49      ! [A: rat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.49       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.28/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_le_imp_le_exp
% 0.28/0.49  thf(fact_599_power__le__imp__le__exp,axiom,
% 0.28/0.49      ! [A: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.49       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.28/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_le_imp_le_exp
% 0.28/0.49  thf(fact_600_power__le__imp__le__exp,axiom,
% 0.28/0.49      ! [A: int,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.49       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.28/0.49         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power_le_imp_le_exp
% 0.28/0.49  thf(fact_601_one__power2,axiom,
% 0.28/0.49      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49      = one_one_rat ) ).
% 0.28/0.49  
% 0.28/0.49  % one_power2
% 0.28/0.49  thf(fact_602_one__power2,axiom,
% 0.28/0.49      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49      = one_one_nat ) ).
% 0.28/0.49  
% 0.28/0.49  % one_power2
% 0.28/0.49  thf(fact_603_one__power2,axiom,
% 0.28/0.49      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49      = one_one_real ) ).
% 0.28/0.49  
% 0.28/0.49  % one_power2
% 0.28/0.49  thf(fact_604_one__power2,axiom,
% 0.28/0.49      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49      = one_one_int ) ).
% 0.28/0.49  
% 0.28/0.49  % one_power2
% 0.28/0.49  thf(fact_605_one__power2,axiom,
% 0.28/0.49      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49      = one_one_complex ) ).
% 0.28/0.49  
% 0.28/0.49  % one_power2
% 0.28/0.49  thf(fact_606_nat__1__add__1,axiom,
% 0.28/0.49      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.28/0.49      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_1_add_1
% 0.28/0.49  thf(fact_607_power2__sum,axiom,
% 0.28/0.49      ! [X: complex,Y: complex] :
% 0.28/0.49        ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_sum
% 0.28/0.49  thf(fact_608_power2__sum,axiom,
% 0.28/0.49      ! [X: real,Y: real] :
% 0.28/0.49        ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_sum
% 0.28/0.49  thf(fact_609_power2__sum,axiom,
% 0.28/0.49      ! [X: rat,Y: rat] :
% 0.28/0.49        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_sum
% 0.28/0.49  thf(fact_610_power2__sum,axiom,
% 0.28/0.49      ! [X: nat,Y: nat] :
% 0.28/0.49        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_sum
% 0.28/0.49  thf(fact_611_power2__sum,axiom,
% 0.28/0.49      ! [X: int,Y: int] :
% 0.28/0.49        ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.49        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % power2_sum
% 0.28/0.49  thf(fact_612_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( ord_less_eq_real @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(3)
% 0.28/0.49  thf(fact_613_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( ord_less_eq_rat @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(3)
% 0.28/0.49  thf(fact_614_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(3)
% 0.28/0.49  thf(fact_615_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( ord_less_eq_int @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(3)
% 0.28/0.49  thf(fact_616_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_eq_real @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(2)
% 0.28/0.49  thf(fact_617_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(2)
% 0.28/0.49  thf(fact_618_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(2)
% 0.28/0.49  thf(fact_619_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_eq_int @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(2)
% 0.28/0.49  thf(fact_620_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( ord_less_eq_real @ I @ J )
% 0.28/0.49          & ( ord_less_eq_real @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(1)
% 0.28/0.49  thf(fact_621_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( ord_less_eq_rat @ I @ J )
% 0.28/0.49          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(1)
% 0.28/0.49  thf(fact_622_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(1)
% 0.28/0.49  thf(fact_623_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( ord_less_eq_int @ I @ J )
% 0.28/0.49          & ( ord_less_eq_int @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_semiring(1)
% 0.28/0.49  thf(fact_624_add__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_real @ C @ D )
% 0.28/0.49         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono
% 0.28/0.49  thf(fact_625_add__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_rat @ C @ D )
% 0.28/0.49         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono
% 0.28/0.49  thf(fact_626_add__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_nat @ C @ D )
% 0.28/0.49         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono
% 0.28/0.49  thf(fact_627_add__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_int @ C @ D )
% 0.28/0.49         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono
% 0.28/0.49  thf(fact_628_add__left__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.49       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_mono
% 0.28/0.49  thf(fact_629_add__left__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.49       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_mono
% 0.28/0.49  thf(fact_630_add__left__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_mono
% 0.28/0.49  thf(fact_631_add__left__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_left_mono
% 0.28/0.49  thf(fact_632_less__eqE,axiom,
% 0.28/0.49      ! [A: nat,B: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.49       => ~ ! [C2: nat] :
% 0.28/0.49              ( B
% 0.28/0.49             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_eqE
% 0.28/0.49  thf(fact_633_add__right__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.49       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_mono
% 0.28/0.49  thf(fact_634_add__right__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.49       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_mono
% 0.28/0.49  thf(fact_635_add__right__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_mono
% 0.28/0.49  thf(fact_636_add__right__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.49       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_right_mono
% 0.28/0.49  thf(fact_637_le__iff__add,axiom,
% 0.28/0.49      ( ord_less_eq_nat
% 0.28/0.49      = ( ^ [A3: nat,B2: nat] :
% 0.28/0.49          ? [C3: nat] :
% 0.28/0.49            ( B2
% 0.28/0.49            = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_iff_add
% 0.28/0.49  thf(fact_638_add__le__imp__le__left,axiom,
% 0.28/0.49      ! [C: real,A: real,B: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.49       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_left
% 0.28/0.49  thf(fact_639_add__le__imp__le__left,axiom,
% 0.28/0.49      ! [C: rat,A: rat,B: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.28/0.49       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_left
% 0.28/0.49  thf(fact_640_add__le__imp__le__left,axiom,
% 0.28/0.49      ! [C: nat,A: nat,B: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.28/0.49       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_left
% 0.28/0.49  thf(fact_641_add__le__imp__le__left,axiom,
% 0.28/0.49      ! [C: int,A: int,B: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.28/0.49       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_left
% 0.28/0.49  thf(fact_642_add__le__imp__le__right,axiom,
% 0.28/0.49      ! [A: real,C: real,B: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.49       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_right
% 0.28/0.49  thf(fact_643_add__le__imp__le__right,axiom,
% 0.28/0.49      ! [A: rat,C: rat,B: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.49       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_right
% 0.28/0.49  thf(fact_644_add__le__imp__le__right,axiom,
% 0.28/0.49      ! [A: nat,C: nat,B: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.49       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_right
% 0.28/0.49  thf(fact_645_add__le__imp__le__right,axiom,
% 0.28/0.49      ! [A: int,C: int,B: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.49       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_imp_le_right
% 0.28/0.49  thf(fact_646_add__mono__thms__linordered__field_I5_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( ord_less_real @ I @ J )
% 0.28/0.49          & ( ord_less_real @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(5)
% 0.28/0.49  thf(fact_647_add__mono__thms__linordered__field_I5_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( ord_less_rat @ I @ J )
% 0.28/0.49          & ( ord_less_rat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(5)
% 0.28/0.49  thf(fact_648_add__mono__thms__linordered__field_I5_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( ord_less_nat @ I @ J )
% 0.28/0.49          & ( ord_less_nat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(5)
% 0.28/0.49  thf(fact_649_add__mono__thms__linordered__field_I5_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( ord_less_int @ I @ J )
% 0.28/0.49          & ( ord_less_int @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(5)
% 0.28/0.49  thf(fact_650_add__mono__thms__linordered__field_I2_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_real @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(2)
% 0.28/0.49  thf(fact_651_add__mono__thms__linordered__field_I2_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_rat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(2)
% 0.28/0.49  thf(fact_652_add__mono__thms__linordered__field_I2_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_nat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(2)
% 0.28/0.49  thf(fact_653_add__mono__thms__linordered__field_I2_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( I = J )
% 0.28/0.49          & ( ord_less_int @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(2)
% 0.28/0.49  thf(fact_654_add__mono__thms__linordered__field_I1_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( ord_less_real @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(1)
% 0.28/0.49  thf(fact_655_add__mono__thms__linordered__field_I1_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( ord_less_rat @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(1)
% 0.28/0.49  thf(fact_656_add__mono__thms__linordered__field_I1_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( ord_less_nat @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(1)
% 0.28/0.49  thf(fact_657_add__mono__thms__linordered__field_I1_J,axiom,
% 0.28/0.49      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.49        ( ( ( ord_less_int @ I @ J )
% 0.28/0.49          & ( K = L2 ) )
% 0.28/0.49       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(1)
% 0.28/0.49  thf(fact_658_add__strict__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.49        ( ( ord_less_real @ A @ B )
% 0.28/0.49       => ( ( ord_less_real @ C @ D )
% 0.28/0.49         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_mono
% 0.28/0.49  thf(fact_659_add__strict__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.49        ( ( ord_less_rat @ A @ B )
% 0.28/0.49       => ( ( ord_less_rat @ C @ D )
% 0.28/0.49         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_mono
% 0.28/0.49  thf(fact_660_add__strict__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.49        ( ( ord_less_nat @ A @ B )
% 0.28/0.49       => ( ( ord_less_nat @ C @ D )
% 0.28/0.49         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_mono
% 0.28/0.49  thf(fact_661_add__strict__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.49        ( ( ord_less_int @ A @ B )
% 0.28/0.49       => ( ( ord_less_int @ C @ D )
% 0.28/0.49         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_mono
% 0.28/0.49  thf(fact_662_add__strict__left__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ord_less_real @ A @ B )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_left_mono
% 0.28/0.49  thf(fact_663_add__strict__left__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ord_less_rat @ A @ B )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_left_mono
% 0.28/0.49  thf(fact_664_add__strict__left__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( ord_less_nat @ A @ B )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_left_mono
% 0.28/0.49  thf(fact_665_add__strict__left__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ord_less_int @ A @ B )
% 0.28/0.49       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_left_mono
% 0.28/0.49  thf(fact_666_add__strict__right__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real] :
% 0.28/0.49        ( ( ord_less_real @ A @ B )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_right_mono
% 0.28/0.49  thf(fact_667_add__strict__right__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat] :
% 0.28/0.49        ( ( ord_less_rat @ A @ B )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_right_mono
% 0.28/0.49  thf(fact_668_add__strict__right__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat] :
% 0.28/0.49        ( ( ord_less_nat @ A @ B )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_right_mono
% 0.28/0.49  thf(fact_669_add__strict__right__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int] :
% 0.28/0.49        ( ( ord_less_int @ A @ B )
% 0.28/0.49       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_strict_right_mono
% 0.28/0.49  thf(fact_670_add__less__imp__less__left,axiom,
% 0.28/0.49      ! [C: real,A: real,B: real] :
% 0.28/0.49        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.49       => ( ord_less_real @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_left
% 0.28/0.49  thf(fact_671_add__less__imp__less__left,axiom,
% 0.28/0.49      ! [C: rat,A: rat,B: rat] :
% 0.28/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.28/0.49       => ( ord_less_rat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_left
% 0.28/0.49  thf(fact_672_add__less__imp__less__left,axiom,
% 0.28/0.49      ! [C: nat,A: nat,B: nat] :
% 0.28/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.28/0.49       => ( ord_less_nat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_left
% 0.28/0.49  thf(fact_673_add__less__imp__less__left,axiom,
% 0.28/0.49      ! [C: int,A: int,B: int] :
% 0.28/0.49        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.28/0.49       => ( ord_less_int @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_left
% 0.28/0.49  thf(fact_674_add__less__imp__less__right,axiom,
% 0.28/0.49      ! [A: real,C: real,B: real] :
% 0.28/0.49        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.49       => ( ord_less_real @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_right
% 0.28/0.49  thf(fact_675_add__less__imp__less__right,axiom,
% 0.28/0.49      ! [A: rat,C: rat,B: rat] :
% 0.28/0.49        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.49       => ( ord_less_rat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_right
% 0.28/0.49  thf(fact_676_add__less__imp__less__right,axiom,
% 0.28/0.49      ! [A: nat,C: nat,B: nat] :
% 0.28/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.49       => ( ord_less_nat @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_right
% 0.28/0.49  thf(fact_677_add__less__imp__less__right,axiom,
% 0.28/0.49      ! [A: int,C: int,B: int] :
% 0.28/0.49        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.49       => ( ord_less_int @ A @ B ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_imp_less_right
% 0.28/0.49  thf(fact_678_nat__less__le,axiom,
% 0.28/0.49      ( ord_less_nat
% 0.28/0.49      = ( ^ [M3: nat,N2: nat] :
% 0.28/0.49            ( ( ord_less_eq_nat @ M3 @ N2 )
% 0.28/0.49            & ( M3 != N2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_less_le
% 0.28/0.49  thf(fact_679_less__imp__le__nat,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ M @ N )
% 0.28/0.49       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_imp_le_nat
% 0.28/0.49  thf(fact_680_le__eq__less__or__eq,axiom,
% 0.28/0.49      ( ord_less_eq_nat
% 0.28/0.49      = ( ^ [M3: nat,N2: nat] :
% 0.28/0.49            ( ( ord_less_nat @ M3 @ N2 )
% 0.28/0.49            | ( M3 = N2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_eq_less_or_eq
% 0.28/0.49  thf(fact_681_less__or__eq__imp__le,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ( ord_less_nat @ M @ N )
% 0.28/0.49          | ( M = N ) )
% 0.28/0.49       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_or_eq_imp_le
% 0.28/0.49  thf(fact_682_le__neq__implies__less,axiom,
% 0.28/0.49      ! [M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.49       => ( ( M != N )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_neq_implies_less
% 0.28/0.49  thf(fact_683_less__mono__imp__le__mono,axiom,
% 0.28/0.49      ! [F: nat > nat,I: nat,J: nat] :
% 0.28/0.49        ( ! [I4: nat,J2: nat] :
% 0.28/0.49            ( ( ord_less_nat @ I4 @ J2 )
% 0.28/0.49           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 0.28/0.49       => ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_mono_imp_le_mono
% 0.28/0.49  thf(fact_684_add__lessD1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.28/0.49       => ( ord_less_nat @ I @ K ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_lessD1
% 0.28/0.49  thf(fact_685_add__less__mono,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ord_less_nat @ I @ J )
% 0.28/0.49       => ( ( ord_less_nat @ K @ L2 )
% 0.28/0.49         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_mono
% 0.28/0.49  thf(fact_686_not__add__less1,axiom,
% 0.28/0.49      ! [I: nat,J: nat] :
% 0.28/0.49        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.28/0.49  
% 0.28/0.49  % not_add_less1
% 0.28/0.49  thf(fact_687_not__add__less2,axiom,
% 0.28/0.49      ! [J: nat,I: nat] :
% 0.28/0.49        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.28/0.49  
% 0.28/0.49  % not_add_less2
% 0.28/0.49  thf(fact_688_add__less__mono1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_nat @ I @ J )
% 0.28/0.49       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_mono1
% 0.28/0.49  thf(fact_689_trans__less__add1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,M: nat] :
% 0.28/0.49        ( ( ord_less_nat @ I @ J )
% 0.28/0.49       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % trans_less_add1
% 0.28/0.49  thf(fact_690_trans__less__add2,axiom,
% 0.28/0.49      ! [I: nat,J: nat,M: nat] :
% 0.28/0.49        ( ( ord_less_nat @ I @ J )
% 0.28/0.49       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % trans_less_add2
% 0.28/0.49  thf(fact_691_less__add__eq__less,axiom,
% 0.28/0.49      ! [K: nat,L2: nat,M: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_nat @ K @ L2 )
% 0.28/0.49       => ( ( ( plus_plus_nat @ M @ L2 )
% 0.28/0.49            = ( plus_plus_nat @ K @ N ) )
% 0.28/0.49         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % less_add_eq_less
% 0.28/0.49  thf(fact_692_add__leE,axiom,
% 0.28/0.49      ! [M: nat,K: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.28/0.49       => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.49           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_leE
% 0.28/0.49  thf(fact_693_le__add1,axiom,
% 0.28/0.49      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_add1
% 0.28/0.49  thf(fact_694_le__add2,axiom,
% 0.28/0.49      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_add2
% 0.28/0.49  thf(fact_695_add__leD1,axiom,
% 0.28/0.49      ! [M: nat,K: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.28/0.49       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_leD1
% 0.28/0.49  thf(fact_696_add__leD2,axiom,
% 0.28/0.49      ! [M: nat,K: nat,N: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.28/0.49       => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_leD2
% 0.28/0.49  thf(fact_697_le__Suc__ex,axiom,
% 0.28/0.49      ! [K: nat,L2: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ K @ L2 )
% 0.28/0.49       => ? [N3: nat] :
% 0.28/0.49            ( L2
% 0.28/0.49            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % le_Suc_ex
% 0.28/0.49  thf(fact_698_add__le__mono,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ( ord_less_eq_nat @ K @ L2 )
% 0.28/0.49         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_mono
% 0.28/0.49  thf(fact_699_add__le__mono1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_mono1
% 0.28/0.49  thf(fact_700_trans__le__add1,axiom,
% 0.28/0.49      ! [I: nat,J: nat,M: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % trans_le_add1
% 0.28/0.49  thf(fact_701_trans__le__add2,axiom,
% 0.28/0.49      ! [I: nat,J: nat,M: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.49       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % trans_le_add2
% 0.28/0.49  thf(fact_702_nat__le__iff__add,axiom,
% 0.28/0.49      ( ord_less_eq_nat
% 0.28/0.49      = ( ^ [M3: nat,N2: nat] :
% 0.28/0.49          ? [K2: nat] :
% 0.28/0.49            ( N2
% 0.28/0.49            = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % nat_le_iff_add
% 0.28/0.49  thf(fact_703_ex__power__ivl1,axiom,
% 0.28/0.49      ! [B: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.28/0.49       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.28/0.49         => ? [N3: nat] :
% 0.28/0.49              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.28/0.49              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ex_power_ivl1
% 0.28/0.49  thf(fact_704_ex__power__ivl2,axiom,
% 0.28/0.49      ! [B: nat,K: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.28/0.49       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.28/0.49         => ? [N3: nat] :
% 0.28/0.49              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.28/0.49              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % ex_power_ivl2
% 0.28/0.49  thf(fact_705_add__less__le__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.49        ( ( ord_less_real @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_real @ C @ D )
% 0.28/0.49         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_le_mono
% 0.28/0.49  thf(fact_706_add__less__le__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.49        ( ( ord_less_rat @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_rat @ C @ D )
% 0.28/0.49         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_le_mono
% 0.28/0.49  thf(fact_707_add__less__le__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.49        ( ( ord_less_nat @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_nat @ C @ D )
% 0.28/0.49         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_le_mono
% 0.28/0.49  thf(fact_708_add__less__le__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.49        ( ( ord_less_int @ A @ B )
% 0.28/0.49       => ( ( ord_less_eq_int @ C @ D )
% 0.28/0.49         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_less_le_mono
% 0.28/0.49  thf(fact_709_add__le__less__mono,axiom,
% 0.28/0.49      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.49        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.49       => ( ( ord_less_real @ C @ D )
% 0.28/0.49         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_less_mono
% 0.28/0.49  thf(fact_710_add__le__less__mono,axiom,
% 0.28/0.49      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.49        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.49       => ( ( ord_less_rat @ C @ D )
% 0.28/0.49         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_less_mono
% 0.28/0.49  thf(fact_711_add__le__less__mono,axiom,
% 0.28/0.49      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.49        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.49       => ( ( ord_less_nat @ C @ D )
% 0.28/0.49         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_less_mono
% 0.28/0.49  thf(fact_712_add__le__less__mono,axiom,
% 0.28/0.49      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.49        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.49       => ( ( ord_less_int @ C @ D )
% 0.28/0.49         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_le_less_mono
% 0.28/0.49  thf(fact_713_add__mono__thms__linordered__field_I3_J,axiom,
% 0.28/0.49      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.49        ( ( ( ord_less_real @ I @ J )
% 0.28/0.49          & ( ord_less_eq_real @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(3)
% 0.28/0.49  thf(fact_714_add__mono__thms__linordered__field_I3_J,axiom,
% 0.28/0.49      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.49        ( ( ( ord_less_rat @ I @ J )
% 0.28/0.49          & ( ord_less_eq_rat @ K @ L2 ) )
% 0.28/0.49       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.49  
% 0.28/0.49  % add_mono_thms_linordered_field(3)
% 0.28/0.49  thf(fact_715_add__mono__thms__linordered__field_I3_J,axiom,
% 0.28/0.49      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.49        ( ( ( ord_less_nat @ I @ J )
% 0.28/0.50          & ( ord_less_eq_nat @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(3)
% 0.28/0.50  thf(fact_716_add__mono__thms__linordered__field_I3_J,axiom,
% 0.28/0.50      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.50        ( ( ( ord_less_int @ I @ J )
% 0.28/0.50          & ( ord_less_eq_int @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(3)
% 0.28/0.50  thf(fact_717_add__mono__thms__linordered__field_I4_J,axiom,
% 0.28/0.50      ! [I: real,J: real,K: real,L2: real] :
% 0.28/0.50        ( ( ( ord_less_eq_real @ I @ J )
% 0.28/0.50          & ( ord_less_real @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(4)
% 0.28/0.50  thf(fact_718_add__mono__thms__linordered__field_I4_J,axiom,
% 0.28/0.50      ! [I: rat,J: rat,K: rat,L2: rat] :
% 0.28/0.50        ( ( ( ord_less_eq_rat @ I @ J )
% 0.28/0.50          & ( ord_less_rat @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(4)
% 0.28/0.50  thf(fact_719_add__mono__thms__linordered__field_I4_J,axiom,
% 0.28/0.50      ! [I: nat,J: nat,K: nat,L2: nat] :
% 0.28/0.50        ( ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.50          & ( ord_less_nat @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(4)
% 0.28/0.50  thf(fact_720_add__mono__thms__linordered__field_I4_J,axiom,
% 0.28/0.50      ! [I: int,J: int,K: int,L2: int] :
% 0.28/0.50        ( ( ( ord_less_eq_int @ I @ J )
% 0.28/0.50          & ( ord_less_int @ K @ L2 ) )
% 0.28/0.50       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono_thms_linordered_field(4)
% 0.28/0.50  thf(fact_721_mono__nat__linear__lb,axiom,
% 0.28/0.50      ! [F: nat > nat,M: nat,K: nat] :
% 0.28/0.50        ( ! [M4: nat,N3: nat] :
% 0.28/0.50            ( ( ord_less_nat @ M4 @ N3 )
% 0.28/0.50           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.28/0.50       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mono_nat_linear_lb
% 0.28/0.50  thf(fact_722_set__vebt__set__vebt_H__valid,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ( vEBT_set_vebt @ T )
% 0.28/0.50          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % set_vebt_set_vebt'_valid
% 0.28/0.50  thf(fact_723_add__self__div__2,axiom,
% 0.28/0.50      ! [M: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.50        = M ) ).
% 0.28/0.50  
% 0.28/0.50  % add_self_div_2
% 0.28/0.50  thf(fact_724_both__member__options__ding,axiom,
% 0.28/0.50      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.50       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.28/0.50         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 0.28/0.50           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % both_member_options_ding
% 0.28/0.50  thf(fact_725_sum__squares__bound,axiom,
% 0.28/0.50      ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % sum_squares_bound
% 0.28/0.50  thf(fact_726_sum__squares__bound,axiom,
% 0.28/0.50      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % sum_squares_bound
% 0.28/0.50  thf(fact_727_div__exp__eq,axiom,
% 0.28/0.50      ! [A: nat,M: nat,N: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.50        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_exp_eq
% 0.28/0.50  thf(fact_728_div__exp__eq,axiom,
% 0.28/0.50      ! [A: int,M: nat,N: nat] :
% 0.28/0.50        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.50        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_exp_eq
% 0.28/0.50  thf(fact_729_field__less__half__sum,axiom,
% 0.28/0.50      ! [X: real,Y: real] :
% 0.28/0.50        ( ( ord_less_real @ X @ Y )
% 0.28/0.50       => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % field_less_half_sum
% 0.28/0.50  thf(fact_730_field__less__half__sum,axiom,
% 0.28/0.50      ! [X: rat,Y: rat] :
% 0.28/0.50        ( ( ord_less_rat @ X @ Y )
% 0.28/0.50       => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % field_less_half_sum
% 0.28/0.50  thf(fact_731_div__by__1,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_1
% 0.28/0.50  thf(fact_732_div__by__1,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( divide_divide_real @ A @ one_one_real )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_1
% 0.28/0.50  thf(fact_733_div__by__1,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_1
% 0.28/0.50  thf(fact_734_div__by__1,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_1
% 0.28/0.50  thf(fact_735_div__by__1,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ A @ one_one_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_1
% 0.28/0.50  thf(fact_736_bits__div__by__1,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_by_1
% 0.28/0.50  thf(fact_737_bits__div__by__1,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ A @ one_one_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_by_1
% 0.28/0.50  thf(fact_738_times__divide__eq__left,axiom,
% 0.28/0.50      ! [B: complex,C: complex,A: complex] :
% 0.28/0.50        ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 0.28/0.50        = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_left
% 0.28/0.50  thf(fact_739_times__divide__eq__left,axiom,
% 0.28/0.50      ! [B: real,C: real,A: real] :
% 0.28/0.50        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.50        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_left
% 0.28/0.50  thf(fact_740_times__divide__eq__left,axiom,
% 0.28/0.50      ! [B: rat,C: rat,A: rat] :
% 0.28/0.50        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.50        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_left
% 0.28/0.50  thf(fact_741_divide__divide__eq__left,axiom,
% 0.28/0.50      ! [A: complex,B: complex,C: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 0.28/0.50        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left
% 0.28/0.50  thf(fact_742_divide__divide__eq__left,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.28/0.50        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left
% 0.28/0.50  thf(fact_743_divide__divide__eq__left,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.28/0.50        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left
% 0.28/0.50  thf(fact_744_divide__divide__eq__right,axiom,
% 0.28/0.50      ! [A: complex,B: complex,C: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.50        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_right
% 0.28/0.50  thf(fact_745_divide__divide__eq__right,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.50        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_right
% 0.28/0.50  thf(fact_746_divide__divide__eq__right,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.50        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_right
% 0.28/0.50  thf(fact_747_times__divide__eq__right,axiom,
% 0.28/0.50      ! [A: complex,B: complex,C: complex] :
% 0.28/0.50        ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.50        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_right
% 0.28/0.50  thf(fact_748_times__divide__eq__right,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.50        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_right
% 0.28/0.50  thf(fact_749_times__divide__eq__right,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.50        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_eq_right
% 0.28/0.50  thf(fact_750_deg__deg__n,axiom,
% 0.28/0.50      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.50       => ( Deg = N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % deg_deg_n
% 0.28/0.50  thf(fact_751_semiring__norm_I13_J,axiom,
% 0.28/0.50      ! [M: num,N: num] :
% 0.28/0.50        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.28/0.50        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % semiring_norm(13)
% 0.28/0.50  thf(fact_752_semiring__norm_I11_J,axiom,
% 0.28/0.50      ! [M: num] :
% 0.28/0.50        ( ( times_times_num @ M @ one )
% 0.28/0.50        = M ) ).
% 0.28/0.50  
% 0.28/0.50  % semiring_norm(11)
% 0.28/0.50  thf(fact_753_semiring__norm_I12_J,axiom,
% 0.28/0.50      ! [N: num] :
% 0.28/0.50        ( ( times_times_num @ one @ N )
% 0.28/0.50        = N ) ).
% 0.28/0.50  
% 0.28/0.50  % semiring_norm(12)
% 0.28/0.50  thf(fact_754_num__double,axiom,
% 0.28/0.50      ! [N: num] :
% 0.28/0.50        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.28/0.50        = ( bit0 @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % num_double
% 0.28/0.50  thf(fact_755_power__mult__numeral,axiom,
% 0.28/0.50      ! [A: nat,M: num,N: num] :
% 0.28/0.50        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.50        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_mult_numeral
% 0.28/0.50  thf(fact_756_power__mult__numeral,axiom,
% 0.28/0.50      ! [A: real,M: num,N: num] :
% 0.28/0.50        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.50        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_mult_numeral
% 0.28/0.50  thf(fact_757_power__mult__numeral,axiom,
% 0.28/0.50      ! [A: int,M: num,N: num] :
% 0.28/0.50        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.50        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_mult_numeral
% 0.28/0.50  thf(fact_758_power__mult__numeral,axiom,
% 0.28/0.50      ! [A: complex,M: num,N: num] :
% 0.28/0.50        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 0.28/0.50        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_mult_numeral
% 0.28/0.50  thf(fact_759_succ__member,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.28/0.50        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.28/0.50        = ( ( vEBT_vebt_member @ T @ Y )
% 0.28/0.50          & ( ord_less_nat @ X @ Y )
% 0.28/0.50          & ! [Z3: nat] :
% 0.28/0.50              ( ( ( vEBT_vebt_member @ T @ Z3 )
% 0.28/0.50                & ( ord_less_nat @ X @ Z3 ) )
% 0.28/0.50             => ( ord_less_eq_nat @ Y @ Z3 ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % succ_member
% 0.28/0.50  thf(fact_760_pred__member,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.28/0.50        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.28/0.50        = ( ( vEBT_vebt_member @ T @ Y )
% 0.28/0.50          & ( ord_less_nat @ Y @ X )
% 0.28/0.50          & ! [Z3: nat] :
% 0.28/0.50              ( ( ( vEBT_vebt_member @ T @ Z3 )
% 0.28/0.50                & ( ord_less_nat @ Z3 @ X ) )
% 0.28/0.50             => ( ord_less_eq_nat @ Z3 @ Y ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % pred_member
% 0.28/0.50  thf(fact_761_two__realpow__ge__one,axiom,
% 0.28/0.50      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % two_realpow_ge_one
% 0.28/0.50  thf(fact_762_four__x__squared,axiom,
% 0.28/0.50      ! [X: real] :
% 0.28/0.50        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.50        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % four_x_squared
% 0.28/0.50  thf(fact_763_L2__set__mult__ineq__lemma,axiom,
% 0.28/0.50      ! [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 ) ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % L2_set_mult_ineq_lemma
% 0.28/0.50  thf(fact_764_div__mult2__numeral__eq,axiom,
% 0.28/0.50      ! [A: nat,K: num,L2: num] :
% 0.28/0.50        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult2_numeral_eq
% 0.28/0.50  thf(fact_765_div__mult2__numeral__eq,axiom,
% 0.28/0.50      ! [A: int,K: num,L2: num] :
% 0.28/0.50        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 0.28/0.50        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult2_numeral_eq
% 0.28/0.50  thf(fact_766_linorder__neqE__linordered__idom,axiom,
% 0.28/0.50      ! [X: real,Y: real] :
% 0.28/0.50        ( ( X != Y )
% 0.28/0.50       => ( ~ ( ord_less_real @ X @ Y )
% 0.28/0.50         => ( ord_less_real @ Y @ X ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % linorder_neqE_linordered_idom
% 0.28/0.50  thf(fact_767_linorder__neqE__linordered__idom,axiom,
% 0.28/0.50      ! [X: rat,Y: rat] :
% 0.28/0.50        ( ( X != Y )
% 0.28/0.50       => ( ~ ( ord_less_rat @ X @ Y )
% 0.28/0.50         => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % linorder_neqE_linordered_idom
% 0.28/0.50  thf(fact_768_linorder__neqE__linordered__idom,axiom,
% 0.28/0.50      ! [X: int,Y: int] :
% 0.28/0.50        ( ( X != Y )
% 0.28/0.50       => ( ~ ( ord_less_int @ X @ Y )
% 0.28/0.50         => ( ord_less_int @ Y @ X ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % linorder_neqE_linordered_idom
% 0.28/0.50  thf(fact_769_linordered__field__no__ub,axiom,
% 0.28/0.50      ! [X4: real] :
% 0.28/0.50      ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 0.28/0.50  
% 0.28/0.50  % linordered_field_no_ub
% 0.28/0.50  thf(fact_770_linordered__field__no__ub,axiom,
% 0.28/0.50      ! [X4: rat] :
% 0.28/0.50      ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 0.28/0.50  
% 0.28/0.50  % linordered_field_no_ub
% 0.28/0.50  thf(fact_771_linordered__field__no__lb,axiom,
% 0.28/0.50      ! [X4: real] :
% 0.28/0.50      ? [Y5: real] : ( ord_less_real @ Y5 @ X4 ) ).
% 0.28/0.50  
% 0.28/0.50  % linordered_field_no_lb
% 0.28/0.50  thf(fact_772_linordered__field__no__lb,axiom,
% 0.28/0.50      ! [X4: rat] :
% 0.28/0.50      ? [Y5: rat] : ( ord_less_rat @ Y5 @ X4 ) ).
% 0.28/0.50  
% 0.28/0.50  % linordered_field_no_lb
% 0.28/0.50  thf(fact_773_combine__common__factor,axiom,
% 0.28/0.50      ! [A: real,E: real,B: real,C: real] :
% 0.28/0.50        ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % combine_common_factor
% 0.28/0.50  thf(fact_774_combine__common__factor,axiom,
% 0.28/0.50      ! [A: rat,E: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % combine_common_factor
% 0.28/0.50  thf(fact_775_combine__common__factor,axiom,
% 0.28/0.50      ! [A: nat,E: nat,B: nat,C: nat] :
% 0.28/0.50        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.28/0.50        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % combine_common_factor
% 0.28/0.50  thf(fact_776_combine__common__factor,axiom,
% 0.28/0.50      ! [A: int,E: int,B: int,C: int] :
% 0.28/0.50        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 0.28/0.50  
% 0.28/0.50  % combine_common_factor
% 0.28/0.50  thf(fact_777_distrib__right,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_right
% 0.28/0.50  thf(fact_778_distrib__right,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_right
% 0.28/0.50  thf(fact_779_distrib__right,axiom,
% 0.28/0.50      ! [A: nat,B: nat,C: nat] :
% 0.28/0.50        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_right
% 0.28/0.50  thf(fact_780_distrib__right,axiom,
% 0.28/0.50      ! [A: int,B: int,C: int] :
% 0.28/0.50        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_right
% 0.28/0.50  thf(fact_781_distrib__left,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_left
% 0.28/0.50  thf(fact_782_distrib__left,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_left
% 0.28/0.50  thf(fact_783_distrib__left,axiom,
% 0.28/0.50      ! [A: nat,B: nat,C: nat] :
% 0.28/0.50        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.50        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_left
% 0.28/0.50  thf(fact_784_distrib__left,axiom,
% 0.28/0.50      ! [A: int,B: int,C: int] :
% 0.28/0.50        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % distrib_left
% 0.28/0.50  thf(fact_785_comm__semiring__class_Odistrib,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % comm_semiring_class.distrib
% 0.28/0.50  thf(fact_786_comm__semiring__class_Odistrib,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % comm_semiring_class.distrib
% 0.28/0.50  thf(fact_787_comm__semiring__class_Odistrib,axiom,
% 0.28/0.50      ! [A: nat,B: nat,C: nat] :
% 0.28/0.50        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % comm_semiring_class.distrib
% 0.28/0.50  thf(fact_788_comm__semiring__class_Odistrib,axiom,
% 0.28/0.50      ! [A: int,B: int,C: int] :
% 0.28/0.50        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % comm_semiring_class.distrib
% 0.28/0.50  thf(fact_789_ring__class_Oring__distribs_I1_J,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(1)
% 0.28/0.50  thf(fact_790_ring__class_Oring__distribs_I1_J,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(1)
% 0.28/0.50  thf(fact_791_ring__class_Oring__distribs_I1_J,axiom,
% 0.28/0.50      ! [A: int,B: int,C: int] :
% 0.28/0.50        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(1)
% 0.28/0.50  thf(fact_792_ring__class_Oring__distribs_I2_J,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(2)
% 0.28/0.50  thf(fact_793_ring__class_Oring__distribs_I2_J,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(2)
% 0.28/0.50  thf(fact_794_ring__class_Oring__distribs_I2_J,axiom,
% 0.28/0.50      ! [A: int,B: int,C: int] :
% 0.28/0.50        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % ring_class.ring_distribs(2)
% 0.28/0.50  thf(fact_795_divide__divide__eq__left_H,axiom,
% 0.28/0.50      ! [A: complex,B: complex,C: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 0.28/0.50        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left'
% 0.28/0.50  thf(fact_796_divide__divide__eq__left_H,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 0.28/0.50        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left'
% 0.28/0.50  thf(fact_797_divide__divide__eq__left_H,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.28/0.50        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_eq_left'
% 0.28/0.50  thf(fact_798_divide__divide__times__eq,axiom,
% 0.28/0.50      ! [X: complex,Y: complex,Z: complex,W: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.28/0.50        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_times_eq
% 0.28/0.50  thf(fact_799_divide__divide__times__eq,axiom,
% 0.28/0.50      ! [X: real,Y: real,Z: real,W: real] :
% 0.28/0.50        ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 0.28/0.50        = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_times_eq
% 0.28/0.50  thf(fact_800_divide__divide__times__eq,axiom,
% 0.28/0.50      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 0.28/0.50        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_divide_times_eq
% 0.28/0.50  thf(fact_801_times__divide__times__eq,axiom,
% 0.28/0.50      ! [X: complex,Y: complex,Z: complex,W: complex] :
% 0.28/0.50        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 0.28/0.50        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_times_eq
% 0.28/0.50  thf(fact_802_times__divide__times__eq,axiom,
% 0.28/0.50      ! [X: real,Y: real,Z: real,W: real] :
% 0.28/0.50        ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 0.28/0.50        = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_times_eq
% 0.28/0.50  thf(fact_803_times__divide__times__eq,axiom,
% 0.28/0.50      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 0.28/0.50        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 0.28/0.50        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % times_divide_times_eq
% 0.28/0.50  thf(fact_804_add__divide__distrib,axiom,
% 0.28/0.50      ! [A: complex,B: complex,C: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_divide_distrib
% 0.28/0.50  thf(fact_805_add__divide__distrib,axiom,
% 0.28/0.50      ! [A: real,B: real,C: real] :
% 0.28/0.50        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_divide_distrib
% 0.28/0.50  thf(fact_806_add__divide__distrib,axiom,
% 0.28/0.50      ! [A: rat,B: rat,C: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.28/0.50        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_divide_distrib
% 0.28/0.50  thf(fact_807_div__le__dividend,axiom,
% 0.28/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.28/0.50  
% 0.28/0.50  % div_le_dividend
% 0.28/0.50  thf(fact_808_div__le__mono,axiom,
% 0.28/0.50      ! [M: nat,N: nat,K: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.50       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_le_mono
% 0.28/0.50  thf(fact_809_div__mult2__eq,axiom,
% 0.28/0.50      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 0.28/0.50        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult2_eq
% 0.28/0.50  thf(fact_810_less__1__mult,axiom,
% 0.28/0.50      ! [M: real,N: real] :
% 0.28/0.50        ( ( ord_less_real @ one_one_real @ M )
% 0.28/0.50       => ( ( ord_less_real @ one_one_real @ N )
% 0.28/0.50         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_1_mult
% 0.28/0.50  thf(fact_811_less__1__mult,axiom,
% 0.28/0.50      ! [M: rat,N: rat] :
% 0.28/0.50        ( ( ord_less_rat @ one_one_rat @ M )
% 0.28/0.50       => ( ( ord_less_rat @ one_one_rat @ N )
% 0.28/0.50         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_1_mult
% 0.28/0.50  thf(fact_812_less__1__mult,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ one_one_nat @ M )
% 0.28/0.50       => ( ( ord_less_nat @ one_one_nat @ N )
% 0.28/0.50         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_1_mult
% 0.28/0.50  thf(fact_813_less__1__mult,axiom,
% 0.28/0.50      ! [M: int,N: int] :
% 0.28/0.50        ( ( ord_less_int @ one_one_int @ M )
% 0.28/0.50       => ( ( ord_less_int @ one_one_int @ N )
% 0.28/0.50         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_1_mult
% 0.28/0.50  thf(fact_814_less__add__one,axiom,
% 0.28/0.50      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_one
% 0.28/0.50  thf(fact_815_less__add__one,axiom,
% 0.28/0.50      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_one
% 0.28/0.50  thf(fact_816_less__add__one,axiom,
% 0.28/0.50      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_one
% 0.28/0.50  thf(fact_817_less__add__one,axiom,
% 0.28/0.50      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_one
% 0.28/0.50  thf(fact_818_add__mono1,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ A @ B )
% 0.28/0.50       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono1
% 0.28/0.50  thf(fact_819_add__mono1,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ A @ B )
% 0.28/0.50       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono1
% 0.28/0.50  thf(fact_820_add__mono1,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_nat @ A @ B )
% 0.28/0.50       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono1
% 0.28/0.50  thf(fact_821_add__mono1,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_int @ A @ B )
% 0.28/0.50       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_mono1
% 0.28/0.50  thf(fact_822_less__mult__imp__div__less,axiom,
% 0.28/0.50      ! [M: nat,I: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 0.28/0.50       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_mult_imp_div_less
% 0.28/0.50  thf(fact_823_div__times__less__eq__dividend,axiom,
% 0.28/0.50      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 0.28/0.50  
% 0.28/0.50  % div_times_less_eq_dividend
% 0.28/0.50  thf(fact_824_times__div__less__eq__dividend,axiom,
% 0.28/0.50      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 0.28/0.50  
% 0.28/0.50  % times_div_less_eq_dividend
% 0.28/0.50  thf(fact_825_gt__half__sum,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ A @ B )
% 0.28/0.50       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % gt_half_sum
% 0.28/0.50  thf(fact_826_gt__half__sum,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ A @ B )
% 0.28/0.50       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % gt_half_sum
% 0.28/0.50  thf(fact_827_less__half__sum,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ A @ B )
% 0.28/0.50       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_half_sum
% 0.28/0.50  thf(fact_828_less__half__sum,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ A @ B )
% 0.28/0.50       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_half_sum
% 0.28/0.50  thf(fact_829_numeral__Bit0__div__2,axiom,
% 0.28/0.50      ! [N: num] :
% 0.28/0.50        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.50        = ( numeral_numeral_nat @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % numeral_Bit0_div_2
% 0.28/0.50  thf(fact_830_numeral__Bit0__div__2,axiom,
% 0.28/0.50      ! [N: num] :
% 0.28/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.50        = ( numeral_numeral_int @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % numeral_Bit0_div_2
% 0.28/0.50  thf(fact_831_field__sum__of__halves,axiom,
% 0.28/0.50      ! [X: real] :
% 0.28/0.50        ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.28/0.50        = X ) ).
% 0.28/0.50  
% 0.28/0.50  % field_sum_of_halves
% 0.28/0.50  thf(fact_832_field__sum__of__halves,axiom,
% 0.28/0.50      ! [X: rat] :
% 0.28/0.50        ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.28/0.50        = X ) ).
% 0.28/0.50  
% 0.28/0.50  % field_sum_of_halves
% 0.28/0.50  thf(fact_833_power__minus__is__div,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.50       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 0.28/0.50          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_minus_is_div
% 0.28/0.50  thf(fact_834_discrete,axiom,
% 0.28/0.50      ( ord_less_nat
% 0.28/0.50      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % discrete
% 0.28/0.50  thf(fact_835_discrete,axiom,
% 0.28/0.50      ( ord_less_int
% 0.28/0.50      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % discrete
% 0.28/0.50  thf(fact_836_low__def,axiom,
% 0.28/0.50      ( vEBT_VEBT_low
% 0.28/0.50      = ( ^ [X3: nat,N2: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % low_def
% 0.28/0.50  thf(fact_837__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_092_060close_062,axiom,
% 0.28/0.50      ( ( some_nat @ maxs )
% 0.28/0.50      = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % \<open>Some maxs = vebt_maxt (vebt_delete summary (high x n))\<close>
% 0.28/0.50  thf(fact_838_dbl__simps_I3_J,axiom,
% 0.28/0.50      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.28/0.50      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(3)
% 0.28/0.50  thf(fact_839_dbl__simps_I3_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_real @ one_one_real )
% 0.28/0.50      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(3)
% 0.28/0.50  thf(fact_840_dbl__simps_I3_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.28/0.50      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(3)
% 0.28/0.50  thf(fact_841_dbl__simps_I3_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.28/0.50      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(3)
% 0.28/0.50  thf(fact_842_power__numeral,axiom,
% 0.28/0.50      ! [K: num,L2: num] :
% 0.28/0.50        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_numeral
% 0.28/0.50  thf(fact_843_power__numeral,axiom,
% 0.28/0.50      ! [K: num,L2: num] :
% 0.28/0.50        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_numeral
% 0.28/0.50  thf(fact_844_power__numeral,axiom,
% 0.28/0.50      ! [K: num,L2: num] :
% 0.28/0.50        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_numeral
% 0.28/0.50  thf(fact_845_power__numeral,axiom,
% 0.28/0.50      ! [K: num,L2: num] :
% 0.28/0.50        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_numeral
% 0.28/0.50  thf(fact_846_power__numeral,axiom,
% 0.28/0.50      ! [K: num,L2: num] :
% 0.28/0.50        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 0.28/0.50        = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_numeral
% 0.28/0.50  thf(fact_847_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.28/0.50      ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.28/0.50        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.50       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.28/0.50         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 0.28/0.50           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % both_member_options_from_chilf_to_complete_tree
% 0.28/0.50  thf(fact_848_arith__geo__mean,axiom,
% 0.28/0.50      ! [U: real,X: real,Y: real] :
% 0.28/0.50        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.50          = ( times_times_real @ X @ Y ) )
% 0.28/0.50       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.50         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.50           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % arith_geo_mean
% 0.28/0.50  thf(fact_849_arith__geo__mean,axiom,
% 0.28/0.50      ! [U: rat,X: rat,Y: rat] :
% 0.28/0.50        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.50          = ( times_times_rat @ X @ Y ) )
% 0.28/0.50       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.50         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.50           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % arith_geo_mean
% 0.28/0.50  thf(fact_850_False,axiom,
% 0.28/0.50      ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 0.28/0.50     != none_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % False
% 0.28/0.50  thf(fact_851_valid__tree__deg__neq__0,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT] :
% 0.28/0.50        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % valid_tree_deg_neq_0
% 0.28/0.50  thf(fact_852_valid__0__not,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT] :
% 0.28/0.50        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % valid_0_not
% 0.28/0.50  thf(fact_853_deg__not__0,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % deg_not_0
% 0.28/0.50  thf(fact_854_maxbmo,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,X: nat] :
% 0.28/0.50        ( ( ( vEBT_vebt_maxt @ T )
% 0.28/0.50          = ( some_nat @ X ) )
% 0.28/0.50       => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 0.28/0.50  
% 0.28/0.50  % maxbmo
% 0.28/0.50  thf(fact_855_power__shift,axiom,
% 0.28/0.50      ! [X: nat,Y: nat,Z: nat] :
% 0.28/0.50        ( ( ( power_power_nat @ X @ Y )
% 0.28/0.50          = Z )
% 0.28/0.50        = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.28/0.50          = ( some_nat @ Z ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % power_shift
% 0.28/0.50  thf(fact_856_maxt__member,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ( ( vEBT_vebt_maxt @ T )
% 0.28/0.50            = ( some_nat @ Maxi ) )
% 0.28/0.50         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % maxt_member
% 0.28/0.50  thf(fact_857_zdiv__numeral__Bit0,axiom,
% 0.28/0.50      ! [V: num,W: num] :
% 0.28/0.50        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.28/0.50        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zdiv_numeral_Bit0
% 0.28/0.50  thf(fact_858_bot__nat__0_Onot__eq__extremum,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( A != zero_zero_nat )
% 0.28/0.50        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % bot_nat_0.not_eq_extremum
% 0.28/0.50  thf(fact_859_neq0__conv,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ( ( N != zero_zero_nat )
% 0.28/0.50        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % neq0_conv
% 0.28/0.50  thf(fact_860_less__nat__zero__code,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % less_nat_zero_code
% 0.28/0.50  thf(fact_861_bot__nat__0_Oextremum,axiom,
% 0.28/0.50      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.28/0.50  
% 0.28/0.50  % bot_nat_0.extremum
% 0.28/0.50  thf(fact_862_le0,axiom,
% 0.28/0.50      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.28/0.50  
% 0.28/0.50  % le0
% 0.28/0.50  thf(fact_863_add__is__0,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ( plus_plus_nat @ M @ N )
% 0.28/0.50          = zero_zero_nat )
% 0.28/0.50        = ( ( M = zero_zero_nat )
% 0.28/0.50          & ( N = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_is_0
% 0.28/0.50  thf(fact_864_Nat_Oadd__0__right,axiom,
% 0.28/0.50      ! [M: nat] :
% 0.28/0.50        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.28/0.50        = M ) ).
% 0.28/0.50  
% 0.28/0.50  % Nat.add_0_right
% 0.28/0.50  thf(fact_865_mod__mod__trivial,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.28/0.50        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_mod_trivial
% 0.28/0.50  thf(fact_866_mod__mod__trivial,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.28/0.50        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_mod_trivial
% 0.28/0.50  thf(fact_867_mod__mod__trivial,axiom,
% 0.28/0.50      ! [A: code_integer,B: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.28/0.50        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_mod_trivial
% 0.28/0.50  thf(fact_868_diff__self__eq__0,axiom,
% 0.28/0.50      ! [M: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ M @ M )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_self_eq_0
% 0.28/0.50  thf(fact_869_diff__0__eq__0,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_0_eq_0
% 0.28/0.50  thf(fact_870_mult__is__0,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ M @ N )
% 0.28/0.50          = zero_zero_nat )
% 0.28/0.50        = ( ( M = zero_zero_nat )
% 0.28/0.50          | ( N = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_is_0
% 0.28/0.50  thf(fact_871_mult__0__right,axiom,
% 0.28/0.50      ! [M: nat] :
% 0.28/0.50        ( ( times_times_nat @ M @ zero_zero_nat )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_0_right
% 0.28/0.50  thf(fact_872_mult__cancel1,axiom,
% 0.28/0.50      ! [K: nat,M: nat,N: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ K @ M )
% 0.28/0.50          = ( times_times_nat @ K @ N ) )
% 0.28/0.50        = ( ( M = N )
% 0.28/0.50          | ( K = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel1
% 0.28/0.50  thf(fact_873_mult__cancel2,axiom,
% 0.28/0.50      ! [M: nat,K: nat,N: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ M @ K )
% 0.28/0.50          = ( times_times_nat @ N @ K ) )
% 0.28/0.50        = ( ( M = N )
% 0.28/0.50          | ( K = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel2
% 0.28/0.50  thf(fact_874_not__real__square__gt__zero,axiom,
% 0.28/0.50      ! [X: real] :
% 0.28/0.50        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 0.28/0.50        = ( X = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % not_real_square_gt_zero
% 0.28/0.50  thf(fact_875_real__divide__square__eq,axiom,
% 0.28/0.50      ! [R: real,A: real] :
% 0.28/0.50        ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 0.28/0.50        = ( divide_divide_real @ A @ R ) ) ).
% 0.28/0.50  
% 0.28/0.50  % real_divide_square_eq
% 0.28/0.50  thf(fact_876_i0__less,axiom,
% 0.28/0.50      ! [N: extended_enat] :
% 0.28/0.50        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.28/0.50        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % i0_less
% 0.28/0.50  thf(fact_877_maxt__corr__help,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ( ( vEBT_vebt_maxt @ T )
% 0.28/0.50            = ( some_nat @ Maxi ) )
% 0.28/0.50         => ( ( vEBT_vebt_member @ T @ X )
% 0.28/0.50           => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % maxt_corr_help
% 0.28/0.50  thf(fact_878_maxt__corr,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ( ( vEBT_vebt_maxt @ T )
% 0.28/0.50            = ( some_nat @ X ) )
% 0.28/0.50         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % maxt_corr
% 0.28/0.50  thf(fact_879_maxt__sound,axiom,
% 0.28/0.50      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.50       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.28/0.50         => ( ( vEBT_vebt_maxt @ T )
% 0.28/0.50            = ( some_nat @ X ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % maxt_sound
% 0.28/0.50  thf(fact_880_mi__eq__ma__no__ch,axiom,
% 0.28/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.28/0.50       => ( ( Mi = Ma )
% 0.28/0.50         => ( ! [X4: vEBT_VEBT] :
% 0.28/0.50                ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.50               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 0.28/0.50            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mi_eq_ma_no_ch
% 0.28/0.50  thf(fact_881_le__zero__eq,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.28/0.50        = ( N = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_zero_eq
% 0.28/0.50  thf(fact_882_not__gr__zero,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.28/0.50        = ( N = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % not_gr_zero
% 0.28/0.50  thf(fact_883_mult__zero__left,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( times_times_complex @ zero_zero_complex @ A )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_left
% 0.28/0.50  thf(fact_884_mult__zero__left,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( times_times_real @ zero_zero_real @ A )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_left
% 0.28/0.50  thf(fact_885_mult__zero__left,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_left
% 0.28/0.50  thf(fact_886_mult__zero__left,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_left
% 0.28/0.50  thf(fact_887_mult__zero__left,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( times_times_int @ zero_zero_int @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_left
% 0.28/0.50  thf(fact_888_mult__zero__right,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( times_times_complex @ A @ zero_zero_complex )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_right
% 0.28/0.50  thf(fact_889_mult__zero__right,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( times_times_real @ A @ zero_zero_real )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_right
% 0.28/0.50  thf(fact_890_mult__zero__right,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_right
% 0.28/0.50  thf(fact_891_mult__zero__right,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_right
% 0.28/0.50  thf(fact_892_mult__zero__right,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( times_times_int @ A @ zero_zero_int )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_zero_right
% 0.28/0.50  thf(fact_893_mult__eq__0__iff,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( ( times_times_complex @ A @ B )
% 0.28/0.50          = zero_zero_complex )
% 0.28/0.50        = ( ( A = zero_zero_complex )
% 0.28/0.50          | ( B = zero_zero_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_eq_0_iff
% 0.28/0.50  thf(fact_894_mult__eq__0__iff,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ( times_times_real @ A @ B )
% 0.28/0.50          = zero_zero_real )
% 0.28/0.50        = ( ( A = zero_zero_real )
% 0.28/0.50          | ( B = zero_zero_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_eq_0_iff
% 0.28/0.50  thf(fact_895_mult__eq__0__iff,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ( times_times_rat @ A @ B )
% 0.28/0.50          = zero_zero_rat )
% 0.28/0.50        = ( ( A = zero_zero_rat )
% 0.28/0.50          | ( B = zero_zero_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_eq_0_iff
% 0.28/0.50  thf(fact_896_mult__eq__0__iff,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ A @ B )
% 0.28/0.50          = zero_zero_nat )
% 0.28/0.50        = ( ( A = zero_zero_nat )
% 0.28/0.50          | ( B = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_eq_0_iff
% 0.28/0.50  thf(fact_897_mult__eq__0__iff,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ( times_times_int @ A @ B )
% 0.28/0.50          = zero_zero_int )
% 0.28/0.50        = ( ( A = zero_zero_int )
% 0.28/0.50          | ( B = zero_zero_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_eq_0_iff
% 0.28/0.50  thf(fact_898_mult__cancel__left,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( ( times_times_complex @ C @ A )
% 0.28/0.50          = ( times_times_complex @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left
% 0.28/0.50  thf(fact_899_mult__cancel__left,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( ( times_times_real @ C @ A )
% 0.28/0.50          = ( times_times_real @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left
% 0.28/0.50  thf(fact_900_mult__cancel__left,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( ( times_times_rat @ C @ A )
% 0.28/0.50          = ( times_times_rat @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left
% 0.28/0.50  thf(fact_901_mult__cancel__left,axiom,
% 0.28/0.50      ! [C: nat,A: nat,B: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ C @ A )
% 0.28/0.50          = ( times_times_nat @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_nat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left
% 0.28/0.50  thf(fact_902_mult__cancel__left,axiom,
% 0.28/0.50      ! [C: int,A: int,B: int] :
% 0.28/0.50        ( ( ( times_times_int @ C @ A )
% 0.28/0.50          = ( times_times_int @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left
% 0.28/0.50  thf(fact_903_mult__cancel__right,axiom,
% 0.28/0.50      ! [A: complex,C: complex,B: complex] :
% 0.28/0.50        ( ( ( times_times_complex @ A @ C )
% 0.28/0.50          = ( times_times_complex @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right
% 0.28/0.50  thf(fact_904_mult__cancel__right,axiom,
% 0.28/0.50      ! [A: real,C: real,B: real] :
% 0.28/0.50        ( ( ( times_times_real @ A @ C )
% 0.28/0.50          = ( times_times_real @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right
% 0.28/0.50  thf(fact_905_mult__cancel__right,axiom,
% 0.28/0.50      ! [A: rat,C: rat,B: rat] :
% 0.28/0.50        ( ( ( times_times_rat @ A @ C )
% 0.28/0.50          = ( times_times_rat @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right
% 0.28/0.50  thf(fact_906_mult__cancel__right,axiom,
% 0.28/0.50      ! [A: nat,C: nat,B: nat] :
% 0.28/0.50        ( ( ( times_times_nat @ A @ C )
% 0.28/0.50          = ( times_times_nat @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_nat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right
% 0.28/0.50  thf(fact_907_mult__cancel__right,axiom,
% 0.28/0.50      ! [A: int,C: int,B: int] :
% 0.28/0.50        ( ( ( times_times_int @ A @ C )
% 0.28/0.50          = ( times_times_int @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right
% 0.28/0.50  thf(fact_908_add_Oright__neutral,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add.right_neutral
% 0.28/0.50  thf(fact_909_add_Oright__neutral,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add.right_neutral
% 0.28/0.50  thf(fact_910_add_Oright__neutral,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add.right_neutral
% 0.28/0.50  thf(fact_911_add_Oright__neutral,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add.right_neutral
% 0.28/0.50  thf(fact_912_add_Oright__neutral,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add.right_neutral
% 0.28/0.50  thf(fact_913_double__zero__sym,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( zero_zero_real
% 0.28/0.50          = ( plus_plus_real @ A @ A ) )
% 0.28/0.50        = ( A = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_zero_sym
% 0.28/0.50  thf(fact_914_double__zero__sym,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( zero_zero_rat
% 0.28/0.50          = ( plus_plus_rat @ A @ A ) )
% 0.28/0.50        = ( A = zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_zero_sym
% 0.28/0.50  thf(fact_915_double__zero__sym,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( zero_zero_int
% 0.28/0.50          = ( plus_plus_int @ A @ A ) )
% 0.28/0.50        = ( A = zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_zero_sym
% 0.28/0.50  thf(fact_916_add__cancel__left__left,axiom,
% 0.28/0.50      ! [B: complex,A: complex] :
% 0.28/0.50        ( ( ( plus_plus_complex @ B @ A )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_complex ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_left
% 0.28/0.50  thf(fact_917_add__cancel__left__left,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( ( plus_plus_real @ B @ A )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_left
% 0.28/0.50  thf(fact_918_add__cancel__left__left,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( ( plus_plus_rat @ B @ A )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_left
% 0.28/0.50  thf(fact_919_add__cancel__left__left,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ( plus_plus_nat @ B @ A )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_left
% 0.28/0.50  thf(fact_920_add__cancel__left__left,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( ( plus_plus_int @ B @ A )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_left
% 0.28/0.50  thf(fact_921_add__cancel__left__right,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( ( plus_plus_complex @ A @ B )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_complex ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_right
% 0.28/0.50  thf(fact_922_add__cancel__left__right,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ( plus_plus_real @ A @ B )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_right
% 0.28/0.50  thf(fact_923_add__cancel__left__right,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ( plus_plus_rat @ A @ B )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_right
% 0.28/0.50  thf(fact_924_add__cancel__left__right,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ( plus_plus_nat @ A @ B )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_right
% 0.28/0.50  thf(fact_925_add__cancel__left__right,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ( plus_plus_int @ A @ B )
% 0.28/0.50          = A )
% 0.28/0.50        = ( B = zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_left_right
% 0.28/0.50  thf(fact_926_add__cancel__right__left,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_complex @ B @ A ) )
% 0.28/0.50        = ( B = zero_zero_complex ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_left
% 0.28/0.50  thf(fact_927_add__cancel__right__left,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_real @ B @ A ) )
% 0.28/0.50        = ( B = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_left
% 0.28/0.50  thf(fact_928_add__cancel__right__left,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_rat @ B @ A ) )
% 0.28/0.50        = ( B = zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_left
% 0.28/0.50  thf(fact_929_add__cancel__right__left,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_nat @ B @ A ) )
% 0.28/0.50        = ( B = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_left
% 0.28/0.50  thf(fact_930_add__cancel__right__left,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_int @ B @ A ) )
% 0.28/0.50        = ( B = zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_left
% 0.28/0.50  thf(fact_931_add__cancel__right__right,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_complex @ A @ B ) )
% 0.28/0.50        = ( B = zero_zero_complex ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_right
% 0.28/0.50  thf(fact_932_add__cancel__right__right,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_real @ A @ B ) )
% 0.28/0.50        = ( B = zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_right
% 0.28/0.50  thf(fact_933_add__cancel__right__right,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_rat @ A @ B ) )
% 0.28/0.50        = ( B = zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_right
% 0.28/0.50  thf(fact_934_add__cancel__right__right,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_nat @ A @ B ) )
% 0.28/0.50        = ( B = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_right
% 0.28/0.50  thf(fact_935_add__cancel__right__right,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( A
% 0.28/0.50          = ( plus_plus_int @ A @ B ) )
% 0.28/0.50        = ( B = zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_cancel_right_right
% 0.28/0.50  thf(fact_936_add__eq__0__iff__both__eq__0,axiom,
% 0.28/0.50      ! [X: nat,Y: nat] :
% 0.28/0.50        ( ( ( plus_plus_nat @ X @ Y )
% 0.28/0.50          = zero_zero_nat )
% 0.28/0.50        = ( ( X = zero_zero_nat )
% 0.28/0.50          & ( Y = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_eq_0_iff_both_eq_0
% 0.28/0.50  thf(fact_937_zero__eq__add__iff__both__eq__0,axiom,
% 0.28/0.50      ! [X: nat,Y: nat] :
% 0.28/0.50        ( ( zero_zero_nat
% 0.28/0.50          = ( plus_plus_nat @ X @ Y ) )
% 0.28/0.50        = ( ( X = zero_zero_nat )
% 0.28/0.50          & ( Y = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_eq_add_iff_both_eq_0
% 0.28/0.50  thf(fact_938_add__0,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_0
% 0.28/0.50  thf(fact_939_add__0,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_0
% 0.28/0.50  thf(fact_940_add__0,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_0
% 0.28/0.50  thf(fact_941_add__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_0
% 0.28/0.50  thf(fact_942_add__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_0
% 0.28/0.50  thf(fact_943_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( minus_minus_complex @ A @ A )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.50  thf(fact_944_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( minus_minus_real @ A @ A )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.50  thf(fact_945_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ A @ A )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.50  thf(fact_946_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ A @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.50  thf(fact_947_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( minus_minus_int @ A @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.50  thf(fact_948_diff__zero,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_zero
% 0.28/0.50  thf(fact_949_diff__zero,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_zero
% 0.28/0.50  thf(fact_950_diff__zero,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_zero
% 0.28/0.50  thf(fact_951_diff__zero,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_zero
% 0.28/0.50  thf(fact_952_diff__zero,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_zero
% 0.28/0.50  thf(fact_953_zero__diff,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_diff
% 0.28/0.50  thf(fact_954_diff__0__right,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_0_right
% 0.28/0.50  thf(fact_955_diff__0__right,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( minus_minus_real @ A @ zero_zero_real )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_0_right
% 0.28/0.50  thf(fact_956_diff__0__right,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_0_right
% 0.28/0.50  thf(fact_957_diff__0__right,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_0_right
% 0.28/0.50  thf(fact_958_diff__self,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( minus_minus_complex @ A @ A )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_self
% 0.28/0.50  thf(fact_959_diff__self,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( minus_minus_real @ A @ A )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_self
% 0.28/0.50  thf(fact_960_diff__self,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ A @ A )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_self
% 0.28/0.50  thf(fact_961_diff__self,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( minus_minus_int @ A @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_self
% 0.28/0.50  thf(fact_962_div__0,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % div_0
% 0.28/0.50  thf(fact_963_div__0,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( divide_divide_real @ zero_zero_real @ A )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % div_0
% 0.28/0.50  thf(fact_964_div__0,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % div_0
% 0.28/0.50  thf(fact_965_div__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % div_0
% 0.28/0.50  thf(fact_966_div__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % div_0
% 0.28/0.50  thf(fact_967_divide__eq__0__iff,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.28/0.50          = zero_zero_complex )
% 0.28/0.50        = ( ( A = zero_zero_complex )
% 0.28/0.50          | ( B = zero_zero_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_eq_0_iff
% 0.28/0.50  thf(fact_968_divide__eq__0__iff,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ( divide_divide_real @ A @ B )
% 0.28/0.50          = zero_zero_real )
% 0.28/0.50        = ( ( A = zero_zero_real )
% 0.28/0.50          | ( B = zero_zero_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_eq_0_iff
% 0.28/0.50  thf(fact_969_divide__eq__0__iff,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ( divide_divide_rat @ A @ B )
% 0.28/0.50          = zero_zero_rat )
% 0.28/0.50        = ( ( A = zero_zero_rat )
% 0.28/0.50          | ( B = zero_zero_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_eq_0_iff
% 0.28/0.50  thf(fact_970_div__by__0,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_0
% 0.28/0.50  thf(fact_971_div__by__0,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_0
% 0.28/0.50  thf(fact_972_div__by__0,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_0
% 0.28/0.50  thf(fact_973_div__by__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_0
% 0.28/0.50  thf(fact_974_div__by__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % div_by_0
% 0.28/0.50  thf(fact_975_divide__cancel__left,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( ( divide1717551699836669952omplex @ C @ A )
% 0.28/0.50          = ( divide1717551699836669952omplex @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_left
% 0.28/0.50  thf(fact_976_divide__cancel__left,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( ( divide_divide_real @ C @ A )
% 0.28/0.50          = ( divide_divide_real @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_left
% 0.28/0.50  thf(fact_977_divide__cancel__left,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( ( divide_divide_rat @ C @ A )
% 0.28/0.50          = ( divide_divide_rat @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_left
% 0.28/0.50  thf(fact_978_divide__cancel__right,axiom,
% 0.28/0.50      ! [A: complex,C: complex,B: complex] :
% 0.28/0.50        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.28/0.50          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_right
% 0.28/0.50  thf(fact_979_divide__cancel__right,axiom,
% 0.28/0.50      ! [A: real,C: real,B: real] :
% 0.28/0.50        ( ( ( divide_divide_real @ A @ C )
% 0.28/0.50          = ( divide_divide_real @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_right
% 0.28/0.50  thf(fact_980_divide__cancel__right,axiom,
% 0.28/0.50      ! [A: rat,C: rat,B: rat] :
% 0.28/0.50        ( ( ( divide_divide_rat @ A @ C )
% 0.28/0.50          = ( divide_divide_rat @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_cancel_right
% 0.28/0.50  thf(fact_981_bits__div__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_0
% 0.28/0.50  thf(fact_982_bits__div__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ zero_zero_int @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_0
% 0.28/0.50  thf(fact_983_bits__div__by__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_by_0
% 0.28/0.50  thf(fact_984_bits__div__by__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( divide_divide_int @ A @ zero_zero_int )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_div_by_0
% 0.28/0.50  thf(fact_985_division__ring__divide__zero,axiom,
% 0.28/0.50      ! [A: complex] :
% 0.28/0.50        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.28/0.50        = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % division_ring_divide_zero
% 0.28/0.50  thf(fact_986_division__ring__divide__zero,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( divide_divide_real @ A @ zero_zero_real )
% 0.28/0.50        = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % division_ring_divide_zero
% 0.28/0.50  thf(fact_987_division__ring__divide__zero,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.28/0.50        = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % division_ring_divide_zero
% 0.28/0.50  thf(fact_988_half__nonnegative__int__iff,axiom,
% 0.28/0.50      ! [K: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.28/0.50        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.28/0.50  
% 0.28/0.50  % half_nonnegative_int_iff
% 0.28/0.50  thf(fact_989_half__negative__int__iff,axiom,
% 0.28/0.50      ! [K: int] :
% 0.28/0.50        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.28/0.50        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % half_negative_int_iff
% 0.28/0.50  thf(fact_990_add__diff__cancel,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel
% 0.28/0.50  thf(fact_991_add__diff__cancel,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel
% 0.28/0.50  thf(fact_992_add__diff__cancel,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel
% 0.28/0.50  thf(fact_993_diff__add__cancel,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_add_cancel
% 0.28/0.50  thf(fact_994_diff__add__cancel,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_add_cancel
% 0.28/0.50  thf(fact_995_diff__add__cancel,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_add_cancel
% 0.28/0.50  thf(fact_996_add__diff__cancel__left,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.28/0.50        = ( minus_minus_real @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left
% 0.28/0.50  thf(fact_997_add__diff__cancel__left,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.28/0.50        = ( minus_minus_rat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left
% 0.28/0.50  thf(fact_998_add__diff__cancel__left,axiom,
% 0.28/0.50      ! [C: nat,A: nat,B: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.28/0.50        = ( minus_minus_nat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left
% 0.28/0.50  thf(fact_999_add__diff__cancel__left,axiom,
% 0.28/0.50      ! [C: int,A: int,B: int] :
% 0.28/0.50        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.28/0.50        = ( minus_minus_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left
% 0.28/0.50  thf(fact_1000_add__diff__cancel__left_H,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.28/0.50        = B ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left'
% 0.28/0.50  thf(fact_1001_add__diff__cancel__left_H,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.28/0.50        = B ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left'
% 0.28/0.50  thf(fact_1002_add__diff__cancel__left_H,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.28/0.50        = B ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left'
% 0.28/0.50  thf(fact_1003_add__diff__cancel__left_H,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.28/0.50        = B ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_left'
% 0.28/0.50  thf(fact_1004_add__diff__cancel__right,axiom,
% 0.28/0.50      ! [A: real,C: real,B: real] :
% 0.28/0.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.28/0.50        = ( minus_minus_real @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right
% 0.28/0.50  thf(fact_1005_add__diff__cancel__right,axiom,
% 0.28/0.50      ! [A: rat,C: rat,B: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.50        = ( minus_minus_rat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right
% 0.28/0.50  thf(fact_1006_add__diff__cancel__right,axiom,
% 0.28/0.50      ! [A: nat,C: nat,B: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.28/0.50        = ( minus_minus_nat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right
% 0.28/0.50  thf(fact_1007_add__diff__cancel__right,axiom,
% 0.28/0.50      ! [A: int,C: int,B: int] :
% 0.28/0.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.28/0.50        = ( minus_minus_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right
% 0.28/0.50  thf(fact_1008_add__diff__cancel__right_H,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right'
% 0.28/0.50  thf(fact_1009_add__diff__cancel__right_H,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right'
% 0.28/0.50  thf(fact_1010_add__diff__cancel__right_H,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right'
% 0.28/0.50  thf(fact_1011_add__diff__cancel__right_H,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % add_diff_cancel_right'
% 0.28/0.50  thf(fact_1012_bits__mod__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_mod_0
% 0.28/0.50  thf(fact_1013_bits__mod__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_mod_0
% 0.28/0.50  thf(fact_1014_bits__mod__0,axiom,
% 0.28/0.50      ! [A: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.50        = zero_z3403309356797280102nteger ) ).
% 0.28/0.50  
% 0.28/0.50  % bits_mod_0
% 0.28/0.50  thf(fact_1015_mod__self,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ A @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_self
% 0.28/0.50  thf(fact_1016_mod__self,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ A @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_self
% 0.28/0.50  thf(fact_1017_mod__self,axiom,
% 0.28/0.50      ! [A: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ A @ A )
% 0.28/0.50        = zero_z3403309356797280102nteger ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_self
% 0.28/0.50  thf(fact_1018_mod__by__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_by_0
% 0.28/0.50  thf(fact_1019_mod__by__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_by_0
% 0.28/0.50  thf(fact_1020_mod__by__0,axiom,
% 0.28/0.50      ! [A: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 0.28/0.50        = A ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_by_0
% 0.28/0.50  thf(fact_1021_mod__0,axiom,
% 0.28/0.50      ! [A: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_0
% 0.28/0.50  thf(fact_1022_mod__0,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.28/0.50        = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_0
% 0.28/0.50  thf(fact_1023_mod__0,axiom,
% 0.28/0.50      ! [A: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.50        = zero_z3403309356797280102nteger ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_0
% 0.28/0.50  thf(fact_1024_insert__simp__mima,axiom,
% 0.28/0.50      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.50        ( ( ( X = Mi )
% 0.28/0.50          | ( X = Ma ) )
% 0.28/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.50         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.50            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % insert_simp_mima
% 0.28/0.50  thf(fact_1025_mod__add__self1,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.28/0.50        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self1
% 0.28/0.50  thf(fact_1026_mod__add__self1,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.28/0.50        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self1
% 0.28/0.50  thf(fact_1027_mod__add__self1,axiom,
% 0.28/0.50      ! [B: code_integer,A: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.28/0.50        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self1
% 0.28/0.50  thf(fact_1028_mod__add__self2,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.28/0.50        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self2
% 0.28/0.50  thf(fact_1029_mod__add__self2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.50        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self2
% 0.28/0.50  thf(fact_1030_mod__add__self2,axiom,
% 0.28/0.50      ! [A: code_integer,B: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.28/0.50        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_add_self2
% 0.28/0.50  thf(fact_1031_minus__mod__self2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.28/0.50        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % minus_mod_self2
% 0.28/0.50  thf(fact_1032_minus__mod__self2,axiom,
% 0.28/0.50      ! [A: code_integer,B: code_integer] :
% 0.28/0.50        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 0.28/0.50        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % minus_mod_self2
% 0.28/0.50  thf(fact_1033_add__gr__0,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.50        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.50          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_gr_0
% 0.28/0.50  thf(fact_1034_zero__less__diff,axiom,
% 0.28/0.50      ! [N: nat,M: nat] :
% 0.28/0.50        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.28/0.50        = ( ord_less_nat @ M @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_less_diff
% 0.28/0.50  thf(fact_1035_mult__less__cancel2,axiom,
% 0.28/0.50      ! [M: nat,K: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.28/0.50        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.50          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_less_cancel2
% 0.28/0.50  thf(fact_1036_nat__0__less__mult__iff,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.28/0.50        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.50          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nat_0_less_mult_iff
% 0.28/0.50  thf(fact_1037_nat__mult__less__cancel__disj,axiom,
% 0.28/0.50      ! [K: nat,M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.50        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.50          & ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nat_mult_less_cancel_disj
% 0.28/0.50  thf(fact_1038_div__less,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ M @ N )
% 0.28/0.50       => ( ( divide_divide_nat @ M @ N )
% 0.28/0.50          = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_less
% 0.28/0.50  thf(fact_1039_diff__is__0__eq_H,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.50       => ( ( minus_minus_nat @ M @ N )
% 0.28/0.50          = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_is_0_eq'
% 0.28/0.50  thf(fact_1040_diff__is__0__eq,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ( minus_minus_nat @ M @ N )
% 0.28/0.50          = zero_zero_nat )
% 0.28/0.50        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_is_0_eq
% 0.28/0.50  thf(fact_1041_diff__diff__cancel,axiom,
% 0.28/0.50      ! [I: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ I @ N )
% 0.28/0.50       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.28/0.50          = I ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_diff_cancel
% 0.28/0.50  thf(fact_1042_less__one,axiom,
% 0.28/0.50      ! [N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ N @ one_one_nat )
% 0.28/0.50        = ( N = zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_one
% 0.28/0.50  thf(fact_1043_diff__diff__left,axiom,
% 0.28/0.50      ! [I: nat,J: nat,K: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.28/0.50        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_diff_left
% 0.28/0.50  thf(fact_1044_nat__zero__less__power__iff,axiom,
% 0.28/0.50      ! [X: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.28/0.50        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.28/0.50          | ( N = zero_zero_nat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nat_zero_less_power_iff
% 0.28/0.50  thf(fact_1045_nat__mult__div__cancel__disj,axiom,
% 0.28/0.50      ! [K: nat,M: nat,N: nat] :
% 0.28/0.50        ( ( ( K = zero_zero_nat )
% 0.28/0.50         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.50            = zero_zero_nat ) )
% 0.28/0.50        & ( ( K != zero_zero_nat )
% 0.28/0.50         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.50            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nat_mult_div_cancel_disj
% 0.28/0.50  thf(fact_1046_mod__less,axiom,
% 0.28/0.50      ! [M: nat,N: nat] :
% 0.28/0.50        ( ( ord_less_nat @ M @ N )
% 0.28/0.50       => ( ( modulo_modulo_nat @ M @ N )
% 0.28/0.50          = M ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mod_less
% 0.28/0.50  thf(fact_1047_delt__out__of__range,axiom,
% 0.28/0.50      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.50        ( ( ( ord_less_nat @ X @ Mi )
% 0.28/0.50          | ( ord_less_nat @ Ma @ X ) )
% 0.28/0.50       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.50         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.50            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % delt_out_of_range
% 0.28/0.50  thf(fact_1048_dbl__simps_I2_J,axiom,
% 0.28/0.50      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 0.28/0.50      = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(2)
% 0.28/0.50  thf(fact_1049_dbl__simps_I2_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.28/0.50      = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(2)
% 0.28/0.50  thf(fact_1050_dbl__simps_I2_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.28/0.50      = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(2)
% 0.28/0.50  thf(fact_1051_dbl__simps_I2_J,axiom,
% 0.28/0.50      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.28/0.50      = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % dbl_simps(2)
% 0.28/0.50  thf(fact_1052__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.28/0.50      ~ ! [Maxs: nat] :
% 0.28/0.50          ( ( some_nat @ Maxs )
% 0.28/0.50         != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % \<open>\<And>thesis. (\<And>maxs. Some maxs = vebt_maxt (vebt_delete summary (high x n)) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.28/0.50  thf(fact_1053_mi__ma__2__deg,axiom,
% 0.28/0.50      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.28/0.50        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.50       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.28/0.50          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mi_ma_2_deg
% 0.28/0.50  thf(fact_1054_add__le__same__cancel1,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel1
% 0.28/0.50  thf(fact_1055_add__le__same__cancel1,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel1
% 0.28/0.50  thf(fact_1056_add__le__same__cancel1,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel1
% 0.28/0.50  thf(fact_1057_add__le__same__cancel1,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel1
% 0.28/0.50  thf(fact_1058_add__le__same__cancel2,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel2
% 0.28/0.50  thf(fact_1059_add__le__same__cancel2,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel2
% 0.28/0.50  thf(fact_1060_add__le__same__cancel2,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel2
% 0.28/0.50  thf(fact_1061_add__le__same__cancel2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_le_same_cancel2
% 0.28/0.50  thf(fact_1062_le__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel1
% 0.28/0.50  thf(fact_1063_le__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel1
% 0.28/0.50  thf(fact_1064_le__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel1
% 0.28/0.50  thf(fact_1065_le__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel1
% 0.28/0.50  thf(fact_1066_le__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.28/0.50        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel2
% 0.28/0.50  thf(fact_1067_le__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.28/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel2
% 0.28/0.50  thf(fact_1068_le__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.28/0.50        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel2
% 0.28/0.50  thf(fact_1069_le__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.28/0.50        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_same_cancel2
% 0.28/0.50  thf(fact_1070_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.28/0.50        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.28/0.50  thf(fact_1071_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.28/0.50        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.28/0.50  thf(fact_1072_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.28/0.50        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_le_zero_iff_single_add_le_zero
% 0.28/0.50  thf(fact_1073_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.28/0.50        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.28/0.50  thf(fact_1074_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.28/0.50        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.28/0.50  thf(fact_1075_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.28/0.50        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_le_double_add_iff_zero_le_single_add
% 0.28/0.50  thf(fact_1076_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.28/0.50        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_less_double_add_iff_zero_less_single_add
% 0.28/0.50  thf(fact_1077_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.28/0.50        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_less_double_add_iff_zero_less_single_add
% 0.28/0.50  thf(fact_1078_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.28/0.50        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % zero_less_double_add_iff_zero_less_single_add
% 0.28/0.50  thf(fact_1079_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.28/0.50      ! [A: real] :
% 0.28/0.50        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.28/0.50        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_less_zero_iff_single_add_less_zero
% 0.28/0.50  thf(fact_1080_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.28/0.50      ! [A: rat] :
% 0.28/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.28/0.50        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_less_zero_iff_single_add_less_zero
% 0.28/0.50  thf(fact_1081_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.28/0.50      ! [A: int] :
% 0.28/0.50        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.28/0.50        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % double_add_less_zero_iff_single_add_less_zero
% 0.28/0.50  thf(fact_1082_less__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.28/0.50        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel2
% 0.28/0.50  thf(fact_1083_less__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.28/0.50        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel2
% 0.28/0.50  thf(fact_1084_less__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.28/0.50        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel2
% 0.28/0.50  thf(fact_1085_less__add__same__cancel2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.28/0.50        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel2
% 0.28/0.50  thf(fact_1086_less__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.28/0.50        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel1
% 0.28/0.50  thf(fact_1087_less__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.28/0.50        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel1
% 0.28/0.50  thf(fact_1088_less__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.28/0.50        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel1
% 0.28/0.50  thf(fact_1089_less__add__same__cancel1,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.28/0.50        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % less_add_same_cancel1
% 0.28/0.50  thf(fact_1090_add__less__same__cancel2,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel2
% 0.28/0.50  thf(fact_1091_add__less__same__cancel2,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel2
% 0.28/0.50  thf(fact_1092_add__less__same__cancel2,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel2
% 0.28/0.50  thf(fact_1093_add__less__same__cancel2,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.50        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel2
% 0.28/0.50  thf(fact_1094_add__less__same__cancel1,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel1
% 0.28/0.50  thf(fact_1095_add__less__same__cancel1,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel1
% 0.28/0.50  thf(fact_1096_add__less__same__cancel1,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel1
% 0.28/0.50  thf(fact_1097_add__less__same__cancel1,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.28/0.50        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.28/0.50  
% 0.28/0.50  % add_less_same_cancel1
% 0.28/0.50  thf(fact_1098_diff__ge__0__iff__ge,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_real @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_ge_0_iff_ge
% 0.28/0.50  thf(fact_1099_diff__ge__0__iff__ge,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_ge_0_iff_ge
% 0.28/0.50  thf(fact_1100_diff__ge__0__iff__ge,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.28/0.50        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_ge_0_iff_ge
% 0.28/0.50  thf(fact_1101_diff__gt__0__iff__gt,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.28/0.50        = ( ord_less_real @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_gt_0_iff_gt
% 0.28/0.50  thf(fact_1102_diff__gt__0__iff__gt,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.28/0.50        = ( ord_less_rat @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_gt_0_iff_gt
% 0.28/0.50  thf(fact_1103_diff__gt__0__iff__gt,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.28/0.50        = ( ord_less_int @ B @ A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_gt_0_iff_gt
% 0.28/0.50  thf(fact_1104_sum__squares__eq__zero__iff,axiom,
% 0.28/0.50      ! [X: real,Y: real] :
% 0.28/0.50        ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.28/0.50          = zero_zero_real )
% 0.28/0.50        = ( ( X = zero_zero_real )
% 0.28/0.50          & ( Y = zero_zero_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % sum_squares_eq_zero_iff
% 0.28/0.50  thf(fact_1105_sum__squares__eq__zero__iff,axiom,
% 0.28/0.50      ! [X: rat,Y: rat] :
% 0.28/0.50        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.28/0.50          = zero_zero_rat )
% 0.28/0.50        = ( ( X = zero_zero_rat )
% 0.28/0.50          & ( Y = zero_zero_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % sum_squares_eq_zero_iff
% 0.28/0.50  thf(fact_1106_sum__squares__eq__zero__iff,axiom,
% 0.28/0.50      ! [X: int,Y: int] :
% 0.28/0.50        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.28/0.50          = zero_zero_int )
% 0.28/0.50        = ( ( X = zero_zero_int )
% 0.28/0.50          & ( Y = zero_zero_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % sum_squares_eq_zero_iff
% 0.28/0.50  thf(fact_1107_mult__cancel__left1,axiom,
% 0.28/0.50      ! [C: complex,B: complex] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_complex @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( B = one_one_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left1
% 0.28/0.50  thf(fact_1108_mult__cancel__left1,axiom,
% 0.28/0.50      ! [C: real,B: real] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_real @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( B = one_one_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left1
% 0.28/0.50  thf(fact_1109_mult__cancel__left1,axiom,
% 0.28/0.50      ! [C: rat,B: rat] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_rat @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( B = one_one_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left1
% 0.28/0.50  thf(fact_1110_mult__cancel__left1,axiom,
% 0.28/0.50      ! [C: int,B: int] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_int @ C @ B ) )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( B = one_one_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left1
% 0.28/0.50  thf(fact_1111_mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: complex,A: complex] :
% 0.28/0.50        ( ( ( times_times_complex @ C @ A )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = one_one_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left2
% 0.28/0.50  thf(fact_1112_mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: real,A: real] :
% 0.28/0.50        ( ( ( times_times_real @ C @ A )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = one_one_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left2
% 0.28/0.50  thf(fact_1113_mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: rat,A: rat] :
% 0.28/0.50        ( ( ( times_times_rat @ C @ A )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = one_one_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left2
% 0.28/0.50  thf(fact_1114_mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: int,A: int] :
% 0.28/0.50        ( ( ( times_times_int @ C @ A )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( A = one_one_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_left2
% 0.28/0.50  thf(fact_1115_mult__cancel__right1,axiom,
% 0.28/0.50      ! [C: complex,B: complex] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_complex @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( B = one_one_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right1
% 0.28/0.50  thf(fact_1116_mult__cancel__right1,axiom,
% 0.28/0.50      ! [C: real,B: real] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_real @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( B = one_one_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right1
% 0.28/0.50  thf(fact_1117_mult__cancel__right1,axiom,
% 0.28/0.50      ! [C: rat,B: rat] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_rat @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( B = one_one_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right1
% 0.28/0.50  thf(fact_1118_mult__cancel__right1,axiom,
% 0.28/0.50      ! [C: int,B: int] :
% 0.28/0.50        ( ( C
% 0.28/0.50          = ( times_times_int @ B @ C ) )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( B = one_one_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right1
% 0.28/0.50  thf(fact_1119_mult__cancel__right2,axiom,
% 0.28/0.50      ! [A: complex,C: complex] :
% 0.28/0.50        ( ( ( times_times_complex @ A @ C )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_complex )
% 0.28/0.50          | ( A = one_one_complex ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right2
% 0.28/0.50  thf(fact_1120_mult__cancel__right2,axiom,
% 0.28/0.50      ! [A: real,C: real] :
% 0.28/0.50        ( ( ( times_times_real @ A @ C )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_real )
% 0.28/0.50          | ( A = one_one_real ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right2
% 0.28/0.50  thf(fact_1121_mult__cancel__right2,axiom,
% 0.28/0.50      ! [A: rat,C: rat] :
% 0.28/0.50        ( ( ( times_times_rat @ A @ C )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_rat )
% 0.28/0.50          | ( A = one_one_rat ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right2
% 0.28/0.50  thf(fact_1122_mult__cancel__right2,axiom,
% 0.28/0.50      ! [A: int,C: int] :
% 0.28/0.50        ( ( ( times_times_int @ A @ C )
% 0.28/0.50          = C )
% 0.28/0.50        = ( ( C = zero_zero_int )
% 0.28/0.50          | ( A = one_one_int ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_cancel_right2
% 0.28/0.50  thf(fact_1123_mult__divide__mult__cancel__left__if,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( ( C = zero_zero_complex )
% 0.28/0.50         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.28/0.50            = zero_zero_complex ) )
% 0.28/0.50        & ( ( C != zero_zero_complex )
% 0.28/0.50         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.28/0.50            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_divide_mult_cancel_left_if
% 0.28/0.50  thf(fact_1124_mult__divide__mult__cancel__left__if,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( ( C = zero_zero_real )
% 0.28/0.50         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.50            = zero_zero_real ) )
% 0.28/0.50        & ( ( C != zero_zero_real )
% 0.28/0.50         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.50            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_divide_mult_cancel_left_if
% 0.28/0.50  thf(fact_1125_mult__divide__mult__cancel__left__if,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( ( C = zero_zero_rat )
% 0.28/0.50         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.50            = zero_zero_rat ) )
% 0.28/0.50        & ( ( C != zero_zero_rat )
% 0.28/0.50         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.50            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % mult_divide_mult_cancel_left_if
% 0.28/0.50  thf(fact_1126_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( C != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.28/0.50          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left
% 0.28/0.50  thf(fact_1127_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( C != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.50          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left
% 0.28/0.50  thf(fact_1128_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( C != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.50          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left
% 0.28/0.50  thf(fact_1129_nonzero__mult__div__cancel__left,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( A != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.28/0.50          = B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_left
% 0.28/0.50  thf(fact_1130_nonzero__mult__div__cancel__left,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( A != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.28/0.50          = B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_left
% 0.28/0.50  thf(fact_1131_nonzero__mult__div__cancel__left,axiom,
% 0.28/0.50      ! [A: rat,B: rat] :
% 0.28/0.50        ( ( A != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.28/0.50          = B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_left
% 0.28/0.50  thf(fact_1132_nonzero__mult__div__cancel__left,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( A != zero_zero_nat )
% 0.28/0.50       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.28/0.50          = B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_left
% 0.28/0.50  thf(fact_1133_nonzero__mult__div__cancel__left,axiom,
% 0.28/0.50      ! [A: int,B: int] :
% 0.28/0.50        ( ( A != zero_zero_int )
% 0.28/0.50       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.28/0.50          = B ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_left
% 0.28/0.50  thf(fact_1134_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( C != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 0.28/0.50          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left2
% 0.28/0.50  thf(fact_1135_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( C != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 0.28/0.50          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left2
% 0.28/0.50  thf(fact_1136_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( C != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.50          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_left2
% 0.28/0.50  thf(fact_1137_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( C != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.28/0.50          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right
% 0.28/0.50  thf(fact_1138_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( C != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.50          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right
% 0.28/0.50  thf(fact_1139_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( C != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.50          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right
% 0.28/0.50  thf(fact_1140_nonzero__mult__div__cancel__right,axiom,
% 0.28/0.50      ! [B: complex,A: complex] :
% 0.28/0.50        ( ( B != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_right
% 0.28/0.50  thf(fact_1141_nonzero__mult__div__cancel__right,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( B != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_right
% 0.28/0.50  thf(fact_1142_nonzero__mult__div__cancel__right,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( B != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_right
% 0.28/0.50  thf(fact_1143_nonzero__mult__div__cancel__right,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( B != zero_zero_nat )
% 0.28/0.50       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_right
% 0.28/0.50  thf(fact_1144_nonzero__mult__div__cancel__right,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( B != zero_zero_int )
% 0.28/0.50       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_div_cancel_right
% 0.28/0.50  thf(fact_1145_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.28/0.50      ! [C: complex,A: complex,B: complex] :
% 0.28/0.50        ( ( C != zero_zero_complex )
% 0.28/0.50       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 0.28/0.50          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right2
% 0.28/0.50  thf(fact_1146_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.28/0.50      ! [C: real,A: real,B: real] :
% 0.28/0.50        ( ( C != zero_zero_real )
% 0.28/0.50       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 0.28/0.50          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right2
% 0.28/0.50  thf(fact_1147_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.28/0.50      ! [C: rat,A: rat,B: rat] :
% 0.28/0.50        ( ( C != zero_zero_rat )
% 0.28/0.50       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.50          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % nonzero_mult_divide_mult_cancel_right2
% 0.28/0.50  thf(fact_1148_div__mult__mult1,axiom,
% 0.28/0.50      ! [C: nat,A: nat,B: nat] :
% 0.28/0.50        ( ( C != zero_zero_nat )
% 0.28/0.50       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.28/0.50          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult1
% 0.28/0.50  thf(fact_1149_div__mult__mult1,axiom,
% 0.28/0.50      ! [C: int,A: int,B: int] :
% 0.28/0.50        ( ( C != zero_zero_int )
% 0.28/0.50       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.50          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult1
% 0.28/0.50  thf(fact_1150_div__mult__mult2,axiom,
% 0.28/0.50      ! [C: nat,A: nat,B: nat] :
% 0.28/0.50        ( ( C != zero_zero_nat )
% 0.28/0.50       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.28/0.50          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult2
% 0.28/0.50  thf(fact_1151_div__mult__mult2,axiom,
% 0.28/0.50      ! [C: int,A: int,B: int] :
% 0.28/0.50        ( ( C != zero_zero_int )
% 0.28/0.50       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.50          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult2
% 0.28/0.50  thf(fact_1152_div__mult__mult1__if,axiom,
% 0.28/0.50      ! [C: nat,A: nat,B: nat] :
% 0.28/0.50        ( ( ( C = zero_zero_nat )
% 0.28/0.50         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.28/0.50            = zero_zero_nat ) )
% 0.28/0.50        & ( ( C != zero_zero_nat )
% 0.28/0.50         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.28/0.50            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult1_if
% 0.28/0.50  thf(fact_1153_div__mult__mult1__if,axiom,
% 0.28/0.50      ! [C: int,A: int,B: int] :
% 0.28/0.50        ( ( ( C = zero_zero_int )
% 0.28/0.50         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.50            = zero_zero_int ) )
% 0.28/0.50        & ( ( C != zero_zero_int )
% 0.28/0.50         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.50            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % div_mult_mult1_if
% 0.28/0.50  thf(fact_1154_le__add__diff__inverse,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.50       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse
% 0.28/0.50  thf(fact_1155_le__add__diff__inverse,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.50       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse
% 0.28/0.50  thf(fact_1156_le__add__diff__inverse,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.50       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse
% 0.28/0.50  thf(fact_1157_le__add__diff__inverse,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.50       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse
% 0.28/0.50  thf(fact_1158_le__add__diff__inverse2,axiom,
% 0.28/0.50      ! [B: real,A: real] :
% 0.28/0.50        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.50       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse2
% 0.28/0.50  thf(fact_1159_le__add__diff__inverse2,axiom,
% 0.28/0.50      ! [B: rat,A: rat] :
% 0.28/0.50        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.50       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse2
% 0.28/0.50  thf(fact_1160_le__add__diff__inverse2,axiom,
% 0.28/0.50      ! [B: nat,A: nat] :
% 0.28/0.50        ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.50       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse2
% 0.28/0.50  thf(fact_1161_le__add__diff__inverse2,axiom,
% 0.28/0.50      ! [B: int,A: int] :
% 0.28/0.50        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.50       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.28/0.50          = A ) ) ).
% 0.28/0.50  
% 0.28/0.50  % le_add_diff_inverse2
% 0.28/0.50  thf(fact_1162_diff__add__zero,axiom,
% 0.28/0.50      ! [A: nat,B: nat] :
% 0.28/0.50        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.28/0.50        = zero_zero_nat ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_add_zero
% 0.28/0.50  thf(fact_1163_diff__numeral__special_I9_J,axiom,
% 0.28/0.50      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.28/0.50      = zero_zero_complex ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_numeral_special(9)
% 0.28/0.50  thf(fact_1164_diff__numeral__special_I9_J,axiom,
% 0.28/0.50      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.28/0.50      = zero_zero_real ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_numeral_special(9)
% 0.28/0.50  thf(fact_1165_diff__numeral__special_I9_J,axiom,
% 0.28/0.50      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.28/0.50      = zero_zero_rat ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_numeral_special(9)
% 0.28/0.50  thf(fact_1166_diff__numeral__special_I9_J,axiom,
% 0.28/0.50      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.28/0.50      = zero_zero_int ) ).
% 0.28/0.50  
% 0.28/0.50  % diff_numeral_special(9)
% 0.28/0.50  thf(fact_1167_divide__eq__1__iff,axiom,
% 0.28/0.50      ! [A: complex,B: complex] :
% 0.28/0.50        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.28/0.50          = one_one_complex )
% 0.28/0.50        = ( ( B != zero_zero_complex )
% 0.28/0.50          & ( A = B ) ) ) ).
% 0.28/0.50  
% 0.28/0.50  % divide_eq_1_iff
% 0.28/0.50  thf(fact_1168_divide__eq__1__iff,axiom,
% 0.28/0.50      ! [A: real,B: real] :
% 0.28/0.50        ( ( ( divide_divide_real @ A @ B )
% 0.28/0.50          = one_one_real )
% 0.28/0.50        = ( ( B != zero_zero_real )
% 0.28/0.50          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_1_iff
% 0.28/0.51  thf(fact_1169_divide__eq__1__iff,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ( divide_divide_rat @ A @ B )
% 0.28/0.51          = one_one_rat )
% 0.28/0.51        = ( ( B != zero_zero_rat )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_1_iff
% 0.28/0.51  thf(fact_1170_div__self,axiom,
% 0.28/0.51      ! [A: complex] :
% 0.28/0.51        ( ( A != zero_zero_complex )
% 0.28/0.51       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.28/0.51          = one_one_complex ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_self
% 0.28/0.51  thf(fact_1171_div__self,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( A != zero_zero_real )
% 0.28/0.51       => ( ( divide_divide_real @ A @ A )
% 0.28/0.51          = one_one_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_self
% 0.28/0.51  thf(fact_1172_div__self,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( A != zero_zero_rat )
% 0.28/0.51       => ( ( divide_divide_rat @ A @ A )
% 0.28/0.51          = one_one_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_self
% 0.28/0.51  thf(fact_1173_div__self,axiom,
% 0.28/0.51      ! [A: nat] :
% 0.28/0.51        ( ( A != zero_zero_nat )
% 0.28/0.51       => ( ( divide_divide_nat @ A @ A )
% 0.28/0.51          = one_one_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_self
% 0.28/0.51  thf(fact_1174_div__self,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( A != zero_zero_int )
% 0.28/0.51       => ( ( divide_divide_int @ A @ A )
% 0.28/0.51          = one_one_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_self
% 0.28/0.51  thf(fact_1175_one__eq__divide__iff,axiom,
% 0.28/0.51      ! [A: complex,B: complex] :
% 0.28/0.51        ( ( one_one_complex
% 0.28/0.51          = ( divide1717551699836669952omplex @ A @ B ) )
% 0.28/0.51        = ( ( B != zero_zero_complex )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % one_eq_divide_iff
% 0.28/0.51  thf(fact_1176_one__eq__divide__iff,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( one_one_real
% 0.28/0.51          = ( divide_divide_real @ A @ B ) )
% 0.28/0.51        = ( ( B != zero_zero_real )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % one_eq_divide_iff
% 0.28/0.51  thf(fact_1177_one__eq__divide__iff,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( one_one_rat
% 0.28/0.51          = ( divide_divide_rat @ A @ B ) )
% 0.28/0.51        = ( ( B != zero_zero_rat )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % one_eq_divide_iff
% 0.28/0.51  thf(fact_1178_divide__self,axiom,
% 0.28/0.51      ! [A: complex] :
% 0.28/0.51        ( ( A != zero_zero_complex )
% 0.28/0.51       => ( ( divide1717551699836669952omplex @ A @ A )
% 0.28/0.51          = one_one_complex ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self
% 0.28/0.51  thf(fact_1179_divide__self,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( A != zero_zero_real )
% 0.28/0.51       => ( ( divide_divide_real @ A @ A )
% 0.28/0.51          = one_one_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self
% 0.28/0.51  thf(fact_1180_divide__self,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( A != zero_zero_rat )
% 0.28/0.51       => ( ( divide_divide_rat @ A @ A )
% 0.28/0.51          = one_one_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self
% 0.28/0.51  thf(fact_1181_divide__self__if,axiom,
% 0.28/0.51      ! [A: complex] :
% 0.28/0.51        ( ( ( A = zero_zero_complex )
% 0.28/0.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.28/0.51            = zero_zero_complex ) )
% 0.28/0.51        & ( ( A != zero_zero_complex )
% 0.28/0.51         => ( ( divide1717551699836669952omplex @ A @ A )
% 0.28/0.51            = one_one_complex ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self_if
% 0.28/0.51  thf(fact_1182_divide__self__if,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ( A = zero_zero_real )
% 0.28/0.51         => ( ( divide_divide_real @ A @ A )
% 0.28/0.51            = zero_zero_real ) )
% 0.28/0.51        & ( ( A != zero_zero_real )
% 0.28/0.51         => ( ( divide_divide_real @ A @ A )
% 0.28/0.51            = one_one_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self_if
% 0.28/0.51  thf(fact_1183_divide__self__if,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ( A = zero_zero_rat )
% 0.28/0.51         => ( ( divide_divide_rat @ A @ A )
% 0.28/0.51            = zero_zero_rat ) )
% 0.28/0.51        & ( ( A != zero_zero_rat )
% 0.28/0.51         => ( ( divide_divide_rat @ A @ A )
% 0.28/0.51            = one_one_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_self_if
% 0.28/0.51  thf(fact_1184_divide__eq__eq__1,axiom,
% 0.28/0.51      ! [B: real,A: real] :
% 0.28/0.51        ( ( ( divide_divide_real @ B @ A )
% 0.28/0.51          = one_one_real )
% 0.28/0.51        = ( ( A != zero_zero_real )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_eq_1
% 0.28/0.51  thf(fact_1185_divide__eq__eq__1,axiom,
% 0.28/0.51      ! [B: rat,A: rat] :
% 0.28/0.51        ( ( ( divide_divide_rat @ B @ A )
% 0.28/0.51          = one_one_rat )
% 0.28/0.51        = ( ( A != zero_zero_rat )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_eq_1
% 0.28/0.51  thf(fact_1186_eq__divide__eq__1,axiom,
% 0.28/0.51      ! [B: real,A: real] :
% 0.28/0.51        ( ( one_one_real
% 0.28/0.51          = ( divide_divide_real @ B @ A ) )
% 0.28/0.51        = ( ( A != zero_zero_real )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_divide_eq_1
% 0.28/0.51  thf(fact_1187_eq__divide__eq__1,axiom,
% 0.28/0.51      ! [B: rat,A: rat] :
% 0.28/0.51        ( ( one_one_rat
% 0.28/0.51          = ( divide_divide_rat @ B @ A ) )
% 0.28/0.51        = ( ( A != zero_zero_rat )
% 0.28/0.51          & ( A = B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_divide_eq_1
% 0.28/0.51  thf(fact_1188_one__divide__eq__0__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ( divide_divide_real @ one_one_real @ A )
% 0.28/0.51          = zero_zero_real )
% 0.28/0.51        = ( A = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % one_divide_eq_0_iff
% 0.28/0.51  thf(fact_1189_one__divide__eq__0__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.28/0.51          = zero_zero_rat )
% 0.28/0.51        = ( A = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % one_divide_eq_0_iff
% 0.28/0.51  thf(fact_1190_zero__eq__1__divide__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( zero_zero_real
% 0.28/0.51          = ( divide_divide_real @ one_one_real @ A ) )
% 0.28/0.51        = ( A = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_1_divide_iff
% 0.28/0.51  thf(fact_1191_zero__eq__1__divide__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( zero_zero_rat
% 0.28/0.51          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.28/0.51        = ( A = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_1_divide_iff
% 0.28/0.51  thf(fact_1192_right__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [V: num,B: complex,C: complex] :
% 0.28/0.51        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 0.28/0.51        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib_numeral
% 0.28/0.51  thf(fact_1193_right__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [V: num,B: real,C: real] :
% 0.28/0.51        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib_numeral
% 0.28/0.51  thf(fact_1194_right__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [V: num,B: rat,C: rat] :
% 0.28/0.51        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib_numeral
% 0.28/0.51  thf(fact_1195_right__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [V: num,B: int,C: int] :
% 0.28/0.51        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib_numeral
% 0.28/0.51  thf(fact_1196_left__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [A: complex,B: complex,V: num] :
% 0.28/0.51        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 0.28/0.51        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib_numeral
% 0.28/0.51  thf(fact_1197_left__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [A: real,B: real,V: num] :
% 0.28/0.51        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib_numeral
% 0.28/0.51  thf(fact_1198_left__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [A: rat,B: rat,V: num] :
% 0.28/0.51        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib_numeral
% 0.28/0.51  thf(fact_1199_left__diff__distrib__numeral,axiom,
% 0.28/0.51      ! [A: int,B: int,V: num] :
% 0.28/0.51        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib_numeral
% 0.28/0.51  thf(fact_1200_power__zero__numeral,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 0.28/0.51        = zero_zero_rat ) ).
% 0.28/0.51  
% 0.28/0.51  % power_zero_numeral
% 0.28/0.51  thf(fact_1201_power__zero__numeral,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % power_zero_numeral
% 0.28/0.51  thf(fact_1202_power__zero__numeral,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 0.28/0.51        = zero_zero_real ) ).
% 0.28/0.51  
% 0.28/0.51  % power_zero_numeral
% 0.28/0.51  thf(fact_1203_power__zero__numeral,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % power_zero_numeral
% 0.28/0.51  thf(fact_1204_power__zero__numeral,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 0.28/0.51        = zero_zero_complex ) ).
% 0.28/0.51  
% 0.28/0.51  % power_zero_numeral
% 0.28/0.51  thf(fact_1205_power__eq__0__iff,axiom,
% 0.28/0.51      ! [A: rat,N: nat] :
% 0.28/0.51        ( ( ( power_power_rat @ A @ N )
% 0.28/0.51          = zero_zero_rat )
% 0.28/0.51        = ( ( A = zero_zero_rat )
% 0.28/0.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_eq_0_iff
% 0.28/0.51  thf(fact_1206_power__eq__0__iff,axiom,
% 0.28/0.51      ! [A: nat,N: nat] :
% 0.28/0.51        ( ( ( power_power_nat @ A @ N )
% 0.28/0.51          = zero_zero_nat )
% 0.28/0.51        = ( ( A = zero_zero_nat )
% 0.28/0.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_eq_0_iff
% 0.28/0.51  thf(fact_1207_power__eq__0__iff,axiom,
% 0.28/0.51      ! [A: real,N: nat] :
% 0.28/0.51        ( ( ( power_power_real @ A @ N )
% 0.28/0.51          = zero_zero_real )
% 0.28/0.51        = ( ( A = zero_zero_real )
% 0.28/0.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_eq_0_iff
% 0.28/0.51  thf(fact_1208_power__eq__0__iff,axiom,
% 0.28/0.51      ! [A: int,N: nat] :
% 0.28/0.51        ( ( ( power_power_int @ A @ N )
% 0.28/0.51          = zero_zero_int )
% 0.28/0.51        = ( ( A = zero_zero_int )
% 0.28/0.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_eq_0_iff
% 0.28/0.51  thf(fact_1209_power__eq__0__iff,axiom,
% 0.28/0.51      ! [A: complex,N: nat] :
% 0.28/0.51        ( ( ( power_power_complex @ A @ N )
% 0.28/0.51          = zero_zero_complex )
% 0.28/0.51        = ( ( A = zero_zero_complex )
% 0.28/0.51          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_eq_0_iff
% 0.28/0.51  thf(fact_1210_mod__mult__self2__is__0,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2_is_0
% 0.28/0.51  thf(fact_1211_mod__mult__self2__is__0,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2_is_0
% 0.28/0.51  thf(fact_1212_mod__mult__self2__is__0,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2_is_0
% 0.28/0.51  thf(fact_1213_mod__mult__self1__is__0,axiom,
% 0.28/0.51      ! [B: nat,A: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1_is_0
% 0.28/0.51  thf(fact_1214_mod__mult__self1__is__0,axiom,
% 0.28/0.51      ! [B: int,A: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1_is_0
% 0.28/0.51  thf(fact_1215_mod__mult__self1__is__0,axiom,
% 0.28/0.51      ! [B: code_integer,A: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1_is_0
% 0.28/0.51  thf(fact_1216_bits__mod__by__1,axiom,
% 0.28/0.51      ! [A: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_by_1
% 0.28/0.51  thf(fact_1217_bits__mod__by__1,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_by_1
% 0.28/0.51  thf(fact_1218_bits__mod__by__1,axiom,
% 0.28/0.51      ! [A: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_by_1
% 0.28/0.51  thf(fact_1219_mod__by__1,axiom,
% 0.28/0.51      ! [A: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_by_1
% 0.28/0.51  thf(fact_1220_mod__by__1,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_by_1
% 0.28/0.51  thf(fact_1221_mod__by__1,axiom,
% 0.28/0.51      ! [A: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_by_1
% 0.28/0.51  thf(fact_1222_mod__div__trivial,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_div_trivial
% 0.28/0.51  thf(fact_1223_mod__div__trivial,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_div_trivial
% 0.28/0.51  thf(fact_1224_mod__div__trivial,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_div_trivial
% 0.28/0.51  thf(fact_1225_bits__mod__div__trivial,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_div_trivial
% 0.28/0.51  thf(fact_1226_bits__mod__div__trivial,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_div_trivial
% 0.28/0.51  thf(fact_1227_bits__mod__div__trivial,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_mod_div_trivial
% 0.28/0.51  thf(fact_1228_mod__mult__self4,axiom,
% 0.28/0.51      ! [B: nat,C: nat,A: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self4
% 0.28/0.51  thf(fact_1229_mod__mult__self4,axiom,
% 0.28/0.51      ! [B: int,C: int,A: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self4
% 0.28/0.51  thf(fact_1230_mod__mult__self4,axiom,
% 0.28/0.51      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self4
% 0.28/0.51  thf(fact_1231_mod__mult__self3,axiom,
% 0.28/0.51      ! [C: nat,B: nat,A: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self3
% 0.28/0.51  thf(fact_1232_mod__mult__self3,axiom,
% 0.28/0.51      ! [C: int,B: int,A: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self3
% 0.28/0.51  thf(fact_1233_mod__mult__self3,axiom,
% 0.28/0.51      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self3
% 0.28/0.51  thf(fact_1234_mod__mult__self2,axiom,
% 0.28/0.51      ! [A: nat,B: nat,C: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2
% 0.28/0.51  thf(fact_1235_mod__mult__self2,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2
% 0.28/0.51  thf(fact_1236_mod__mult__self2,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self2
% 0.28/0.51  thf(fact_1237_mod__mult__self1,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1
% 0.28/0.51  thf(fact_1238_mod__mult__self1,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1
% 0.28/0.51  thf(fact_1239_mod__mult__self1,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_self1
% 0.28/0.51  thf(fact_1240_mult__le__cancel2,axiom,
% 0.28/0.51      ! [M: nat,K: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.28/0.51        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.51         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mult_le_cancel2
% 0.28/0.51  thf(fact_1241_nat__mult__le__cancel__disj,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.51        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.51         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nat_mult_le_cancel_disj
% 0.28/0.51  thf(fact_1242_Nat_Oadd__diff__assoc,axiom,
% 0.28/0.51      ! [K: nat,J: nat,I: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.51       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.28/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % Nat.add_diff_assoc
% 0.28/0.51  thf(fact_1243_Nat_Oadd__diff__assoc2,axiom,
% 0.28/0.51      ! [K: nat,J: nat,I: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.51       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.28/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % Nat.add_diff_assoc2
% 0.28/0.51  thf(fact_1244_Nat_Odiff__diff__right,axiom,
% 0.28/0.51      ! [K: nat,J: nat,I: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.51       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.28/0.51          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % Nat.diff_diff_right
% 0.28/0.51  thf(fact_1245_div__mult__self__is__m,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 0.28/0.51          = M ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self_is_m
% 0.28/0.51  thf(fact_1246_div__mult__self1__is__m,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 0.28/0.51          = M ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self1_is_m
% 0.28/0.51  thf(fact_1247_dbl__simps_I5_J,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.28/0.51        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % dbl_simps(5)
% 0.28/0.51  thf(fact_1248_dbl__simps_I5_J,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.28/0.51        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % dbl_simps(5)
% 0.28/0.51  thf(fact_1249_dbl__simps_I5_J,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 0.28/0.51        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % dbl_simps(5)
% 0.28/0.51  thf(fact_1250_dbl__simps_I5_J,axiom,
% 0.28/0.51      ! [K: num] :
% 0.28/0.51        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 0.28/0.51        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % dbl_simps(5)
% 0.28/0.51  thf(fact_1251_both__member__options__from__complete__tree__to__child,axiom,
% 0.28/0.51      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.28/0.51       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.51         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 0.28/0.51            | ( X = Mi )
% 0.28/0.51            | ( X = Ma ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % both_member_options_from_complete_tree_to_child
% 0.28/0.51  thf(fact_1252__C10_C,axiom,
% 0.28/0.51      vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 0.28/0.51  
% 0.28/0.51  % "10"
% 0.28/0.51  thf(fact_1253_member__inv,axiom,
% 0.28/0.51      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.28/0.51        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.51       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.51          & ( ( X = Mi )
% 0.28/0.51            | ( X = Ma )
% 0.28/0.51            | ( ( ord_less_nat @ X @ Ma )
% 0.28/0.51              & ( ord_less_nat @ Mi @ X )
% 0.28/0.51              & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.51              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % member_inv
% 0.28/0.51  thf(fact_1254_zero__le__divide__1__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.28/0.51        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_le_divide_1_iff
% 0.28/0.51  thf(fact_1255_zero__le__divide__1__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.28/0.51        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_le_divide_1_iff
% 0.28/0.51  thf(fact_1256_divide__le__0__1__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.28/0.51        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_0_1_iff
% 0.28/0.51  thf(fact_1257_divide__le__0__1__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.28/0.51        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_0_1_iff
% 0.28/0.51  thf(fact_1258_divide__less__0__1__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.28/0.51        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_0_1_iff
% 0.28/0.51  thf(fact_1259_divide__less__0__1__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.28/0.51        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_0_1_iff
% 0.28/0.51  thf(fact_1260_divide__less__eq__1__neg,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.51          = ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_eq_1_neg
% 0.28/0.51  thf(fact_1261_divide__less__eq__1__neg,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_eq_1_neg
% 0.28/0.51  thf(fact_1262_divide__less__eq__1__pos,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.51          = ( ord_less_real @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_eq_1_pos
% 0.28/0.51  thf(fact_1263_divide__less__eq__1__pos,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.51       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_less_eq_1_pos
% 0.28/0.51  thf(fact_1264_less__divide__eq__1__neg,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.51          = ( ord_less_real @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_divide_eq_1_neg
% 0.28/0.51  thf(fact_1265_less__divide__eq__1__neg,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.51          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_divide_eq_1_neg
% 0.28/0.51  thf(fact_1266_less__divide__eq__1__pos,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.51          = ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_divide_eq_1_pos
% 0.28/0.51  thf(fact_1267_less__divide__eq__1__pos,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.51       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.51          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_divide_eq_1_pos
% 0.28/0.51  thf(fact_1268_zero__less__divide__1__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.28/0.51        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_divide_1_iff
% 0.28/0.51  thf(fact_1269_zero__less__divide__1__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.28/0.51        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_divide_1_iff
% 0.28/0.51  thf(fact_1270_divide__eq__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [B: complex,W: num,A: complex] :
% 0.28/0.51        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.28/0.51             != zero_zero_complex )
% 0.28/0.51           => ( B
% 0.28/0.51              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.28/0.51          & ( ( ( numera6690914467698888265omplex @ W )
% 0.28/0.51              = zero_zero_complex )
% 0.28/0.51           => ( A = zero_zero_complex ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_eq_numeral1(1)
% 0.28/0.51  thf(fact_1271_divide__eq__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [B: real,W: num,A: real] :
% 0.28/0.51        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( ( ( numeral_numeral_real @ W )
% 0.28/0.51             != zero_zero_real )
% 0.28/0.51           => ( B
% 0.28/0.51              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 0.28/0.51          & ( ( ( numeral_numeral_real @ W )
% 0.28/0.51              = zero_zero_real )
% 0.28/0.51           => ( A = zero_zero_real ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_eq_numeral1(1)
% 0.28/0.51  thf(fact_1272_divide__eq__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [B: rat,W: num,A: rat] :
% 0.28/0.51        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( ( ( numeral_numeral_rat @ W )
% 0.28/0.51             != zero_zero_rat )
% 0.28/0.51           => ( B
% 0.28/0.51              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 0.28/0.51          & ( ( ( numeral_numeral_rat @ W )
% 0.28/0.51              = zero_zero_rat )
% 0.28/0.51           => ( A = zero_zero_rat ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_eq_eq_numeral1(1)
% 0.28/0.51  thf(fact_1273_eq__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [A: complex,B: complex,W: num] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 0.28/0.51        = ( ( ( ( numera6690914467698888265omplex @ W )
% 0.28/0.51             != zero_zero_complex )
% 0.28/0.51           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 0.28/0.51              = B ) )
% 0.28/0.51          & ( ( ( numera6690914467698888265omplex @ W )
% 0.28/0.51              = zero_zero_complex )
% 0.28/0.51           => ( A = zero_zero_complex ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_divide_eq_numeral1(1)
% 0.28/0.51  thf(fact_1274_eq__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [A: real,B: real,W: num] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 0.28/0.51        = ( ( ( ( numeral_numeral_real @ W )
% 0.28/0.51             != zero_zero_real )
% 0.28/0.51           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 0.28/0.51              = B ) )
% 0.28/0.51          & ( ( ( numeral_numeral_real @ W )
% 0.28/0.51              = zero_zero_real )
% 0.28/0.51           => ( A = zero_zero_real ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_divide_eq_numeral1(1)
% 0.28/0.51  thf(fact_1275_eq__divide__eq__numeral1_I1_J,axiom,
% 0.28/0.51      ! [A: rat,B: rat,W: num] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.28/0.51        = ( ( ( ( numeral_numeral_rat @ W )
% 0.28/0.51             != zero_zero_rat )
% 0.28/0.51           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 0.28/0.51              = B ) )
% 0.28/0.51          & ( ( ( numeral_numeral_rat @ W )
% 0.28/0.51              = zero_zero_rat )
% 0.28/0.51           => ( A = zero_zero_rat ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_divide_eq_numeral1(1)
% 0.28/0.51  thf(fact_1276_div__mult__self4,axiom,
% 0.28/0.51      ! [B: nat,C: nat,A: nat] :
% 0.28/0.51        ( ( B != zero_zero_nat )
% 0.28/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.28/0.51          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self4
% 0.28/0.51  thf(fact_1277_div__mult__self4,axiom,
% 0.28/0.51      ! [B: int,C: int,A: int] :
% 0.28/0.51        ( ( B != zero_zero_int )
% 0.28/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.28/0.51          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self4
% 0.28/0.51  thf(fact_1278_div__mult__self3,axiom,
% 0.28/0.51      ! [B: nat,C: nat,A: nat] :
% 0.28/0.51        ( ( B != zero_zero_nat )
% 0.28/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.28/0.51          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self3
% 0.28/0.51  thf(fact_1279_div__mult__self3,axiom,
% 0.28/0.51      ! [B: int,C: int,A: int] :
% 0.28/0.51        ( ( B != zero_zero_int )
% 0.28/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.28/0.51          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self3
% 0.28/0.51  thf(fact_1280_div__mult__self2,axiom,
% 0.28/0.51      ! [B: nat,A: nat,C: nat] :
% 0.28/0.51        ( ( B != zero_zero_nat )
% 0.28/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.28/0.51          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self2
% 0.28/0.51  thf(fact_1281_div__mult__self2,axiom,
% 0.28/0.51      ! [B: int,A: int,C: int] :
% 0.28/0.51        ( ( B != zero_zero_int )
% 0.28/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.28/0.51          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self2
% 0.28/0.51  thf(fact_1282_div__mult__self1,axiom,
% 0.28/0.51      ! [B: nat,A: nat,C: nat] :
% 0.28/0.51        ( ( B != zero_zero_nat )
% 0.28/0.51       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.28/0.51          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self1
% 0.28/0.51  thf(fact_1283_div__mult__self1,axiom,
% 0.28/0.51      ! [B: int,A: int,C: int] :
% 0.28/0.51        ( ( B != zero_zero_int )
% 0.28/0.51       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.28/0.51          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % div_mult_self1
% 0.28/0.51  thf(fact_1284_nonzero__divide__mult__cancel__left,axiom,
% 0.28/0.51      ! [A: complex,B: complex] :
% 0.28/0.51        ( ( A != zero_zero_complex )
% 0.28/0.51       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.28/0.51          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_left
% 0.28/0.51  thf(fact_1285_nonzero__divide__mult__cancel__left,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( A != zero_zero_real )
% 0.28/0.51       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.28/0.51          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_left
% 0.28/0.51  thf(fact_1286_nonzero__divide__mult__cancel__left,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( A != zero_zero_rat )
% 0.28/0.51       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.28/0.51          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_left
% 0.28/0.51  thf(fact_1287_nonzero__divide__mult__cancel__right,axiom,
% 0.28/0.51      ! [B: complex,A: complex] :
% 0.28/0.51        ( ( B != zero_zero_complex )
% 0.28/0.51       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.28/0.51          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_right
% 0.28/0.51  thf(fact_1288_nonzero__divide__mult__cancel__right,axiom,
% 0.28/0.51      ! [B: real,A: real] :
% 0.28/0.51        ( ( B != zero_zero_real )
% 0.28/0.51       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.28/0.51          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_right
% 0.28/0.51  thf(fact_1289_nonzero__divide__mult__cancel__right,axiom,
% 0.28/0.51      ! [B: rat,A: rat] :
% 0.28/0.51        ( ( B != zero_zero_rat )
% 0.28/0.51       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.28/0.51          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nonzero_divide_mult_cancel_right
% 0.28/0.51  thf(fact_1290_power__mono__iff,axiom,
% 0.28/0.51      ! [A: real,B: real,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.51         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.28/0.51              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mono_iff
% 0.28/0.51  thf(fact_1291_power__mono__iff,axiom,
% 0.28/0.51      ! [A: rat,B: rat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.51         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.28/0.51              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mono_iff
% 0.28/0.51  thf(fact_1292_power__mono__iff,axiom,
% 0.28/0.51      ! [A: nat,B: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.51         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.28/0.51              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mono_iff
% 0.28/0.51  thf(fact_1293_power__mono__iff,axiom,
% 0.28/0.51      ! [A: int,B: int,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.51         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.28/0.51              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mono_iff
% 0.28/0.51  thf(fact_1294_lesseq__shift,axiom,
% 0.28/0.51      ( ord_less_eq_nat
% 0.28/0.51      = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % lesseq_shift
% 0.28/0.51  thf(fact_1295_le__divide__eq__1__pos,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_divide_eq_1_pos
% 0.28/0.51  thf(fact_1296_le__divide__eq__1__pos,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_divide_eq_1_pos
% 0.28/0.51  thf(fact_1297_le__divide__eq__1__neg,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.51       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_divide_eq_1_neg
% 0.28/0.51  thf(fact_1298_le__divide__eq__1__neg,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.51       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_divide_eq_1_neg
% 0.28/0.51  thf(fact_1299_divide__le__eq__1__pos,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.51          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_eq_1_pos
% 0.28/0.51  thf(fact_1300_divide__le__eq__1__pos,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.51          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_eq_1_pos
% 0.28/0.51  thf(fact_1301_divide__le__eq__1__neg,axiom,
% 0.28/0.51      ! [A: real,B: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.51       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.51          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_eq_1_neg
% 0.28/0.51  thf(fact_1302_divide__le__eq__1__neg,axiom,
% 0.28/0.51      ! [A: rat,B: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.51       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.51          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_le_eq_1_neg
% 0.28/0.51  thf(fact_1303_power__strict__decreasing__iff,axiom,
% 0.28/0.51      ! [B: real,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.51       => ( ( ord_less_real @ B @ one_one_real )
% 0.28/0.51         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.28/0.51            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_strict_decreasing_iff
% 0.28/0.51  thf(fact_1304_power__strict__decreasing__iff,axiom,
% 0.28/0.51      ! [B: rat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.51       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.28/0.51         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.28/0.51            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_strict_decreasing_iff
% 0.28/0.51  thf(fact_1305_power__strict__decreasing__iff,axiom,
% 0.28/0.51      ! [B: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.51       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.28/0.51         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.28/0.51            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_strict_decreasing_iff
% 0.28/0.51  thf(fact_1306_power__strict__decreasing__iff,axiom,
% 0.28/0.51      ! [B: int,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.51       => ( ( ord_less_int @ B @ one_one_int )
% 0.28/0.51         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.28/0.51            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_strict_decreasing_iff
% 0.28/0.51  thf(fact_1307_zero__eq__power2,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = zero_zero_rat )
% 0.28/0.51        = ( A = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_power2
% 0.28/0.51  thf(fact_1308_zero__eq__power2,axiom,
% 0.28/0.51      ! [A: nat] :
% 0.28/0.51        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = zero_zero_nat )
% 0.28/0.51        = ( A = zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_power2
% 0.28/0.51  thf(fact_1309_zero__eq__power2,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = zero_zero_real )
% 0.28/0.51        = ( A = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_power2
% 0.28/0.51  thf(fact_1310_zero__eq__power2,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = zero_zero_int )
% 0.28/0.51        = ( A = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_power2
% 0.28/0.51  thf(fact_1311_zero__eq__power2,axiom,
% 0.28/0.51      ! [A: complex] :
% 0.28/0.51        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = zero_zero_complex )
% 0.28/0.51        = ( A = zero_zero_complex ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_eq_power2
% 0.28/0.51  thf(fact_1312_bits__one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_one_mod_two_eq_one
% 0.28/0.51  thf(fact_1313_bits__one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_int ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_one_mod_two_eq_one
% 0.28/0.51  thf(fact_1314_bits__one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_Code_integer ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_one_mod_two_eq_one
% 0.28/0.51  thf(fact_1315_one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % one_mod_two_eq_one
% 0.28/0.51  thf(fact_1316_one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_int ) ).
% 0.28/0.51  
% 0.28/0.51  % one_mod_two_eq_one
% 0.28/0.51  thf(fact_1317_one__mod__two__eq__one,axiom,
% 0.28/0.51      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.51      = one_one_Code_integer ) ).
% 0.28/0.51  
% 0.28/0.51  % one_mod_two_eq_one
% 0.28/0.51  thf(fact_1318_add__self__mod__2,axiom,
% 0.28/0.51      ! [M: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % add_self_mod_2
% 0.28/0.51  thf(fact_1319_bits__1__div__2,axiom,
% 0.28/0.51      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51      = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_1_div_2
% 0.28/0.51  thf(fact_1320_bits__1__div__2,axiom,
% 0.28/0.51      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.51      = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % bits_1_div_2
% 0.28/0.51  thf(fact_1321_one__div__two__eq__zero,axiom,
% 0.28/0.51      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51      = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % one_div_two_eq_zero
% 0.28/0.51  thf(fact_1322_one__div__two__eq__zero,axiom,
% 0.28/0.51      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.51      = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % one_div_two_eq_zero
% 0.28/0.51  thf(fact_1323_power2__less__eq__zero__iff,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.28/0.51        = ( A = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_less_eq_zero_iff
% 0.28/0.51  thf(fact_1324_power2__less__eq__zero__iff,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.28/0.51        = ( A = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_less_eq_zero_iff
% 0.28/0.51  thf(fact_1325_power2__less__eq__zero__iff,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.28/0.51        = ( A = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_less_eq_zero_iff
% 0.28/0.51  thf(fact_1326_power2__eq__iff__nonneg,axiom,
% 0.28/0.51      ! [X: real,Y: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.51       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.51         => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51            = ( X = Y ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_eq_iff_nonneg
% 0.28/0.51  thf(fact_1327_power2__eq__iff__nonneg,axiom,
% 0.28/0.51      ! [X: rat,Y: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.51       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.51         => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51            = ( X = Y ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_eq_iff_nonneg
% 0.28/0.51  thf(fact_1328_power2__eq__iff__nonneg,axiom,
% 0.28/0.51      ! [X: nat,Y: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.28/0.51       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.28/0.51         => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51            = ( X = Y ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_eq_iff_nonneg
% 0.28/0.51  thf(fact_1329_power2__eq__iff__nonneg,axiom,
% 0.28/0.51      ! [X: int,Y: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.51       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.51         => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51            = ( X = Y ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power2_eq_iff_nonneg
% 0.28/0.51  thf(fact_1330_power__decreasing__iff,axiom,
% 0.28/0.51      ! [B: real,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.51       => ( ( ord_less_real @ B @ one_one_real )
% 0.28/0.51         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.28/0.51            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_decreasing_iff
% 0.28/0.51  thf(fact_1331_power__decreasing__iff,axiom,
% 0.28/0.51      ! [B: rat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.51       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.28/0.51         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.28/0.51            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_decreasing_iff
% 0.28/0.51  thf(fact_1332_power__decreasing__iff,axiom,
% 0.28/0.51      ! [B: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.51       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.28/0.51         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.28/0.51            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_decreasing_iff
% 0.28/0.51  thf(fact_1333_power__decreasing__iff,axiom,
% 0.28/0.51      ! [B: int,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.51       => ( ( ord_less_int @ B @ one_one_int )
% 0.28/0.51         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.28/0.51            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_decreasing_iff
% 0.28/0.51  thf(fact_1334_zero__less__power2,axiom,
% 0.28/0.51      ! [A: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51        = ( A != zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_power2
% 0.28/0.51  thf(fact_1335_zero__less__power2,axiom,
% 0.28/0.51      ! [A: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51        = ( A != zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_power2
% 0.28/0.51  thf(fact_1336_zero__less__power2,axiom,
% 0.28/0.51      ! [A: int] :
% 0.28/0.51        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51        = ( A != zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_power2
% 0.28/0.51  thf(fact_1337_sum__power2__eq__zero__iff,axiom,
% 0.28/0.51      ! [X: rat,Y: rat] :
% 0.28/0.51        ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51          = zero_zero_rat )
% 0.28/0.51        = ( ( X = zero_zero_rat )
% 0.28/0.51          & ( Y = zero_zero_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % sum_power2_eq_zero_iff
% 0.28/0.51  thf(fact_1338_sum__power2__eq__zero__iff,axiom,
% 0.28/0.51      ! [X: real,Y: real] :
% 0.28/0.51        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51          = zero_zero_real )
% 0.28/0.51        = ( ( X = zero_zero_real )
% 0.28/0.51          & ( Y = zero_zero_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % sum_power2_eq_zero_iff
% 0.28/0.51  thf(fact_1339_sum__power2__eq__zero__iff,axiom,
% 0.28/0.51      ! [X: int,Y: int] :
% 0.28/0.51        ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51          = zero_zero_int )
% 0.28/0.51        = ( ( X = zero_zero_int )
% 0.28/0.51          & ( Y = zero_zero_int ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % sum_power2_eq_zero_iff
% 0.28/0.51  thf(fact_1340_mod2__gr__0,axiom,
% 0.28/0.51      ! [M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.51        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.51          = one_one_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod2_gr_0
% 0.28/0.51  thf(fact_1341_real__arch__pow,axiom,
% 0.28/0.51      ! [X: real,Y: real] :
% 0.28/0.51        ( ( ord_less_real @ one_one_real @ X )
% 0.28/0.51       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N3 ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % real_arch_pow
% 0.28/0.51  thf(fact_1342_less__eq__real__def,axiom,
% 0.28/0.51      ( ord_less_eq_real
% 0.28/0.51      = ( ^ [X3: real,Y3: real] :
% 0.28/0.51            ( ( ord_less_real @ X3 @ Y3 )
% 0.28/0.51            | ( X3 = Y3 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_eq_real_def
% 0.28/0.51  thf(fact_1343_real__arch__pow__inv,axiom,
% 0.28/0.51      ! [Y: real,X: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.51       => ( ( ord_less_real @ X @ one_one_real )
% 0.28/0.51         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % real_arch_pow_inv
% 0.28/0.51  thf(fact_1344_complete__real,axiom,
% 0.28/0.51      ! [S2: set_real] :
% 0.28/0.51        ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 0.28/0.51       => ( ? [Z4: real] :
% 0.28/0.51            ! [X6: real] :
% 0.28/0.51              ( ( member_real @ X6 @ S2 )
% 0.28/0.51             => ( ord_less_eq_real @ X6 @ Z4 ) )
% 0.28/0.51         => ? [Y5: real] :
% 0.28/0.51              ( ! [X4: real] :
% 0.28/0.51                  ( ( member_real @ X4 @ S2 )
% 0.28/0.51                 => ( ord_less_eq_real @ X4 @ Y5 ) )
% 0.28/0.51              & ! [Z4: real] :
% 0.28/0.51                  ( ! [X6: real] :
% 0.28/0.51                      ( ( member_real @ X6 @ S2 )
% 0.28/0.51                     => ( ord_less_eq_real @ X6 @ Z4 ) )
% 0.28/0.51                 => ( ord_less_eq_real @ Y5 @ Z4 ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % complete_real
% 0.28/0.51  thf(fact_1345_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.51       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.28/0.51  thf(fact_1346_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.51       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.28/0.51  thf(fact_1347_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.51       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.28/0.51  thf(fact_1348_mod__eq__0D,axiom,
% 0.28/0.51      ! [M: nat,D: nat] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ M @ D )
% 0.28/0.51          = zero_zero_nat )
% 0.28/0.51       => ? [Q3: nat] :
% 0.28/0.51            ( M
% 0.28/0.51            = ( times_times_nat @ D @ Q3 ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_eq_0D
% 0.28/0.51  thf(fact_1349_mod__diff__right__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_right_eq
% 0.28/0.51  thf(fact_1350_mod__diff__right__eq,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_right_eq
% 0.28/0.51  thf(fact_1351_mod__diff__left__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_left_eq
% 0.28/0.51  thf(fact_1352_mod__diff__left__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_left_eq
% 0.28/0.51  thf(fact_1353_mod__diff__cong,axiom,
% 0.28/0.51      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ A @ C )
% 0.28/0.51          = ( modulo_modulo_int @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo_modulo_int @ B @ C )
% 0.28/0.51            = ( modulo_modulo_int @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.51            = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_cong
% 0.28/0.51  thf(fact_1354_mod__diff__cong,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.28/0.51        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.28/0.51          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_cong
% 0.28/0.51  thf(fact_1355_mod__diff__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_eq
% 0.28/0.51  thf(fact_1356_mod__diff__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_diff_eq
% 0.28/0.51  thf(fact_1357_diffs0__imp__equal,axiom,
% 0.28/0.51      ! [M: nat,N: nat] :
% 0.28/0.51        ( ( ( minus_minus_nat @ M @ N )
% 0.28/0.51          = zero_zero_nat )
% 0.28/0.51       => ( ( ( minus_minus_nat @ N @ M )
% 0.28/0.51            = zero_zero_nat )
% 0.28/0.51         => ( M = N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diffs0_imp_equal
% 0.28/0.51  thf(fact_1358_zero__reorient,axiom,
% 0.28/0.51      ! [X: complex] :
% 0.28/0.51        ( ( zero_zero_complex = X )
% 0.28/0.51        = ( X = zero_zero_complex ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_reorient
% 0.28/0.51  thf(fact_1359_zero__reorient,axiom,
% 0.28/0.51      ! [X: real] :
% 0.28/0.51        ( ( zero_zero_real = X )
% 0.28/0.51        = ( X = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_reorient
% 0.28/0.51  thf(fact_1360_zero__reorient,axiom,
% 0.28/0.51      ! [X: rat] :
% 0.28/0.51        ( ( zero_zero_rat = X )
% 0.28/0.51        = ( X = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_reorient
% 0.28/0.51  thf(fact_1361_zero__reorient,axiom,
% 0.28/0.51      ! [X: nat] :
% 0.28/0.51        ( ( zero_zero_nat = X )
% 0.28/0.51        = ( X = zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_reorient
% 0.28/0.51  thf(fact_1362_zero__reorient,axiom,
% 0.28/0.51      ! [X: int] :
% 0.28/0.51        ( ( zero_zero_int = X )
% 0.28/0.51        = ( X = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_reorient
% 0.28/0.51  thf(fact_1363_diff__commute,axiom,
% 0.28/0.51      ! [I: nat,J: nat,K: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.28/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_commute
% 0.28/0.51  thf(fact_1364_diff__right__commute,axiom,
% 0.28/0.51      ! [A: real,C: real,B: real] :
% 0.28/0.51        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.28/0.51        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_commute
% 0.28/0.51  thf(fact_1365_diff__right__commute,axiom,
% 0.28/0.51      ! [A: rat,C: rat,B: rat] :
% 0.28/0.51        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.28/0.51        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_commute
% 0.28/0.51  thf(fact_1366_diff__right__commute,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.28/0.51        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_commute
% 0.28/0.51  thf(fact_1367_diff__right__commute,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.28/0.51        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_commute
% 0.28/0.51  thf(fact_1368_eq__iff__diff__eq__0,axiom,
% 0.28/0.51      ( ( ^ [Y4: complex,Z2: complex] : ( Y4 = Z2 ) )
% 0.28/0.51      = ( ^ [A3: complex,B2: complex] :
% 0.28/0.51            ( ( minus_minus_complex @ A3 @ B2 )
% 0.28/0.51            = zero_zero_complex ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_iff_diff_eq_0
% 0.28/0.51  thf(fact_1369_eq__iff__diff__eq__0,axiom,
% 0.28/0.51      ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 0.28/0.51      = ( ^ [A3: real,B2: real] :
% 0.28/0.51            ( ( minus_minus_real @ A3 @ B2 )
% 0.28/0.51            = zero_zero_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_iff_diff_eq_0
% 0.28/0.51  thf(fact_1370_eq__iff__diff__eq__0,axiom,
% 0.28/0.51      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 0.28/0.51      = ( ^ [A3: rat,B2: rat] :
% 0.28/0.51            ( ( minus_minus_rat @ A3 @ B2 )
% 0.28/0.51            = zero_zero_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_iff_diff_eq_0
% 0.28/0.51  thf(fact_1371_eq__iff__diff__eq__0,axiom,
% 0.28/0.51      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.28/0.51      = ( ^ [A3: int,B2: int] :
% 0.28/0.51            ( ( minus_minus_int @ A3 @ B2 )
% 0.28/0.51            = zero_zero_int ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_iff_diff_eq_0
% 0.28/0.51  thf(fact_1372_diff__eq__diff__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.51        ( ( ( minus_minus_real @ A @ B )
% 0.28/0.51          = ( minus_minus_real @ C @ D ) )
% 0.28/0.51       => ( ( A = B )
% 0.28/0.51          = ( C = D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_eq
% 0.28/0.51  thf(fact_1373_diff__eq__diff__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.51        ( ( ( minus_minus_rat @ A @ B )
% 0.28/0.51          = ( minus_minus_rat @ C @ D ) )
% 0.28/0.51       => ( ( A = B )
% 0.28/0.51          = ( C = D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_eq
% 0.28/0.51  thf(fact_1374_diff__eq__diff__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.51        ( ( ( minus_minus_int @ A @ B )
% 0.28/0.51          = ( minus_minus_int @ C @ D ) )
% 0.28/0.51       => ( ( A = B )
% 0.28/0.51          = ( C = D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_eq
% 0.28/0.51  thf(fact_1375_minus__nat_Odiff__0,axiom,
% 0.28/0.51      ! [M: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.28/0.51        = M ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_nat.diff_0
% 0.28/0.51  thf(fact_1376_mod__geq,axiom,
% 0.28/0.51      ! [M: nat,N: nat] :
% 0.28/0.51        ( ~ ( ord_less_nat @ M @ N )
% 0.28/0.51       => ( ( modulo_modulo_nat @ M @ N )
% 0.28/0.51          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_geq
% 0.28/0.51  thf(fact_1377_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.28/0.51      ! [B: nat,A: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.51       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.28/0.51  thf(fact_1378_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.28/0.51      ! [B: int,A: int] :
% 0.28/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.51       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.28/0.51  thf(fact_1379_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.28/0.51      ! [B: code_integer,A: code_integer] :
% 0.28/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.51       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.28/0.51  thf(fact_1380_mod__if,axiom,
% 0.28/0.51      ( modulo_modulo_nat
% 0.28/0.51      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N2 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_if
% 0.28/0.51  thf(fact_1381_le__mod__geq,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.51       => ( ( modulo_modulo_nat @ M @ N )
% 0.28/0.51          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_mod_geq
% 0.28/0.51  thf(fact_1382_mod__eq__self__iff__div__eq__0,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ A @ B )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( divide_divide_nat @ A @ B )
% 0.28/0.51          = zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_eq_self_iff_div_eq_0
% 0.28/0.51  thf(fact_1383_mod__eq__self__iff__div__eq__0,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ A @ B )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( divide_divide_int @ A @ B )
% 0.28/0.51          = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_eq_self_iff_div_eq_0
% 0.28/0.51  thf(fact_1384_mod__eq__self__iff__div__eq__0,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.28/0.51          = A )
% 0.28/0.51        = ( ( divide6298287555418463151nteger @ A @ B )
% 0.28/0.51          = zero_z3403309356797280102nteger ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_eq_self_iff_div_eq_0
% 0.28/0.51  thf(fact_1385_le__iff__diff__le__0,axiom,
% 0.28/0.51      ( ord_less_eq_real
% 0.28/0.51      = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_iff_diff_le_0
% 0.28/0.51  thf(fact_1386_le__iff__diff__le__0,axiom,
% 0.28/0.51      ( ord_less_eq_rat
% 0.28/0.51      = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_iff_diff_le_0
% 0.28/0.51  thf(fact_1387_le__iff__diff__le__0,axiom,
% 0.28/0.51      ( ord_less_eq_int
% 0.28/0.51      = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_iff_diff_le_0
% 0.28/0.51  thf(fact_1388_less__iff__diff__less__0,axiom,
% 0.28/0.51      ( ord_less_real
% 0.28/0.51      = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_iff_diff_less_0
% 0.28/0.51  thf(fact_1389_less__iff__diff__less__0,axiom,
% 0.28/0.51      ( ord_less_rat
% 0.28/0.51      = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_iff_diff_less_0
% 0.28/0.51  thf(fact_1390_less__iff__diff__less__0,axiom,
% 0.28/0.51      ( ord_less_int
% 0.28/0.51      = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_iff_diff_less_0
% 0.28/0.51  thf(fact_1391_mod__less__divisor,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_less_divisor
% 0.28/0.51  thf(fact_1392_diff__less,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.51         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_less
% 0.28/0.51  thf(fact_1393_diff__add__0,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_0
% 0.28/0.51  thf(fact_1394_realpow__pos__nth__unique,axiom,
% 0.28/0.51      ! [N: nat,A: real] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51         => ? [X6: real] :
% 0.28/0.51              ( ( ord_less_real @ zero_zero_real @ X6 )
% 0.28/0.51              & ( ( power_power_real @ X6 @ N )
% 0.28/0.51                = A )
% 0.28/0.51              & ! [Y2: real] :
% 0.28/0.51                  ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.28/0.51                    & ( ( power_power_real @ Y2 @ N )
% 0.28/0.51                      = A ) )
% 0.28/0.51                 => ( Y2 = X6 ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % realpow_pos_nth_unique
% 0.28/0.51  thf(fact_1395_realpow__pos__nth,axiom,
% 0.28/0.51      ! [N: nat,A: real] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.51         => ? [R2: real] :
% 0.28/0.51              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.28/0.51              & ( ( power_power_real @ R2 @ N )
% 0.28/0.51                = A ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % realpow_pos_nth
% 0.28/0.51  thf(fact_1396_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.28/0.51      ! [B: code_integer,A: code_integer] :
% 0.28/0.51        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.51       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.28/0.51  thf(fact_1397_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.28/0.51      ! [B: nat,A: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.51       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.28/0.51  thf(fact_1398_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.28/0.51      ! [B: int,A: int] :
% 0.28/0.51        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.51       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.28/0.51  thf(fact_1399_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.51       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.28/0.51         => ( ( modulo364778990260209775nteger @ A @ B )
% 0.28/0.51            = A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.28/0.51  thf(fact_1400_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.51       => ( ( ord_less_nat @ A @ B )
% 0.28/0.51         => ( ( modulo_modulo_nat @ A @ B )
% 0.28/0.51            = A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.28/0.51  thf(fact_1401_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.51       => ( ( ord_less_int @ A @ B )
% 0.28/0.51         => ( ( modulo_modulo_int @ A @ B )
% 0.28/0.51            = A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % unique_euclidean_semiring_numeral_class.mod_less
% 0.28/0.51  thf(fact_1402_cong__exp__iff__simps_I2_J,axiom,
% 0.28/0.51      ! [N: num,Q2: num] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.28/0.51          = zero_zero_nat )
% 0.28/0.51        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.28/0.51          = zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(2)
% 0.28/0.51  thf(fact_1403_cong__exp__iff__simps_I2_J,axiom,
% 0.28/0.51      ! [N: num,Q2: num] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.28/0.51          = zero_zero_int )
% 0.28/0.51        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.28/0.51          = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(2)
% 0.28/0.51  thf(fact_1404_cong__exp__iff__simps_I2_J,axiom,
% 0.28/0.51      ! [N: num,Q2: num] :
% 0.28/0.51        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.28/0.51          = zero_z3403309356797280102nteger )
% 0.28/0.51        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.28/0.51          = zero_z3403309356797280102nteger ) ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(2)
% 0.28/0.51  thf(fact_1405_cong__exp__iff__simps_I1_J,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 0.28/0.51        = zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(1)
% 0.28/0.51  thf(fact_1406_cong__exp__iff__simps_I1_J,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 0.28/0.51        = zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(1)
% 0.28/0.51  thf(fact_1407_cong__exp__iff__simps_I1_J,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 0.28/0.51        = zero_z3403309356797280102nteger ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(1)
% 0.28/0.51  thf(fact_1408_minus__div__mult__eq__mod,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_div_mult_eq_mod
% 0.28/0.51  thf(fact_1409_minus__div__mult__eq__mod,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_div_mult_eq_mod
% 0.28/0.51  thf(fact_1410_minus__div__mult__eq__mod,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_div_mult_eq_mod
% 0.28/0.51  thf(fact_1411_minus__mod__eq__div__mult,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.28/0.51        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_div_mult
% 0.28/0.51  thf(fact_1412_minus__mod__eq__div__mult,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.51        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_div_mult
% 0.28/0.51  thf(fact_1413_minus__mod__eq__div__mult,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.28/0.51        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_div_mult
% 0.28/0.51  thf(fact_1414_minus__mod__eq__mult__div,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.28/0.51        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_mult_div
% 0.28/0.51  thf(fact_1415_minus__mod__eq__mult__div,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.51        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_mult_div
% 0.28/0.51  thf(fact_1416_minus__mod__eq__mult__div,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.28/0.51        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mod_eq_mult_div
% 0.28/0.51  thf(fact_1417_minus__mult__div__eq__mod,axiom,
% 0.28/0.51      ! [A: nat,B: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.28/0.51        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mult_div_eq_mod
% 0.28/0.51  thf(fact_1418_minus__mult__div__eq__mod,axiom,
% 0.28/0.51      ! [A: int,B: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.28/0.51        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mult_div_eq_mod
% 0.28/0.51  thf(fact_1419_minus__mult__div__eq__mod,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.28/0.51        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % minus_mult_div_eq_mod
% 0.28/0.51  thf(fact_1420_add__divide__eq__if__simps_I4_J,axiom,
% 0.28/0.51      ! [Z: complex,A: complex,B: complex] :
% 0.28/0.51        ( ( ( Z = zero_zero_complex )
% 0.28/0.51         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.28/0.51            = A ) )
% 0.28/0.51        & ( ( Z != zero_zero_complex )
% 0.28/0.51         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.28/0.51            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_divide_eq_if_simps(4)
% 0.28/0.51  thf(fact_1421_add__divide__eq__if__simps_I4_J,axiom,
% 0.28/0.51      ! [Z: real,A: real,B: real] :
% 0.28/0.51        ( ( ( Z = zero_zero_real )
% 0.28/0.51         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.28/0.51            = A ) )
% 0.28/0.51        & ( ( Z != zero_zero_real )
% 0.28/0.51         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.28/0.51            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_divide_eq_if_simps(4)
% 0.28/0.51  thf(fact_1422_add__divide__eq__if__simps_I4_J,axiom,
% 0.28/0.51      ! [Z: rat,A: rat,B: rat] :
% 0.28/0.51        ( ( ( Z = zero_zero_rat )
% 0.28/0.51         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.28/0.51            = A ) )
% 0.28/0.51        & ( ( Z != zero_zero_rat )
% 0.28/0.51         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.28/0.51            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_divide_eq_if_simps(4)
% 0.28/0.51  thf(fact_1423_diff__frac__eq,axiom,
% 0.28/0.51      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 0.28/0.51        ( ( Y != zero_zero_complex )
% 0.28/0.51       => ( ( Z != zero_zero_complex )
% 0.28/0.51         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.28/0.51            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_frac_eq
% 0.28/0.51  thf(fact_1424_diff__frac__eq,axiom,
% 0.28/0.51      ! [Y: real,Z: real,X: real,W: real] :
% 0.28/0.51        ( ( Y != zero_zero_real )
% 0.28/0.51       => ( ( Z != zero_zero_real )
% 0.28/0.51         => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.28/0.51            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_frac_eq
% 0.28/0.51  thf(fact_1425_diff__frac__eq,axiom,
% 0.28/0.51      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.28/0.51        ( ( Y != zero_zero_rat )
% 0.28/0.51       => ( ( Z != zero_zero_rat )
% 0.28/0.51         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.28/0.51            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_frac_eq
% 0.28/0.51  thf(fact_1426_diff__divide__eq__iff,axiom,
% 0.28/0.51      ! [Z: complex,X: complex,Y: complex] :
% 0.28/0.51        ( ( Z != zero_zero_complex )
% 0.28/0.51       => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 0.28/0.51          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_eq_iff
% 0.28/0.51  thf(fact_1427_diff__divide__eq__iff,axiom,
% 0.28/0.51      ! [Z: real,X: real,Y: real] :
% 0.28/0.51        ( ( Z != zero_zero_real )
% 0.28/0.51       => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 0.28/0.51          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_eq_iff
% 0.28/0.51  thf(fact_1428_diff__divide__eq__iff,axiom,
% 0.28/0.51      ! [Z: rat,X: rat,Y: rat] :
% 0.28/0.51        ( ( Z != zero_zero_rat )
% 0.28/0.51       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 0.28/0.51          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_eq_iff
% 0.28/0.51  thf(fact_1429_divide__diff__eq__iff,axiom,
% 0.28/0.51      ! [Z: complex,X: complex,Y: complex] :
% 0.28/0.51        ( ( Z != zero_zero_complex )
% 0.28/0.51       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 0.28/0.51          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_diff_eq_iff
% 0.28/0.51  thf(fact_1430_divide__diff__eq__iff,axiom,
% 0.28/0.51      ! [Z: real,X: real,Y: real] :
% 0.28/0.51        ( ( Z != zero_zero_real )
% 0.28/0.51       => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 0.28/0.51          = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_diff_eq_iff
% 0.28/0.51  thf(fact_1431_divide__diff__eq__iff,axiom,
% 0.28/0.51      ! [Z: rat,X: rat,Y: rat] :
% 0.28/0.51        ( ( Z != zero_zero_rat )
% 0.28/0.51       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 0.28/0.51          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % divide_diff_eq_iff
% 0.28/0.51  thf(fact_1432_modulo__nat__def,axiom,
% 0.28/0.51      ( modulo_modulo_nat
% 0.28/0.51      = ( ^ [M3: nat,N2: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % modulo_nat_def
% 0.28/0.51  thf(fact_1433_mod__le__divisor,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_le_divisor
% 0.28/0.51  thf(fact_1434_nat__diff__split__asm,axiom,
% 0.28/0.51      ! [P: nat > $o,A: nat,B: nat] :
% 0.28/0.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.28/0.51        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.28/0.51                & ~ ( P @ zero_zero_nat ) )
% 0.28/0.51              | ? [D2: nat] :
% 0.28/0.51                  ( ( A
% 0.28/0.51                    = ( plus_plus_nat @ B @ D2 ) )
% 0.28/0.51                  & ~ ( P @ D2 ) ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nat_diff_split_asm
% 0.28/0.51  thf(fact_1435_nat__diff__split,axiom,
% 0.28/0.51      ! [P: nat > $o,A: nat,B: nat] :
% 0.28/0.51        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.28/0.51        = ( ( ( ord_less_nat @ A @ B )
% 0.28/0.51           => ( P @ zero_zero_nat ) )
% 0.28/0.51          & ! [D2: nat] :
% 0.28/0.51              ( ( A
% 0.28/0.51                = ( plus_plus_nat @ B @ D2 ) )
% 0.28/0.51             => ( P @ D2 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % nat_diff_split
% 0.28/0.51  thf(fact_1436_power__0__left,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ( N = zero_zero_nat )
% 0.28/0.51         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.28/0.51            = one_one_rat ) )
% 0.28/0.51        & ( ( N != zero_zero_nat )
% 0.28/0.51         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.28/0.51            = zero_zero_rat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_0_left
% 0.28/0.51  thf(fact_1437_power__0__left,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ( N = zero_zero_nat )
% 0.28/0.51         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.28/0.51            = one_one_nat ) )
% 0.28/0.51        & ( ( N != zero_zero_nat )
% 0.28/0.51         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.28/0.51            = zero_zero_nat ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_0_left
% 0.28/0.51  thf(fact_1438_power__0__left,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ( N = zero_zero_nat )
% 0.28/0.51         => ( ( power_power_real @ zero_zero_real @ N )
% 0.28/0.51            = one_one_real ) )
% 0.28/0.51        & ( ( N != zero_zero_nat )
% 0.28/0.51         => ( ( power_power_real @ zero_zero_real @ N )
% 0.28/0.51            = zero_zero_real ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_0_left
% 0.28/0.51  thf(fact_1439_power__0__left,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ( N = zero_zero_nat )
% 0.28/0.51         => ( ( power_power_int @ zero_zero_int @ N )
% 0.28/0.51            = one_one_int ) )
% 0.28/0.51        & ( ( N != zero_zero_nat )
% 0.28/0.51         => ( ( power_power_int @ zero_zero_int @ N )
% 0.28/0.51            = zero_zero_int ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_0_left
% 0.28/0.51  thf(fact_1440_power__0__left,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ( N = zero_zero_nat )
% 0.28/0.51         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.28/0.51            = one_one_complex ) )
% 0.28/0.51        & ( ( N != zero_zero_nat )
% 0.28/0.51         => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.28/0.51            = zero_zero_complex ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_0_left
% 0.28/0.51  thf(fact_1441_zero__power,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.28/0.51          = zero_zero_rat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_power
% 0.28/0.51  thf(fact_1442_zero__power,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.28/0.51          = zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_power
% 0.28/0.51  thf(fact_1443_zero__power,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( power_power_real @ zero_zero_real @ N )
% 0.28/0.51          = zero_zero_real ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_power
% 0.28/0.51  thf(fact_1444_zero__power,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( power_power_int @ zero_zero_int @ N )
% 0.28/0.51          = zero_zero_int ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_power
% 0.28/0.51  thf(fact_1445_zero__power,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51       => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.28/0.51          = zero_zero_complex ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_power
% 0.28/0.51  thf(fact_1446_mod__mult__eq,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_eq
% 0.28/0.51  thf(fact_1447_mod__mult__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_eq
% 0.28/0.51  thf(fact_1448_mod__mult__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_eq
% 0.28/0.51  thf(fact_1449_mod__mult__cong,axiom,
% 0.28/0.51      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ A @ C )
% 0.28/0.51          = ( modulo_modulo_nat @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.28/0.51            = ( modulo_modulo_nat @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.28/0.51            = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_cong
% 0.28/0.51  thf(fact_1450_mod__mult__cong,axiom,
% 0.28/0.51      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ A @ C )
% 0.28/0.51          = ( modulo_modulo_int @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo_modulo_int @ B @ C )
% 0.28/0.51            = ( modulo_modulo_int @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 0.28/0.51            = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_cong
% 0.28/0.51  thf(fact_1451_mod__mult__cong,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.28/0.51        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.28/0.51          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_cong
% 0.28/0.51  thf(fact_1452_mod__mult__mult2,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.28/0.51        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_mult2
% 0.28/0.51  thf(fact_1453_mod__mult__mult2,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.51        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_mult2
% 0.28/0.51  thf(fact_1454_mod__mult__mult2,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.28/0.51        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_mult2
% 0.28/0.51  thf(fact_1455_mult__mod__right,axiom,
% 0.28/0.51      ! [C: nat,A: nat,B: nat] :
% 0.28/0.51        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.28/0.51        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mult_mod_right
% 0.28/0.51  thf(fact_1456_mult__mod__right,axiom,
% 0.28/0.51      ! [C: int,A: int,B: int] :
% 0.28/0.51        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.51        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mult_mod_right
% 0.28/0.51  thf(fact_1457_mult__mod__right,axiom,
% 0.28/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.28/0.51        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mult_mod_right
% 0.28/0.51  thf(fact_1458_mod__mult__left__eq,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_left_eq
% 0.28/0.51  thf(fact_1459_mod__mult__left__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_left_eq
% 0.28/0.51  thf(fact_1460_mod__mult__left__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_left_eq
% 0.28/0.51  thf(fact_1461_mod__mult__right__eq,axiom,
% 0.28/0.51      ! [A: nat,B: nat,C: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_right_eq
% 0.28/0.51  thf(fact_1462_mod__mult__right__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_right_eq
% 0.28/0.51  thf(fact_1463_mod__mult__right__eq,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_mult_right_eq
% 0.28/0.51  thf(fact_1464_mod__add__eq,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_eq
% 0.28/0.51  thf(fact_1465_mod__add__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_eq
% 0.28/0.51  thf(fact_1466_mod__add__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_eq
% 0.28/0.51  thf(fact_1467_mod__add__cong,axiom,
% 0.28/0.51      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ A @ C )
% 0.28/0.51          = ( modulo_modulo_nat @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.28/0.51            = ( modulo_modulo_nat @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.51            = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_cong
% 0.28/0.51  thf(fact_1468_mod__add__cong,axiom,
% 0.28/0.51      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ A @ C )
% 0.28/0.51          = ( modulo_modulo_int @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo_modulo_int @ B @ C )
% 0.28/0.51            = ( modulo_modulo_int @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.51            = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_cong
% 0.28/0.51  thf(fact_1469_mod__add__cong,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 0.28/0.51        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.28/0.51          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 0.28/0.51       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 0.28/0.51         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.28/0.51            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_cong
% 0.28/0.51  thf(fact_1470_mod__add__left__eq,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_left_eq
% 0.28/0.51  thf(fact_1471_mod__add__left__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_left_eq
% 0.28/0.51  thf(fact_1472_mod__add__left__eq,axiom,
% 0.28/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_left_eq
% 0.28/0.51  thf(fact_1473_mod__add__right__eq,axiom,
% 0.28/0.51      ! [A: nat,B: nat,C: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_right_eq
% 0.28/0.51  thf(fact_1474_mod__add__right__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_right_eq
% 0.28/0.51  thf(fact_1475_mod__add__right__eq,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_add_right_eq
% 0.28/0.51  thf(fact_1476_power__mod,axiom,
% 0.28/0.51      ! [A: nat,B: nat,N: nat] :
% 0.28/0.51        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 0.28/0.51        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mod
% 0.28/0.51  thf(fact_1477_power__mod,axiom,
% 0.28/0.51      ! [A: int,B: int,N: nat] :
% 0.28/0.51        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 0.28/0.51        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mod
% 0.28/0.51  thf(fact_1478_power__mod,axiom,
% 0.28/0.51      ! [A: code_integer,B: code_integer,N: nat] :
% 0.28/0.51        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 0.28/0.51        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % power_mod
% 0.28/0.51  thf(fact_1479_diff__mono,axiom,
% 0.28/0.51      ! [A: real,B: real,D: real,C: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.51       => ( ( ord_less_eq_real @ D @ C )
% 0.28/0.51         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_mono
% 0.28/0.51  thf(fact_1480_diff__mono,axiom,
% 0.28/0.51      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.51       => ( ( ord_less_eq_rat @ D @ C )
% 0.28/0.51         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_mono
% 0.28/0.51  thf(fact_1481_diff__mono,axiom,
% 0.28/0.51      ! [A: int,B: int,D: int,C: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.51       => ( ( ord_less_eq_int @ D @ C )
% 0.28/0.51         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_mono
% 0.28/0.51  thf(fact_1482_diff__left__mono,axiom,
% 0.28/0.51      ! [B: real,A: real,C: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.51       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_left_mono
% 0.28/0.51  thf(fact_1483_diff__left__mono,axiom,
% 0.28/0.51      ! [B: rat,A: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.51       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_left_mono
% 0.28/0.51  thf(fact_1484_diff__left__mono,axiom,
% 0.28/0.51      ! [B: int,A: int,C: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.51       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_left_mono
% 0.28/0.51  thf(fact_1485_diff__right__mono,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.51       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_mono
% 0.28/0.51  thf(fact_1486_diff__right__mono,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.51       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_mono
% 0.28/0.51  thf(fact_1487_diff__right__mono,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.51       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_right_mono
% 0.28/0.51  thf(fact_1488_diff__eq__diff__less__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.51        ( ( ( minus_minus_real @ A @ B )
% 0.28/0.51          = ( minus_minus_real @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_eq_real @ A @ B )
% 0.28/0.51          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less_eq
% 0.28/0.51  thf(fact_1489_diff__eq__diff__less__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.51        ( ( ( minus_minus_rat @ A @ B )
% 0.28/0.51          = ( minus_minus_rat @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.51          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less_eq
% 0.28/0.51  thf(fact_1490_diff__eq__diff__less__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.51        ( ( ( minus_minus_int @ A @ B )
% 0.28/0.51          = ( minus_minus_int @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_eq_int @ A @ B )
% 0.28/0.51          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less_eq
% 0.28/0.51  thf(fact_1491_diff__strict__mono,axiom,
% 0.28/0.51      ! [A: real,B: real,D: real,C: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ B )
% 0.28/0.51       => ( ( ord_less_real @ D @ C )
% 0.28/0.51         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_mono
% 0.28/0.51  thf(fact_1492_diff__strict__mono,axiom,
% 0.28/0.51      ! [A: rat,B: rat,D: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ B )
% 0.28/0.51       => ( ( ord_less_rat @ D @ C )
% 0.28/0.51         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_mono
% 0.28/0.51  thf(fact_1493_diff__strict__mono,axiom,
% 0.28/0.51      ! [A: int,B: int,D: int,C: int] :
% 0.28/0.51        ( ( ord_less_int @ A @ B )
% 0.28/0.51       => ( ( ord_less_int @ D @ C )
% 0.28/0.51         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_mono
% 0.28/0.51  thf(fact_1494_diff__eq__diff__less,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.51        ( ( ( minus_minus_real @ A @ B )
% 0.28/0.51          = ( minus_minus_real @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_real @ A @ B )
% 0.28/0.51          = ( ord_less_real @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less
% 0.28/0.51  thf(fact_1495_diff__eq__diff__less,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.51        ( ( ( minus_minus_rat @ A @ B )
% 0.28/0.51          = ( minus_minus_rat @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_rat @ A @ B )
% 0.28/0.51          = ( ord_less_rat @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less
% 0.28/0.51  thf(fact_1496_diff__eq__diff__less,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.51        ( ( ( minus_minus_int @ A @ B )
% 0.28/0.51          = ( minus_minus_int @ C @ D ) )
% 0.28/0.51       => ( ( ord_less_int @ A @ B )
% 0.28/0.51          = ( ord_less_int @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_diff_less
% 0.28/0.51  thf(fact_1497_diff__strict__left__mono,axiom,
% 0.28/0.51      ! [B: real,A: real,C: real] :
% 0.28/0.51        ( ( ord_less_real @ B @ A )
% 0.28/0.51       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_left_mono
% 0.28/0.51  thf(fact_1498_diff__strict__left__mono,axiom,
% 0.28/0.51      ! [B: rat,A: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_rat @ B @ A )
% 0.28/0.51       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_left_mono
% 0.28/0.51  thf(fact_1499_diff__strict__left__mono,axiom,
% 0.28/0.51      ! [B: int,A: int,C: int] :
% 0.28/0.51        ( ( ord_less_int @ B @ A )
% 0.28/0.51       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_left_mono
% 0.28/0.51  thf(fact_1500_diff__strict__right__mono,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( ord_less_real @ A @ B )
% 0.28/0.51       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_right_mono
% 0.28/0.51  thf(fact_1501_diff__strict__right__mono,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( ord_less_rat @ A @ B )
% 0.28/0.51       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_right_mono
% 0.28/0.51  thf(fact_1502_diff__strict__right__mono,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( ord_less_int @ A @ B )
% 0.28/0.51       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_strict_right_mono
% 0.28/0.51  thf(fact_1503_left__diff__distrib,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib
% 0.28/0.51  thf(fact_1504_left__diff__distrib,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib
% 0.28/0.51  thf(fact_1505_left__diff__distrib,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib
% 0.28/0.51  thf(fact_1506_right__diff__distrib,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib
% 0.28/0.51  thf(fact_1507_right__diff__distrib,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib
% 0.28/0.51  thf(fact_1508_right__diff__distrib,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib
% 0.28/0.51  thf(fact_1509_left__diff__distrib_H,axiom,
% 0.28/0.51      ! [B: real,C: real,A: real] :
% 0.28/0.51        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib'
% 0.28/0.51  thf(fact_1510_left__diff__distrib_H,axiom,
% 0.28/0.51      ! [B: rat,C: rat,A: rat] :
% 0.28/0.51        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib'
% 0.28/0.51  thf(fact_1511_left__diff__distrib_H,axiom,
% 0.28/0.51      ! [B: nat,C: nat,A: nat] :
% 0.28/0.51        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.28/0.51        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib'
% 0.28/0.51  thf(fact_1512_left__diff__distrib_H,axiom,
% 0.28/0.51      ! [B: int,C: int,A: int] :
% 0.28/0.51        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % left_diff_distrib'
% 0.28/0.51  thf(fact_1513_right__diff__distrib_H,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib'
% 0.28/0.51  thf(fact_1514_right__diff__distrib_H,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib'
% 0.28/0.51  thf(fact_1515_right__diff__distrib_H,axiom,
% 0.28/0.51      ! [A: nat,B: nat,C: nat] :
% 0.28/0.51        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib'
% 0.28/0.51  thf(fact_1516_right__diff__distrib_H,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % right_diff_distrib'
% 0.28/0.51  thf(fact_1517_group__cancel_Osub1,axiom,
% 0.28/0.51      ! [A2: real,K: real,A: real,B: real] :
% 0.28/0.51        ( ( A2
% 0.28/0.51          = ( plus_plus_real @ K @ A ) )
% 0.28/0.51       => ( ( minus_minus_real @ A2 @ B )
% 0.28/0.51          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % group_cancel.sub1
% 0.28/0.51  thf(fact_1518_group__cancel_Osub1,axiom,
% 0.28/0.51      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.28/0.51        ( ( A2
% 0.28/0.51          = ( plus_plus_rat @ K @ A ) )
% 0.28/0.51       => ( ( minus_minus_rat @ A2 @ B )
% 0.28/0.51          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % group_cancel.sub1
% 0.28/0.51  thf(fact_1519_group__cancel_Osub1,axiom,
% 0.28/0.51      ! [A2: int,K: int,A: int,B: int] :
% 0.28/0.51        ( ( A2
% 0.28/0.51          = ( plus_plus_int @ K @ A ) )
% 0.28/0.51       => ( ( minus_minus_int @ A2 @ B )
% 0.28/0.51          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % group_cancel.sub1
% 0.28/0.51  thf(fact_1520_diff__eq__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( ( minus_minus_real @ A @ B )
% 0.28/0.51          = C )
% 0.28/0.51        = ( A
% 0.28/0.51          = ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_eq
% 0.28/0.51  thf(fact_1521_diff__eq__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( ( minus_minus_rat @ A @ B )
% 0.28/0.51          = C )
% 0.28/0.51        = ( A
% 0.28/0.51          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_eq
% 0.28/0.51  thf(fact_1522_diff__eq__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( ( minus_minus_int @ A @ B )
% 0.28/0.51          = C )
% 0.28/0.51        = ( A
% 0.28/0.51          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_eq_eq
% 0.28/0.51  thf(fact_1523_eq__diff__eq,axiom,
% 0.28/0.51      ! [A: real,C: real,B: real] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( minus_minus_real @ C @ B ) )
% 0.28/0.51        = ( ( plus_plus_real @ A @ B )
% 0.28/0.51          = C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_diff_eq
% 0.28/0.51  thf(fact_1524_eq__diff__eq,axiom,
% 0.28/0.51      ! [A: rat,C: rat,B: rat] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( minus_minus_rat @ C @ B ) )
% 0.28/0.51        = ( ( plus_plus_rat @ A @ B )
% 0.28/0.51          = C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_diff_eq
% 0.28/0.51  thf(fact_1525_eq__diff__eq,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int] :
% 0.28/0.51        ( ( A
% 0.28/0.51          = ( minus_minus_int @ C @ B ) )
% 0.28/0.51        = ( ( plus_plus_int @ A @ B )
% 0.28/0.51          = C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_diff_eq
% 0.28/0.51  thf(fact_1526_add__diff__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_eq
% 0.28/0.51  thf(fact_1527_add__diff__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_eq
% 0.28/0.51  thf(fact_1528_add__diff__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_eq
% 0.28/0.51  thf(fact_1529_diff__diff__eq2,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq2
% 0.28/0.51  thf(fact_1530_diff__diff__eq2,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq2
% 0.28/0.51  thf(fact_1531_diff__diff__eq2,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq2
% 0.28/0.51  thf(fact_1532_diff__add__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq
% 0.28/0.51  thf(fact_1533_diff__add__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq
% 0.28/0.51  thf(fact_1534_diff__add__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq
% 0.28/0.51  thf(fact_1535_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.28/0.51        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq_diff_diff_swap
% 0.28/0.51  thf(fact_1536_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.28/0.51        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq_diff_diff_swap
% 0.28/0.51  thf(fact_1537_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.28/0.51        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_eq_diff_diff_swap
% 0.28/0.51  thf(fact_1538_add__implies__diff,axiom,
% 0.28/0.51      ! [C: real,B: real,A: real] :
% 0.28/0.51        ( ( ( plus_plus_real @ C @ B )
% 0.28/0.51          = A )
% 0.28/0.51       => ( C
% 0.28/0.51          = ( minus_minus_real @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_implies_diff
% 0.28/0.51  thf(fact_1539_add__implies__diff,axiom,
% 0.28/0.51      ! [C: rat,B: rat,A: rat] :
% 0.28/0.51        ( ( ( plus_plus_rat @ C @ B )
% 0.28/0.51          = A )
% 0.28/0.51       => ( C
% 0.28/0.51          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_implies_diff
% 0.28/0.51  thf(fact_1540_add__implies__diff,axiom,
% 0.28/0.51      ! [C: nat,B: nat,A: nat] :
% 0.28/0.51        ( ( ( plus_plus_nat @ C @ B )
% 0.28/0.51          = A )
% 0.28/0.51       => ( C
% 0.28/0.51          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_implies_diff
% 0.28/0.51  thf(fact_1541_add__implies__diff,axiom,
% 0.28/0.51      ! [C: int,B: int,A: int] :
% 0.28/0.51        ( ( ( plus_plus_int @ C @ B )
% 0.28/0.51          = A )
% 0.28/0.51       => ( C
% 0.28/0.51          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_implies_diff
% 0.28/0.51  thf(fact_1542_diff__diff__eq,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq
% 0.28/0.51  thf(fact_1543_diff__diff__eq,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq
% 0.28/0.51  thf(fact_1544_diff__diff__eq,axiom,
% 0.28/0.51      ! [A: nat,B: nat,C: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq
% 0.28/0.51  thf(fact_1545_diff__diff__eq,axiom,
% 0.28/0.51      ! [A: int,B: int,C: int] :
% 0.28/0.51        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_diff_eq
% 0.28/0.51  thf(fact_1546_add__diff__add,axiom,
% 0.28/0.51      ! [A: real,C: real,B: real,D: real] :
% 0.28/0.51        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 0.28/0.51        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_add
% 0.28/0.51  thf(fact_1547_add__diff__add,axiom,
% 0.28/0.51      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.28/0.51        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 0.28/0.51        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_add
% 0.28/0.51  thf(fact_1548_add__diff__add,axiom,
% 0.28/0.51      ! [A: int,C: int,B: int,D: int] :
% 0.28/0.51        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 0.28/0.51        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % add_diff_add
% 0.28/0.51  thf(fact_1549_mod__less__eq__dividend,axiom,
% 0.28/0.51      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 0.28/0.51  
% 0.28/0.51  % mod_less_eq_dividend
% 0.28/0.51  thf(fact_1550_diff__divide__distrib,axiom,
% 0.28/0.51      ! [A: complex,B: complex,C: complex] :
% 0.28/0.51        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_distrib
% 0.28/0.51  thf(fact_1551_diff__divide__distrib,axiom,
% 0.28/0.51      ! [A: real,B: real,C: real] :
% 0.28/0.51        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_distrib
% 0.28/0.51  thf(fact_1552_diff__divide__distrib,axiom,
% 0.28/0.51      ! [A: rat,B: rat,C: rat] :
% 0.28/0.51        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.51        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_divide_distrib
% 0.28/0.51  thf(fact_1553_diff__less__mono2,axiom,
% 0.28/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.28/0.51        ( ( ord_less_nat @ M @ N )
% 0.28/0.51       => ( ( ord_less_nat @ M @ L2 )
% 0.28/0.51         => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_less_mono2
% 0.28/0.51  thf(fact_1554_less__imp__diff__less,axiom,
% 0.28/0.51      ! [J: nat,K: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ J @ K )
% 0.28/0.51       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.28/0.51  
% 0.28/0.51  % less_imp_diff_less
% 0.28/0.51  thf(fact_1555_eq__diff__iff,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.28/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.51         => ( ( ( minus_minus_nat @ M @ K )
% 0.28/0.51              = ( minus_minus_nat @ N @ K ) )
% 0.28/0.51            = ( M = N ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % eq_diff_iff
% 0.28/0.51  thf(fact_1556_le__diff__iff,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.28/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.51         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.28/0.51            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_diff_iff
% 0.28/0.51  thf(fact_1557_Nat_Odiff__diff__eq,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ K @ M )
% 0.28/0.51       => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.51         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.28/0.51            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % Nat.diff_diff_eq
% 0.28/0.51  thf(fact_1558_diff__le__mono,axiom,
% 0.28/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_le_mono
% 0.28/0.51  thf(fact_1559_diff__le__self,axiom,
% 0.28/0.51      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_le_self
% 0.28/0.51  thf(fact_1560_le__diff__iff_H,axiom,
% 0.28/0.51      ! [A: nat,C: nat,B: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ A @ C )
% 0.28/0.51       => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.51         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.28/0.51            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % le_diff_iff'
% 0.28/0.51  thf(fact_1561_diff__le__mono2,axiom,
% 0.28/0.51      ! [M: nat,N: nat,L2: nat] :
% 0.28/0.51        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.51       => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_le_mono2
% 0.28/0.51  thf(fact_1562_Nat_Odiff__cancel,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.28/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % Nat.diff_cancel
% 0.28/0.51  thf(fact_1563_diff__cancel2,axiom,
% 0.28/0.51      ! [M: nat,K: nat,N: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.28/0.51        = ( minus_minus_nat @ M @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_cancel2
% 0.28/0.51  thf(fact_1564_diff__add__inverse,axiom,
% 0.28/0.51      ! [N: nat,M: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.28/0.51        = M ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_inverse
% 0.28/0.51  thf(fact_1565_diff__add__inverse2,axiom,
% 0.28/0.51      ! [M: nat,N: nat] :
% 0.28/0.51        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.28/0.51        = M ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_add_inverse2
% 0.28/0.51  thf(fact_1566_diff__mult__distrib,axiom,
% 0.28/0.51      ! [M: nat,N: nat,K: nat] :
% 0.28/0.51        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.28/0.51        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_mult_distrib
% 0.28/0.51  thf(fact_1567_diff__mult__distrib2,axiom,
% 0.28/0.51      ! [K: nat,M: nat,N: nat] :
% 0.28/0.51        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.51        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % diff_mult_distrib2
% 0.28/0.51  thf(fact_1568_zero__le,axiom,
% 0.28/0.51      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_le
% 0.28/0.51  thf(fact_1569_le__numeral__extra_I3_J,axiom,
% 0.28/0.51      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.28/0.51  
% 0.28/0.51  % le_numeral_extra(3)
% 0.28/0.51  thf(fact_1570_le__numeral__extra_I3_J,axiom,
% 0.28/0.51      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.28/0.51  
% 0.28/0.51  % le_numeral_extra(3)
% 0.28/0.51  thf(fact_1571_le__numeral__extra_I3_J,axiom,
% 0.28/0.51      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.28/0.51  
% 0.28/0.51  % le_numeral_extra(3)
% 0.28/0.51  thf(fact_1572_le__numeral__extra_I3_J,axiom,
% 0.28/0.51      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.28/0.51  
% 0.28/0.51  % le_numeral_extra(3)
% 0.28/0.51  thf(fact_1573_gr__zeroI,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( N != zero_zero_nat )
% 0.28/0.51       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % gr_zeroI
% 0.28/0.51  thf(fact_1574_not__less__zero,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % not_less_zero
% 0.28/0.51  thf(fact_1575_gr__implies__not__zero,axiom,
% 0.28/0.51      ! [M: nat,N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ M @ N )
% 0.28/0.51       => ( N != zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % gr_implies_not_zero
% 0.28/0.51  thf(fact_1576_zero__less__iff__neq__zero,axiom,
% 0.28/0.51      ! [N: nat] :
% 0.28/0.51        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.51        = ( N != zero_zero_nat ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_less_iff_neq_zero
% 0.28/0.51  thf(fact_1577_less__numeral__extra_I3_J,axiom,
% 0.28/0.51      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.28/0.51  
% 0.28/0.51  % less_numeral_extra(3)
% 0.28/0.51  thf(fact_1578_less__numeral__extra_I3_J,axiom,
% 0.28/0.51      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.28/0.51  
% 0.28/0.51  % less_numeral_extra(3)
% 0.28/0.51  thf(fact_1579_less__numeral__extra_I3_J,axiom,
% 0.28/0.51      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.28/0.51  
% 0.28/0.51  % less_numeral_extra(3)
% 0.28/0.51  thf(fact_1580_less__numeral__extra_I3_J,axiom,
% 0.28/0.51      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.28/0.51  
% 0.28/0.51  % less_numeral_extra(3)
% 0.28/0.51  thf(fact_1581_field__lbound__gt__zero,axiom,
% 0.28/0.51      ! [D1: real,D22: real] :
% 0.28/0.51        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.28/0.51       => ( ( ord_less_real @ zero_zero_real @ D22 )
% 0.28/0.51         => ? [E2: real] :
% 0.28/0.51              ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.28/0.51              & ( ord_less_real @ E2 @ D1 )
% 0.28/0.51              & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % field_lbound_gt_zero
% 0.28/0.51  thf(fact_1582_field__lbound__gt__zero,axiom,
% 0.28/0.51      ! [D1: rat,D22: rat] :
% 0.28/0.51        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.28/0.51       => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 0.28/0.51         => ? [E2: rat] :
% 0.28/0.51              ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.28/0.51              & ( ord_less_rat @ E2 @ D1 )
% 0.28/0.51              & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % field_lbound_gt_zero
% 0.28/0.51  thf(fact_1583_zero__neq__numeral,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( zero_zero_complex
% 0.28/0.51       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_neq_numeral
% 0.28/0.51  thf(fact_1584_zero__neq__numeral,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( zero_zero_real
% 0.28/0.51       != ( numeral_numeral_real @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_neq_numeral
% 0.28/0.51  thf(fact_1585_zero__neq__numeral,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( zero_zero_rat
% 0.28/0.51       != ( numeral_numeral_rat @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_neq_numeral
% 0.28/0.51  thf(fact_1586_zero__neq__numeral,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( zero_zero_nat
% 0.28/0.51       != ( numeral_numeral_nat @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_neq_numeral
% 0.28/0.51  thf(fact_1587_zero__neq__numeral,axiom,
% 0.28/0.51      ! [N: num] :
% 0.28/0.51        ( zero_zero_int
% 0.28/0.51       != ( numeral_numeral_int @ N ) ) ).
% 0.28/0.51  
% 0.28/0.51  % zero_neq_numeral
% 0.28/0.51  thf(fact_1588_cong__exp__iff__simps_I9_J,axiom,
% 0.28/0.51      ! [M: num,Q2: num,N: num] :
% 0.28/0.51        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.28/0.51          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.28/0.51        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.28/0.51          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.28/0.51  
% 0.28/0.51  % cong_exp_iff_simps(9)
% 0.28/0.51  thf(fact_1589_cong__exp__iff__simps_I9_J,axiom,
% 0.28/0.51      ! [M: num,Q2: num,N: num] :
% 0.28/0.51        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.28/0.52          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.28/0.52        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.28/0.52          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(9)
% 0.28/0.52  thf(fact_1590_cong__exp__iff__simps_I9_J,axiom,
% 0.28/0.52      ! [M: num,Q2: num,N: num] :
% 0.28/0.52        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.28/0.52          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.28/0.52        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.28/0.52          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(9)
% 0.28/0.52  thf(fact_1591_cong__exp__iff__simps_I4_J,axiom,
% 0.28/0.52      ! [M: num,N: num] :
% 0.28/0.52        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 0.28/0.52        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(4)
% 0.28/0.52  thf(fact_1592_cong__exp__iff__simps_I4_J,axiom,
% 0.28/0.52      ! [M: num,N: num] :
% 0.28/0.52        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 0.28/0.52        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(4)
% 0.28/0.52  thf(fact_1593_cong__exp__iff__simps_I4_J,axiom,
% 0.28/0.52      ! [M: num,N: num] :
% 0.28/0.52        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 0.28/0.52        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(4)
% 0.28/0.52  thf(fact_1594_mult__not__zero,axiom,
% 0.28/0.52      ! [A: complex,B: complex] :
% 0.28/0.52        ( ( ( times_times_complex @ A @ B )
% 0.28/0.52         != zero_zero_complex )
% 0.28/0.52       => ( ( A != zero_zero_complex )
% 0.28/0.52          & ( B != zero_zero_complex ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_not_zero
% 0.28/0.52  thf(fact_1595_mult__not__zero,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ( times_times_real @ A @ B )
% 0.28/0.52         != zero_zero_real )
% 0.28/0.52       => ( ( A != zero_zero_real )
% 0.28/0.52          & ( B != zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_not_zero
% 0.28/0.52  thf(fact_1596_mult__not__zero,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ( times_times_rat @ A @ B )
% 0.28/0.52         != zero_zero_rat )
% 0.28/0.52       => ( ( A != zero_zero_rat )
% 0.28/0.52          & ( B != zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_not_zero
% 0.28/0.52  thf(fact_1597_mult__not__zero,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ( times_times_nat @ A @ B )
% 0.28/0.52         != zero_zero_nat )
% 0.28/0.52       => ( ( A != zero_zero_nat )
% 0.28/0.52          & ( B != zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_not_zero
% 0.28/0.52  thf(fact_1598_mult__not__zero,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ( times_times_int @ A @ B )
% 0.28/0.52         != zero_zero_int )
% 0.28/0.52       => ( ( A != zero_zero_int )
% 0.28/0.52          & ( B != zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_not_zero
% 0.28/0.52  thf(fact_1599_divisors__zero,axiom,
% 0.28/0.52      ! [A: complex,B: complex] :
% 0.28/0.52        ( ( ( times_times_complex @ A @ B )
% 0.28/0.52          = zero_zero_complex )
% 0.28/0.52       => ( ( A = zero_zero_complex )
% 0.28/0.52          | ( B = zero_zero_complex ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divisors_zero
% 0.28/0.52  thf(fact_1600_divisors__zero,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ( times_times_real @ A @ B )
% 0.28/0.52          = zero_zero_real )
% 0.28/0.52       => ( ( A = zero_zero_real )
% 0.28/0.52          | ( B = zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divisors_zero
% 0.28/0.52  thf(fact_1601_divisors__zero,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ( times_times_rat @ A @ B )
% 0.28/0.52          = zero_zero_rat )
% 0.28/0.52       => ( ( A = zero_zero_rat )
% 0.28/0.52          | ( B = zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divisors_zero
% 0.28/0.52  thf(fact_1602_divisors__zero,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ( times_times_nat @ A @ B )
% 0.28/0.52          = zero_zero_nat )
% 0.28/0.52       => ( ( A = zero_zero_nat )
% 0.28/0.52          | ( B = zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divisors_zero
% 0.28/0.52  thf(fact_1603_divisors__zero,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ( times_times_int @ A @ B )
% 0.28/0.52          = zero_zero_int )
% 0.28/0.52       => ( ( A = zero_zero_int )
% 0.28/0.52          | ( B = zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divisors_zero
% 0.28/0.52  thf(fact_1604_no__zero__divisors,axiom,
% 0.28/0.52      ! [A: complex,B: complex] :
% 0.28/0.52        ( ( A != zero_zero_complex )
% 0.28/0.52       => ( ( B != zero_zero_complex )
% 0.28/0.52         => ( ( times_times_complex @ A @ B )
% 0.28/0.52           != zero_zero_complex ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % no_zero_divisors
% 0.28/0.52  thf(fact_1605_no__zero__divisors,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( A != zero_zero_real )
% 0.28/0.52       => ( ( B != zero_zero_real )
% 0.28/0.52         => ( ( times_times_real @ A @ B )
% 0.28/0.52           != zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % no_zero_divisors
% 0.28/0.52  thf(fact_1606_no__zero__divisors,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( A != zero_zero_rat )
% 0.28/0.52       => ( ( B != zero_zero_rat )
% 0.28/0.52         => ( ( times_times_rat @ A @ B )
% 0.28/0.52           != zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % no_zero_divisors
% 0.28/0.52  thf(fact_1607_no__zero__divisors,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( A != zero_zero_nat )
% 0.28/0.52       => ( ( B != zero_zero_nat )
% 0.28/0.52         => ( ( times_times_nat @ A @ B )
% 0.28/0.52           != zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % no_zero_divisors
% 0.28/0.52  thf(fact_1608_no__zero__divisors,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( A != zero_zero_int )
% 0.28/0.52       => ( ( B != zero_zero_int )
% 0.28/0.52         => ( ( times_times_int @ A @ B )
% 0.28/0.52           != zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % no_zero_divisors
% 0.28/0.52  thf(fact_1609_mult__left__cancel,axiom,
% 0.28/0.52      ! [C: complex,A: complex,B: complex] :
% 0.28/0.52        ( ( C != zero_zero_complex )
% 0.28/0.52       => ( ( ( times_times_complex @ C @ A )
% 0.28/0.52            = ( times_times_complex @ C @ B ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_cancel
% 0.28/0.52  thf(fact_1610_mult__left__cancel,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( C != zero_zero_real )
% 0.28/0.52       => ( ( ( times_times_real @ C @ A )
% 0.28/0.52            = ( times_times_real @ C @ B ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_cancel
% 0.28/0.52  thf(fact_1611_mult__left__cancel,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( C != zero_zero_rat )
% 0.28/0.52       => ( ( ( times_times_rat @ C @ A )
% 0.28/0.52            = ( times_times_rat @ C @ B ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_cancel
% 0.28/0.52  thf(fact_1612_mult__left__cancel,axiom,
% 0.28/0.52      ! [C: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( C != zero_zero_nat )
% 0.28/0.52       => ( ( ( times_times_nat @ C @ A )
% 0.28/0.52            = ( times_times_nat @ C @ B ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_cancel
% 0.28/0.52  thf(fact_1613_mult__left__cancel,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( C != zero_zero_int )
% 0.28/0.52       => ( ( ( times_times_int @ C @ A )
% 0.28/0.52            = ( times_times_int @ C @ B ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_cancel
% 0.28/0.52  thf(fact_1614_mult__right__cancel,axiom,
% 0.28/0.52      ! [C: complex,A: complex,B: complex] :
% 0.28/0.52        ( ( C != zero_zero_complex )
% 0.28/0.52       => ( ( ( times_times_complex @ A @ C )
% 0.28/0.52            = ( times_times_complex @ B @ C ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_cancel
% 0.28/0.52  thf(fact_1615_mult__right__cancel,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( C != zero_zero_real )
% 0.28/0.52       => ( ( ( times_times_real @ A @ C )
% 0.28/0.52            = ( times_times_real @ B @ C ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_cancel
% 0.28/0.52  thf(fact_1616_mult__right__cancel,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( C != zero_zero_rat )
% 0.28/0.52       => ( ( ( times_times_rat @ A @ C )
% 0.28/0.52            = ( times_times_rat @ B @ C ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_cancel
% 0.28/0.52  thf(fact_1617_mult__right__cancel,axiom,
% 0.28/0.52      ! [C: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( C != zero_zero_nat )
% 0.28/0.52       => ( ( ( times_times_nat @ A @ C )
% 0.28/0.52            = ( times_times_nat @ B @ C ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_cancel
% 0.28/0.52  thf(fact_1618_mult__right__cancel,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( C != zero_zero_int )
% 0.28/0.52       => ( ( ( times_times_int @ A @ C )
% 0.28/0.52            = ( times_times_int @ B @ C ) )
% 0.28/0.52          = ( A = B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_cancel
% 0.28/0.52  thf(fact_1619_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.52      ! [A: complex] :
% 0.28/0.52        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % comm_monoid_add_class.add_0
% 0.28/0.52  thf(fact_1620_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.52      ! [A: real] :
% 0.28/0.52        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % comm_monoid_add_class.add_0
% 0.28/0.52  thf(fact_1621_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.52      ! [A: rat] :
% 0.28/0.52        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % comm_monoid_add_class.add_0
% 0.28/0.52  thf(fact_1622_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.52      ! [A: nat] :
% 0.28/0.52        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % comm_monoid_add_class.add_0
% 0.28/0.52  thf(fact_1623_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.52      ! [A: int] :
% 0.28/0.52        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % comm_monoid_add_class.add_0
% 0.28/0.52  thf(fact_1624_add_Ocomm__neutral,axiom,
% 0.28/0.52      ! [A: complex] :
% 0.28/0.52        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.comm_neutral
% 0.28/0.52  thf(fact_1625_add_Ocomm__neutral,axiom,
% 0.28/0.52      ! [A: real] :
% 0.28/0.52        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.comm_neutral
% 0.28/0.52  thf(fact_1626_add_Ocomm__neutral,axiom,
% 0.28/0.52      ! [A: rat] :
% 0.28/0.52        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.comm_neutral
% 0.28/0.52  thf(fact_1627_add_Ocomm__neutral,axiom,
% 0.28/0.52      ! [A: nat] :
% 0.28/0.52        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.comm_neutral
% 0.28/0.52  thf(fact_1628_add_Ocomm__neutral,axiom,
% 0.28/0.52      ! [A: int] :
% 0.28/0.52        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.comm_neutral
% 0.28/0.52  thf(fact_1629_add_Ogroup__left__neutral,axiom,
% 0.28/0.52      ! [A: complex] :
% 0.28/0.52        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.group_left_neutral
% 0.28/0.52  thf(fact_1630_add_Ogroup__left__neutral,axiom,
% 0.28/0.52      ! [A: real] :
% 0.28/0.52        ( ( plus_plus_real @ zero_zero_real @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.group_left_neutral
% 0.28/0.52  thf(fact_1631_add_Ogroup__left__neutral,axiom,
% 0.28/0.52      ! [A: rat] :
% 0.28/0.52        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.group_left_neutral
% 0.28/0.52  thf(fact_1632_add_Ogroup__left__neutral,axiom,
% 0.28/0.52      ! [A: int] :
% 0.28/0.52        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.28/0.52        = A ) ).
% 0.28/0.52  
% 0.28/0.52  % add.group_left_neutral
% 0.28/0.52  thf(fact_1633_zero__neq__one,axiom,
% 0.28/0.52      zero_zero_complex != one_one_complex ).
% 0.28/0.52  
% 0.28/0.52  % zero_neq_one
% 0.28/0.52  thf(fact_1634_zero__neq__one,axiom,
% 0.28/0.52      zero_zero_real != one_one_real ).
% 0.28/0.52  
% 0.28/0.52  % zero_neq_one
% 0.28/0.52  thf(fact_1635_zero__neq__one,axiom,
% 0.28/0.52      zero_zero_rat != one_one_rat ).
% 0.28/0.52  
% 0.28/0.52  % zero_neq_one
% 0.28/0.52  thf(fact_1636_zero__neq__one,axiom,
% 0.28/0.52      zero_zero_nat != one_one_nat ).
% 0.28/0.52  
% 0.28/0.52  % zero_neq_one
% 0.28/0.52  thf(fact_1637_zero__neq__one,axiom,
% 0.28/0.52      zero_zero_int != one_one_int ).
% 0.28/0.52  
% 0.28/0.52  % zero_neq_one
% 0.28/0.52  thf(fact_1638_power__not__zero,axiom,
% 0.28/0.52      ! [A: rat,N: nat] :
% 0.28/0.52        ( ( A != zero_zero_rat )
% 0.28/0.52       => ( ( power_power_rat @ A @ N )
% 0.28/0.52         != zero_zero_rat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_not_zero
% 0.28/0.52  thf(fact_1639_power__not__zero,axiom,
% 0.28/0.52      ! [A: nat,N: nat] :
% 0.28/0.52        ( ( A != zero_zero_nat )
% 0.28/0.52       => ( ( power_power_nat @ A @ N )
% 0.28/0.52         != zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_not_zero
% 0.28/0.52  thf(fact_1640_power__not__zero,axiom,
% 0.28/0.52      ! [A: real,N: nat] :
% 0.28/0.52        ( ( A != zero_zero_real )
% 0.28/0.52       => ( ( power_power_real @ A @ N )
% 0.28/0.52         != zero_zero_real ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_not_zero
% 0.28/0.52  thf(fact_1641_power__not__zero,axiom,
% 0.28/0.52      ! [A: int,N: nat] :
% 0.28/0.52        ( ( A != zero_zero_int )
% 0.28/0.52       => ( ( power_power_int @ A @ N )
% 0.28/0.52         != zero_zero_int ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_not_zero
% 0.28/0.52  thf(fact_1642_power__not__zero,axiom,
% 0.28/0.52      ! [A: complex,N: nat] :
% 0.28/0.52        ( ( A != zero_zero_complex )
% 0.28/0.52       => ( ( power_power_complex @ A @ N )
% 0.28/0.52         != zero_zero_complex ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_not_zero
% 0.28/0.52  thf(fact_1643_num_Osize_I4_J,axiom,
% 0.28/0.52      ( ( size_size_num @ one )
% 0.28/0.52      = zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % num.size(4)
% 0.28/0.52  thf(fact_1644_bot__nat__0_Oextremum__strict,axiom,
% 0.28/0.52      ! [A: nat] :
% 0.28/0.52        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % bot_nat_0.extremum_strict
% 0.28/0.52  thf(fact_1645_gr0I,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ( ( N != zero_zero_nat )
% 0.28/0.52       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % gr0I
% 0.28/0.52  thf(fact_1646_not__gr0,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.28/0.52        = ( N = zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % not_gr0
% 0.28/0.52  thf(fact_1647_not__less0,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_less0
% 0.28/0.52  thf(fact_1648_less__zeroE,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % less_zeroE
% 0.28/0.52  thf(fact_1649_gr__implies__not0,axiom,
% 0.28/0.52      ! [M: nat,N: nat] :
% 0.28/0.52        ( ( ord_less_nat @ M @ N )
% 0.28/0.52       => ( N != zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % gr_implies_not0
% 0.28/0.52  thf(fact_1650_infinite__descent0,axiom,
% 0.28/0.52      ! [P: nat > $o,N: nat] :
% 0.28/0.52        ( ( P @ zero_zero_nat )
% 0.28/0.52       => ( ! [N3: nat] :
% 0.28/0.52              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.28/0.52             => ( ~ ( P @ N3 )
% 0.28/0.52               => ? [M2: nat] :
% 0.28/0.52                    ( ( ord_less_nat @ M2 @ N3 )
% 0.28/0.52                    & ~ ( P @ M2 ) ) ) )
% 0.28/0.52         => ( P @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % infinite_descent0
% 0.28/0.52  thf(fact_1651_less__eq__nat_Osimps_I1_J,axiom,
% 0.28/0.52      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.28/0.52  
% 0.28/0.52  % less_eq_nat.simps(1)
% 0.28/0.52  thf(fact_1652_bot__nat__0_Oextremum__unique,axiom,
% 0.28/0.52      ! [A: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52        = ( A = zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % bot_nat_0.extremum_unique
% 0.28/0.52  thf(fact_1653_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.28/0.52      ! [A: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( A = zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % bot_nat_0.extremum_uniqueI
% 0.28/0.52  thf(fact_1654_le__0__eq,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.28/0.52        = ( N = zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_0_eq
% 0.28/0.52  thf(fact_1655_plus__nat_Oadd__0,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.28/0.52        = N ) ).
% 0.28/0.52  
% 0.28/0.52  % plus_nat.add_0
% 0.28/0.52  thf(fact_1656_add__eq__self__zero,axiom,
% 0.28/0.52      ! [M: nat,N: nat] :
% 0.28/0.52        ( ( ( plus_plus_nat @ M @ N )
% 0.28/0.52          = M )
% 0.28/0.52       => ( N = zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_eq_self_zero
% 0.28/0.52  thf(fact_1657_nat__mult__eq__cancel__disj,axiom,
% 0.28/0.52      ! [K: nat,M: nat,N: nat] :
% 0.28/0.52        ( ( ( times_times_nat @ K @ M )
% 0.28/0.52          = ( times_times_nat @ K @ N ) )
% 0.28/0.52        = ( ( K = zero_zero_nat )
% 0.28/0.52          | ( M = N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % nat_mult_eq_cancel_disj
% 0.28/0.52  thf(fact_1658_mult__0,axiom,
% 0.28/0.52      ! [N: nat] :
% 0.28/0.52        ( ( times_times_nat @ zero_zero_nat @ N )
% 0.28/0.52        = zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_0
% 0.28/0.52  thf(fact_1659_nat__mod__eq__iff,axiom,
% 0.28/0.52      ! [X: nat,N: nat,Y: nat] :
% 0.28/0.52        ( ( ( modulo_modulo_nat @ X @ N )
% 0.28/0.52          = ( modulo_modulo_nat @ Y @ N ) )
% 0.28/0.52        = ( ? [Q1: nat,Q22: nat] :
% 0.28/0.52              ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 0.28/0.52              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % nat_mod_eq_iff
% 0.28/0.52  thf(fact_1660_pos__zdiv__mult__2,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( 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 ) )
% 0.28/0.52          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % pos_zdiv_mult_2
% 0.28/0.52  thf(fact_1661_neg__zdiv__mult__2,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( 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 ) )
% 0.28/0.52          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % neg_zdiv_mult_2
% 0.28/0.52  thf(fact_1662_frac__le__eq,axiom,
% 0.28/0.52      ! [Y: real,Z: real,X: real,W: real] :
% 0.28/0.52        ( ( Y != zero_zero_real )
% 0.28/0.52       => ( ( Z != zero_zero_real )
% 0.28/0.52         => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.28/0.52            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % frac_le_eq
% 0.28/0.52  thf(fact_1663_frac__le__eq,axiom,
% 0.28/0.52      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.28/0.52        ( ( Y != zero_zero_rat )
% 0.28/0.52       => ( ( Z != zero_zero_rat )
% 0.28/0.52         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.28/0.52            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % frac_le_eq
% 0.28/0.52  thf(fact_1664_frac__less__eq,axiom,
% 0.28/0.52      ! [Y: real,Z: real,X: real,W: real] :
% 0.28/0.52        ( ( Y != zero_zero_real )
% 0.28/0.52       => ( ( Z != zero_zero_real )
% 0.28/0.52         => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.28/0.52            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % frac_less_eq
% 0.28/0.52  thf(fact_1665_frac__less__eq,axiom,
% 0.28/0.52      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.28/0.52        ( ( Y != zero_zero_rat )
% 0.28/0.52       => ( ( Z != zero_zero_rat )
% 0.28/0.52         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.28/0.52            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % frac_less_eq
% 0.28/0.52  thf(fact_1666_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.28/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.28/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.28/0.52       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.28/0.52          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.28/0.52  thf(fact_1667_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.28/0.52      ! [C: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.28/0.52          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.28/0.52  thf(fact_1668_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.28/0.52          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.28/0.52  thf(fact_1669_not__iless0,axiom,
% 0.28/0.52      ! [N: extended_enat] :
% 0.28/0.52        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_iless0
% 0.28/0.52  thf(fact_1670_enat__0__less__mult__iff,axiom,
% 0.28/0.52      ! [M: extended_enat,N: extended_enat] :
% 0.28/0.52        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 0.28/0.52        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.28/0.52          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % enat_0_less_mult_iff
% 0.28/0.52  thf(fact_1671_power__diff,axiom,
% 0.28/0.52      ! [A: complex,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_complex )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff
% 0.28/0.52  thf(fact_1672_power__diff,axiom,
% 0.28/0.52      ! [A: real,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff
% 0.28/0.52  thf(fact_1673_power__diff,axiom,
% 0.28/0.52      ! [A: rat,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff
% 0.28/0.52  thf(fact_1674_power__diff,axiom,
% 0.28/0.52      ! [A: nat,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff
% 0.28/0.52  thf(fact_1675_power__diff,axiom,
% 0.28/0.52      ! [A: int,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff
% 0.28/0.52  thf(fact_1676_split__mod,axiom,
% 0.28/0.52      ! [P: nat > $o,M: nat,N: nat] :
% 0.28/0.52        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 0.28/0.52        = ( ( ( N = zero_zero_nat )
% 0.28/0.52           => ( P @ M ) )
% 0.28/0.52          & ( ( N != zero_zero_nat )
% 0.28/0.52           => ! [I5: nat,J3: nat] :
% 0.28/0.52                ( ( ord_less_nat @ J3 @ N )
% 0.28/0.52               => ( ( M
% 0.28/0.52                    = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 0.28/0.52                 => ( P @ J3 ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mod
% 0.28/0.52  thf(fact_1677_i0__lb,axiom,
% 0.28/0.52      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 0.28/0.52  
% 0.28/0.52  % i0_lb
% 0.28/0.52  thf(fact_1678_ile0__eq,axiom,
% 0.28/0.52      ! [N: extended_enat] :
% 0.28/0.52        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.28/0.52        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ile0_eq
% 0.28/0.52  thf(fact_1679_divmod__digit__1_I2_J,axiom,
% 0.28/0.52      ! [A: code_integer,B: code_integer] :
% 0.28/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.52       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.52         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.52           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_1(2)
% 0.28/0.52  thf(fact_1680_divmod__digit__1_I2_J,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.52           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_1(2)
% 0.28/0.52  thf(fact_1681_divmod__digit__1_I2_J,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.52           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_1(2)
% 0.28/0.52  thf(fact_1682_power__eq__iff__eq__base,axiom,
% 0.28/0.52      ! [N: nat,A: real,B: real] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52           => ( ( ( power_power_real @ A @ N )
% 0.28/0.52                = ( power_power_real @ B @ N ) )
% 0.28/0.52              = ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_iff_eq_base
% 0.28/0.52  thf(fact_1683_power__eq__iff__eq__base,axiom,
% 0.28/0.52      ! [N: nat,A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52           => ( ( ( power_power_rat @ A @ N )
% 0.28/0.52                = ( power_power_rat @ B @ N ) )
% 0.28/0.52              = ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_iff_eq_base
% 0.28/0.52  thf(fact_1684_power__eq__iff__eq__base,axiom,
% 0.28/0.52      ! [N: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52           => ( ( ( power_power_nat @ A @ N )
% 0.28/0.52                = ( power_power_nat @ B @ N ) )
% 0.28/0.52              = ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_iff_eq_base
% 0.28/0.52  thf(fact_1685_power__eq__iff__eq__base,axiom,
% 0.28/0.52      ! [N: nat,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52           => ( ( ( power_power_int @ A @ N )
% 0.28/0.52                = ( power_power_int @ B @ N ) )
% 0.28/0.52              = ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_iff_eq_base
% 0.28/0.52  thf(fact_1686_power__eq__imp__eq__base,axiom,
% 0.28/0.52      ! [A: real,N: nat,B: real] :
% 0.28/0.52        ( ( ( power_power_real @ A @ N )
% 0.28/0.52          = ( power_power_real @ B @ N ) )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52             => ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_imp_eq_base
% 0.28/0.52  thf(fact_1687_power__eq__imp__eq__base,axiom,
% 0.28/0.52      ! [A: rat,N: nat,B: rat] :
% 0.28/0.52        ( ( ( power_power_rat @ A @ N )
% 0.28/0.52          = ( power_power_rat @ B @ N ) )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52             => ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_imp_eq_base
% 0.28/0.52  thf(fact_1688_power__eq__imp__eq__base,axiom,
% 0.28/0.52      ! [A: nat,N: nat,B: nat] :
% 0.28/0.52        ( ( ( power_power_nat @ A @ N )
% 0.28/0.52          = ( power_power_nat @ B @ N ) )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52             => ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_imp_eq_base
% 0.28/0.52  thf(fact_1689_power__eq__imp__eq__base,axiom,
% 0.28/0.52      ! [A: int,N: nat,B: int] :
% 0.28/0.52        ( ( ( power_power_int @ A @ N )
% 0.28/0.52          = ( power_power_int @ B @ N ) )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52             => ( A = B ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_imp_eq_base
% 0.28/0.52  thf(fact_1690_mult__eq__if,axiom,
% 0.28/0.52      ( times_times_nat
% 0.28/0.52      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_eq_if
% 0.28/0.52  thf(fact_1691_divmod__digit__0_I2_J,axiom,
% 0.28/0.52      ! [B: nat,A: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.28/0.52            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_0(2)
% 0.28/0.52  thf(fact_1692_divmod__digit__0_I2_J,axiom,
% 0.28/0.52      ! [B: int,A: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.28/0.52            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_0(2)
% 0.28/0.52  thf(fact_1693_divmod__digit__0_I2_J,axiom,
% 0.28/0.52      ! [B: code_integer,A: code_integer] :
% 0.28/0.52        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.52       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.52         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 0.28/0.52            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % divmod_digit_0(2)
% 0.28/0.52  thf(fact_1694_cong__exp__iff__simps_I8_J,axiom,
% 0.28/0.52      ! [M: num,Q2: num] :
% 0.28/0.52        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(8)
% 0.28/0.52  thf(fact_1695_cong__exp__iff__simps_I8_J,axiom,
% 0.28/0.52      ! [M: num,Q2: num] :
% 0.28/0.52        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(8)
% 0.28/0.52  thf(fact_1696_cong__exp__iff__simps_I8_J,axiom,
% 0.28/0.52      ! [M: num,Q2: num] :
% 0.28/0.52        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(8)
% 0.28/0.52  thf(fact_1697_cong__exp__iff__simps_I6_J,axiom,
% 0.28/0.52      ! [Q2: num,N: num] :
% 0.28/0.52        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(6)
% 0.28/0.52  thf(fact_1698_cong__exp__iff__simps_I6_J,axiom,
% 0.28/0.52      ! [Q2: num,N: num] :
% 0.28/0.52        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(6)
% 0.28/0.52  thf(fact_1699_cong__exp__iff__simps_I6_J,axiom,
% 0.28/0.52      ! [Q2: num,N: num] :
% 0.28/0.52        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.28/0.52       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % cong_exp_iff_simps(6)
% 0.28/0.52  thf(fact_1700_scaling__mono,axiom,
% 0.28/0.52      ! [U: real,V: real,R: real,S: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ U @ V )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 0.28/0.52         => ( ( ord_less_eq_real @ R @ S )
% 0.28/0.52           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % scaling_mono
% 0.28/0.52  thf(fact_1701_scaling__mono,axiom,
% 0.28/0.52      ! [U: rat,V: rat,R: rat,S: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ U @ V )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 0.28/0.52         => ( ( ord_less_eq_rat @ R @ S )
% 0.28/0.52           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % scaling_mono
% 0.28/0.52  thf(fact_1702_mod__eqE,axiom,
% 0.28/0.52      ! [A: int,C: int,B: int] :
% 0.28/0.52        ( ( ( modulo_modulo_int @ A @ C )
% 0.28/0.52          = ( modulo_modulo_int @ B @ C ) )
% 0.28/0.52       => ~ ! [D3: int] :
% 0.28/0.52              ( B
% 0.28/0.52             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mod_eqE
% 0.28/0.52  thf(fact_1703_mod__eqE,axiom,
% 0.28/0.52      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.28/0.52        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.28/0.52          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.28/0.52       => ~ ! [D3: code_integer] :
% 0.28/0.52              ( B
% 0.28/0.52             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mod_eqE
% 0.28/0.52  thf(fact_1704_div__add1__eq,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.28/0.52        = ( 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 ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % div_add1_eq
% 0.28/0.52  thf(fact_1705_div__add1__eq,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.28/0.52        = ( 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 ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % div_add1_eq
% 0.28/0.52  thf(fact_1706_div__add1__eq,axiom,
% 0.28/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.52        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.28/0.52        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % div_add1_eq
% 0.28/0.52  thf(fact_1707_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.28/0.52      ! [N: nat,M: nat] :
% 0.28/0.52        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.28/0.52         != zero_zero_nat )
% 0.28/0.52       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.28/0.52         != zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % exp_not_zero_imp_exp_diff_not_zero
% 0.28/0.52  thf(fact_1708_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.28/0.52      ! [N: nat,M: nat] :
% 0.28/0.52        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.28/0.52         != zero_zero_int )
% 0.28/0.52       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 0.28/0.52         != zero_zero_int ) ) ).
% 0.28/0.52  
% 0.28/0.52  % exp_not_zero_imp_exp_diff_not_zero
% 0.28/0.52  thf(fact_1709_power__diff__power__eq,axiom,
% 0.28/0.52      ! [A: nat,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_nat )
% 0.28/0.52       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.28/0.52              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.28/0.52          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.28/0.52           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.28/0.52              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff_power_eq
% 0.28/0.52  thf(fact_1710_power__diff__power__eq,axiom,
% 0.28/0.52      ! [A: int,N: nat,M: nat] :
% 0.28/0.52        ( ( A != zero_zero_int )
% 0.28/0.52       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.28/0.52              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.28/0.52          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.28/0.52           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.28/0.52              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_diff_power_eq
% 0.28/0.52  thf(fact_1711_power__eq__if,axiom,
% 0.28/0.52      ( power_power_complex
% 0.28/0.52      = ( ^ [P2: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P2 @ ( power_power_complex @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_if
% 0.28/0.52  thf(fact_1712_power__eq__if,axiom,
% 0.28/0.52      ( power_power_real
% 0.28/0.52      = ( ^ [P2: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P2 @ ( power_power_real @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_if
% 0.28/0.52  thf(fact_1713_power__eq__if,axiom,
% 0.28/0.52      ( power_power_rat
% 0.28/0.52      = ( ^ [P2: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P2 @ ( power_power_rat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_if
% 0.28/0.52  thf(fact_1714_power__eq__if,axiom,
% 0.28/0.52      ( power_power_nat
% 0.28/0.52      = ( ^ [P2: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P2 @ ( power_power_nat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_if
% 0.28/0.52  thf(fact_1715_power__eq__if,axiom,
% 0.28/0.52      ( power_power_int
% 0.28/0.52      = ( ^ [P2: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P2 @ ( power_power_int @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_eq_if
% 0.28/0.52  thf(fact_1716_diff__le__eq,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_le_eq
% 0.28/0.52  thf(fact_1717_diff__le__eq,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_le_eq
% 0.28/0.52  thf(fact_1718_diff__le__eq,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_le_eq
% 0.28/0.52  thf(fact_1719_le__diff__eq,axiom,
% 0.28/0.52      ! [A: real,C: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.28/0.52        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_diff_eq
% 0.28/0.52  thf(fact_1720_le__diff__eq,axiom,
% 0.28/0.52      ! [A: rat,C: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.28/0.52        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_diff_eq
% 0.28/0.52  thf(fact_1721_le__diff__eq,axiom,
% 0.28/0.52      ! [A: int,C: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.28/0.52        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_diff_eq
% 0.28/0.52  thf(fact_1722_diff__add,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.28/0.52          = B ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_add
% 0.28/0.52  thf(fact_1723_le__add__diff,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_add_diff
% 0.28/0.52  thf(fact_1724_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.28/0.52          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.28/0.52  thf(fact_1725_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.28/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.28/0.52  thf(fact_1726_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.28/0.52          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.28/0.52  thf(fact_1727_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.28/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.28/0.52  thf(fact_1728_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.28/0.52          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.28/0.52  thf(fact_1729_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.28/0.52          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.28/0.52  thf(fact_1730_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.28/0.52          = B ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.28/0.52  thf(fact_1731_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52         => ( ( ( minus_minus_nat @ B @ A )
% 0.28/0.52              = C )
% 0.28/0.52            = ( B
% 0.28/0.52              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.28/0.52  thf(fact_1732_add__le__imp__le__diff,axiom,
% 0.28/0.52      ! [I: real,K: real,N: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.28/0.52       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_imp_le_diff
% 0.28/0.52  thf(fact_1733_add__le__imp__le__diff,axiom,
% 0.28/0.52      ! [I: rat,K: rat,N: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.28/0.52       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_imp_le_diff
% 0.28/0.52  thf(fact_1734_add__le__imp__le__diff,axiom,
% 0.28/0.52      ! [I: nat,K: nat,N: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.28/0.52       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_imp_le_diff
% 0.28/0.52  thf(fact_1735_add__le__imp__le__diff,axiom,
% 0.28/0.52      ! [I: int,K: int,N: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.28/0.52       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_imp_le_diff
% 0.28/0.52  thf(fact_1736_add__le__add__imp__diff__le,axiom,
% 0.28/0.52      ! [I: real,K: real,N: real,J: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.28/0.52       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.28/0.52         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.28/0.52           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.28/0.52             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_add_imp_diff_le
% 0.28/0.52  thf(fact_1737_add__le__add__imp__diff__le,axiom,
% 0.28/0.52      ! [I: rat,K: rat,N: rat,J: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.28/0.52       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.28/0.52         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.28/0.52           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.28/0.52             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_add_imp_diff_le
% 0.28/0.52  thf(fact_1738_add__le__add__imp__diff__le,axiom,
% 0.28/0.52      ! [I: nat,K: nat,N: nat,J: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.28/0.52         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.28/0.52           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.28/0.52             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_add_imp_diff_le
% 0.28/0.52  thf(fact_1739_add__le__add__imp__diff__le,axiom,
% 0.28/0.52      ! [I: int,K: int,N: int,J: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.28/0.52       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.28/0.52         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.28/0.52           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.28/0.52             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_le_add_imp_diff_le
% 0.28/0.52  thf(fact_1740_power__minus__mult,axiom,
% 0.28/0.52      ! [N: nat,A: complex] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.28/0.52          = ( power_power_complex @ A @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_minus_mult
% 0.28/0.52  thf(fact_1741_power__minus__mult,axiom,
% 0.28/0.52      ! [N: nat,A: real] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.28/0.52          = ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_minus_mult
% 0.28/0.52  thf(fact_1742_power__minus__mult,axiom,
% 0.28/0.52      ! [N: nat,A: rat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.28/0.52          = ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_minus_mult
% 0.28/0.52  thf(fact_1743_power__minus__mult,axiom,
% 0.28/0.52      ! [N: nat,A: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.28/0.52          = ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_minus_mult
% 0.28/0.52  thf(fact_1744_power__minus__mult,axiom,
% 0.28/0.52      ! [N: nat,A: int] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.28/0.52          = ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_minus_mult
% 0.28/0.52  thf(fact_1745_less__diff__eq,axiom,
% 0.28/0.52      ! [A: real,C: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.28/0.52        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % less_diff_eq
% 0.28/0.52  thf(fact_1746_less__diff__eq,axiom,
% 0.28/0.52      ! [A: rat,C: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.28/0.52        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % less_diff_eq
% 0.28/0.52  thf(fact_1747_less__diff__eq,axiom,
% 0.28/0.52      ! [A: int,C: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.28/0.52        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.28/0.52  
% 0.28/0.52  % less_diff_eq
% 0.28/0.52  thf(fact_1748_diff__less__eq,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_less_eq
% 0.28/0.52  thf(fact_1749_diff__less__eq,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_less_eq
% 0.28/0.52  thf(fact_1750_diff__less__eq,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.28/0.52        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_less_eq
% 0.28/0.52  thf(fact_1751_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ~ ( ord_less_real @ A @ B )
% 0.28/0.52       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.28/0.52          = A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_semidom_class.add_diff_inverse
% 0.28/0.52  thf(fact_1752_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ~ ( ord_less_rat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.28/0.52          = A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_semidom_class.add_diff_inverse
% 0.28/0.52  thf(fact_1753_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ~ ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.28/0.52          = A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_semidom_class.add_diff_inverse
% 0.28/0.52  thf(fact_1754_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ~ ( ord_less_int @ A @ B )
% 0.28/0.52       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.28/0.52          = A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_semidom_class.add_diff_inverse
% 0.28/0.52  thf(fact_1755_mult__diff__mult,axiom,
% 0.28/0.52      ! [X: real,Y: real,A: real,B: real] :
% 0.28/0.52        ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 0.28/0.52        = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_diff_mult
% 0.28/0.52  thf(fact_1756_mult__diff__mult,axiom,
% 0.28/0.52      ! [X: rat,Y: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 0.28/0.52        = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_diff_mult
% 0.28/0.52  thf(fact_1757_mult__diff__mult,axiom,
% 0.28/0.52      ! [X: int,Y: int,A: int,B: int] :
% 0.28/0.52        ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 0.28/0.52        = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_diff_mult
% 0.28/0.52  thf(fact_1758_square__diff__square__factored,axiom,
% 0.28/0.52      ! [X: real,Y: real] :
% 0.28/0.52        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.28/0.52        = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % square_diff_square_factored
% 0.28/0.52  thf(fact_1759_square__diff__square__factored,axiom,
% 0.28/0.52      ! [X: rat,Y: rat] :
% 0.28/0.52        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.28/0.52        = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % square_diff_square_factored
% 0.28/0.52  thf(fact_1760_square__diff__square__factored,axiom,
% 0.28/0.52      ! [X: int,Y: int] :
% 0.28/0.52        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.28/0.52        = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % square_diff_square_factored
% 0.28/0.52  thf(fact_1761_eq__add__iff2,axiom,
% 0.28/0.52      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.52        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.52        = ( C
% 0.28/0.52          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff2
% 0.28/0.52  thf(fact_1762_eq__add__iff2,axiom,
% 0.28/0.52      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.52        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.52        = ( C
% 0.28/0.52          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff2
% 0.28/0.52  thf(fact_1763_eq__add__iff2,axiom,
% 0.28/0.52      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.52        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.52        = ( C
% 0.28/0.52          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff2
% 0.28/0.52  thf(fact_1764_eq__add__iff1,axiom,
% 0.28/0.52      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.52        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.52        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 0.28/0.52          = D ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff1
% 0.28/0.52  thf(fact_1765_eq__add__iff1,axiom,
% 0.28/0.52      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.52        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.52        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 0.28/0.52          = D ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff1
% 0.28/0.52  thf(fact_1766_eq__add__iff1,axiom,
% 0.28/0.52      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.52        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 0.28/0.52          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.52        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 0.28/0.52          = D ) ) ).
% 0.28/0.52  
% 0.28/0.52  % eq_add_iff1
% 0.28/0.52  thf(fact_1767_power__strict__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,N: nat] :
% 0.28/0.52        ( ( ord_less_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_strict_mono
% 0.28/0.52  thf(fact_1768_power__strict__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,N: nat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_strict_mono
% 0.28/0.52  thf(fact_1769_power__strict__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,N: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_strict_mono
% 0.28/0.52  thf(fact_1770_power__strict__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,N: nat] :
% 0.28/0.52        ( ( ord_less_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.52           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % power_strict_mono
% 0.28/0.52  thf(fact_1771_mod__eq__nat1E,axiom,
% 0.28/0.52      ! [M: nat,Q2: nat,N: nat] :
% 0.28/0.52        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.28/0.52          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.28/0.52       => ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.52         => ~ ! [S3: nat] :
% 0.28/0.52                ( M
% 0.28/0.52               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mod_eq_nat1E
% 0.28/0.52  thf(fact_1772_mod__eq__nat2E,axiom,
% 0.28/0.52      ! [M: nat,Q2: nat,N: nat] :
% 0.28/0.52        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.28/0.52          = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.28/0.52       => ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.52         => ~ ! [S3: nat] :
% 0.28/0.52                ( N
% 0.28/0.52               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mod_eq_nat2E
% 0.28/0.52  thf(fact_1773_nat__mod__eq__lemma,axiom,
% 0.28/0.52      ! [X: nat,N: nat,Y: nat] :
% 0.28/0.52        ( ( ( modulo_modulo_nat @ X @ N )
% 0.28/0.52          = ( modulo_modulo_nat @ Y @ N ) )
% 0.28/0.52       => ( ( ord_less_eq_nat @ Y @ X )
% 0.28/0.52         => ? [Q3: nat] :
% 0.28/0.52              ( X
% 0.28/0.52              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % nat_mod_eq_lemma
% 0.28/0.52  thf(fact_1774_div__positive,axiom,
% 0.28/0.52      ! [B: nat,A: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.52         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % div_positive
% 0.28/0.52  thf(fact_1775_div__positive,axiom,
% 0.28/0.52      ! [B: int,A: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ A )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % div_positive
% 0.28/0.52  thf(fact_1776_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ A @ B )
% 0.28/0.52         => ( ( divide_divide_nat @ A @ B )
% 0.28/0.52            = zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.div_less
% 0.28/0.52  thf(fact_1777_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ A @ B )
% 0.28/0.52         => ( ( divide_divide_int @ A @ B )
% 0.28/0.52            = zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.div_less
% 0.28/0.52  thf(fact_1778_diff__less__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ C @ A )
% 0.28/0.52         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % diff_less_mono
% 0.28/0.52  thf(fact_1779_less__diff__iff,axiom,
% 0.28/0.52      ! [K: nat,M: nat,N: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ K @ M )
% 0.28/0.52       => ( ( ord_less_eq_nat @ K @ N )
% 0.28/0.52         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.28/0.52            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % less_diff_iff
% 0.28/0.52  thf(fact_1780_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.28/0.52      ! [C: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.28/0.52          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.28/0.52  thf(fact_1781_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.28/0.52          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.28/0.52  thf(fact_1782_add__diff__inverse__nat,axiom,
% 0.28/0.52      ! [M: nat,N: nat] :
% 0.28/0.52        ( ~ ( ord_less_nat @ M @ N )
% 0.28/0.52       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.28/0.52          = M ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_diff_inverse_nat
% 0.28/0.52  thf(fact_1783_less__diff__conv,axiom,
% 0.28/0.52      ! [I: nat,J: nat,K: nat] :
% 0.28/0.52        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.28/0.52        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.28/0.52  
% 0.28/0.52  % less_diff_conv
% 0.28/0.52  thf(fact_1784_le__diff__conv,axiom,
% 0.28/0.52      ! [J: nat,K: nat,I: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.28/0.52        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % le_diff_conv
% 0.28/0.52  thf(fact_1785_Nat_Ole__diff__conv2,axiom,
% 0.28/0.52      ! [K: nat,J: nat,I: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.52       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.28/0.52          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % Nat.le_diff_conv2
% 0.28/0.52  thf(fact_1786_Nat_Odiff__add__assoc,axiom,
% 0.28/0.52      ! [K: nat,J: nat,I: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.28/0.52          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % Nat.diff_add_assoc
% 0.28/0.52  thf(fact_1787_Nat_Odiff__add__assoc2,axiom,
% 0.28/0.52      ! [K: nat,J: nat,I: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.52       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.28/0.52          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % Nat.diff_add_assoc2
% 0.28/0.52  thf(fact_1788_Nat_Ole__imp__diff__is__add,axiom,
% 0.28/0.52      ! [I: nat,J: nat,K: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.52       => ( ( ( minus_minus_nat @ J @ I )
% 0.28/0.52            = K )
% 0.28/0.52          = ( J
% 0.28/0.52            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % Nat.le_imp_diff_is_add
% 0.28/0.52  thf(fact_1789_dbl__def,axiom,
% 0.28/0.52      ( neg_numeral_dbl_real
% 0.28/0.52      = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % dbl_def
% 0.28/0.52  thf(fact_1790_dbl__def,axiom,
% 0.28/0.52      ( neg_numeral_dbl_rat
% 0.28/0.52      = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % dbl_def
% 0.28/0.52  thf(fact_1791_dbl__def,axiom,
% 0.28/0.52      ( neg_numeral_dbl_int
% 0.28/0.52      = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % dbl_def
% 0.28/0.52  thf(fact_1792_not__numeral__le__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_le_zero
% 0.28/0.52  thf(fact_1793_not__numeral__le__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_le_zero
% 0.28/0.52  thf(fact_1794_not__numeral__le__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_le_zero
% 0.28/0.52  thf(fact_1795_not__numeral__le__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_le_zero
% 0.28/0.52  thf(fact_1796_zero__le__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_numeral
% 0.28/0.52  thf(fact_1797_zero__le__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_numeral
% 0.28/0.52  thf(fact_1798_zero__le__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_numeral
% 0.28/0.52  thf(fact_1799_zero__le__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_numeral
% 0.28/0.52  thf(fact_1800_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.28/0.52  thf(fact_1801_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.28/0.52  thf(fact_1802_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.28/0.52  thf(fact_1803_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.28/0.52  thf(fact_1804_zero__le__mult__iff,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_mult_iff
% 0.28/0.52  thf(fact_1805_zero__le__mult__iff,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_mult_iff
% 0.28/0.52  thf(fact_1806_zero__le__mult__iff,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_mult_iff
% 0.28/0.52  thf(fact_1807_mult__nonneg__nonpos2,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos2
% 0.28/0.52  thf(fact_1808_mult__nonneg__nonpos2,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos2
% 0.28/0.52  thf(fact_1809_mult__nonneg__nonpos2,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos2
% 0.28/0.52  thf(fact_1810_mult__nonneg__nonpos2,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos2
% 0.28/0.52  thf(fact_1811_mult__nonpos__nonneg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonneg
% 0.28/0.52  thf(fact_1812_mult__nonpos__nonneg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonneg
% 0.28/0.52  thf(fact_1813_mult__nonpos__nonneg,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonneg
% 0.28/0.52  thf(fact_1814_mult__nonpos__nonneg,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonneg
% 0.28/0.52  thf(fact_1815_mult__nonneg__nonpos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos
% 0.28/0.52  thf(fact_1816_mult__nonneg__nonpos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos
% 0.28/0.52  thf(fact_1817_mult__nonneg__nonpos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos
% 0.28/0.52  thf(fact_1818_mult__nonneg__nonpos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonpos
% 0.28/0.52  thf(fact_1819_mult__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonneg
% 0.28/0.52  thf(fact_1820_mult__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonneg
% 0.28/0.52  thf(fact_1821_mult__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonneg
% 0.28/0.52  thf(fact_1822_mult__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonneg_nonneg
% 0.28/0.52  thf(fact_1823_split__mult__neg__le,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.28/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.28/0.52       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_neg_le
% 0.28/0.52  thf(fact_1824_split__mult__neg__le,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.28/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.28/0.52       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_neg_le
% 0.28/0.52  thf(fact_1825_split__mult__neg__le,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.28/0.52          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.28/0.52       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_neg_le
% 0.28/0.52  thf(fact_1826_split__mult__neg__le,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.28/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.28/0.52       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_neg_le
% 0.28/0.52  thf(fact_1827_mult__le__0__iff,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.28/0.52        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.28/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_le_0_iff
% 0.28/0.52  thf(fact_1828_mult__le__0__iff,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.28/0.52        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.28/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_le_0_iff
% 0.28/0.52  thf(fact_1829_mult__le__0__iff,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.28/0.52        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.28/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_le_0_iff
% 0.28/0.52  thf(fact_1830_mult__right__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono
% 0.28/0.52  thf(fact_1831_mult__right__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono
% 0.28/0.52  thf(fact_1832_mult__right__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono
% 0.28/0.52  thf(fact_1833_mult__right__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono
% 0.28/0.52  thf(fact_1834_mult__right__mono__neg,axiom,
% 0.28/0.52      ! [B: real,A: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono_neg
% 0.28/0.52  thf(fact_1835_mult__right__mono__neg,axiom,
% 0.28/0.52      ! [B: rat,A: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono_neg
% 0.28/0.52  thf(fact_1836_mult__right__mono__neg,axiom,
% 0.28/0.52      ! [B: int,A: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_right_mono_neg
% 0.28/0.52  thf(fact_1837_mult__left__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono
% 0.28/0.52  thf(fact_1838_mult__left__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono
% 0.28/0.52  thf(fact_1839_mult__left__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono
% 0.28/0.52  thf(fact_1840_mult__left__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono
% 0.28/0.52  thf(fact_1841_mult__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonpos
% 0.28/0.52  thf(fact_1842_mult__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonpos
% 0.28/0.52  thf(fact_1843_mult__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_nonpos_nonpos
% 0.28/0.52  thf(fact_1844_mult__left__mono__neg,axiom,
% 0.28/0.52      ! [B: real,A: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono_neg
% 0.28/0.52  thf(fact_1845_mult__left__mono__neg,axiom,
% 0.28/0.52      ! [B: rat,A: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono_neg
% 0.28/0.52  thf(fact_1846_mult__left__mono__neg,axiom,
% 0.28/0.52      ! [B: int,A: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_left_mono_neg
% 0.28/0.52  thf(fact_1847_split__mult__pos__le,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.28/0.52       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_pos_le
% 0.28/0.52  thf(fact_1848_split__mult__pos__le,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.28/0.52       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_pos_le
% 0.28/0.52  thf(fact_1849_split__mult__pos__le,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.28/0.52          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.28/0.52       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % split_mult_pos_le
% 0.28/0.52  thf(fact_1850_zero__le__square,axiom,
% 0.28/0.52      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_square
% 0.28/0.52  thf(fact_1851_zero__le__square,axiom,
% 0.28/0.52      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_square
% 0.28/0.52  thf(fact_1852_zero__le__square,axiom,
% 0.28/0.52      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_le_square
% 0.28/0.52  thf(fact_1853_mult__mono_H,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono'
% 0.28/0.52  thf(fact_1854_mult__mono_H,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono'
% 0.28/0.52  thf(fact_1855_mult__mono_H,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono'
% 0.28/0.52  thf(fact_1856_mult__mono_H,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono'
% 0.28/0.52  thf(fact_1857_mult__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_real @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono
% 0.28/0.52  thf(fact_1858_mult__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_rat @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono
% 0.28/0.52  thf(fact_1859_mult__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_nat @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono
% 0.28/0.52  thf(fact_1860_mult__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_eq_int @ C @ D )
% 0.28/0.52         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_mono
% 0.28/0.52  thf(fact_1861_zero__less__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_numeral
% 0.28/0.52  thf(fact_1862_zero__less__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_numeral
% 0.28/0.52  thf(fact_1863_zero__less__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_numeral
% 0.28/0.52  thf(fact_1864_zero__less__numeral,axiom,
% 0.28/0.52      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_numeral
% 0.28/0.52  thf(fact_1865_not__numeral__less__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_less_zero
% 0.28/0.52  thf(fact_1866_not__numeral__less__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_less_zero
% 0.28/0.52  thf(fact_1867_not__numeral__less__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_less_zero
% 0.28/0.52  thf(fact_1868_not__numeral__less__zero,axiom,
% 0.28/0.52      ! [N: num] :
% 0.28/0.52        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.28/0.52  
% 0.28/0.52  % not_numeral_less_zero
% 0.28/0.52  thf(fact_1869_add__decreasing,axiom,
% 0.28/0.52      ! [A: real,C: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ C @ B )
% 0.28/0.52         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing
% 0.28/0.52  thf(fact_1870_add__decreasing,axiom,
% 0.28/0.52      ! [A: rat,C: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ C @ B )
% 0.28/0.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing
% 0.28/0.52  thf(fact_1871_add__decreasing,axiom,
% 0.28/0.52      ! [A: nat,C: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ C @ B )
% 0.28/0.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing
% 0.28/0.52  thf(fact_1872_add__decreasing,axiom,
% 0.28/0.52      ! [A: int,C: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ C @ B )
% 0.28/0.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing
% 0.28/0.52  thf(fact_1873_add__increasing,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ C )
% 0.28/0.52         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing
% 0.28/0.52  thf(fact_1874_add__increasing,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ C )
% 0.28/0.52         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing
% 0.28/0.52  thf(fact_1875_add__increasing,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.52         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing
% 0.28/0.52  thf(fact_1876_add__increasing,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ C )
% 0.28/0.52         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing
% 0.28/0.52  thf(fact_1877_add__decreasing2,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ A @ B )
% 0.28/0.52         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing2
% 0.28/0.52  thf(fact_1878_add__decreasing2,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing2
% 0.28/0.52  thf(fact_1879_add__decreasing2,axiom,
% 0.28/0.52      ! [C: nat,A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing2
% 0.28/0.52  thf(fact_1880_add__decreasing2,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ A @ B )
% 0.28/0.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_decreasing2
% 0.28/0.52  thf(fact_1881_add__increasing2,axiom,
% 0.28/0.52      ! [C: real,B: real,A: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ A )
% 0.28/0.52         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing2
% 0.28/0.52  thf(fact_1882_add__increasing2,axiom,
% 0.28/0.52      ! [C: rat,B: rat,A: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.52         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing2
% 0.28/0.52  thf(fact_1883_add__increasing2,axiom,
% 0.28/0.52      ! [C: nat,B: nat,A: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ A )
% 0.28/0.52         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing2
% 0.28/0.52  thf(fact_1884_add__increasing2,axiom,
% 0.28/0.52      ! [C: int,B: int,A: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ A )
% 0.28/0.52         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_increasing2
% 0.28/0.52  thf(fact_1885_add__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_nonneg
% 0.28/0.52  thf(fact_1886_add__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_nonneg
% 0.28/0.52  thf(fact_1887_add__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_nonneg
% 0.28/0.52  thf(fact_1888_add__nonneg__nonneg,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_nonneg
% 0.28/0.52  thf(fact_1889_add__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_nonpos
% 0.28/0.52  thf(fact_1890_add__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_nonpos
% 0.28/0.52  thf(fact_1891_add__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_nonpos
% 0.28/0.52  thf(fact_1892_add__nonpos__nonpos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_nonpos
% 0.28/0.52  thf(fact_1893_add__nonneg__eq__0__iff,axiom,
% 0.28/0.52      ! [X: real,Y: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.52       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.52         => ( ( ( plus_plus_real @ X @ Y )
% 0.28/0.52              = zero_zero_real )
% 0.28/0.52            = ( ( X = zero_zero_real )
% 0.28/0.52              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_eq_0_iff
% 0.28/0.52  thf(fact_1894_add__nonneg__eq__0__iff,axiom,
% 0.28/0.52      ! [X: rat,Y: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.52       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.52         => ( ( ( plus_plus_rat @ X @ Y )
% 0.28/0.52              = zero_zero_rat )
% 0.28/0.52            = ( ( X = zero_zero_rat )
% 0.28/0.52              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_eq_0_iff
% 0.28/0.52  thf(fact_1895_add__nonneg__eq__0__iff,axiom,
% 0.28/0.52      ! [X: nat,Y: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.28/0.52       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.28/0.52         => ( ( ( plus_plus_nat @ X @ Y )
% 0.28/0.52              = zero_zero_nat )
% 0.28/0.52            = ( ( X = zero_zero_nat )
% 0.28/0.52              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_eq_0_iff
% 0.28/0.52  thf(fact_1896_add__nonneg__eq__0__iff,axiom,
% 0.28/0.52      ! [X: int,Y: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.52       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.52         => ( ( ( plus_plus_int @ X @ Y )
% 0.28/0.52              = zero_zero_int )
% 0.28/0.52            = ( ( X = zero_zero_int )
% 0.28/0.52              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonneg_eq_0_iff
% 0.28/0.52  thf(fact_1897_add__nonpos__eq__0__iff,axiom,
% 0.28/0.52      ! [X: real,Y: real] :
% 0.28/0.52        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.28/0.52         => ( ( ( plus_plus_real @ X @ Y )
% 0.28/0.52              = zero_zero_real )
% 0.28/0.52            = ( ( X = zero_zero_real )
% 0.28/0.52              & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_eq_0_iff
% 0.28/0.52  thf(fact_1898_add__nonpos__eq__0__iff,axiom,
% 0.28/0.52      ! [X: rat,Y: rat] :
% 0.28/0.52        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.28/0.52         => ( ( ( plus_plus_rat @ X @ Y )
% 0.28/0.52              = zero_zero_rat )
% 0.28/0.52            = ( ( X = zero_zero_rat )
% 0.28/0.52              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_eq_0_iff
% 0.28/0.52  thf(fact_1899_add__nonpos__eq__0__iff,axiom,
% 0.28/0.52      ! [X: nat,Y: nat] :
% 0.28/0.52        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.28/0.52         => ( ( ( plus_plus_nat @ X @ Y )
% 0.28/0.52              = zero_zero_nat )
% 0.28/0.52            = ( ( X = zero_zero_nat )
% 0.28/0.52              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_eq_0_iff
% 0.28/0.52  thf(fact_1900_add__nonpos__eq__0__iff,axiom,
% 0.28/0.52      ! [X: int,Y: int] :
% 0.28/0.52        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.28/0.52         => ( ( ( plus_plus_int @ X @ Y )
% 0.28/0.52              = zero_zero_int )
% 0.28/0.52            = ( ( X = zero_zero_int )
% 0.28/0.52              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_nonpos_eq_0_iff
% 0.28/0.52  thf(fact_1901_not__one__le__zero,axiom,
% 0.28/0.52      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.28/0.52  
% 0.28/0.52  % not_one_le_zero
% 0.28/0.52  thf(fact_1902_not__one__le__zero,axiom,
% 0.28/0.52      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_one_le_zero
% 0.28/0.52  thf(fact_1903_not__one__le__zero,axiom,
% 0.28/0.52      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_one_le_zero
% 0.28/0.52  thf(fact_1904_not__one__le__zero,axiom,
% 0.28/0.52      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.28/0.52  
% 0.28/0.52  % not_one_le_zero
% 0.28/0.52  thf(fact_1905_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.28/0.52  
% 0.28/0.52  % linordered_nonzero_semiring_class.zero_le_one
% 0.28/0.52  thf(fact_1906_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.28/0.52  
% 0.28/0.52  % linordered_nonzero_semiring_class.zero_le_one
% 0.28/0.52  thf(fact_1907_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.28/0.52  
% 0.28/0.52  % linordered_nonzero_semiring_class.zero_le_one
% 0.28/0.52  thf(fact_1908_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.28/0.52  
% 0.28/0.52  % linordered_nonzero_semiring_class.zero_le_one
% 0.28/0.52  thf(fact_1909_zero__less__one__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_one_class.zero_le_one
% 0.28/0.52  thf(fact_1910_zero__less__one__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_one_class.zero_le_one
% 0.28/0.52  thf(fact_1911_zero__less__one__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_one_class.zero_le_one
% 0.28/0.52  thf(fact_1912_zero__less__one__class_Ozero__le__one,axiom,
% 0.28/0.52      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_one_class.zero_le_one
% 0.28/0.52  thf(fact_1913_mult__neg__neg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_neg
% 0.28/0.52  thf(fact_1914_mult__neg__neg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_neg
% 0.28/0.52  thf(fact_1915_mult__neg__neg,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_neg
% 0.28/0.52  thf(fact_1916_not__square__less__zero,axiom,
% 0.28/0.52      ! [A: real] :
% 0.28/0.52        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.28/0.52  
% 0.28/0.52  % not_square_less_zero
% 0.28/0.52  thf(fact_1917_not__square__less__zero,axiom,
% 0.28/0.52      ! [A: rat] :
% 0.28/0.52        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.28/0.52  
% 0.28/0.52  % not_square_less_zero
% 0.28/0.52  thf(fact_1918_not__square__less__zero,axiom,
% 0.28/0.52      ! [A: int] :
% 0.28/0.52        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.28/0.52  
% 0.28/0.52  % not_square_less_zero
% 0.28/0.52  thf(fact_1919_mult__less__0__iff,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.28/0.52        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.28/0.52          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_0_iff
% 0.28/0.52  thf(fact_1920_mult__less__0__iff,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.28/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.28/0.52          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_0_iff
% 0.28/0.52  thf(fact_1921_mult__less__0__iff,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.28/0.52        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.28/0.52          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_0_iff
% 0.28/0.52  thf(fact_1922_mult__neg__pos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_pos
% 0.28/0.52  thf(fact_1923_mult__neg__pos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_pos
% 0.28/0.52  thf(fact_1924_mult__neg__pos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_pos
% 0.28/0.52  thf(fact_1925_mult__neg__pos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_neg_pos
% 0.28/0.52  thf(fact_1926_mult__pos__neg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg
% 0.28/0.52  thf(fact_1927_mult__pos__neg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg
% 0.28/0.52  thf(fact_1928_mult__pos__neg,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg
% 0.28/0.52  thf(fact_1929_mult__pos__neg,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg
% 0.28/0.52  thf(fact_1930_mult__pos__pos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_pos
% 0.28/0.52  thf(fact_1931_mult__pos__pos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_pos
% 0.28/0.52  thf(fact_1932_mult__pos__pos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_pos
% 0.28/0.52  thf(fact_1933_mult__pos__pos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_pos
% 0.28/0.52  thf(fact_1934_mult__pos__neg2,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg2
% 0.28/0.52  thf(fact_1935_mult__pos__neg2,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg2
% 0.28/0.52  thf(fact_1936_mult__pos__neg2,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg2
% 0.28/0.52  thf(fact_1937_mult__pos__neg2,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_pos_neg2
% 0.28/0.52  thf(fact_1938_zero__less__mult__iff,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.28/0.52          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.52            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_iff
% 0.28/0.52  thf(fact_1939_zero__less__mult__iff,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.28/0.52          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_iff
% 0.28/0.52  thf(fact_1940_zero__less__mult__iff,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.28/0.52        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.28/0.52          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.52            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_iff
% 0.28/0.52  thf(fact_1941_zero__less__mult__pos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos
% 0.28/0.52  thf(fact_1942_zero__less__mult__pos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos
% 0.28/0.52  thf(fact_1943_zero__less__mult__pos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos
% 0.28/0.52  thf(fact_1944_zero__less__mult__pos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos
% 0.28/0.52  thf(fact_1945_zero__less__mult__pos2,axiom,
% 0.28/0.52      ! [B: real,A: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos2
% 0.28/0.52  thf(fact_1946_zero__less__mult__pos2,axiom,
% 0.28/0.52      ! [B: rat,A: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos2
% 0.28/0.52  thf(fact_1947_zero__less__mult__pos2,axiom,
% 0.28/0.52      ! [B: nat,A: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos2
% 0.28/0.52  thf(fact_1948_zero__less__mult__pos2,axiom,
% 0.28/0.52      ! [B: int,A: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % zero_less_mult_pos2
% 0.28/0.52  thf(fact_1949_mult__less__cancel__left__neg,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.52          = ( ord_less_real @ B @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_neg
% 0.28/0.52  thf(fact_1950_mult__less__cancel__left__neg,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.52          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_neg
% 0.28/0.52  thf(fact_1951_mult__less__cancel__left__neg,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.52       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.52          = ( ord_less_int @ B @ A ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_neg
% 0.28/0.52  thf(fact_1952_mult__less__cancel__left__pos,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.52          = ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_pos
% 0.28/0.52  thf(fact_1953_mult__less__cancel__left__pos,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.52          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_pos
% 0.28/0.52  thf(fact_1954_mult__less__cancel__left__pos,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.52          = ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_pos
% 0.28/0.52  thf(fact_1955_mult__strict__left__mono__neg,axiom,
% 0.28/0.52      ! [B: real,A: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ B @ A )
% 0.28/0.52       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono_neg
% 0.28/0.52  thf(fact_1956_mult__strict__left__mono__neg,axiom,
% 0.28/0.52      ! [B: rat,A: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ B @ A )
% 0.28/0.52       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono_neg
% 0.28/0.52  thf(fact_1957_mult__strict__left__mono__neg,axiom,
% 0.28/0.52      ! [B: int,A: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ B @ A )
% 0.28/0.52       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono_neg
% 0.28/0.52  thf(fact_1958_mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono
% 0.28/0.52  thf(fact_1959_mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono
% 0.28/0.52  thf(fact_1960_mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono
% 0.28/0.52  thf(fact_1961_mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_left_mono
% 0.28/0.52  thf(fact_1962_mult__less__cancel__left__disj,axiom,
% 0.28/0.52      ! [C: real,A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.52        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52            & ( ord_less_real @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.52            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_disj
% 0.28/0.52  thf(fact_1963_mult__less__cancel__left__disj,axiom,
% 0.28/0.52      ! [C: rat,A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52            & ( ord_less_rat @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_disj
% 0.28/0.52  thf(fact_1964_mult__less__cancel__left__disj,axiom,
% 0.28/0.52      ! [C: int,A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.52        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52            & ( ord_less_int @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.52            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_left_disj
% 0.28/0.52  thf(fact_1965_mult__strict__right__mono__neg,axiom,
% 0.28/0.52      ! [B: real,A: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ B @ A )
% 0.28/0.52       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono_neg
% 0.28/0.52  thf(fact_1966_mult__strict__right__mono__neg,axiom,
% 0.28/0.52      ! [B: rat,A: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ B @ A )
% 0.28/0.52       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono_neg
% 0.28/0.52  thf(fact_1967_mult__strict__right__mono__neg,axiom,
% 0.28/0.52      ! [B: int,A: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ B @ A )
% 0.28/0.52       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono_neg
% 0.28/0.52  thf(fact_1968_mult__strict__right__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono
% 0.28/0.52  thf(fact_1969_mult__strict__right__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono
% 0.28/0.52  thf(fact_1970_mult__strict__right__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono
% 0.28/0.52  thf(fact_1971_mult__strict__right__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_strict_right_mono
% 0.28/0.52  thf(fact_1972_mult__less__cancel__right__disj,axiom,
% 0.28/0.52      ! [A: real,C: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.52        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52            & ( ord_less_real @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.52            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_right_disj
% 0.28/0.52  thf(fact_1973_mult__less__cancel__right__disj,axiom,
% 0.28/0.52      ! [A: rat,C: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52            & ( ord_less_rat @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.52            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_right_disj
% 0.28/0.52  thf(fact_1974_mult__less__cancel__right__disj,axiom,
% 0.28/0.52      ! [A: int,C: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.52        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52            & ( ord_less_int @ A @ B ) )
% 0.28/0.52          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.52            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % mult_less_cancel_right_disj
% 0.28/0.52  thf(fact_1975_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ B )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.52         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.28/0.52  thf(fact_1976_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ B )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.52         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.28/0.52  thf(fact_1977_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.52         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.28/0.52  thf(fact_1978_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ A @ B )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.52         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.28/0.52  thf(fact_1979_pos__add__strict,axiom,
% 0.28/0.52      ! [A: real,B: real,C: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_real @ B @ C )
% 0.28/0.52         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % pos_add_strict
% 0.28/0.52  thf(fact_1980_pos__add__strict,axiom,
% 0.28/0.52      ! [A: rat,B: rat,C: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_rat @ B @ C )
% 0.28/0.52         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % pos_add_strict
% 0.28/0.52  thf(fact_1981_pos__add__strict,axiom,
% 0.28/0.52      ! [A: nat,B: nat,C: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ B @ C )
% 0.28/0.52         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % pos_add_strict
% 0.28/0.52  thf(fact_1982_pos__add__strict,axiom,
% 0.28/0.52      ! [A: int,B: int,C: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ B @ C )
% 0.28/0.52         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % pos_add_strict
% 0.28/0.52  thf(fact_1983_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ B )
% 0.28/0.52       => ~ ! [C2: nat] :
% 0.28/0.52              ( ( B
% 0.28/0.52                = ( plus_plus_nat @ A @ C2 ) )
% 0.28/0.52             => ( C2 = zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % canonically_ordered_monoid_add_class.lessE
% 0.28/0.52  thf(fact_1984_add__pos__pos,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.52       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.52         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_pos_pos
% 0.28/0.52  thf(fact_1985_add__pos__pos,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.52       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.52         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_pos_pos
% 0.28/0.52  thf(fact_1986_add__pos__pos,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.52       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.52         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_pos_pos
% 0.28/0.52  thf(fact_1987_add__pos__pos,axiom,
% 0.28/0.52      ! [A: int,B: int] :
% 0.28/0.52        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.52       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.52         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_pos_pos
% 0.28/0.52  thf(fact_1988_add__neg__neg,axiom,
% 0.28/0.52      ! [A: real,B: real] :
% 0.28/0.52        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.52       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.28/0.52         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_neg_neg
% 0.28/0.52  thf(fact_1989_add__neg__neg,axiom,
% 0.28/0.52      ! [A: rat,B: rat] :
% 0.28/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.52       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.28/0.52         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_neg_neg
% 0.28/0.52  thf(fact_1990_add__neg__neg,axiom,
% 0.28/0.52      ! [A: nat,B: nat] :
% 0.28/0.52        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.28/0.52       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.28/0.52         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.52  
% 0.28/0.52  % add_neg_neg
% 0.28/0.52  thf(fact_1991_add__neg__neg,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_neg_neg
% 0.28/0.53  thf(fact_1992_add__less__zeroD,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.28/0.53          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_less_zeroD
% 0.28/0.53  thf(fact_1993_add__less__zeroD,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.28/0.53          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_less_zeroD
% 0.28/0.53  thf(fact_1994_add__less__zeroD,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 0.28/0.53       => ( ( ord_less_int @ X @ zero_zero_int )
% 0.28/0.53          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_less_zeroD
% 0.28/0.53  thf(fact_1995_less__numeral__extra_I1_J,axiom,
% 0.28/0.53      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.28/0.53  
% 0.28/0.53  % less_numeral_extra(1)
% 0.28/0.53  thf(fact_1996_less__numeral__extra_I1_J,axiom,
% 0.28/0.53      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.28/0.53  
% 0.28/0.53  % less_numeral_extra(1)
% 0.28/0.53  thf(fact_1997_less__numeral__extra_I1_J,axiom,
% 0.28/0.53      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.28/0.53  
% 0.28/0.53  % less_numeral_extra(1)
% 0.28/0.53  thf(fact_1998_less__numeral__extra_I1_J,axiom,
% 0.28/0.53      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.28/0.53  
% 0.28/0.53  % less_numeral_extra(1)
% 0.28/0.53  thf(fact_1999_zero__less__one,axiom,
% 0.28/0.53      ord_less_real @ zero_zero_real @ one_one_real ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_one
% 0.28/0.53  thf(fact_2000_zero__less__one,axiom,
% 0.28/0.53      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_one
% 0.28/0.53  thf(fact_2001_zero__less__one,axiom,
% 0.28/0.53      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_one
% 0.28/0.53  thf(fact_2002_zero__less__one,axiom,
% 0.28/0.53      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_one
% 0.28/0.53  thf(fact_2003_not__one__less__zero,axiom,
% 0.28/0.53      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.28/0.53  
% 0.28/0.53  % not_one_less_zero
% 0.28/0.53  thf(fact_2004_not__one__less__zero,axiom,
% 0.28/0.53      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.28/0.53  
% 0.28/0.53  % not_one_less_zero
% 0.28/0.53  thf(fact_2005_not__one__less__zero,axiom,
% 0.28/0.53      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.28/0.53  
% 0.28/0.53  % not_one_less_zero
% 0.28/0.53  thf(fact_2006_not__one__less__zero,axiom,
% 0.28/0.53      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.28/0.53  
% 0.28/0.53  % not_one_less_zero
% 0.28/0.53  thf(fact_2007_divide__right__mono__neg,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_right_mono_neg
% 0.28/0.53  thf(fact_2008_divide__right__mono__neg,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_right_mono_neg
% 0.28/0.53  thf(fact_2009_divide__nonpos__nonpos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_nonpos
% 0.28/0.53  thf(fact_2010_divide__nonpos__nonpos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_nonpos
% 0.28/0.53  thf(fact_2011_divide__nonpos__nonneg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_nonneg
% 0.28/0.53  thf(fact_2012_divide__nonpos__nonneg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_nonneg
% 0.28/0.53  thf(fact_2013_divide__nonneg__nonpos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_nonpos
% 0.28/0.53  thf(fact_2014_divide__nonneg__nonpos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_nonpos
% 0.28/0.53  thf(fact_2015_divide__nonneg__nonneg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_nonneg
% 0.28/0.53  thf(fact_2016_divide__nonneg__nonneg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_nonneg
% 0.28/0.53  thf(fact_2017_zero__le__divide__iff,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.28/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.28/0.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_divide_iff
% 0.28/0.53  thf(fact_2018_zero__le__divide__iff,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.28/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.28/0.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_divide_iff
% 0.28/0.53  thf(fact_2019_divide__right__mono,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_right_mono
% 0.28/0.53  thf(fact_2020_divide__right__mono,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_right_mono
% 0.28/0.53  thf(fact_2021_divide__le__0__iff,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.28/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.28/0.53          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_le_0_iff
% 0.28/0.53  thf(fact_2022_divide__le__0__iff,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.28/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.28/0.53          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_le_0_iff
% 0.28/0.53  thf(fact_2023_divide__neg__neg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_neg_neg
% 0.28/0.53  thf(fact_2024_divide__neg__neg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_neg_neg
% 0.28/0.53  thf(fact_2025_divide__neg__pos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_neg_pos
% 0.28/0.53  thf(fact_2026_divide__neg__pos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_neg_pos
% 0.28/0.53  thf(fact_2027_divide__pos__neg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_pos_neg
% 0.28/0.53  thf(fact_2028_divide__pos__neg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_pos_neg
% 0.28/0.53  thf(fact_2029_divide__pos__pos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_pos_pos
% 0.28/0.53  thf(fact_2030_divide__pos__pos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_pos_pos
% 0.28/0.53  thf(fact_2031_divide__less__0__iff,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_real @ B @ zero_zero_real ) )
% 0.28/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_0_iff
% 0.28/0.53  thf(fact_2032_divide__less__0__iff,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.28/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_0_iff
% 0.28/0.53  thf(fact_2033_divide__less__cancel,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_real @ B @ A ) )
% 0.28/0.53          & ( C != zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_cancel
% 0.28/0.53  thf(fact_2034_divide__less__cancel,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_rat @ B @ A ) )
% 0.28/0.53          & ( C != zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_cancel
% 0.28/0.53  thf(fact_2035_zero__less__divide__iff,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_real @ zero_zero_real @ B ) )
% 0.28/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_divide_iff
% 0.28/0.53  thf(fact_2036_zero__less__divide__iff,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.28/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_divide_iff
% 0.28/0.53  thf(fact_2037_divide__strict__right__mono,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_right_mono
% 0.28/0.53  thf(fact_2038_divide__strict__right__mono,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_right_mono
% 0.28/0.53  thf(fact_2039_divide__strict__right__mono__neg,axiom,
% 0.28/0.53      ! [B: real,A: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ B @ A )
% 0.28/0.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_right_mono_neg
% 0.28/0.53  thf(fact_2040_divide__strict__right__mono__neg,axiom,
% 0.28/0.53      ! [B: rat,A: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ B @ A )
% 0.28/0.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_right_mono_neg
% 0.28/0.53  thf(fact_2041_zero__le__power,axiom,
% 0.28/0.53      ! [A: real,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_power
% 0.28/0.53  thf(fact_2042_zero__le__power,axiom,
% 0.28/0.53      ! [A: rat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_power
% 0.28/0.53  thf(fact_2043_zero__le__power,axiom,
% 0.28/0.53      ! [A: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_power
% 0.28/0.53  thf(fact_2044_zero__le__power,axiom,
% 0.28/0.53      ! [A: int,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_le_power
% 0.28/0.53  thf(fact_2045_power__mono,axiom,
% 0.28/0.53      ! [A: real,B: real,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_mono
% 0.28/0.53  thf(fact_2046_power__mono,axiom,
% 0.28/0.53      ! [A: rat,B: rat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_mono
% 0.28/0.53  thf(fact_2047_power__mono,axiom,
% 0.28/0.53      ! [A: nat,B: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_mono
% 0.28/0.53  thf(fact_2048_power__mono,axiom,
% 0.28/0.53      ! [A: int,B: int,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_mono
% 0.28/0.53  thf(fact_2049_zero__less__power,axiom,
% 0.28/0.53      ! [A: real,N: nat] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_power
% 0.28/0.53  thf(fact_2050_zero__less__power,axiom,
% 0.28/0.53      ! [A: rat,N: nat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_power
% 0.28/0.53  thf(fact_2051_zero__less__power,axiom,
% 0.28/0.53      ! [A: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_power
% 0.28/0.53  thf(fact_2052_zero__less__power,axiom,
% 0.28/0.53      ! [A: int,N: nat] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_power
% 0.28/0.53  thf(fact_2053_frac__eq__eq,axiom,
% 0.28/0.53      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 0.28/0.53        ( ( Y != zero_zero_complex )
% 0.28/0.53       => ( ( Z != zero_zero_complex )
% 0.28/0.53         => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 0.28/0.53              = ( divide1717551699836669952omplex @ W @ Z ) )
% 0.28/0.53            = ( ( times_times_complex @ X @ Z )
% 0.28/0.53              = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_eq_eq
% 0.28/0.53  thf(fact_2054_frac__eq__eq,axiom,
% 0.28/0.53      ! [Y: real,Z: real,X: real,W: real] :
% 0.28/0.53        ( ( Y != zero_zero_real )
% 0.28/0.53       => ( ( Z != zero_zero_real )
% 0.28/0.53         => ( ( ( divide_divide_real @ X @ Y )
% 0.28/0.53              = ( divide_divide_real @ W @ Z ) )
% 0.28/0.53            = ( ( times_times_real @ X @ Z )
% 0.28/0.53              = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_eq_eq
% 0.28/0.53  thf(fact_2055_frac__eq__eq,axiom,
% 0.28/0.53      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.28/0.53        ( ( Y != zero_zero_rat )
% 0.28/0.53       => ( ( Z != zero_zero_rat )
% 0.28/0.53         => ( ( ( divide_divide_rat @ X @ Y )
% 0.28/0.53              = ( divide_divide_rat @ W @ Z ) )
% 0.28/0.53            = ( ( times_times_rat @ X @ Z )
% 0.28/0.53              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_eq_eq
% 0.28/0.53  thf(fact_2056_divide__eq__eq,axiom,
% 0.28/0.53      ! [B: complex,C: complex,A: complex] :
% 0.28/0.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.28/0.53          = A )
% 0.28/0.53        = ( ( ( C != zero_zero_complex )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_complex @ A @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_complex )
% 0.28/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq
% 0.28/0.53  thf(fact_2057_divide__eq__eq,axiom,
% 0.28/0.53      ! [B: real,C: real,A: real] :
% 0.28/0.53        ( ( ( divide_divide_real @ B @ C )
% 0.28/0.53          = A )
% 0.28/0.53        = ( ( ( C != zero_zero_real )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_real @ A @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_real )
% 0.28/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq
% 0.28/0.53  thf(fact_2058_divide__eq__eq,axiom,
% 0.28/0.53      ! [B: rat,C: rat,A: rat] :
% 0.28/0.53        ( ( ( divide_divide_rat @ B @ C )
% 0.28/0.53          = A )
% 0.28/0.53        = ( ( ( C != zero_zero_rat )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_rat @ A @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_rat )
% 0.28/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq
% 0.28/0.53  thf(fact_2059_eq__divide__eq,axiom,
% 0.28/0.53      ! [A: complex,B: complex,C: complex] :
% 0.28/0.53        ( ( A
% 0.28/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_complex )
% 0.28/0.53           => ( ( times_times_complex @ A @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_complex )
% 0.28/0.53           => ( A = zero_zero_complex ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq
% 0.28/0.53  thf(fact_2060_eq__divide__eq,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( A
% 0.28/0.53          = ( divide_divide_real @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_real )
% 0.28/0.53           => ( ( times_times_real @ A @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_real )
% 0.28/0.53           => ( A = zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq
% 0.28/0.53  thf(fact_2061_eq__divide__eq,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( A
% 0.28/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_rat )
% 0.28/0.53           => ( ( times_times_rat @ A @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_rat )
% 0.28/0.53           => ( A = zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq
% 0.28/0.53  thf(fact_2062_divide__eq__imp,axiom,
% 0.28/0.53      ! [C: complex,B: complex,A: complex] :
% 0.28/0.53        ( ( C != zero_zero_complex )
% 0.28/0.53       => ( ( B
% 0.28/0.53            = ( times_times_complex @ A @ C ) )
% 0.28/0.53         => ( ( divide1717551699836669952omplex @ B @ C )
% 0.28/0.53            = A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_imp
% 0.28/0.53  thf(fact_2063_divide__eq__imp,axiom,
% 0.28/0.53      ! [C: real,B: real,A: real] :
% 0.28/0.53        ( ( C != zero_zero_real )
% 0.28/0.53       => ( ( B
% 0.28/0.53            = ( times_times_real @ A @ C ) )
% 0.28/0.53         => ( ( divide_divide_real @ B @ C )
% 0.28/0.53            = A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_imp
% 0.28/0.53  thf(fact_2064_divide__eq__imp,axiom,
% 0.28/0.53      ! [C: rat,B: rat,A: rat] :
% 0.28/0.53        ( ( C != zero_zero_rat )
% 0.28/0.53       => ( ( B
% 0.28/0.53            = ( times_times_rat @ A @ C ) )
% 0.28/0.53         => ( ( divide_divide_rat @ B @ C )
% 0.28/0.53            = A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_imp
% 0.28/0.53  thf(fact_2065_eq__divide__imp,axiom,
% 0.28/0.53      ! [C: complex,A: complex,B: complex] :
% 0.28/0.53        ( ( C != zero_zero_complex )
% 0.28/0.53       => ( ( ( times_times_complex @ A @ C )
% 0.28/0.53            = B )
% 0.28/0.53         => ( A
% 0.28/0.53            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_imp
% 0.28/0.53  thf(fact_2066_eq__divide__imp,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( C != zero_zero_real )
% 0.28/0.53       => ( ( ( times_times_real @ A @ C )
% 0.28/0.53            = B )
% 0.28/0.53         => ( A
% 0.28/0.53            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_imp
% 0.28/0.53  thf(fact_2067_eq__divide__imp,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( C != zero_zero_rat )
% 0.28/0.53       => ( ( ( times_times_rat @ A @ C )
% 0.28/0.53            = B )
% 0.28/0.53         => ( A
% 0.28/0.53            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_imp
% 0.28/0.53  thf(fact_2068_nonzero__divide__eq__eq,axiom,
% 0.28/0.53      ! [C: complex,B: complex,A: complex] :
% 0.28/0.53        ( ( C != zero_zero_complex )
% 0.28/0.53       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.28/0.53            = A )
% 0.28/0.53          = ( B
% 0.28/0.53            = ( times_times_complex @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_divide_eq_eq
% 0.28/0.53  thf(fact_2069_nonzero__divide__eq__eq,axiom,
% 0.28/0.53      ! [C: real,B: real,A: real] :
% 0.28/0.53        ( ( C != zero_zero_real )
% 0.28/0.53       => ( ( ( divide_divide_real @ B @ C )
% 0.28/0.53            = A )
% 0.28/0.53          = ( B
% 0.28/0.53            = ( times_times_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_divide_eq_eq
% 0.28/0.53  thf(fact_2070_nonzero__divide__eq__eq,axiom,
% 0.28/0.53      ! [C: rat,B: rat,A: rat] :
% 0.28/0.53        ( ( C != zero_zero_rat )
% 0.28/0.53       => ( ( ( divide_divide_rat @ B @ C )
% 0.28/0.53            = A )
% 0.28/0.53          = ( B
% 0.28/0.53            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_divide_eq_eq
% 0.28/0.53  thf(fact_2071_nonzero__eq__divide__eq,axiom,
% 0.28/0.53      ! [C: complex,A: complex,B: complex] :
% 0.28/0.53        ( ( C != zero_zero_complex )
% 0.28/0.53       => ( ( A
% 0.28/0.53            = ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.53          = ( ( times_times_complex @ A @ C )
% 0.28/0.53            = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_eq_divide_eq
% 0.28/0.53  thf(fact_2072_nonzero__eq__divide__eq,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( C != zero_zero_real )
% 0.28/0.53       => ( ( A
% 0.28/0.53            = ( divide_divide_real @ B @ C ) )
% 0.28/0.53          = ( ( times_times_real @ A @ C )
% 0.28/0.53            = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_eq_divide_eq
% 0.28/0.53  thf(fact_2073_nonzero__eq__divide__eq,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( C != zero_zero_rat )
% 0.28/0.53       => ( ( A
% 0.28/0.53            = ( divide_divide_rat @ B @ C ) )
% 0.28/0.53          = ( ( times_times_rat @ A @ C )
% 0.28/0.53            = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nonzero_eq_divide_eq
% 0.28/0.53  thf(fact_2074_right__inverse__eq,axiom,
% 0.28/0.53      ! [B: complex,A: complex] :
% 0.28/0.53        ( ( B != zero_zero_complex )
% 0.28/0.53       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.28/0.53            = one_one_complex )
% 0.28/0.53          = ( A = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % right_inverse_eq
% 0.28/0.53  thf(fact_2075_right__inverse__eq,axiom,
% 0.28/0.53      ! [B: real,A: real] :
% 0.28/0.53        ( ( B != zero_zero_real )
% 0.28/0.53       => ( ( ( divide_divide_real @ A @ B )
% 0.28/0.53            = one_one_real )
% 0.28/0.53          = ( A = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % right_inverse_eq
% 0.28/0.53  thf(fact_2076_right__inverse__eq,axiom,
% 0.28/0.53      ! [B: rat,A: rat] :
% 0.28/0.53        ( ( B != zero_zero_rat )
% 0.28/0.53       => ( ( ( divide_divide_rat @ A @ B )
% 0.28/0.53            = one_one_rat )
% 0.28/0.53          = ( A = B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % right_inverse_eq
% 0.28/0.53  thf(fact_2077_not__exp__less__eq__0__int,axiom,
% 0.28/0.53      ! [N: nat] :
% 0.28/0.53        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 0.28/0.53  
% 0.28/0.53  % not_exp_less_eq_0_int
% 0.28/0.53  thf(fact_2078_power__0,axiom,
% 0.28/0.53      ! [A: rat] :
% 0.28/0.53        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.28/0.53        = one_one_rat ) ).
% 0.28/0.53  
% 0.28/0.53  % power_0
% 0.28/0.53  thf(fact_2079_power__0,axiom,
% 0.28/0.53      ! [A: nat] :
% 0.28/0.53        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.28/0.53        = one_one_nat ) ).
% 0.28/0.53  
% 0.28/0.53  % power_0
% 0.28/0.53  thf(fact_2080_power__0,axiom,
% 0.28/0.53      ! [A: real] :
% 0.28/0.53        ( ( power_power_real @ A @ zero_zero_nat )
% 0.28/0.53        = one_one_real ) ).
% 0.28/0.53  
% 0.28/0.53  % power_0
% 0.28/0.53  thf(fact_2081_power__0,axiom,
% 0.28/0.53      ! [A: int] :
% 0.28/0.53        ( ( power_power_int @ A @ zero_zero_nat )
% 0.28/0.53        = one_one_int ) ).
% 0.28/0.53  
% 0.28/0.53  % power_0
% 0.28/0.53  thf(fact_2082_power__0,axiom,
% 0.28/0.53      ! [A: complex] :
% 0.28/0.53        ( ( power_power_complex @ A @ zero_zero_nat )
% 0.28/0.53        = one_one_complex ) ).
% 0.28/0.53  
% 0.28/0.53  % power_0
% 0.28/0.53  thf(fact_2083_divmod__digit__0_I1_J,axiom,
% 0.28/0.53      ! [B: nat,A: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.53       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.53         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.53            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divmod_digit_0(1)
% 0.28/0.53  thf(fact_2084_divmod__digit__0_I1_J,axiom,
% 0.28/0.53      ! [B: int,A: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.53       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.53         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.53            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divmod_digit_0(1)
% 0.28/0.53  thf(fact_2085_divmod__digit__0_I1_J,axiom,
% 0.28/0.53      ! [B: code_integer,A: code_integer] :
% 0.28/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.53       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.28/0.53         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.53            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divmod_digit_0(1)
% 0.28/0.53  thf(fact_2086_ex__least__nat__le,axiom,
% 0.28/0.53      ! [P: nat > $o,N: nat] :
% 0.28/0.53        ( ( P @ N )
% 0.28/0.53       => ( ~ ( P @ zero_zero_nat )
% 0.28/0.53         => ? [K3: nat] :
% 0.28/0.53              ( ( ord_less_eq_nat @ K3 @ N )
% 0.28/0.53              & ! [I2: nat] :
% 0.28/0.53                  ( ( ord_less_nat @ I2 @ K3 )
% 0.28/0.53                 => ~ ( P @ I2 ) )
% 0.28/0.53              & ( P @ K3 ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ex_least_nat_le
% 0.28/0.53  thf(fact_2087_less__imp__add__positive,axiom,
% 0.28/0.53      ! [I: nat,J: nat] :
% 0.28/0.53        ( ( ord_less_nat @ I @ J )
% 0.28/0.53       => ? [K3: nat] :
% 0.28/0.53            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 0.28/0.53            & ( ( plus_plus_nat @ I @ K3 )
% 0.28/0.53              = J ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_imp_add_positive
% 0.28/0.53  thf(fact_2088_mult__less__mono1,axiom,
% 0.28/0.53      ! [I: nat,J: nat,K: nat] :
% 0.28/0.53        ( ( ord_less_nat @ I @ J )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_mono1
% 0.28/0.53  thf(fact_2089_mult__less__mono2,axiom,
% 0.28/0.53      ! [I: nat,J: nat,K: nat] :
% 0.28/0.53        ( ( ord_less_nat @ I @ J )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_mono2
% 0.28/0.53  thf(fact_2090_nat__mult__less__cancel1,axiom,
% 0.28/0.53      ! [K: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.53          = ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_mult_less_cancel1
% 0.28/0.53  thf(fact_2091_nat__mult__eq__cancel1,axiom,
% 0.28/0.53      ! [K: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53       => ( ( ( times_times_nat @ K @ M )
% 0.28/0.53            = ( times_times_nat @ K @ N ) )
% 0.28/0.53          = ( M = N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_mult_eq_cancel1
% 0.28/0.53  thf(fact_2092_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.28/0.53      ! [M: nat,N: nat] :
% 0.28/0.53        ( ( ( divide_divide_nat @ M @ N )
% 0.28/0.53          = zero_zero_nat )
% 0.28/0.53        = ( ( ord_less_nat @ M @ N )
% 0.28/0.53          | ( N = zero_zero_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % Euclidean_Division.div_eq_0_iff
% 0.28/0.53  thf(fact_2093_nat__power__less__imp__less,axiom,
% 0.28/0.53      ! [I: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ I )
% 0.28/0.53       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.28/0.53         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_power_less_imp_less
% 0.28/0.53  thf(fact_2094_bits__stable__imp__add__self,axiom,
% 0.28/0.53      ! [A: nat] :
% 0.28/0.53        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.53          = A )
% 0.28/0.53       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.53          = zero_zero_nat ) ) ).
% 0.28/0.53  
% 0.28/0.53  % bits_stable_imp_add_self
% 0.28/0.53  thf(fact_2095_bits__stable__imp__add__self,axiom,
% 0.28/0.53      ! [A: int] :
% 0.28/0.53        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.53          = A )
% 0.28/0.53       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.28/0.53          = zero_zero_int ) ) ).
% 0.28/0.53  
% 0.28/0.53  % bits_stable_imp_add_self
% 0.28/0.53  thf(fact_2096_bits__stable__imp__add__self,axiom,
% 0.28/0.53      ! [A: code_integer] :
% 0.28/0.53        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.53          = A )
% 0.28/0.53       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.28/0.53          = zero_z3403309356797280102nteger ) ) ).
% 0.28/0.53  
% 0.28/0.53  % bits_stable_imp_add_self
% 0.28/0.53  thf(fact_2097_mult__eq__self__implies__10,axiom,
% 0.28/0.53      ! [M: nat,N: nat] :
% 0.28/0.53        ( ( M
% 0.28/0.53          = ( times_times_nat @ M @ N ) )
% 0.28/0.53       => ( ( N = one_one_nat )
% 0.28/0.53          | ( M = zero_zero_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_eq_self_implies_10
% 0.28/0.53  thf(fact_2098_pow_Osimps_I1_J,axiom,
% 0.28/0.53      ! [X: num] :
% 0.28/0.53        ( ( pow @ X @ one )
% 0.28/0.53        = X ) ).
% 0.28/0.53  
% 0.28/0.53  % pow.simps(1)
% 0.28/0.53  thf(fact_2099_mod__double__modulus,axiom,
% 0.28/0.53      ! [M: code_integer,X: code_integer] :
% 0.28/0.53        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 0.28/0.53       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.28/0.53         => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( modulo364778990260209775nteger @ X @ M ) )
% 0.28/0.53            | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_double_modulus
% 0.28/0.53  thf(fact_2100_mod__double__modulus,axiom,
% 0.28/0.53      ! [M: nat,X: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.28/0.53         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( modulo_modulo_nat @ X @ M ) )
% 0.28/0.53            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_double_modulus
% 0.28/0.53  thf(fact_2101_mod__double__modulus,axiom,
% 0.28/0.53      ! [M: int,X: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ M )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.53         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( modulo_modulo_int @ X @ M ) )
% 0.28/0.53            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.53              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_double_modulus
% 0.28/0.53  thf(fact_2102_mult__exp__mod__exp__eq,axiom,
% 0.28/0.53      ! [M: nat,N: nat,A: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.53       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.53          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_exp_mod_exp_eq
% 0.28/0.53  thf(fact_2103_mult__exp__mod__exp__eq,axiom,
% 0.28/0.53      ! [M: nat,N: nat,A: int] :
% 0.28/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.53       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.53          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_exp_mod_exp_eq
% 0.28/0.53  thf(fact_2104_mult__exp__mod__exp__eq,axiom,
% 0.28/0.53      ! [M: nat,N: nat,A: code_integer] :
% 0.28/0.53        ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.53       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.28/0.53          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_exp_mod_exp_eq
% 0.28/0.53  thf(fact_2105_div__mult1__eq,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat] :
% 0.28/0.53        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.28/0.53        = ( 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 ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult1_eq
% 0.28/0.53  thf(fact_2106_div__mult1__eq,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int] :
% 0.28/0.53        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.28/0.53        = ( 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 ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult1_eq
% 0.28/0.53  thf(fact_2107_div__mult1__eq,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.53        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.28/0.53        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult1_eq
% 0.28/0.53  thf(fact_2108_mult__div__mod__eq,axiom,
% 0.28/0.53      ! [B: nat,A: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_div_mod_eq
% 0.28/0.53  thf(fact_2109_mult__div__mod__eq,axiom,
% 0.28/0.53      ! [B: int,A: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_div_mod_eq
% 0.28/0.53  thf(fact_2110_mult__div__mod__eq,axiom,
% 0.28/0.53      ! [B: code_integer,A: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_div_mod_eq
% 0.28/0.53  thf(fact_2111_mod__mult__div__eq,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_mult_div_eq
% 0.28/0.53  thf(fact_2112_mod__mult__div__eq,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_mult_div_eq
% 0.28/0.53  thf(fact_2113_mod__mult__div__eq,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_mult_div_eq
% 0.28/0.53  thf(fact_2114_mod__div__mult__eq,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_mult_eq
% 0.28/0.53  thf(fact_2115_mod__div__mult__eq,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_mult_eq
% 0.28/0.53  thf(fact_2116_mod__div__mult__eq,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_mult_eq
% 0.28/0.53  thf(fact_2117_div__mult__mod__eq,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult_mod_eq
% 0.28/0.53  thf(fact_2118_div__mult__mod__eq,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult_mod_eq
% 0.28/0.53  thf(fact_2119_div__mult__mod__eq,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.28/0.53        = A ) ).
% 0.28/0.53  
% 0.28/0.53  % div_mult_mod_eq
% 0.28/0.53  thf(fact_2120_mod__div__decomp,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( A
% 0.28/0.53        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_decomp
% 0.28/0.53  thf(fact_2121_mod__div__decomp,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( A
% 0.28/0.53        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_decomp
% 0.28/0.53  thf(fact_2122_mod__div__decomp,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer] :
% 0.28/0.53        ( A
% 0.28/0.53        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_div_decomp
% 0.28/0.53  thf(fact_2123_cancel__div__mod__rules_I1_J,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_plus_nat @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(1)
% 0.28/0.53  thf(fact_2124_cancel__div__mod__rules_I1_J,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_plus_int @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(1)
% 0.28/0.53  thf(fact_2125_cancel__div__mod__rules_I1_J,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(1)
% 0.28/0.53  thf(fact_2126_cancel__div__mod__rules_I2_J,axiom,
% 0.28/0.53      ! [B: nat,A: nat,C: nat] :
% 0.28/0.53        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_plus_nat @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(2)
% 0.28/0.53  thf(fact_2127_cancel__div__mod__rules_I2_J,axiom,
% 0.28/0.53      ! [B: int,A: int,C: int] :
% 0.28/0.53        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_plus_int @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(2)
% 0.28/0.53  thf(fact_2128_cancel__div__mod__rules_I2_J,axiom,
% 0.28/0.53      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.28/0.53        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.28/0.53        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.28/0.53  
% 0.28/0.53  % cancel_div_mod_rules(2)
% 0.28/0.53  thf(fact_2129_ordered__ring__class_Ole__add__iff1,axiom,
% 0.28/0.53      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff1
% 0.28/0.53  thf(fact_2130_ordered__ring__class_Ole__add__iff1,axiom,
% 0.28/0.53      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff1
% 0.28/0.53  thf(fact_2131_ordered__ring__class_Ole__add__iff1,axiom,
% 0.28/0.53      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff1
% 0.28/0.53  thf(fact_2132_ordered__ring__class_Ole__add__iff2,axiom,
% 0.28/0.53      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff2
% 0.28/0.53  thf(fact_2133_ordered__ring__class_Ole__add__iff2,axiom,
% 0.28/0.53      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff2
% 0.28/0.53  thf(fact_2134_ordered__ring__class_Ole__add__iff2,axiom,
% 0.28/0.53      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % ordered_ring_class.le_add_iff2
% 0.28/0.53  thf(fact_2135_less__add__iff2,axiom,
% 0.28/0.53      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff2
% 0.28/0.53  thf(fact_2136_less__add__iff2,axiom,
% 0.28/0.53      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff2
% 0.28/0.53  thf(fact_2137_less__add__iff2,axiom,
% 0.28/0.53      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff2
% 0.28/0.53  thf(fact_2138_less__add__iff1,axiom,
% 0.28/0.53      ! [A: real,E: real,C: real,B: real,D: real] :
% 0.28/0.53        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff1
% 0.28/0.53  thf(fact_2139_less__add__iff1,axiom,
% 0.28/0.53      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff1
% 0.28/0.53  thf(fact_2140_less__add__iff1,axiom,
% 0.28/0.53      ! [A: int,E: int,C: int,B: int,D: int] :
% 0.28/0.53        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.28/0.53        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_add_iff1
% 0.28/0.53  thf(fact_2141_square__diff__one__factored,axiom,
% 0.28/0.53      ! [X: complex] :
% 0.28/0.53        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 0.28/0.53        = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % square_diff_one_factored
% 0.28/0.53  thf(fact_2142_square__diff__one__factored,axiom,
% 0.28/0.53      ! [X: real] :
% 0.28/0.53        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 0.28/0.53        = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % square_diff_one_factored
% 0.28/0.53  thf(fact_2143_square__diff__one__factored,axiom,
% 0.28/0.53      ! [X: rat] :
% 0.28/0.53        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 0.28/0.53        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % square_diff_one_factored
% 0.28/0.53  thf(fact_2144_square__diff__one__factored,axiom,
% 0.28/0.53      ! [X: int] :
% 0.28/0.53        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 0.28/0.53        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % square_diff_one_factored
% 0.28/0.53  thf(fact_2145_mod__mult2__eq,axiom,
% 0.28/0.53      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.53        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 0.28/0.53        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mod_mult2_eq
% 0.28/0.53  thf(fact_2146_less__diff__conv2,axiom,
% 0.28/0.53      ! [K: nat,J: nat,I: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.53       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.28/0.53          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_diff_conv2
% 0.28/0.53  thf(fact_2147_nat__eq__add__iff1,axiom,
% 0.28/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.28/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.28/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.28/0.53            = N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_eq_add_iff1
% 0.28/0.53  thf(fact_2148_nat__eq__add__iff2,axiom,
% 0.28/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.53       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.28/0.53            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( M
% 0.28/0.53            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_eq_add_iff2
% 0.28/0.53  thf(fact_2149_nat__le__add__iff1,axiom,
% 0.28/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.28/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_le_add_iff1
% 0.28/0.53  thf(fact_2150_nat__le__add__iff2,axiom,
% 0.28/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.53       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_le_add_iff2
% 0.28/0.53  thf(fact_2151_nat__diff__add__eq1,axiom,
% 0.28/0.53      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ J @ I )
% 0.28/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_diff_add_eq1
% 0.28/0.53  thf(fact_2152_nat__diff__add__eq2,axiom,
% 0.28/0.53      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.53       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.53          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_diff_add_eq2
% 0.28/0.53  thf(fact_2153_mult__less__le__imp__less,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_real @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53           => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_le_imp_less
% 0.28/0.53  thf(fact_2154_mult__less__le__imp__less,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_rat @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_le_imp_less
% 0.28/0.53  thf(fact_2155_mult__less__le__imp__less,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.53        ( ( ord_less_nat @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_nat @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_le_imp_less
% 0.28/0.53  thf(fact_2156_mult__less__le__imp__less,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.53        ( ( ord_less_int @ A @ B )
% 0.28/0.53       => ( ( ord_less_eq_int @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_le_imp_less
% 0.28/0.53  thf(fact_2157_mult__le__less__imp__less,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_real @ C @ D )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_less_imp_less
% 0.28/0.53  thf(fact_2158_mult__le__less__imp__less,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_rat @ C @ D )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_less_imp_less
% 0.28/0.53  thf(fact_2159_mult__le__less__imp__less,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.28/0.53       => ( ( ord_less_nat @ C @ D )
% 0.28/0.53         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_less_imp_less
% 0.28/0.53  thf(fact_2160_mult__le__less__imp__less,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.53       => ( ( ord_less_int @ C @ D )
% 0.28/0.53         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_less_imp_less
% 0.28/0.53  thf(fact_2161_mult__right__le__imp__le,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_imp_le
% 0.28/0.53  thf(fact_2162_mult__right__le__imp__le,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_imp_le
% 0.28/0.53  thf(fact_2163_mult__right__le__imp__le,axiom,
% 0.28/0.53      ! [A: nat,C: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_imp_le
% 0.28/0.53  thf(fact_2164_mult__right__le__imp__le,axiom,
% 0.28/0.53      ! [A: int,C: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_imp_le
% 0.28/0.53  thf(fact_2165_mult__left__le__imp__le,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_imp_le
% 0.28/0.53  thf(fact_2166_mult__left__le__imp__le,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_imp_le
% 0.28/0.53  thf(fact_2167_mult__left__le__imp__le,axiom,
% 0.28/0.53      ! [C: nat,A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.28/0.53         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_imp_le
% 0.28/0.53  thf(fact_2168_mult__left__le__imp__le,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_imp_le
% 0.28/0.53  thf(fact_2169_mult__le__cancel__left__pos,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_pos
% 0.28/0.53  thf(fact_2170_mult__le__cancel__left__pos,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_pos
% 0.28/0.53  thf(fact_2171_mult__le__cancel__left__pos,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_pos
% 0.28/0.53  thf(fact_2172_mult__le__cancel__left__neg,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_neg
% 0.28/0.53  thf(fact_2173_mult__le__cancel__left__neg,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_neg
% 0.28/0.53  thf(fact_2174_mult__le__cancel__left__neg,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.53       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left_neg
% 0.28/0.53  thf(fact_2175_mult__less__cancel__right,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_right
% 0.28/0.53  thf(fact_2176_mult__less__cancel__right,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_right
% 0.28/0.53  thf(fact_2177_mult__less__cancel__right,axiom,
% 0.28/0.53      ! [A: int,C: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53           => ( ord_less_int @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_right
% 0.28/0.53  thf(fact_2178_mult__strict__mono_H,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_real @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono'
% 0.28/0.53  thf(fact_2179_mult__strict__mono_H,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_rat @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono'
% 0.28/0.53  thf(fact_2180_mult__strict__mono_H,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.53        ( ( ord_less_nat @ A @ B )
% 0.28/0.53       => ( ( ord_less_nat @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono'
% 0.28/0.53  thf(fact_2181_mult__strict__mono_H,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.53        ( ( ord_less_int @ A @ B )
% 0.28/0.53       => ( ( ord_less_int @ C @ D )
% 0.28/0.53         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono'
% 0.28/0.53  thf(fact_2182_mult__right__less__imp__less,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_less_imp_less
% 0.28/0.53  thf(fact_2183_mult__right__less__imp__less,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_less_imp_less
% 0.28/0.53  thf(fact_2184_mult__right__less__imp__less,axiom,
% 0.28/0.53      ! [A: nat,C: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_less_imp_less
% 0.28/0.53  thf(fact_2185_mult__right__less__imp__less,axiom,
% 0.28/0.53      ! [A: int,C: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_less_imp_less
% 0.28/0.53  thf(fact_2186_mult__less__cancel__left,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_left
% 0.28/0.53  thf(fact_2187_mult__less__cancel__left,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_left
% 0.28/0.53  thf(fact_2188_mult__less__cancel__left,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53           => ( ord_less_int @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.53           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_less_cancel_left
% 0.28/0.53  thf(fact_2189_mult__strict__mono,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_real @ C @ D )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.53           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono
% 0.28/0.53  thf(fact_2190_mult__strict__mono,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_rat @ C @ D )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.53           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono
% 0.28/0.53  thf(fact_2191_mult__strict__mono,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.53        ( ( ord_less_nat @ A @ B )
% 0.28/0.53       => ( ( ord_less_nat @ C @ D )
% 0.28/0.53         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.53           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.53             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono
% 0.28/0.53  thf(fact_2192_mult__strict__mono,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.53        ( ( ord_less_int @ A @ B )
% 0.28/0.53       => ( ( ord_less_int @ C @ D )
% 0.28/0.53         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.53           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_strict_mono
% 0.28/0.53  thf(fact_2193_mult__left__less__imp__less,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_less_imp_less
% 0.28/0.53  thf(fact_2194_mult__left__less__imp__less,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_less_imp_less
% 0.28/0.53  thf(fact_2195_mult__left__less__imp__less,axiom,
% 0.28/0.53      ! [C: nat,A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.28/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_less_imp_less
% 0.28/0.53  thf(fact_2196_mult__left__less__imp__less,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_less_imp_less
% 0.28/0.53  thf(fact_2197_mult__le__cancel__right,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_eq_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_right
% 0.28/0.53  thf(fact_2198_mult__le__cancel__right,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_eq_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_right
% 0.28/0.53  thf(fact_2199_mult__le__cancel__right,axiom,
% 0.28/0.53      ! [A: int,C: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53           => ( ord_less_eq_int @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_right
% 0.28/0.53  thf(fact_2200_mult__le__cancel__left,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_eq_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left
% 0.28/0.53  thf(fact_2201_mult__le__cancel__left,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_eq_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left
% 0.28/0.53  thf(fact_2202_mult__le__cancel__left,axiom,
% 0.28/0.53      ! [C: int,A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.28/0.53        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.53           => ( ord_less_eq_int @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.53           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_cancel_left
% 0.28/0.53  thf(fact_2203_add__strict__increasing2,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ( ord_less_real @ B @ C )
% 0.28/0.53         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing2
% 0.28/0.53  thf(fact_2204_add__strict__increasing2,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ( ord_less_rat @ B @ C )
% 0.28/0.53         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing2
% 0.28/0.53  thf(fact_2205_add__strict__increasing2,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_nat @ B @ C )
% 0.28/0.53         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing2
% 0.28/0.53  thf(fact_2206_add__strict__increasing2,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_int @ B @ C )
% 0.28/0.53         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing2
% 0.28/0.53  thf(fact_2207_add__strict__increasing,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ( ord_less_eq_real @ B @ C )
% 0.28/0.53         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing
% 0.28/0.53  thf(fact_2208_add__strict__increasing,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.28/0.53         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing
% 0.28/0.53  thf(fact_2209_add__strict__increasing,axiom,
% 0.28/0.53      ! [A: nat,B: nat,C: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.28/0.53         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing
% 0.28/0.53  thf(fact_2210_add__strict__increasing,axiom,
% 0.28/0.53      ! [A: int,B: int,C: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.28/0.53         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_strict_increasing
% 0.28/0.53  thf(fact_2211_add__pos__nonneg,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.53         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_pos_nonneg
% 0.28/0.53  thf(fact_2212_add__pos__nonneg,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.53         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_pos_nonneg
% 0.28/0.53  thf(fact_2213_add__pos__nonneg,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.53         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_pos_nonneg
% 0.28/0.53  thf(fact_2214_add__pos__nonneg,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.53         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_pos_nonneg
% 0.28/0.53  thf(fact_2215_add__nonpos__neg,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ B @ zero_zero_real )
% 0.28/0.53         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonpos_neg
% 0.28/0.53  thf(fact_2216_add__nonpos__neg,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonpos_neg
% 0.28/0.53  thf(fact_2217_add__nonpos__neg,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.28/0.53       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.28/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonpos_neg
% 0.28/0.53  thf(fact_2218_add__nonpos__neg,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.53       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonpos_neg
% 0.28/0.53  thf(fact_2219_add__nonneg__pos,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.28/0.53         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonneg_pos
% 0.28/0.53  thf(fact_2220_add__nonneg__pos,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.28/0.53         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonneg_pos
% 0.28/0.53  thf(fact_2221_add__nonneg__pos,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.53         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonneg_pos
% 0.28/0.53  thf(fact_2222_add__nonneg__pos,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.53         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_nonneg_pos
% 0.28/0.53  thf(fact_2223_add__neg__nonpos,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.28/0.53         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_neg_nonpos
% 0.28/0.53  thf(fact_2224_add__neg__nonpos,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_neg_nonpos
% 0.28/0.53  thf(fact_2225_add__neg__nonpos,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.28/0.53       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.28/0.53         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_neg_nonpos
% 0.28/0.53  thf(fact_2226_add__neg__nonpos,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.53       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.28/0.53         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_neg_nonpos
% 0.28/0.53  thf(fact_2227_field__le__epsilon,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ! [E2: real] :
% 0.28/0.53            ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.28/0.53           => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 0.28/0.53       => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.28/0.53  
% 0.28/0.53  % field_le_epsilon
% 0.28/0.53  thf(fact_2228_field__le__epsilon,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ! [E2: rat] :
% 0.28/0.53            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.28/0.53           => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 0.28/0.53       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.28/0.53  
% 0.28/0.53  % field_le_epsilon
% 0.28/0.53  thf(fact_2229_divide__nonpos__pos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_pos
% 0.28/0.53  thf(fact_2230_divide__nonpos__pos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_pos
% 0.28/0.53  thf(fact_2231_divide__nonpos__neg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_neg
% 0.28/0.53  thf(fact_2232_divide__nonpos__neg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonpos_neg
% 0.28/0.53  thf(fact_2233_divide__nonneg__pos,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_pos
% 0.28/0.53  thf(fact_2234_divide__nonneg__pos,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_pos
% 0.28/0.53  thf(fact_2235_divide__nonneg__neg,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.28/0.53         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_neg
% 0.28/0.53  thf(fact_2236_divide__nonneg__neg,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_nonneg_neg
% 0.28/0.53  thf(fact_2237_divide__le__cancel,axiom,
% 0.28/0.53      ! [A: real,C: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_eq_real @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_le_cancel
% 0.28/0.53  thf(fact_2238_divide__le__cancel,axiom,
% 0.28/0.53      ! [A: rat,C: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_eq_rat @ A @ B ) )
% 0.28/0.53          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_le_cancel
% 0.28/0.53  thf(fact_2239_frac__less2,axiom,
% 0.28/0.53      ! [X: real,Y: real,W: real,Z: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_eq_real @ X @ Y )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.28/0.53           => ( ( ord_less_real @ W @ Z )
% 0.28/0.53             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_less2
% 0.28/0.53  thf(fact_2240_frac__less2,axiom,
% 0.28/0.53      ! [X: rat,Y: rat,W: rat,Z: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_eq_rat @ X @ Y )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.28/0.53           => ( ( ord_less_rat @ W @ Z )
% 0.28/0.53             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_less2
% 0.28/0.53  thf(fact_2241_frac__less,axiom,
% 0.28/0.53      ! [X: real,Y: real,W: real,Z: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_real @ X @ Y )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.28/0.53           => ( ( ord_less_eq_real @ W @ Z )
% 0.28/0.53             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_less
% 0.28/0.53  thf(fact_2242_frac__less,axiom,
% 0.28/0.53      ! [X: rat,Y: rat,W: rat,Z: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_rat @ X @ Y )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.28/0.53           => ( ( ord_less_eq_rat @ W @ Z )
% 0.28/0.53             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_less
% 0.28/0.53  thf(fact_2243_frac__le,axiom,
% 0.28/0.53      ! [Y: real,X: real,W: real,Z: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.53       => ( ( ord_less_eq_real @ X @ Y )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ W )
% 0.28/0.53           => ( ( ord_less_eq_real @ W @ Z )
% 0.28/0.53             => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_le
% 0.28/0.53  thf(fact_2244_frac__le,axiom,
% 0.28/0.53      ! [Y: rat,X: rat,W: rat,Z: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.53       => ( ( ord_less_eq_rat @ X @ Y )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 0.28/0.53           => ( ( ord_less_eq_rat @ W @ Z )
% 0.28/0.53             => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % frac_le
% 0.28/0.53  thf(fact_2245_sum__squares__le__zero__iff,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 0.28/0.53        = ( ( X = zero_zero_real )
% 0.28/0.53          & ( Y = zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_le_zero_iff
% 0.28/0.53  thf(fact_2246_sum__squares__le__zero__iff,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.28/0.53        = ( ( X = zero_zero_rat )
% 0.28/0.53          & ( Y = zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_le_zero_iff
% 0.28/0.53  thf(fact_2247_sum__squares__le__zero__iff,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.28/0.53        = ( ( X = zero_zero_int )
% 0.28/0.53          & ( Y = zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_le_zero_iff
% 0.28/0.53  thf(fact_2248_sum__squares__ge__zero,axiom,
% 0.28/0.53      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_ge_zero
% 0.28/0.53  thf(fact_2249_sum__squares__ge__zero,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_ge_zero
% 0.28/0.53  thf(fact_2250_sum__squares__ge__zero,axiom,
% 0.28/0.53      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_ge_zero
% 0.28/0.53  thf(fact_2251_mult__left__le,axiom,
% 0.28/0.53      ! [C: real,A: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ C @ one_one_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le
% 0.28/0.53  thf(fact_2252_mult__left__le,axiom,
% 0.28/0.53      ! [C: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le
% 0.28/0.53  thf(fact_2253_mult__left__le,axiom,
% 0.28/0.53      ! [C: nat,A: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le
% 0.28/0.53  thf(fact_2254_mult__left__le,axiom,
% 0.28/0.53      ! [C: int,A: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le
% 0.28/0.53  thf(fact_2255_mult__le__one,axiom,
% 0.28/0.53      ! [A: real,B: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ A @ one_one_real )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.53         => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.28/0.53           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_one
% 0.28/0.53  thf(fact_2256_mult__le__one,axiom,
% 0.28/0.53      ! [A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.53         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_one
% 0.28/0.53  thf(fact_2257_mult__le__one,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.53         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.28/0.53           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_one
% 0.28/0.53  thf(fact_2258_mult__le__one,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.53         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.28/0.53           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_le_one
% 0.28/0.53  thf(fact_2259_mult__right__le__one__le,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.28/0.53           => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_one_le
% 0.28/0.53  thf(fact_2260_mult__right__le__one__le,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_one_le
% 0.28/0.53  thf(fact_2261_mult__right__le__one__le,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.53         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.28/0.53           => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_right_le_one_le
% 0.28/0.53  thf(fact_2262_mult__left__le__one__le,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.53         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.28/0.53           => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_one_le
% 0.28/0.53  thf(fact_2263_mult__left__le__one__le,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.53         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.28/0.53           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_one_le
% 0.28/0.53  thf(fact_2264_mult__left__le__one__le,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.53         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.28/0.53           => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_left_le_one_le
% 0.28/0.53  thf(fact_2265_power__less__imp__less__base,axiom,
% 0.28/0.53      ! [A: real,N: nat,B: real] :
% 0.28/0.53        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.28/0.53       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.28/0.53         => ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_less_imp_less_base
% 0.28/0.53  thf(fact_2266_power__less__imp__less__base,axiom,
% 0.28/0.53      ! [A: rat,N: nat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.28/0.53       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.28/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_less_imp_less_base
% 0.28/0.53  thf(fact_2267_power__less__imp__less__base,axiom,
% 0.28/0.53      ! [A: nat,N: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.28/0.53       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.28/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_less_imp_less_base
% 0.28/0.53  thf(fact_2268_power__less__imp__less__base,axiom,
% 0.28/0.53      ! [A: int,N: nat,B: int] :
% 0.28/0.53        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.28/0.53       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.28/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_less_imp_less_base
% 0.28/0.53  thf(fact_2269_sum__squares__gt__zero__iff,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 0.28/0.53        = ( ( X != zero_zero_real )
% 0.28/0.53          | ( Y != zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_gt_zero_iff
% 0.28/0.53  thf(fact_2270_sum__squares__gt__zero__iff,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.28/0.53        = ( ( X != zero_zero_rat )
% 0.28/0.53          | ( Y != zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_gt_zero_iff
% 0.28/0.53  thf(fact_2271_sum__squares__gt__zero__iff,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 0.28/0.53        = ( ( X != zero_zero_int )
% 0.28/0.53          | ( Y != zero_zero_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % sum_squares_gt_zero_iff
% 0.28/0.53  thf(fact_2272_not__sum__squares__lt__zero,axiom,
% 0.28/0.53      ! [X: real,Y: real] :
% 0.28/0.53        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 0.28/0.53  
% 0.28/0.53  % not_sum_squares_lt_zero
% 0.28/0.53  thf(fact_2273_not__sum__squares__lt__zero,axiom,
% 0.28/0.53      ! [X: rat,Y: rat] :
% 0.28/0.53        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.28/0.53  
% 0.28/0.53  % not_sum_squares_lt_zero
% 0.28/0.53  thf(fact_2274_not__sum__squares__lt__zero,axiom,
% 0.28/0.53      ! [X: int,Y: int] :
% 0.28/0.53        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.28/0.53  
% 0.28/0.53  % not_sum_squares_lt_zero
% 0.28/0.53  thf(fact_2275_zero__less__two,axiom,
% 0.28/0.53      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_two
% 0.28/0.53  thf(fact_2276_zero__less__two,axiom,
% 0.28/0.53      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_two
% 0.28/0.53  thf(fact_2277_zero__less__two,axiom,
% 0.28/0.53      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_two
% 0.28/0.53  thf(fact_2278_zero__less__two,axiom,
% 0.28/0.53      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.28/0.53  
% 0.28/0.53  % zero_less_two
% 0.28/0.53  thf(fact_2279_divide__less__eq,axiom,
% 0.28/0.53      ! [B: real,C: real,A: real] :
% 0.28/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.28/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.28/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_eq
% 0.28/0.53  thf(fact_2280_divide__less__eq,axiom,
% 0.28/0.53      ! [B: rat,C: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.28/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.28/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_eq
% 0.28/0.53  thf(fact_2281_less__divide__eq,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.28/0.53          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.28/0.53              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_divide_eq
% 0.28/0.53  thf(fact_2282_less__divide__eq,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.28/0.53          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.28/0.53              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_divide_eq
% 0.28/0.53  thf(fact_2283_neg__divide__less__eq,axiom,
% 0.28/0.53      ! [C: real,B: real,A: real] :
% 0.28/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % neg_divide_less_eq
% 0.28/0.53  thf(fact_2284_neg__divide__less__eq,axiom,
% 0.28/0.53      ! [C: rat,B: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % neg_divide_less_eq
% 0.28/0.53  thf(fact_2285_neg__less__divide__eq,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % neg_less_divide_eq
% 0.28/0.53  thf(fact_2286_neg__less__divide__eq,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % neg_less_divide_eq
% 0.28/0.53  thf(fact_2287_pos__divide__less__eq,axiom,
% 0.28/0.53      ! [C: real,B: real,A: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.53          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % pos_divide_less_eq
% 0.28/0.53  thf(fact_2288_pos__divide__less__eq,axiom,
% 0.28/0.53      ! [C: rat,B: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.53          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % pos_divide_less_eq
% 0.28/0.53  thf(fact_2289_pos__less__divide__eq,axiom,
% 0.28/0.53      ! [C: real,A: real,B: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.53          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % pos_less_divide_eq
% 0.28/0.53  thf(fact_2290_pos__less__divide__eq,axiom,
% 0.28/0.53      ! [C: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.53          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % pos_less_divide_eq
% 0.28/0.53  thf(fact_2291_mult__imp__div__pos__less,axiom,
% 0.28/0.53      ! [Y: real,X: real,Z: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53       => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 0.28/0.53         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_imp_div_pos_less
% 0.28/0.53  thf(fact_2292_mult__imp__div__pos__less,axiom,
% 0.28/0.53      ! [Y: rat,X: rat,Z: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 0.28/0.53         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_imp_div_pos_less
% 0.28/0.53  thf(fact_2293_mult__imp__less__div__pos,axiom,
% 0.28/0.53      ! [Y: real,Z: real,X: real] :
% 0.28/0.53        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.53       => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 0.28/0.53         => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_imp_less_div_pos
% 0.28/0.53  thf(fact_2294_mult__imp__less__div__pos,axiom,
% 0.28/0.53      ! [Y: rat,Z: rat,X: rat] :
% 0.28/0.53        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.53       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 0.28/0.53         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % mult_imp_less_div_pos
% 0.28/0.53  thf(fact_2295_divide__strict__left__mono,axiom,
% 0.28/0.53      ! [B: real,A: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ B @ A )
% 0.28/0.53       => ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_left_mono
% 0.28/0.53  thf(fact_2296_divide__strict__left__mono,axiom,
% 0.28/0.53      ! [B: rat,A: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ B @ A )
% 0.28/0.53       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_left_mono
% 0.28/0.53  thf(fact_2297_divide__strict__left__mono__neg,axiom,
% 0.28/0.53      ! [A: real,B: real,C: real] :
% 0.28/0.53        ( ( ord_less_real @ A @ B )
% 0.28/0.53       => ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.53         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.53           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_left_mono_neg
% 0.28/0.53  thf(fact_2298_divide__strict__left__mono__neg,axiom,
% 0.28/0.53      ! [A: rat,B: rat,C: rat] :
% 0.28/0.53        ( ( ord_less_rat @ A @ B )
% 0.28/0.53       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.53         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.53           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_strict_left_mono_neg
% 0.28/0.53  thf(fact_2299_divide__less__eq__1,axiom,
% 0.28/0.53      ! [B: real,A: real] :
% 0.28/0.53        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_real @ B @ A ) )
% 0.28/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_real @ A @ B ) )
% 0.28/0.53          | ( A = zero_zero_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_eq_1
% 0.28/0.53  thf(fact_2300_divide__less__eq__1,axiom,
% 0.28/0.53      ! [B: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_rat @ B @ A ) )
% 0.28/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_rat @ A @ B ) )
% 0.28/0.53          | ( A = zero_zero_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_less_eq_1
% 0.28/0.53  thf(fact_2301_less__divide__eq__1,axiom,
% 0.28/0.53      ! [B: real,A: real] :
% 0.28/0.53        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.53        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.53            & ( ord_less_real @ A @ B ) )
% 0.28/0.53          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.53            & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_divide_eq_1
% 0.28/0.53  thf(fact_2302_less__divide__eq__1,axiom,
% 0.28/0.53      ! [B: rat,A: rat] :
% 0.28/0.53        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.53        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.53            & ( ord_less_rat @ A @ B ) )
% 0.28/0.53          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.53            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % less_divide_eq_1
% 0.28/0.53  thf(fact_2303_power__le__one,axiom,
% 0.28/0.53      ! [A: real,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.53       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.28/0.53         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_le_one
% 0.28/0.53  thf(fact_2304_power__le__one,axiom,
% 0.28/0.53      ! [A: rat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.53       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.28/0.53         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_le_one
% 0.28/0.53  thf(fact_2305_power__le__one,axiom,
% 0.28/0.53      ! [A: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.28/0.53         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_le_one
% 0.28/0.53  thf(fact_2306_power__le__one,axiom,
% 0.28/0.53      ! [A: int,N: nat] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.28/0.53         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % power_le_one
% 0.28/0.53  thf(fact_2307_divide__eq__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [B: complex,C: complex,W: num] :
% 0.28/0.53        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.28/0.53          = ( numera6690914467698888265omplex @ W ) )
% 0.28/0.53        = ( ( ( C != zero_zero_complex )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_complex )
% 0.28/0.53           => ( ( numera6690914467698888265omplex @ W )
% 0.28/0.53              = zero_zero_complex ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq_numeral(1)
% 0.28/0.53  thf(fact_2308_divide__eq__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [B: real,C: real,W: num] :
% 0.28/0.53        ( ( ( divide_divide_real @ B @ C )
% 0.28/0.53          = ( numeral_numeral_real @ W ) )
% 0.28/0.53        = ( ( ( C != zero_zero_real )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_real )
% 0.28/0.53           => ( ( numeral_numeral_real @ W )
% 0.28/0.53              = zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq_numeral(1)
% 0.28/0.53  thf(fact_2309_divide__eq__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [B: rat,C: rat,W: num] :
% 0.28/0.53        ( ( ( divide_divide_rat @ B @ C )
% 0.28/0.53          = ( numeral_numeral_rat @ W ) )
% 0.28/0.53        = ( ( ( C != zero_zero_rat )
% 0.28/0.53           => ( B
% 0.28/0.53              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.28/0.53          & ( ( C = zero_zero_rat )
% 0.28/0.53           => ( ( numeral_numeral_rat @ W )
% 0.28/0.53              = zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_eq_eq_numeral(1)
% 0.28/0.53  thf(fact_2310_eq__divide__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [W: num,B: complex,C: complex] :
% 0.28/0.53        ( ( ( numera6690914467698888265omplex @ W )
% 0.28/0.53          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_complex )
% 0.28/0.53           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_complex )
% 0.28/0.53           => ( ( numera6690914467698888265omplex @ W )
% 0.28/0.53              = zero_zero_complex ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq_numeral(1)
% 0.28/0.53  thf(fact_2311_eq__divide__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [W: num,B: real,C: real] :
% 0.28/0.53        ( ( ( numeral_numeral_real @ W )
% 0.28/0.53          = ( divide_divide_real @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_real )
% 0.28/0.53           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_real )
% 0.28/0.53           => ( ( numeral_numeral_real @ W )
% 0.28/0.53              = zero_zero_real ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq_numeral(1)
% 0.28/0.53  thf(fact_2312_eq__divide__eq__numeral_I1_J,axiom,
% 0.28/0.53      ! [W: num,B: rat,C: rat] :
% 0.28/0.53        ( ( ( numeral_numeral_rat @ W )
% 0.28/0.53          = ( divide_divide_rat @ B @ C ) )
% 0.28/0.53        = ( ( ( C != zero_zero_rat )
% 0.28/0.53           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 0.28/0.53              = B ) )
% 0.28/0.53          & ( ( C = zero_zero_rat )
% 0.28/0.53           => ( ( numeral_numeral_rat @ W )
% 0.28/0.53              = zero_zero_rat ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % eq_divide_eq_numeral(1)
% 0.28/0.53  thf(fact_2313_divide__add__eq__iff,axiom,
% 0.28/0.53      ! [Z: complex,X: complex,Y: complex] :
% 0.28/0.53        ( ( Z != zero_zero_complex )
% 0.28/0.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 0.28/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_add_eq_iff
% 0.28/0.53  thf(fact_2314_divide__add__eq__iff,axiom,
% 0.28/0.53      ! [Z: real,X: real,Y: real] :
% 0.28/0.53        ( ( Z != zero_zero_real )
% 0.28/0.53       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 0.28/0.53          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_add_eq_iff
% 0.28/0.53  thf(fact_2315_divide__add__eq__iff,axiom,
% 0.28/0.53      ! [Z: rat,X: rat,Y: rat] :
% 0.28/0.53        ( ( Z != zero_zero_rat )
% 0.28/0.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 0.28/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divide_add_eq_iff
% 0.28/0.53  thf(fact_2316_add__divide__eq__iff,axiom,
% 0.28/0.53      ! [Z: complex,X: complex,Y: complex] :
% 0.28/0.53        ( ( Z != zero_zero_complex )
% 0.28/0.53       => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 0.28/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_iff
% 0.28/0.53  thf(fact_2317_add__divide__eq__iff,axiom,
% 0.28/0.53      ! [Z: real,X: real,Y: real] :
% 0.28/0.53        ( ( Z != zero_zero_real )
% 0.28/0.53       => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 0.28/0.53          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_iff
% 0.28/0.53  thf(fact_2318_add__divide__eq__iff,axiom,
% 0.28/0.53      ! [Z: rat,X: rat,Y: rat] :
% 0.28/0.53        ( ( Z != zero_zero_rat )
% 0.28/0.53       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 0.28/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_iff
% 0.28/0.53  thf(fact_2319_add__num__frac,axiom,
% 0.28/0.53      ! [Y: complex,Z: complex,X: complex] :
% 0.28/0.53        ( ( Y != zero_zero_complex )
% 0.28/0.53       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.28/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_num_frac
% 0.28/0.53  thf(fact_2320_add__num__frac,axiom,
% 0.28/0.53      ! [Y: real,Z: real,X: real] :
% 0.28/0.53        ( ( Y != zero_zero_real )
% 0.28/0.53       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 0.28/0.53          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_num_frac
% 0.28/0.53  thf(fact_2321_add__num__frac,axiom,
% 0.28/0.53      ! [Y: rat,Z: rat,X: rat] :
% 0.28/0.53        ( ( Y != zero_zero_rat )
% 0.28/0.53       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 0.28/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_num_frac
% 0.28/0.53  thf(fact_2322_add__frac__num,axiom,
% 0.28/0.53      ! [Y: complex,X: complex,Z: complex] :
% 0.28/0.53        ( ( Y != zero_zero_complex )
% 0.28/0.53       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 0.28/0.53          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_num
% 0.28/0.53  thf(fact_2323_add__frac__num,axiom,
% 0.28/0.53      ! [Y: real,X: real,Z: real] :
% 0.28/0.53        ( ( Y != zero_zero_real )
% 0.28/0.53       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 0.28/0.53          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_num
% 0.28/0.53  thf(fact_2324_add__frac__num,axiom,
% 0.28/0.53      ! [Y: rat,X: rat,Z: rat] :
% 0.28/0.53        ( ( Y != zero_zero_rat )
% 0.28/0.53       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 0.28/0.53          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_num
% 0.28/0.53  thf(fact_2325_add__frac__eq,axiom,
% 0.28/0.53      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 0.28/0.53        ( ( Y != zero_zero_complex )
% 0.28/0.53       => ( ( Z != zero_zero_complex )
% 0.28/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 0.28/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_eq
% 0.28/0.53  thf(fact_2326_add__frac__eq,axiom,
% 0.28/0.53      ! [Y: real,Z: real,X: real,W: real] :
% 0.28/0.53        ( ( Y != zero_zero_real )
% 0.28/0.53       => ( ( Z != zero_zero_real )
% 0.28/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 0.28/0.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_eq
% 0.28/0.53  thf(fact_2327_add__frac__eq,axiom,
% 0.28/0.53      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.28/0.53        ( ( Y != zero_zero_rat )
% 0.28/0.53       => ( ( Z != zero_zero_rat )
% 0.28/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.28/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_frac_eq
% 0.28/0.53  thf(fact_2328_add__divide__eq__if__simps_I1_J,axiom,
% 0.28/0.53      ! [Z: complex,A: complex,B: complex] :
% 0.28/0.53        ( ( ( Z = zero_zero_complex )
% 0.28/0.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.28/0.53            = A ) )
% 0.28/0.53        & ( ( Z != zero_zero_complex )
% 0.28/0.53         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 0.28/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(1)
% 0.28/0.53  thf(fact_2329_add__divide__eq__if__simps_I1_J,axiom,
% 0.28/0.53      ! [Z: real,A: real,B: real] :
% 0.28/0.53        ( ( ( Z = zero_zero_real )
% 0.28/0.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.28/0.53            = A ) )
% 0.28/0.53        & ( ( Z != zero_zero_real )
% 0.28/0.53         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 0.28/0.53            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(1)
% 0.28/0.53  thf(fact_2330_add__divide__eq__if__simps_I1_J,axiom,
% 0.28/0.53      ! [Z: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ( Z = zero_zero_rat )
% 0.28/0.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.28/0.53            = A ) )
% 0.28/0.53        & ( ( Z != zero_zero_rat )
% 0.28/0.53         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.28/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(1)
% 0.28/0.53  thf(fact_2331_add__divide__eq__if__simps_I2_J,axiom,
% 0.28/0.53      ! [Z: complex,A: complex,B: complex] :
% 0.28/0.53        ( ( ( Z = zero_zero_complex )
% 0.28/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.28/0.53            = B ) )
% 0.28/0.53        & ( ( Z != zero_zero_complex )
% 0.28/0.53         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.28/0.53            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(2)
% 0.28/0.53  thf(fact_2332_add__divide__eq__if__simps_I2_J,axiom,
% 0.28/0.53      ! [Z: real,A: real,B: real] :
% 0.28/0.53        ( ( ( Z = zero_zero_real )
% 0.28/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.28/0.53            = B ) )
% 0.28/0.53        & ( ( Z != zero_zero_real )
% 0.28/0.53         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.28/0.53            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(2)
% 0.28/0.53  thf(fact_2333_add__divide__eq__if__simps_I2_J,axiom,
% 0.28/0.53      ! [Z: rat,A: rat,B: rat] :
% 0.28/0.53        ( ( ( Z = zero_zero_rat )
% 0.28/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.28/0.53            = B ) )
% 0.28/0.53        & ( ( Z != zero_zero_rat )
% 0.28/0.53         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.28/0.53            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % add_divide_eq_if_simps(2)
% 0.28/0.53  thf(fact_2334_div__add__self2,axiom,
% 0.28/0.53      ! [B: nat,A: nat] :
% 0.28/0.53        ( ( B != zero_zero_nat )
% 0.28/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.28/0.53          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_add_self2
% 0.28/0.53  thf(fact_2335_div__add__self2,axiom,
% 0.28/0.53      ! [B: int,A: int] :
% 0.28/0.53        ( ( B != zero_zero_int )
% 0.28/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.28/0.53          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_add_self2
% 0.28/0.53  thf(fact_2336_div__add__self1,axiom,
% 0.28/0.53      ! [B: nat,A: nat] :
% 0.28/0.53        ( ( B != zero_zero_nat )
% 0.28/0.53       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.28/0.53          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_add_self1
% 0.28/0.53  thf(fact_2337_div__add__self1,axiom,
% 0.28/0.53      ! [B: int,A: int] :
% 0.28/0.53        ( ( B != zero_zero_int )
% 0.28/0.53       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.28/0.53          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_add_self1
% 0.28/0.53  thf(fact_2338_bounded__Max__nat,axiom,
% 0.28/0.53      ! [P: nat > $o,X: nat,M5: nat] :
% 0.28/0.53        ( ( P @ X )
% 0.28/0.53       => ( ! [X6: nat] :
% 0.28/0.53              ( ( P @ X6 )
% 0.28/0.53             => ( ord_less_eq_nat @ X6 @ M5 ) )
% 0.28/0.53         => ~ ! [M4: nat] :
% 0.28/0.53                ( ( P @ M4 )
% 0.28/0.53               => ~ ! [X4: nat] :
% 0.28/0.53                      ( ( P @ X4 )
% 0.28/0.53                     => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % bounded_Max_nat
% 0.28/0.53  thf(fact_2339_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: complex,Xs: list_complex] :
% 0.28/0.53        ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2340_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: real,Xs: list_real] :
% 0.28/0.53        ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2341_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: set_nat,Xs: list_set_nat] :
% 0.28/0.53        ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2342_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.28/0.53        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2343_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: $o,Xs: list_o] :
% 0.28/0.53        ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2344_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: nat,Xs: list_nat] :
% 0.28/0.53        ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2345_length__pos__if__in__set,axiom,
% 0.28/0.53      ! [X: int,Xs: list_int] :
% 0.28/0.53        ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.28/0.53       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % length_pos_if_in_set
% 0.28/0.53  thf(fact_2346_nat__mult__le__cancel1,axiom,
% 0.28/0.53      ! [K: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.53          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_mult_le_cancel1
% 0.28/0.53  thf(fact_2347_div__greater__zero__iff,axiom,
% 0.28/0.53      ! [M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.28/0.53        = ( ( ord_less_eq_nat @ N @ M )
% 0.28/0.53          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_greater_zero_iff
% 0.28/0.53  thf(fact_2348_div__le__mono2,axiom,
% 0.28/0.53      ! [M: nat,N: nat,K: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.53       => ( ( ord_less_eq_nat @ M @ N )
% 0.28/0.53         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_le_mono2
% 0.28/0.53  thf(fact_2349_nat__mult__div__cancel1,axiom,
% 0.28/0.53      ! [K: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.28/0.53       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.28/0.53          = ( divide_divide_nat @ M @ N ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % nat_mult_div_cancel1
% 0.28/0.53  thf(fact_2350_div__less__iff__less__mult,axiom,
% 0.28/0.53      ! [Q2: nat,M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.28/0.53       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 0.28/0.53          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_less_iff_less_mult
% 0.28/0.53  thf(fact_2351_div__less__dividend,axiom,
% 0.28/0.53      ! [N: nat,M: nat] :
% 0.28/0.53        ( ( ord_less_nat @ one_one_nat @ N )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.53         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_less_dividend
% 0.28/0.53  thf(fact_2352_div__eq__dividend__iff,axiom,
% 0.28/0.53      ! [M: nat,N: nat] :
% 0.28/0.53        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.53       => ( ( ( divide_divide_nat @ M @ N )
% 0.28/0.53            = M )
% 0.28/0.53          = ( N = one_one_nat ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % div_eq_dividend_iff
% 0.28/0.53  thf(fact_2353_divmod__digit__1_I1_J,axiom,
% 0.28/0.53      ! [A: code_integer,B: code_integer] :
% 0.28/0.53        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.28/0.53       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.28/0.53         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.53           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.28/0.53              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divmod_digit_1(1)
% 0.28/0.53  thf(fact_2354_divmod__digit__1_I1_J,axiom,
% 0.28/0.53      ! [A: nat,B: nat] :
% 0.28/0.53        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.53       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.28/0.53         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.53           => ( ( 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 )
% 0.28/0.53              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.28/0.53  
% 0.28/0.53  % divmod_digit_1(1)
% 0.28/0.53  thf(fact_2355_divmod__digit__1_I1_J,axiom,
% 0.28/0.53      ! [A: int,B: int] :
% 0.28/0.53        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.53       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.53         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.28/0.54           => ( ( 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 )
% 0.28/0.54              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divmod_digit_1(1)
% 0.28/0.54  thf(fact_2356_power2__commute,axiom,
% 0.28/0.54      ! [X: complex,Y: complex] :
% 0.28/0.54        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_commute
% 0.28/0.54  thf(fact_2357_power2__commute,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_commute
% 0.28/0.54  thf(fact_2358_power2__commute,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_commute
% 0.28/0.54  thf(fact_2359_power2__commute,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_commute
% 0.28/0.54  thf(fact_2360_nat__less__add__iff2,axiom,
% 0.28/0.54      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ I @ J )
% 0.28/0.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.54          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_less_add_iff2
% 0.28/0.54  thf(fact_2361_nat__less__add__iff1,axiom,
% 0.28/0.54      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ J @ I )
% 0.28/0.54       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.28/0.54          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_less_add_iff1
% 0.28/0.54  thf(fact_2362_field__le__mult__one__interval,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ! [Z5: real] :
% 0.28/0.54            ( ( ord_less_real @ zero_zero_real @ Z5 )
% 0.28/0.54           => ( ( ord_less_real @ Z5 @ one_one_real )
% 0.28/0.54             => ( ord_less_eq_real @ ( times_times_real @ Z5 @ X ) @ Y ) ) )
% 0.28/0.54       => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.28/0.54  
% 0.28/0.54  % field_le_mult_one_interval
% 0.28/0.54  thf(fact_2363_field__le__mult__one__interval,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ! [Z5: rat] :
% 0.28/0.54            ( ( ord_less_rat @ zero_zero_rat @ Z5 )
% 0.28/0.54           => ( ( ord_less_rat @ Z5 @ one_one_rat )
% 0.28/0.54             => ( ord_less_eq_rat @ ( times_times_rat @ Z5 @ X ) @ Y ) ) )
% 0.28/0.54       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.28/0.54  
% 0.28/0.54  % field_le_mult_one_interval
% 0.28/0.54  thf(fact_2364_mult__less__cancel__right2,axiom,
% 0.28/0.54      ! [A: real,C: real] :
% 0.28/0.54        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ A @ one_one_real ) )
% 0.28/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right2
% 0.28/0.54  thf(fact_2365_mult__less__cancel__right2,axiom,
% 0.28/0.54      ! [A: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.28/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right2
% 0.28/0.54  thf(fact_2366_mult__less__cancel__right2,axiom,
% 0.28/0.54      ! [A: int,C: int] :
% 0.28/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_int @ A @ one_one_int ) )
% 0.28/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right2
% 0.28/0.54  thf(fact_2367_mult__less__cancel__right1,axiom,
% 0.28/0.54      ! [C: real,B: real] :
% 0.28/0.54        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ one_one_real @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right1
% 0.28/0.54  thf(fact_2368_mult__less__cancel__right1,axiom,
% 0.28/0.54      ! [C: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right1
% 0.28/0.54  thf(fact_2369_mult__less__cancel__right1,axiom,
% 0.28/0.54      ! [C: int,B: int] :
% 0.28/0.54        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_int @ one_one_int @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_right1
% 0.28/0.54  thf(fact_2370_mult__less__cancel__left2,axiom,
% 0.28/0.54      ! [C: real,A: real] :
% 0.28/0.54        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ A @ one_one_real ) )
% 0.28/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left2
% 0.28/0.54  thf(fact_2371_mult__less__cancel__left2,axiom,
% 0.28/0.54      ! [C: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.28/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left2
% 0.28/0.54  thf(fact_2372_mult__less__cancel__left2,axiom,
% 0.28/0.54      ! [C: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_int @ A @ one_one_int ) )
% 0.28/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left2
% 0.28/0.54  thf(fact_2373_mult__less__cancel__left1,axiom,
% 0.28/0.54      ! [C: real,B: real] :
% 0.28/0.54        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ one_one_real @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left1
% 0.28/0.54  thf(fact_2374_mult__less__cancel__left1,axiom,
% 0.28/0.54      ! [C: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left1
% 0.28/0.54  thf(fact_2375_mult__less__cancel__left1,axiom,
% 0.28/0.54      ! [C: int,B: int] :
% 0.28/0.54        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_int @ one_one_int @ B ) )
% 0.28/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_less_cancel_left1
% 0.28/0.54  thf(fact_2376_mult__le__cancel__right2,axiom,
% 0.28/0.54      ! [A: real,C: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.28/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right2
% 0.28/0.54  thf(fact_2377_mult__le__cancel__right2,axiom,
% 0.28/0.54      ! [A: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.28/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right2
% 0.28/0.54  thf(fact_2378_mult__le__cancel__right2,axiom,
% 0.28/0.54      ! [A: int,C: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.28/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.28/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right2
% 0.28/0.54  thf(fact_2379_mult__le__cancel__right1,axiom,
% 0.28/0.54      ! [C: real,B: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.28/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right1
% 0.28/0.54  thf(fact_2380_mult__le__cancel__right1,axiom,
% 0.28/0.54      ! [C: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.28/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right1
% 0.28/0.54  thf(fact_2381_mult__le__cancel__right1,axiom,
% 0.28/0.54      ! [C: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.28/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_right1
% 0.28/0.54  thf(fact_2382_mult__le__cancel__left2,axiom,
% 0.28/0.54      ! [C: real,A: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.28/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left2
% 0.28/0.54  thf(fact_2383_mult__le__cancel__left2,axiom,
% 0.28/0.54      ! [C: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.28/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left2
% 0.28/0.54  thf(fact_2384_mult__le__cancel__left2,axiom,
% 0.28/0.54      ! [C: int,A: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.28/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.28/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left2
% 0.28/0.54  thf(fact_2385_mult__le__cancel__left1,axiom,
% 0.28/0.54      ! [C: real,B: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.28/0.54          & ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left1
% 0.28/0.54  thf(fact_2386_mult__le__cancel__left1,axiom,
% 0.28/0.54      ! [C: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.28/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left1
% 0.28/0.54  thf(fact_2387_mult__le__cancel__left1,axiom,
% 0.28/0.54      ! [C: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.28/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.28/0.54           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.28/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.28/0.54           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_le_cancel_left1
% 0.28/0.54  thf(fact_2388_divide__left__mono__neg,axiom,
% 0.28/0.54      ! [A: real,B: real,C: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.54       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.28/0.54         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.54           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_left_mono_neg
% 0.28/0.54  thf(fact_2389_divide__left__mono__neg,axiom,
% 0.28/0.54      ! [A: rat,B: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.28/0.54       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.28/0.54         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.54           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_left_mono_neg
% 0.28/0.54  thf(fact_2390_mult__imp__le__div__pos,axiom,
% 0.28/0.54      ! [Y: real,Z: real,X: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.54       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 0.28/0.54         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_imp_le_div_pos
% 0.28/0.54  thf(fact_2391_mult__imp__le__div__pos,axiom,
% 0.28/0.54      ! [Y: rat,Z: rat,X: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 0.28/0.54         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_imp_le_div_pos
% 0.28/0.54  thf(fact_2392_mult__imp__div__pos__le,axiom,
% 0.28/0.54      ! [Y: real,X: real,Z: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.28/0.54       => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 0.28/0.54         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_imp_div_pos_le
% 0.28/0.54  thf(fact_2393_mult__imp__div__pos__le,axiom,
% 0.28/0.54      ! [Y: rat,X: rat,Z: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.28/0.54       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 0.28/0.54         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mult_imp_div_pos_le
% 0.28/0.54  thf(fact_2394_pos__le__divide__eq,axiom,
% 0.28/0.54      ! [C: real,A: real,B: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.54          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_le_divide_eq
% 0.28/0.54  thf(fact_2395_pos__le__divide__eq,axiom,
% 0.28/0.54      ! [C: rat,A: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.54          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_le_divide_eq
% 0.28/0.54  thf(fact_2396_pos__divide__le__eq,axiom,
% 0.28/0.54      ! [C: real,B: real,A: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.54          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_divide_le_eq
% 0.28/0.54  thf(fact_2397_pos__divide__le__eq,axiom,
% 0.28/0.54      ! [C: rat,B: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.54          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_divide_le_eq
% 0.28/0.54  thf(fact_2398_neg__le__divide__eq,axiom,
% 0.28/0.54      ! [C: real,A: real,B: real] :
% 0.28/0.54        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.54          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_le_divide_eq
% 0.28/0.54  thf(fact_2399_neg__le__divide__eq,axiom,
% 0.28/0.54      ! [C: rat,A: rat,B: rat] :
% 0.28/0.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.54          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_le_divide_eq
% 0.28/0.54  thf(fact_2400_neg__divide__le__eq,axiom,
% 0.28/0.54      ! [C: real,B: real,A: real] :
% 0.28/0.54        ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.54          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_divide_le_eq
% 0.28/0.54  thf(fact_2401_neg__divide__le__eq,axiom,
% 0.28/0.54      ! [C: rat,B: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.54          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_divide_le_eq
% 0.28/0.54  thf(fact_2402_divide__left__mono,axiom,
% 0.28/0.54      ! [B: real,A: real,C: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.28/0.54         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.28/0.54           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_left_mono
% 0.28/0.54  thf(fact_2403_divide__left__mono,axiom,
% 0.28/0.54      ! [B: rat,A: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.28/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.28/0.54         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.28/0.54           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_left_mono
% 0.28/0.54  thf(fact_2404_le__divide__eq,axiom,
% 0.28/0.54      ! [A: real,B: real,C: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq
% 0.28/0.54  thf(fact_2405_le__divide__eq,axiom,
% 0.28/0.54      ! [A: rat,B: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq
% 0.28/0.54  thf(fact_2406_divide__le__eq,axiom,
% 0.28/0.54      ! [B: real,C: real,A: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq
% 0.28/0.54  thf(fact_2407_divide__le__eq,axiom,
% 0.28/0.54      ! [B: rat,C: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq
% 0.28/0.54  thf(fact_2408_le__divide__eq__1,axiom,
% 0.28/0.54      ! [B: real,A: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.54            & ( ord_less_eq_real @ A @ B ) )
% 0.28/0.54          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.54            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq_1
% 0.28/0.54  thf(fact_2409_le__divide__eq__1,axiom,
% 0.28/0.54      ! [B: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.54            & ( ord_less_eq_rat @ A @ B ) )
% 0.28/0.54          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.54            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq_1
% 0.28/0.54  thf(fact_2410_divide__le__eq__1,axiom,
% 0.28/0.54      ! [B: real,A: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.54            & ( ord_less_eq_real @ B @ A ) )
% 0.28/0.54          | ( ( ord_less_real @ A @ zero_zero_real )
% 0.28/0.54            & ( ord_less_eq_real @ A @ B ) )
% 0.28/0.54          | ( A = zero_zero_real ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq_1
% 0.28/0.54  thf(fact_2411_divide__le__eq__1,axiom,
% 0.28/0.54      ! [B: rat,A: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.54            & ( ord_less_eq_rat @ B @ A ) )
% 0.28/0.54          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.28/0.54            & ( ord_less_eq_rat @ A @ B ) )
% 0.28/0.54          | ( A = zero_zero_rat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq_1
% 0.28/0.54  thf(fact_2412_convex__bound__le,axiom,
% 0.28/0.54      ! [X: real,A: real,Y: real,U: real,V: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ X @ A )
% 0.28/0.54       => ( ( ord_less_eq_real @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.28/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.28/0.54             => ( ( ( plus_plus_real @ U @ V )
% 0.28/0.54                  = one_one_real )
% 0.28/0.54               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_le
% 0.28/0.54  thf(fact_2413_convex__bound__le,axiom,
% 0.28/0.54      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ X @ A )
% 0.28/0.54       => ( ( ord_less_eq_rat @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.28/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.28/0.54             => ( ( ( plus_plus_rat @ U @ V )
% 0.28/0.54                  = one_one_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_le
% 0.28/0.54  thf(fact_2414_convex__bound__le,axiom,
% 0.28/0.54      ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ X @ A )
% 0.28/0.54       => ( ( ord_less_eq_int @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.28/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.28/0.54             => ( ( ( plus_plus_int @ U @ V )
% 0.28/0.54                  = one_one_int )
% 0.28/0.54               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_le
% 0.28/0.54  thf(fact_2415_divide__less__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [B: real,C: real,W: num] :
% 0.28/0.54        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_less_eq_numeral(1)
% 0.28/0.54  thf(fact_2416_divide__less__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [B: rat,C: rat,W: num] :
% 0.28/0.54        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_less_eq_numeral(1)
% 0.28/0.54  thf(fact_2417_less__divide__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [W: num,B: real,C: real] :
% 0.28/0.54        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % less_divide_eq_numeral(1)
% 0.28/0.54  thf(fact_2418_less__divide__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [W: num,B: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % less_divide_eq_numeral(1)
% 0.28/0.54  thf(fact_2419_power__Suc__less,axiom,
% 0.28/0.54      ! [A: real,N: nat] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.54       => ( ( ord_less_real @ A @ one_one_real )
% 0.28/0.54         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_Suc_less
% 0.28/0.54  thf(fact_2420_power__Suc__less,axiom,
% 0.28/0.54      ! [A: rat,N: nat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.54       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.28/0.54         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_Suc_less
% 0.28/0.54  thf(fact_2421_power__Suc__less,axiom,
% 0.28/0.54      ! [A: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.54       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.28/0.54         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_Suc_less
% 0.28/0.54  thf(fact_2422_power__Suc__less,axiom,
% 0.28/0.54      ! [A: int,N: nat] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.54       => ( ( ord_less_int @ A @ one_one_int )
% 0.28/0.54         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_Suc_less
% 0.28/0.54  thf(fact_2423_power__strict__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: real] :
% 0.28/0.54        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.54         => ( ( ord_less_real @ A @ one_one_real )
% 0.28/0.54           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_strict_decreasing
% 0.28/0.54  thf(fact_2424_power__strict__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: rat] :
% 0.28/0.54        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.54         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.28/0.54           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_strict_decreasing
% 0.28/0.54  thf(fact_2425_power__strict__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: nat] :
% 0.28/0.54        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.28/0.54         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.28/0.54           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_strict_decreasing
% 0.28/0.54  thf(fact_2426_power__strict__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: int] :
% 0.28/0.54        ( ( ord_less_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.28/0.54         => ( ( ord_less_int @ A @ one_one_int )
% 0.28/0.54           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_strict_decreasing
% 0.28/0.54  thf(fact_2427_power__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: real] :
% 0.28/0.54        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.28/0.54         => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.28/0.54           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_decreasing
% 0.28/0.54  thf(fact_2428_power__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: rat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.28/0.54         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.28/0.54           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_decreasing
% 0.28/0.54  thf(fact_2429_power__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.28/0.54         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.28/0.54           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_decreasing
% 0.28/0.54  thf(fact_2430_power__decreasing,axiom,
% 0.28/0.54      ! [N: nat,N4: nat,A: int] :
% 0.28/0.54        ( ( ord_less_eq_nat @ N @ N4 )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.54         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.28/0.54           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power_decreasing
% 0.28/0.54  thf(fact_2431_zero__power2,axiom,
% 0.28/0.54      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54      = zero_zero_rat ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_power2
% 0.28/0.54  thf(fact_2432_zero__power2,axiom,
% 0.28/0.54      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54      = zero_zero_nat ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_power2
% 0.28/0.54  thf(fact_2433_zero__power2,axiom,
% 0.28/0.54      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54      = zero_zero_real ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_power2
% 0.28/0.54  thf(fact_2434_zero__power2,axiom,
% 0.28/0.54      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54      = zero_zero_int ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_power2
% 0.28/0.54  thf(fact_2435_zero__power2,axiom,
% 0.28/0.54      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54      = zero_zero_complex ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_power2
% 0.28/0.54  thf(fact_2436_self__le__power,axiom,
% 0.28/0.54      ! [A: real,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_real @ one_one_real @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % self_le_power
% 0.28/0.54  thf(fact_2437_self__le__power,axiom,
% 0.28/0.54      ! [A: rat,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % self_le_power
% 0.28/0.54  thf(fact_2438_self__le__power,axiom,
% 0.28/0.54      ! [A: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % self_le_power
% 0.28/0.54  thf(fact_2439_self__le__power,axiom,
% 0.28/0.54      ! [A: int,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % self_le_power
% 0.28/0.54  thf(fact_2440_one__less__power,axiom,
% 0.28/0.54      ! [A: real,N: nat] :
% 0.28/0.54        ( ( ord_less_real @ one_one_real @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % one_less_power
% 0.28/0.54  thf(fact_2441_one__less__power,axiom,
% 0.28/0.54      ! [A: rat,N: nat] :
% 0.28/0.54        ( ( ord_less_rat @ one_one_rat @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % one_less_power
% 0.28/0.54  thf(fact_2442_one__less__power,axiom,
% 0.28/0.54      ! [A: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_nat @ one_one_nat @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % one_less_power
% 0.28/0.54  thf(fact_2443_one__less__power,axiom,
% 0.28/0.54      ! [A: int,N: nat] :
% 0.28/0.54        ( ( ord_less_int @ one_one_int @ A )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % one_less_power
% 0.28/0.54  thf(fact_2444_pos2,axiom,
% 0.28/0.54      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos2
% 0.28/0.54  thf(fact_2445_less__eq__div__iff__mult__less__eq,axiom,
% 0.28/0.54      ! [Q2: nat,M: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.28/0.54       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 0.28/0.54          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % less_eq_div_iff_mult_less_eq
% 0.28/0.54  thf(fact_2446_dividend__less__times__div,axiom,
% 0.28/0.54      ! [N: nat,M: nat] :
% 0.28/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % dividend_less_times_div
% 0.28/0.54  thf(fact_2447_dividend__less__div__times,axiom,
% 0.28/0.54      ! [N: nat,M: nat] :
% 0.28/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % dividend_less_div_times
% 0.28/0.54  thf(fact_2448_split__div,axiom,
% 0.28/0.54      ! [P: nat > $o,M: nat,N: nat] :
% 0.28/0.54        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.28/0.54        = ( ( ( N = zero_zero_nat )
% 0.28/0.54           => ( P @ zero_zero_nat ) )
% 0.28/0.54          & ( ( N != zero_zero_nat )
% 0.28/0.54           => ! [I5: nat,J3: nat] :
% 0.28/0.54                ( ( ord_less_nat @ J3 @ N )
% 0.28/0.54               => ( ( M
% 0.28/0.54                    = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 0.28/0.54                 => ( P @ I5 ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_div
% 0.28/0.54  thf(fact_2449_diff__le__diff__pow,axiom,
% 0.28/0.54      ! [K: nat,M: nat,N: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.28/0.54       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % diff_le_diff_pow
% 0.28/0.54  thf(fact_2450_le__divide__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [W: num,B: real,C: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq_numeral(1)
% 0.28/0.54  thf(fact_2451_le__divide__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [W: num,B: rat,C: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % le_divide_eq_numeral(1)
% 0.28/0.54  thf(fact_2452_divide__le__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [B: real,C: real,W: num] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 0.28/0.54        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.28/0.54           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.28/0.54               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq_numeral(1)
% 0.28/0.54  thf(fact_2453_divide__le__eq__numeral_I1_J,axiom,
% 0.28/0.54      ! [B: rat,C: rat,W: num] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.28/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.28/0.54          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.28/0.54           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.28/0.54              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.28/0.54               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divide_le_eq_numeral(1)
% 0.28/0.54  thf(fact_2454_convex__bound__lt,axiom,
% 0.28/0.54      ! [X: real,A: real,Y: real,U: real,V: real] :
% 0.28/0.54        ( ( ord_less_real @ X @ A )
% 0.28/0.54       => ( ( ord_less_real @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.28/0.54           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 0.28/0.54             => ( ( ( plus_plus_real @ U @ V )
% 0.28/0.54                  = one_one_real )
% 0.28/0.54               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_lt
% 0.28/0.54  thf(fact_2455_convex__bound__lt,axiom,
% 0.28/0.54      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.28/0.54        ( ( ord_less_rat @ X @ A )
% 0.28/0.54       => ( ( ord_less_rat @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.28/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.28/0.54             => ( ( ( plus_plus_rat @ U @ V )
% 0.28/0.54                  = one_one_rat )
% 0.28/0.54               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_lt
% 0.28/0.54  thf(fact_2456_convex__bound__lt,axiom,
% 0.28/0.54      ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.28/0.54        ( ( ord_less_int @ X @ A )
% 0.28/0.54       => ( ( ord_less_int @ Y @ A )
% 0.28/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.28/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.28/0.54             => ( ( ( plus_plus_int @ U @ V )
% 0.28/0.54                  = one_one_int )
% 0.28/0.54               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % convex_bound_lt
% 0.28/0.54  thf(fact_2457_half__gt__zero,axiom,
% 0.28/0.54      ! [A: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ A )
% 0.28/0.54       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % half_gt_zero
% 0.28/0.54  thf(fact_2458_half__gt__zero,axiom,
% 0.28/0.54      ! [A: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.28/0.54       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % half_gt_zero
% 0.28/0.54  thf(fact_2459_half__gt__zero__iff,axiom,
% 0.28/0.54      ! [A: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.28/0.54        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.28/0.54  
% 0.28/0.54  % half_gt_zero_iff
% 0.28/0.54  thf(fact_2460_half__gt__zero__iff,axiom,
% 0.28/0.54      ! [A: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.28/0.54        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.28/0.54  
% 0.28/0.54  % half_gt_zero_iff
% 0.28/0.54  thf(fact_2461_zero__le__power2,axiom,
% 0.28/0.54      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_power2
% 0.28/0.54  thf(fact_2462_zero__le__power2,axiom,
% 0.28/0.54      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_power2
% 0.28/0.54  thf(fact_2463_zero__le__power2,axiom,
% 0.28/0.54      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_power2
% 0.28/0.54  thf(fact_2464_power2__eq__imp__eq,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.28/0.54         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.54           => ( X = Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_eq_imp_eq
% 0.28/0.54  thf(fact_2465_power2__eq__imp__eq,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.28/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.54           => ( X = Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_eq_imp_eq
% 0.28/0.54  thf(fact_2466_power2__eq__imp__eq,axiom,
% 0.28/0.54      ! [X: nat,Y: nat] :
% 0.28/0.54        ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.28/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.28/0.54           => ( X = Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_eq_imp_eq
% 0.28/0.54  thf(fact_2467_power2__eq__imp__eq,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.28/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.54           => ( X = Y ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_eq_imp_eq
% 0.28/0.54  thf(fact_2468_power2__le__imp__le,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.54         => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_le_imp_le
% 0.28/0.54  thf(fact_2469_power2__le__imp__le,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.54         => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_le_imp_le
% 0.28/0.54  thf(fact_2470_power2__le__imp__le,axiom,
% 0.28/0.54      ! [X: nat,Y: nat] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.28/0.54         => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_le_imp_le
% 0.28/0.54  thf(fact_2471_power2__le__imp__le,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.54         => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_le_imp_le
% 0.28/0.54  thf(fact_2472_power2__less__0,axiom,
% 0.28/0.54      ! [A: real] :
% 0.28/0.54        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_0
% 0.28/0.54  thf(fact_2473_power2__less__0,axiom,
% 0.28/0.54      ! [A: rat] :
% 0.28/0.54        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_0
% 0.28/0.54  thf(fact_2474_power2__less__0,axiom,
% 0.28/0.54      ! [A: int] :
% 0.28/0.54        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_0
% 0.28/0.54  thf(fact_2475_exp__add__not__zero__imp__left,axiom,
% 0.28/0.54      ! [M: nat,N: nat] :
% 0.28/0.54        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.54         != zero_zero_nat )
% 0.28/0.54       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.28/0.54         != zero_zero_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % exp_add_not_zero_imp_left
% 0.28/0.54  thf(fact_2476_exp__add__not__zero__imp__left,axiom,
% 0.28/0.54      ! [M: nat,N: nat] :
% 0.28/0.54        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.54         != zero_zero_int )
% 0.28/0.54       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.28/0.54         != zero_zero_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % exp_add_not_zero_imp_left
% 0.28/0.54  thf(fact_2477_exp__add__not__zero__imp__right,axiom,
% 0.28/0.54      ! [M: nat,N: nat] :
% 0.28/0.54        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.54         != zero_zero_nat )
% 0.28/0.54       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.28/0.54         != zero_zero_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % exp_add_not_zero_imp_right
% 0.28/0.54  thf(fact_2478_exp__add__not__zero__imp__right,axiom,
% 0.28/0.54      ! [M: nat,N: nat] :
% 0.28/0.54        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 0.28/0.54         != zero_zero_int )
% 0.28/0.54       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.28/0.54         != zero_zero_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % exp_add_not_zero_imp_right
% 0.28/0.54  thf(fact_2479_div__exp__mod__exp__eq,axiom,
% 0.28/0.54      ! [A: nat,N: nat,M: nat] :
% 0.28/0.54        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_exp_mod_exp_eq
% 0.28/0.54  thf(fact_2480_div__exp__mod__exp__eq,axiom,
% 0.28/0.54      ! [A: int,N: nat,M: nat] :
% 0.28/0.54        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_exp_mod_exp_eq
% 0.28/0.54  thf(fact_2481_div__exp__mod__exp__eq,axiom,
% 0.28/0.54      ! [A: code_integer,N: nat,M: nat] :
% 0.28/0.54        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_exp_mod_exp_eq
% 0.28/0.54  thf(fact_2482_power2__less__imp__less,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.28/0.54         => ( ord_less_real @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_imp_less
% 0.28/0.54  thf(fact_2483_power2__less__imp__less,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.28/0.54         => ( ord_less_rat @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_imp_less
% 0.28/0.54  thf(fact_2484_power2__less__imp__less,axiom,
% 0.28/0.54      ! [X: nat,Y: nat] :
% 0.28/0.54        ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.28/0.54         => ( ord_less_nat @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_imp_less
% 0.28/0.54  thf(fact_2485_power2__less__imp__less,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.28/0.54         => ( ord_less_int @ X @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_less_imp_less
% 0.28/0.54  thf(fact_2486_sum__power2__ge__zero,axiom,
% 0.28/0.54      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_ge_zero
% 0.28/0.54  thf(fact_2487_sum__power2__ge__zero,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_ge_zero
% 0.28/0.54  thf(fact_2488_sum__power2__ge__zero,axiom,
% 0.28/0.54      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_ge_zero
% 0.28/0.54  thf(fact_2489_sum__power2__le__zero__iff,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.28/0.54        = ( ( X = zero_zero_real )
% 0.28/0.54          & ( Y = zero_zero_real ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_le_zero_iff
% 0.28/0.54  thf(fact_2490_sum__power2__le__zero__iff,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.28/0.54        = ( ( X = zero_zero_rat )
% 0.28/0.54          & ( Y = zero_zero_rat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_le_zero_iff
% 0.28/0.54  thf(fact_2491_sum__power2__le__zero__iff,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.28/0.54        = ( ( X = zero_zero_int )
% 0.28/0.54          & ( Y = zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_le_zero_iff
% 0.28/0.54  thf(fact_2492_not__sum__power2__lt__zero,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.28/0.54  
% 0.28/0.54  % not_sum_power2_lt_zero
% 0.28/0.54  thf(fact_2493_not__sum__power2__lt__zero,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.28/0.54  
% 0.28/0.54  % not_sum_power2_lt_zero
% 0.28/0.54  thf(fact_2494_not__sum__power2__lt__zero,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.28/0.54  
% 0.28/0.54  % not_sum_power2_lt_zero
% 0.28/0.54  thf(fact_2495_sum__power2__gt__zero__iff,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54        = ( ( X != zero_zero_real )
% 0.28/0.54          | ( Y != zero_zero_real ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_gt_zero_iff
% 0.28/0.54  thf(fact_2496_sum__power2__gt__zero__iff,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54        = ( ( X != zero_zero_rat )
% 0.28/0.54          | ( Y != zero_zero_rat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_gt_zero_iff
% 0.28/0.54  thf(fact_2497_sum__power2__gt__zero__iff,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54        = ( ( X != zero_zero_int )
% 0.28/0.54          | ( Y != zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % sum_power2_gt_zero_iff
% 0.28/0.54  thf(fact_2498_zero__le__even__power_H,axiom,
% 0.28/0.54      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_even_power'
% 0.28/0.54  thf(fact_2499_zero__le__even__power_H,axiom,
% 0.28/0.54      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_even_power'
% 0.28/0.54  thf(fact_2500_zero__le__even__power_H,axiom,
% 0.28/0.54      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zero_le_even_power'
% 0.28/0.54  thf(fact_2501_power2__diff,axiom,
% 0.28/0.54      ! [X: complex,Y: complex] :
% 0.28/0.54        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_diff
% 0.28/0.54  thf(fact_2502_power2__diff,axiom,
% 0.28/0.54      ! [X: real,Y: real] :
% 0.28/0.54        ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_diff
% 0.28/0.54  thf(fact_2503_power2__diff,axiom,
% 0.28/0.54      ! [X: rat,Y: rat] :
% 0.28/0.54        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_diff
% 0.28/0.54  thf(fact_2504_power2__diff,axiom,
% 0.28/0.54      ! [X: int,Y: int] :
% 0.28/0.54        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % power2_diff
% 0.28/0.54  thf(fact_2505_invar__vebt_Ointros_I4_J,axiom,
% 0.28/0.54      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.28/0.54        ( ! [X6: vEBT_VEBT] :
% 0.28/0.54            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.54           => ( vEBT_invar_vebt @ X6 @ N ) )
% 0.28/0.54       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.28/0.54         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.28/0.54              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54           => ( ( M = N )
% 0.28/0.54             => ( ( Deg
% 0.28/0.54                  = ( plus_plus_nat @ N @ M ) )
% 0.28/0.54               => ( ! [I4: nat] :
% 0.28/0.54                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 0.28/0.54                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.28/0.54                 => ( ( ( Mi = Ma )
% 0.28/0.54                     => ! [X6: vEBT_VEBT] :
% 0.28/0.54                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.54                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 0.28/0.54                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.28/0.54                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.28/0.54                       => ( ( ( Mi != Ma )
% 0.28/0.54                           => ! [I4: nat] :
% 0.28/0.54                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.54                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.28/0.54                                      = I4 )
% 0.28/0.54                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.28/0.54                                  & ! [X6: nat] :
% 0.28/0.54                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 0.28/0.54                                          = I4 )
% 0.28/0.54                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 0.28/0.54                                     => ( ( ord_less_nat @ Mi @ X6 )
% 0.28/0.54                                        & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 0.28/0.54                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % invar_vebt.intros(4)
% 0.28/0.54  thf(fact_2506_pred__list__to__short,axiom,
% 0.28/0.54      ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54              = none_nat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pred_list_to_short
% 0.28/0.54  thf(fact_2507_succ__list__to__short,axiom,
% 0.28/0.54      ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54              = none_nat ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % succ_list_to_short
% 0.28/0.54  thf(fact_2508_not__mod__2__eq__0__eq__1,axiom,
% 0.28/0.54      ! [A: nat] :
% 0.28/0.54        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54         != zero_zero_nat )
% 0.28/0.54        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = one_one_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_0_eq_1
% 0.28/0.54  thf(fact_2509_not__mod__2__eq__0__eq__1,axiom,
% 0.28/0.54      ! [A: int] :
% 0.28/0.54        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.54         != zero_zero_int )
% 0.28/0.54        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.54          = one_one_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_0_eq_1
% 0.28/0.54  thf(fact_2510_not__mod__2__eq__0__eq__1,axiom,
% 0.28/0.54      ! [A: code_integer] :
% 0.28/0.54        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.54         != zero_z3403309356797280102nteger )
% 0.28/0.54        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.54          = one_one_Code_integer ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_0_eq_1
% 0.28/0.54  thf(fact_2511_not__mod__2__eq__1__eq__0,axiom,
% 0.28/0.54      ! [A: nat] :
% 0.28/0.54        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54         != one_one_nat )
% 0.28/0.54        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.54          = zero_zero_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_1_eq_0
% 0.28/0.54  thf(fact_2512_not__mod__2__eq__1__eq__0,axiom,
% 0.28/0.54      ! [A: int] :
% 0.28/0.54        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.54         != one_one_int )
% 0.28/0.54        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.28/0.54          = zero_zero_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_1_eq_0
% 0.28/0.54  thf(fact_2513_not__mod__2__eq__1__eq__0,axiom,
% 0.28/0.54      ! [A: code_integer] :
% 0.28/0.54        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.54         != one_one_Code_integer )
% 0.28/0.54        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.28/0.54          = zero_z3403309356797280102nteger ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_mod_2_eq_1_eq_0
% 0.28/0.54  thf(fact_2514_pred__max,axiom,
% 0.28/0.54      ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54       => ( ( ord_less_nat @ Ma @ X )
% 0.28/0.54         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54            = ( some_nat @ Ma ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pred_max
% 0.28/0.54  thf(fact_2515_succ__min,axiom,
% 0.28/0.54      ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54       => ( ( ord_less_nat @ X @ Mi )
% 0.28/0.54         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54            = ( some_nat @ Mi ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % succ_min
% 0.28/0.54  thf(fact_2516_del__x__not__mi__newnode__not__nil,axiom,
% 0.28/0.54      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ( ord_less_nat @ Mi @ X )
% 0.28/0.54          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.28/0.54       => ( ( Mi != Ma )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54                = H2 )
% 0.28/0.54             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54                  = L2 )
% 0.28/0.54               => ( ( Newnode
% 0.28/0.54                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.54                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.54                   => ( ( Newlist
% 0.28/0.54                        = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.54                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.54                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % del_x_not_mi_newnode_not_nil
% 0.28/0.54  thf(fact_2517_greater__shift,axiom,
% 0.28/0.54      ( ord_less_nat
% 0.28/0.54      = ( ^ [Y3: nat,X3: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % greater_shift
% 0.28/0.54  thf(fact_2518_less__shift,axiom,
% 0.28/0.54      ( ord_less_nat
% 0.28/0.54      = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_less @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % less_shift
% 0.28/0.54  thf(fact_2519_helpyd,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.28/0.54            = ( some_nat @ Y ) )
% 0.28/0.54         => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % helpyd
% 0.28/0.54  thf(fact_2520_VEBT_Oinject_I1_J,axiom,
% 0.28/0.54      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 0.28/0.54        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.28/0.54          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.28/0.54        = ( ( X11 = Y11 )
% 0.28/0.54          & ( X12 = Y12 )
% 0.28/0.54          & ( X13 = Y13 )
% 0.28/0.54          & ( X14 = Y14 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % VEBT.inject(1)
% 0.28/0.54  thf(fact_2521_idiff__0__right,axiom,
% 0.28/0.54      ! [N: extended_enat] :
% 0.28/0.54        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.28/0.54        = N ) ).
% 0.28/0.54  
% 0.28/0.54  % idiff_0_right
% 0.28/0.54  thf(fact_2522_idiff__0,axiom,
% 0.28/0.54      ! [N: extended_enat] :
% 0.28/0.54        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.28/0.54        = zero_z5237406670263579293d_enat ) ).
% 0.28/0.54  
% 0.28/0.54  % idiff_0
% 0.28/0.54  thf(fact_2523_succ__corr,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.28/0.54            = ( some_nat @ Sx ) )
% 0.28/0.54          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % succ_corr
% 0.28/0.54  thf(fact_2524_pred__corr,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.28/0.54            = ( some_nat @ Px ) )
% 0.28/0.54          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pred_corr
% 0.28/0.54  thf(fact_2525_succ__correct,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.28/0.54            = ( some_nat @ Sx ) )
% 0.28/0.54          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % succ_correct
% 0.28/0.54  thf(fact_2526_pred__correct,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.28/0.54            = ( some_nat @ Sx ) )
% 0.28/0.54          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pred_correct
% 0.28/0.54  thf(fact_2527_geqmaxNone,axiom,
% 0.28/0.54      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.54       => ( ( ord_less_eq_nat @ Ma @ X )
% 0.28/0.54         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54            = none_nat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % geqmaxNone
% 0.28/0.54  thf(fact_2528_helpypredd,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.28/0.54            = ( some_nat @ Y ) )
% 0.28/0.54         => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % helpypredd
% 0.28/0.54  thf(fact_2529_summaxma,axiom,
% 0.28/0.54      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.28/0.54       => ( ( Mi != Ma )
% 0.28/0.54         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 0.28/0.54            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % summaxma
% 0.28/0.54  thf(fact_2530_mod__neg__neg__trivial,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ L2 @ K )
% 0.28/0.54         => ( ( modulo_modulo_int @ K @ L2 )
% 0.28/0.54            = K ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mod_neg_neg_trivial
% 0.28/0.54  thf(fact_2531_mod__pos__pos__trivial,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.28/0.54       => ( ( ord_less_int @ K @ L2 )
% 0.28/0.54         => ( ( modulo_modulo_int @ K @ L2 )
% 0.28/0.54            = K ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mod_pos_pos_trivial
% 0.28/0.54  thf(fact_2532_zmod__numeral__Bit0,axiom,
% 0.28/0.54      ! [V: num,W: num] :
% 0.28/0.54        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.28/0.54        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_numeral_Bit0
% 0.28/0.54  thf(fact_2533_div__neg__neg__trivial,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ L2 @ K )
% 0.28/0.54         => ( ( divide_divide_int @ K @ L2 )
% 0.28/0.54            = zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_neg_neg_trivial
% 0.28/0.54  thf(fact_2534_div__pos__pos__trivial,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.28/0.54       => ( ( ord_less_int @ K @ L2 )
% 0.28/0.54         => ( ( divide_divide_int @ K @ L2 )
% 0.28/0.54            = zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_pos_pos_trivial
% 0.28/0.54  thf(fact_2535_local_Opower__def,axiom,
% 0.28/0.54      ( vEBT_VEBT_power
% 0.28/0.54      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % local.power_def
% 0.28/0.54  thf(fact_2536_split__zdiv,axiom,
% 0.28/0.54      ! [P: int > $o,N: int,K: int] :
% 0.28/0.54        ( ( P @ ( divide_divide_int @ N @ K ) )
% 0.28/0.54        = ( ( ( K = zero_zero_int )
% 0.28/0.54           => ( P @ zero_zero_int ) )
% 0.28/0.54          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.54           => ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.28/0.54                  & ( ord_less_int @ J3 @ K )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ I5 ) ) )
% 0.28/0.54          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.28/0.54           => ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.28/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ I5 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_zdiv
% 0.28/0.54  thf(fact_2537_split__zmod,axiom,
% 0.28/0.54      ! [P: int > $o,N: int,K: int] :
% 0.28/0.54        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 0.28/0.54        = ( ( ( K = zero_zero_int )
% 0.28/0.54           => ( P @ N ) )
% 0.28/0.54          & ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.54           => ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.28/0.54                  & ( ord_less_int @ J3 @ K )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ J3 ) ) )
% 0.28/0.54          & ( ( ord_less_int @ K @ zero_zero_int )
% 0.28/0.54           => ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.28/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ J3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_zmod
% 0.28/0.54  thf(fact_2538_zdiv__mono1,axiom,
% 0.28/0.54      ! [A: int,A4: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ A @ A4 )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono1
% 0.28/0.54  thf(fact_2539_zdiv__mono2,axiom,
% 0.28/0.54      ! [A: int,B4: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.28/0.54         => ( ( ord_less_eq_int @ B4 @ B )
% 0.28/0.54           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono2
% 0.28/0.54  thf(fact_2540_div__pos__geq,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.28/0.54       => ( ( ord_less_eq_int @ L2 @ K )
% 0.28/0.54         => ( ( divide_divide_int @ K @ L2 )
% 0.28/0.54            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_pos_geq
% 0.28/0.54  thf(fact_2541_mod__pos__geq,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.28/0.54       => ( ( ord_less_eq_int @ L2 @ K )
% 0.28/0.54         => ( ( modulo_modulo_int @ K @ L2 )
% 0.28/0.54            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mod_pos_geq
% 0.28/0.54  thf(fact_2542_q__pos__lemma,axiom,
% 0.28/0.54      ! [B4: int,Q4: int,R3: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 0.28/0.54       => ( ( ord_less_int @ R3 @ B4 )
% 0.28/0.54         => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.28/0.54           => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % q_pos_lemma
% 0.28/0.54  thf(fact_2543_neg__mod__conj,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.28/0.54          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_mod_conj
% 0.28/0.54  thf(fact_2544_pos__mod__conj,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.28/0.54          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_mod_conj
% 0.28/0.54  thf(fact_2545_zdiv__eq__0__iff,axiom,
% 0.28/0.54      ! [I: int,K: int] :
% 0.28/0.54        ( ( ( divide_divide_int @ I @ K )
% 0.28/0.54          = zero_zero_int )
% 0.28/0.54        = ( ( K = zero_zero_int )
% 0.28/0.54          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.28/0.54            & ( ord_less_int @ I @ K ) )
% 0.28/0.54          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.28/0.54            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_eq_0_iff
% 0.28/0.54  thf(fact_2546_int__div__neg__eq,axiom,
% 0.28/0.54      ! [A: int,B: int,Q2: int,R: int] :
% 0.28/0.54        ( ( A
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.28/0.54         => ( ( ord_less_int @ B @ R )
% 0.28/0.54           => ( ( divide_divide_int @ A @ B )
% 0.28/0.54              = Q2 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_div_neg_eq
% 0.28/0.54  thf(fact_2547_int__div__pos__eq,axiom,
% 0.28/0.54      ! [A: int,B: int,Q2: int,R: int] :
% 0.28/0.54        ( ( A
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.28/0.54         => ( ( ord_less_int @ R @ B )
% 0.28/0.54           => ( ( divide_divide_int @ A @ B )
% 0.28/0.54              = Q2 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_div_pos_eq
% 0.28/0.54  thf(fact_2548_int__mod__neg__eq,axiom,
% 0.28/0.54      ! [A: int,B: int,Q2: int,R: int] :
% 0.28/0.54        ( ( A
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.28/0.54         => ( ( ord_less_int @ B @ R )
% 0.28/0.54           => ( ( modulo_modulo_int @ A @ B )
% 0.28/0.54              = R ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_mod_neg_eq
% 0.28/0.54  thf(fact_2549_int__mod__pos__eq,axiom,
% 0.28/0.54      ! [A: int,B: int,Q2: int,R: int] :
% 0.28/0.54        ( ( A
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.28/0.54         => ( ( ord_less_int @ R @ B )
% 0.28/0.54           => ( ( modulo_modulo_int @ A @ B )
% 0.28/0.54              = R ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_mod_pos_eq
% 0.28/0.54  thf(fact_2550_zdiv__mono1__neg,axiom,
% 0.28/0.54      ! [A: int,A4: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ A @ A4 )
% 0.28/0.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.54         => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono1_neg
% 0.28/0.54  thf(fact_2551_zdiv__mono2__neg,axiom,
% 0.28/0.54      ! [A: int,B4: int,B: int] :
% 0.28/0.54        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.28/0.54         => ( ( ord_less_eq_int @ B4 @ B )
% 0.28/0.54           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono2_neg
% 0.28/0.54  thf(fact_2552_div__int__pos__iff,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 0.28/0.54        = ( ( K = zero_zero_int )
% 0.28/0.54          | ( L2 = zero_zero_int )
% 0.28/0.54          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.28/0.54            & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 0.28/0.54          | ( ( ord_less_int @ K @ zero_zero_int )
% 0.28/0.54            & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_int_pos_iff
% 0.28/0.54  thf(fact_2553_split__neg__lemma,axiom,
% 0.28/0.54      ! [K: int,P: int > int > $o,N: int] :
% 0.28/0.54        ( ( ord_less_int @ K @ zero_zero_int )
% 0.28/0.54       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.28/0.54          = ( ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_int @ K @ J3 )
% 0.28/0.54                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_neg_lemma
% 0.28/0.54  thf(fact_2554_split__pos__lemma,axiom,
% 0.28/0.54      ! [K: int,P: int > int > $o,N: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.54       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.28/0.54          = ( ! [I5: int,J3: int] :
% 0.28/0.54                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.28/0.54                  & ( ord_less_int @ J3 @ K )
% 0.28/0.54                  & ( N
% 0.28/0.54                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 0.28/0.54               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_pos_lemma
% 0.28/0.54  thf(fact_2555_div__positive__int,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ L2 @ K )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.28/0.54         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_positive_int
% 0.28/0.54  thf(fact_2556_zdiv__mono2__lemma,axiom,
% 0.28/0.54      ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 0.28/0.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 0.28/0.54         => ( ( ord_less_int @ R3 @ B4 )
% 0.28/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.28/0.54             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.28/0.54               => ( ( ord_less_eq_int @ B4 @ B )
% 0.28/0.54                 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono2_lemma
% 0.28/0.54  thf(fact_2557_zmod__trivial__iff,axiom,
% 0.28/0.54      ! [I: int,K: int] :
% 0.28/0.54        ( ( ( modulo_modulo_int @ I @ K )
% 0.28/0.54          = I )
% 0.28/0.54        = ( ( K = zero_zero_int )
% 0.28/0.54          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.28/0.54            & ( ord_less_int @ I @ K ) )
% 0.28/0.54          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.28/0.54            & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_trivial_iff
% 0.28/0.54  thf(fact_2558_div__neg__pos__less0,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_int @ A @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_neg_pos_less0
% 0.28/0.54  thf(fact_2559_int__div__less__self,axiom,
% 0.28/0.54      ! [X: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ X )
% 0.28/0.54       => ( ( ord_less_int @ one_one_int @ K )
% 0.28/0.54         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_div_less_self
% 0.28/0.54  thf(fact_2560_div__nonneg__neg__le0,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.54       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.54         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_nonneg_neg_le0
% 0.28/0.54  thf(fact_2561_div__nonpos__pos__le0,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % div_nonpos_pos_le0
% 0.28/0.54  thf(fact_2562_neg__imp__zdiv__neg__iff,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.28/0.54          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_imp_zdiv_neg_iff
% 0.28/0.54  thf(fact_2563_pos__imp__zdiv__neg__iff,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.28/0.54          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_imp_zdiv_neg_iff
% 0.28/0.54  thf(fact_2564_pos__imp__zdiv__pos__iff,axiom,
% 0.28/0.54      ! [K: int,I: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 0.28/0.54          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_imp_zdiv_pos_iff
% 0.28/0.54  thf(fact_2565_zdiv__mono2__neg__lemma,axiom,
% 0.28/0.54      ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 0.28/0.54        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 0.28/0.54       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) @ zero_zero_int )
% 0.28/0.54         => ( ( ord_less_int @ R @ B )
% 0.28/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.28/0.54             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 0.28/0.54               => ( ( ord_less_eq_int @ B4 @ B )
% 0.28/0.54                 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_mono2_neg_lemma
% 0.28/0.54  thf(fact_2566_unique__quotient__lemma,axiom,
% 0.28/0.54      ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.28/0.54         => ( ( ord_less_int @ R3 @ B )
% 0.28/0.54           => ( ( ord_less_int @ R @ B )
% 0.28/0.54             => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % unique_quotient_lemma
% 0.28/0.54  thf(fact_2567_neg__imp__zdiv__nonneg__iff,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ B @ zero_zero_int )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.28/0.54          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_imp_zdiv_nonneg_iff
% 0.28/0.54  thf(fact_2568_pos__imp__zdiv__nonneg__iff,axiom,
% 0.28/0.54      ! [B: int,A: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ B )
% 0.28/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.28/0.54          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_imp_zdiv_nonneg_iff
% 0.28/0.54  thf(fact_2569_neg__mod__sign,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.28/0.54       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_mod_sign
% 0.28/0.54  thf(fact_2570_Euclidean__Division_Opos__mod__sign,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.28/0.54       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % Euclidean_Division.pos_mod_sign
% 0.28/0.54  thf(fact_2571_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.54       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.28/0.54          = ( ( ord_less_eq_int @ B @ A )
% 0.28/0.54            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nonneg1_imp_zdiv_pos_iff
% 0.28/0.54  thf(fact_2572_neg__mod__bound,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.28/0.54       => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_mod_bound
% 0.28/0.54  thf(fact_2573_Euclidean__Division_Opos__mod__bound,axiom,
% 0.28/0.54      ! [L2: int,K: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.28/0.54       => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % Euclidean_Division.pos_mod_bound
% 0.28/0.54  thf(fact_2574_unique__quotient__lemma__neg,axiom,
% 0.28/0.54      ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 0.28/0.54       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.28/0.54         => ( ( ord_less_int @ B @ R )
% 0.28/0.54           => ( ( ord_less_int @ B @ R3 )
% 0.28/0.54             => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % unique_quotient_lemma_neg
% 0.28/0.54  thf(fact_2575_mod__pos__neg__trivial,axiom,
% 0.28/0.54      ! [K: int,L2: int] :
% 0.28/0.54        ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.54       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 0.28/0.54         => ( ( modulo_modulo_int @ K @ L2 )
% 0.28/0.54            = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mod_pos_neg_trivial
% 0.28/0.54  thf(fact_2576_zmod__zmult2__eq,axiom,
% 0.28/0.54      ! [C: int,A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.28/0.54          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_zmult2_eq
% 0.28/0.54  thf(fact_2577_zdiv__zmult2__eq,axiom,
% 0.28/0.54      ! [C: int,A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.28/0.54       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.28/0.54          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zdiv_zmult2_eq
% 0.28/0.54  thf(fact_2578_zmod__le__nonneg__dividend,axiom,
% 0.28/0.54      ! [M: int,K: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.28/0.54       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_le_nonneg_dividend
% 0.28/0.54  thf(fact_2579_zero__one__enat__neq_I1_J,axiom,
% 0.28/0.54      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 0.28/0.54  
% 0.28/0.54  % zero_one_enat_neq(1)
% 0.28/0.54  thf(fact_2580_zmod__eq__0D,axiom,
% 0.28/0.54      ! [M: int,D: int] :
% 0.28/0.54        ( ( ( modulo_modulo_int @ M @ D )
% 0.28/0.54          = zero_zero_int )
% 0.28/0.54       => ? [Q3: int] :
% 0.28/0.54            ( M
% 0.28/0.54            = ( times_times_int @ D @ Q3 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_eq_0D
% 0.28/0.54  thf(fact_2581_zmod__eq__0__iff,axiom,
% 0.28/0.54      ! [M: int,D: int] :
% 0.28/0.54        ( ( ( modulo_modulo_int @ M @ D )
% 0.28/0.54          = zero_zero_int )
% 0.28/0.54        = ( ? [Q5: int] :
% 0.28/0.54              ( M
% 0.28/0.54              = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zmod_eq_0_iff
% 0.28/0.54  thf(fact_2582_imult__is__0,axiom,
% 0.28/0.54      ! [M: extended_enat,N: extended_enat] :
% 0.28/0.54        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 0.28/0.54          = zero_z5237406670263579293d_enat )
% 0.28/0.54        = ( ( M = zero_z5237406670263579293d_enat )
% 0.28/0.54          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % imult_is_0
% 0.28/0.54  thf(fact_2583_iadd__is__0,axiom,
% 0.28/0.54      ! [M: extended_enat,N: extended_enat] :
% 0.28/0.54        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 0.28/0.54          = zero_z5237406670263579293d_enat )
% 0.28/0.54        = ( ( M = zero_z5237406670263579293d_enat )
% 0.28/0.54          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % iadd_is_0
% 0.28/0.54  thf(fact_2584_neg__zmod__mult__2,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.28/0.54       => ( ( 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 ) )
% 0.28/0.54          = ( 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 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % neg_zmod_mult_2
% 0.28/0.54  thf(fact_2585_add__diff__assoc__enat,axiom,
% 0.28/0.54      ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 0.28/0.54        ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 0.28/0.54       => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 0.28/0.54          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % add_diff_assoc_enat
% 0.28/0.54  thf(fact_2586_pos__zmod__mult__2,axiom,
% 0.28/0.54      ! [A: int,B: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.28/0.54       => ( ( 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 ) )
% 0.28/0.54          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % pos_zmod_mult_2
% 0.28/0.54  thf(fact_2587_nat__induct2,axiom,
% 0.28/0.54      ! [P: nat > $o,N: nat] :
% 0.28/0.54        ( ( P @ zero_zero_nat )
% 0.28/0.54       => ( ( P @ one_one_nat )
% 0.28/0.54         => ( ! [N3: nat] :
% 0.28/0.54                ( ( P @ N3 )
% 0.28/0.54               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.54           => ( P @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_induct2
% 0.28/0.54  thf(fact_2588_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.28/0.54      ! [X: nat,N: nat,M: nat] :
% 0.28/0.54        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.54           => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % VEBT_internal.exp_split_high_low(1)
% 0.28/0.54  thf(fact_2589_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.28/0.54      ! [X: nat,N: nat,M: nat] :
% 0.28/0.54        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.28/0.54       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.54         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.28/0.54           => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % VEBT_internal.exp_split_high_low(2)
% 0.28/0.54  thf(fact_2590_del__x__mi__lets__in__not__minNull,axiom,
% 0.28/0.54      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.28/0.54        ( ( ( X = Mi )
% 0.28/0.54          & ( ord_less_nat @ X @ Ma ) )
% 0.28/0.54       => ( ( Mi != Ma )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54                = H2 )
% 0.28/0.54             => ( ( Xn
% 0.28/0.54                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.28/0.54               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.54                    = L2 )
% 0.28/0.54                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.54                   => ( ( Newnode
% 0.28/0.54                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.54                     => ( ( Newlist
% 0.28/0.54                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.54                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.54                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % del_x_mi_lets_in_not_minNull
% 0.28/0.54  thf(fact_2591_real__average__minus__first,axiom,
% 0.28/0.54      ! [A: real,B: real] :
% 0.28/0.54        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.28/0.54        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % real_average_minus_first
% 0.28/0.54  thf(fact_2592_real__average__minus__second,axiom,
% 0.28/0.54      ! [B: real,A: real] :
% 0.28/0.54        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 0.28/0.54        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % real_average_minus_second
% 0.28/0.54  thf(fact_2593_insert__simp__norm,axiom,
% 0.28/0.54      ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.54       => ( ( ord_less_nat @ Mi @ X )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54           => ( ( X != Ma )
% 0.28/0.54             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % insert_simp_norm
% 0.28/0.54  thf(fact_2594_insert__simp__excp,axiom,
% 0.28/0.54      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.54       => ( ( ord_less_nat @ X @ Mi )
% 0.28/0.54         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54           => ( ( X != Ma )
% 0.28/0.54             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % insert_simp_excp
% 0.28/0.54  thf(fact_2595_zle__add1__eq__le,axiom,
% 0.28/0.54      ! [W: int,Z: int] :
% 0.28/0.54        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.28/0.54        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zle_add1_eq_le
% 0.28/0.54  thf(fact_2596_divmod__step__eq,axiom,
% 0.28/0.54      ! [L2: num,R: nat,Q2: nat] :
% 0.28/0.54        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 0.28/0.54         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.28/0.54            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 0.28/0.54         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.28/0.54            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divmod_step_eq
% 0.28/0.54  thf(fact_2597_divmod__step__eq,axiom,
% 0.28/0.54      ! [L2: num,R: int,Q2: int] :
% 0.28/0.54        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 0.28/0.54         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.28/0.54            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 0.28/0.54         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.28/0.54            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divmod_step_eq
% 0.28/0.54  thf(fact_2598_divmod__step__eq,axiom,
% 0.28/0.54      ! [L2: num,R: code_integer,Q2: code_integer] :
% 0.28/0.54        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 0.28/0.54         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 0.28/0.54            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 0.28/0.54        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 0.28/0.54         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 0.28/0.54            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % divmod_step_eq
% 0.28/0.54  thf(fact_2599_mintlistlength,axiom,
% 0.28/0.54      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.54       => ( ( Mi != Ma )
% 0.28/0.54         => ( ( ord_less_nat @ Mi @ Ma )
% 0.28/0.54            & ? [M4: nat] :
% 0.28/0.54                ( ( ( some_nat @ M4 )
% 0.28/0.54                  = ( vEBT_vebt_mint @ Summary ) )
% 0.28/0.54                & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mintlistlength
% 0.28/0.54  thf(fact_2600_option_Ocollapse,axiom,
% 0.28/0.54      ! [Option: option_nat] :
% 0.28/0.54        ( ( Option != none_nat )
% 0.28/0.54       => ( ( some_nat @ ( the_nat @ Option ) )
% 0.28/0.54          = Option ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.collapse
% 0.28/0.54  thf(fact_2601_option_Ocollapse,axiom,
% 0.28/0.54      ! [Option: option4927543243414619207at_nat] :
% 0.28/0.54        ( ( Option != none_P5556105721700978146at_nat )
% 0.28/0.54       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 0.28/0.54          = Option ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.collapse
% 0.28/0.54  thf(fact_2602_option_Ocollapse,axiom,
% 0.28/0.54      ! [Option: option_num] :
% 0.28/0.54        ( ( Option != none_num )
% 0.28/0.54       => ( ( some_num @ ( the_num @ Option ) )
% 0.28/0.54          = Option ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.collapse
% 0.28/0.54  thf(fact_2603_minNullmin,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT] :
% 0.28/0.54        ( ( vEBT_VEBT_minNull @ T )
% 0.28/0.54       => ( ( vEBT_vebt_mint @ T )
% 0.28/0.54          = none_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % minNullmin
% 0.28/0.54  thf(fact_2604_minminNull,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT] :
% 0.28/0.54        ( ( ( vEBT_vebt_mint @ T )
% 0.28/0.54          = none_nat )
% 0.28/0.54       => ( vEBT_VEBT_minNull @ T ) ) ).
% 0.28/0.54  
% 0.28/0.54  % minminNull
% 0.28/0.54  thf(fact_2605_mint__member,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_mint @ T )
% 0.28/0.54            = ( some_nat @ Maxi ) )
% 0.28/0.54         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mint_member
% 0.28/0.54  thf(fact_2606_option_Oinject,axiom,
% 0.28/0.54      ! [X22: nat,Y22: nat] :
% 0.28/0.54        ( ( ( some_nat @ X22 )
% 0.28/0.54          = ( some_nat @ Y22 ) )
% 0.28/0.54        = ( X22 = Y22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.inject
% 0.28/0.54  thf(fact_2607_option_Oinject,axiom,
% 0.28/0.54      ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 0.28/0.54        ( ( ( some_P7363390416028606310at_nat @ X22 )
% 0.28/0.54          = ( some_P7363390416028606310at_nat @ Y22 ) )
% 0.28/0.54        = ( X22 = Y22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.inject
% 0.28/0.54  thf(fact_2608_option_Oinject,axiom,
% 0.28/0.54      ! [X22: num,Y22: num] :
% 0.28/0.54        ( ( ( some_num @ X22 )
% 0.28/0.54          = ( some_num @ Y22 ) )
% 0.28/0.54        = ( X22 = Y22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.inject
% 0.28/0.54  thf(fact_2609_mint__corr__help,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_mint @ T )
% 0.28/0.54            = ( some_nat @ Mini ) )
% 0.28/0.54         => ( ( vEBT_vebt_member @ T @ X )
% 0.28/0.54           => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mint_corr_help
% 0.28/0.54  thf(fact_2610_mint__corr,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( vEBT_vebt_mint @ T )
% 0.28/0.54            = ( some_nat @ X ) )
% 0.28/0.54         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mint_corr
% 0.28/0.54  thf(fact_2611_mint__sound,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.28/0.54         => ( ( vEBT_vebt_mint @ T )
% 0.28/0.54            = ( some_nat @ X ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % mint_sound
% 0.28/0.54  thf(fact_2612_double__eq__0__iff,axiom,
% 0.28/0.54      ! [A: real] :
% 0.28/0.54        ( ( ( plus_plus_real @ A @ A )
% 0.28/0.54          = zero_zero_real )
% 0.28/0.54        = ( A = zero_zero_real ) ) ).
% 0.28/0.54  
% 0.28/0.54  % double_eq_0_iff
% 0.28/0.54  thf(fact_2613_double__eq__0__iff,axiom,
% 0.28/0.54      ! [A: rat] :
% 0.28/0.54        ( ( ( plus_plus_rat @ A @ A )
% 0.28/0.54          = zero_zero_rat )
% 0.28/0.54        = ( A = zero_zero_rat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % double_eq_0_iff
% 0.28/0.54  thf(fact_2614_double__eq__0__iff,axiom,
% 0.28/0.54      ! [A: int] :
% 0.28/0.54        ( ( ( plus_plus_int @ A @ A )
% 0.28/0.54          = zero_zero_int )
% 0.28/0.54        = ( A = zero_zero_int ) ) ).
% 0.28/0.54  
% 0.28/0.54  % double_eq_0_iff
% 0.28/0.54  thf(fact_2615_del__single__cont,axiom,
% 0.28/0.54      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.54        ( ( ( X = Mi )
% 0.28/0.54          & ( X = Ma ) )
% 0.28/0.54       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.54         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.54            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % del_single_cont
% 0.28/0.54  thf(fact_2616_misiz,axiom,
% 0.28/0.54      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 0.28/0.54        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.54       => ( ( ( some_nat @ M )
% 0.28/0.54            = ( vEBT_vebt_mint @ T ) )
% 0.28/0.54         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % misiz
% 0.28/0.54  thf(fact_2617_not__None__eq,axiom,
% 0.28/0.54      ! [X: option_nat] :
% 0.28/0.54        ( ( X != none_nat )
% 0.28/0.54        = ( ? [Y3: nat] :
% 0.28/0.54              ( X
% 0.28/0.54              = ( some_nat @ Y3 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_None_eq
% 0.28/0.54  thf(fact_2618_not__None__eq,axiom,
% 0.28/0.54      ! [X: option4927543243414619207at_nat] :
% 0.28/0.54        ( ( X != none_P5556105721700978146at_nat )
% 0.28/0.54        = ( ? [Y3: product_prod_nat_nat] :
% 0.28/0.54              ( X
% 0.28/0.54              = ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_None_eq
% 0.28/0.54  thf(fact_2619_not__None__eq,axiom,
% 0.28/0.54      ! [X: option_num] :
% 0.28/0.54        ( ( X != none_num )
% 0.28/0.54        = ( ? [Y3: num] :
% 0.28/0.54              ( X
% 0.28/0.54              = ( some_num @ Y3 ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_None_eq
% 0.28/0.54  thf(fact_2620_not__Some__eq,axiom,
% 0.28/0.54      ! [X: option_nat] :
% 0.28/0.54        ( ( ! [Y3: nat] :
% 0.28/0.54              ( X
% 0.28/0.54             != ( some_nat @ Y3 ) ) )
% 0.28/0.54        = ( X = none_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_Some_eq
% 0.28/0.54  thf(fact_2621_not__Some__eq,axiom,
% 0.28/0.54      ! [X: option4927543243414619207at_nat] :
% 0.28/0.54        ( ( ! [Y3: product_prod_nat_nat] :
% 0.28/0.54              ( X
% 0.28/0.54             != ( some_P7363390416028606310at_nat @ Y3 ) ) )
% 0.28/0.54        = ( X = none_P5556105721700978146at_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_Some_eq
% 0.28/0.54  thf(fact_2622_not__Some__eq,axiom,
% 0.28/0.54      ! [X: option_num] :
% 0.28/0.54        ( ( ! [Y3: num] :
% 0.28/0.54              ( X
% 0.28/0.54             != ( some_num @ Y3 ) ) )
% 0.28/0.54        = ( X = none_num ) ) ).
% 0.28/0.54  
% 0.28/0.54  % not_Some_eq
% 0.28/0.54  thf(fact_2623_max__nat_Oeq__neutr__iff,axiom,
% 0.28/0.54      ! [A: nat,B: nat] :
% 0.28/0.54        ( ( ( ord_max_nat @ A @ B )
% 0.28/0.54          = zero_zero_nat )
% 0.28/0.54        = ( ( A = zero_zero_nat )
% 0.28/0.54          & ( B = zero_zero_nat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_nat.eq_neutr_iff
% 0.28/0.54  thf(fact_2624_max__nat_Oleft__neutral,axiom,
% 0.28/0.54      ! [A: nat] :
% 0.28/0.54        ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.28/0.54        = A ) ).
% 0.28/0.54  
% 0.28/0.54  % max_nat.left_neutral
% 0.28/0.54  thf(fact_2625_max__nat_Oneutr__eq__iff,axiom,
% 0.28/0.54      ! [A: nat,B: nat] :
% 0.28/0.54        ( ( zero_zero_nat
% 0.28/0.54          = ( ord_max_nat @ A @ B ) )
% 0.28/0.54        = ( ( A = zero_zero_nat )
% 0.28/0.54          & ( B = zero_zero_nat ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_nat.neutr_eq_iff
% 0.28/0.54  thf(fact_2626_max__nat_Oright__neutral,axiom,
% 0.28/0.54      ! [A: nat] :
% 0.28/0.54        ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.28/0.54        = A ) ).
% 0.28/0.54  
% 0.28/0.54  % max_nat.right_neutral
% 0.28/0.54  thf(fact_2627_max__0L,axiom,
% 0.28/0.54      ! [N: nat] :
% 0.28/0.54        ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.28/0.54        = N ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0L
% 0.28/0.54  thf(fact_2628_max__0R,axiom,
% 0.28/0.54      ! [N: nat] :
% 0.28/0.54        ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.28/0.54        = N ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0R
% 0.28/0.54  thf(fact_2629_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.28/0.54         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.28/0.54            = ( numera1916890842035813515d_enat @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.28/0.54         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 0.28/0.54            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2630_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.28/0.54         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.28/0.54            = ( numera6620942414471956472nteger @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.28/0.54         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 0.28/0.54            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2631_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.54         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.54            = ( numeral_numeral_real @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.54         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 0.28/0.54            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2632_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.54         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.54            = ( numeral_numeral_rat @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.54         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 0.28/0.54            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2633_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.28/0.54         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.28/0.54            = ( numeral_numeral_nat @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.28/0.54         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 0.28/0.54            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2634_max__number__of_I1_J,axiom,
% 0.28/0.54      ! [U: num,V: num] :
% 0.28/0.54        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.54         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.54            = ( numeral_numeral_int @ V ) ) )
% 0.28/0.54        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.54         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 0.28/0.54            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_number_of(1)
% 0.28/0.54  thf(fact_2635_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.28/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2636_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.28/0.54        = ( numera6620942414471956472nteger @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2637_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 0.28/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2638_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 0.28/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2639_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 0.28/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2640_max__0__1_I3_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 0.28/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(3)
% 0.28/0.54  thf(fact_2641_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 0.28/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2642_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 0.28/0.54        = ( numera6620942414471956472nteger @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2643_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 0.28/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2644_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 0.28/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2645_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 0.28/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2646_max__0__1_I4_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 0.28/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(4)
% 0.28/0.54  thf(fact_2647_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.28/0.54      = one_one_real ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2648_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.28/0.54      = one_one_rat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2649_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.28/0.54      = one_one_nat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2650_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 0.28/0.54      = one_on7984719198319812577d_enat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2651_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.28/0.54      = one_one_int ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2652_max__0__1_I1_J,axiom,
% 0.28/0.54      ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.28/0.54      = one_one_Code_integer ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(1)
% 0.28/0.54  thf(fact_2653_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.28/0.54      = one_one_real ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2654_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.28/0.54      = one_one_rat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2655_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.28/0.54      = one_one_nat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2656_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 0.28/0.54      = one_on7984719198319812577d_enat ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2657_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.28/0.54      = one_one_int ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2658_max__0__1_I2_J,axiom,
% 0.28/0.54      ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.28/0.54      = one_one_Code_integer ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(2)
% 0.28/0.54  thf(fact_2659_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.28/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2660_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.28/0.54        = ( numera6620942414471956472nteger @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2661_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.28/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2662_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.28/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2663_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.28/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2664_max__0__1_I5_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.28/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(5)
% 0.28/0.54  thf(fact_2665_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 0.28/0.54        = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2666_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 0.28/0.54        = ( numera6620942414471956472nteger @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2667_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 0.28/0.54        = ( numeral_numeral_real @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2668_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 0.28/0.54        = ( numeral_numeral_rat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2669_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 0.28/0.54        = ( numeral_numeral_nat @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2670_max__0__1_I6_J,axiom,
% 0.28/0.54      ! [X: num] :
% 0.28/0.54        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 0.28/0.54        = ( numeral_numeral_int @ X ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_0_1(6)
% 0.28/0.54  thf(fact_2671_zle__diff1__eq,axiom,
% 0.28/0.54      ! [W: int,Z: int] :
% 0.28/0.54        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.28/0.54        = ( ord_less_int @ W @ Z ) ) ).
% 0.28/0.54  
% 0.28/0.54  % zle_diff1_eq
% 0.28/0.54  thf(fact_2672_max__add__distrib__left,axiom,
% 0.28/0.54      ! [X: real,Y: real,Z: real] :
% 0.28/0.54        ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_left
% 0.28/0.54  thf(fact_2673_max__add__distrib__left,axiom,
% 0.28/0.54      ! [X: rat,Y: rat,Z: rat] :
% 0.28/0.54        ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_left
% 0.28/0.54  thf(fact_2674_max__add__distrib__left,axiom,
% 0.28/0.54      ! [X: nat,Y: nat,Z: nat] :
% 0.28/0.54        ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_left
% 0.28/0.54  thf(fact_2675_max__add__distrib__left,axiom,
% 0.28/0.54      ! [X: int,Y: int,Z: int] :
% 0.28/0.54        ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_left
% 0.28/0.54  thf(fact_2676_max__add__distrib__left,axiom,
% 0.28/0.54      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.28/0.54        ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_left
% 0.28/0.54  thf(fact_2677_max__add__distrib__right,axiom,
% 0.28/0.54      ! [X: real,Y: real,Z: real] :
% 0.28/0.54        ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 0.28/0.54        = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_right
% 0.28/0.54  thf(fact_2678_max__add__distrib__right,axiom,
% 0.28/0.54      ! [X: rat,Y: rat,Z: rat] :
% 0.28/0.54        ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 0.28/0.54        = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_right
% 0.28/0.54  thf(fact_2679_max__add__distrib__right,axiom,
% 0.28/0.54      ! [X: nat,Y: nat,Z: nat] :
% 0.28/0.54        ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 0.28/0.54        = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_right
% 0.28/0.54  thf(fact_2680_max__add__distrib__right,axiom,
% 0.28/0.54      ! [X: int,Y: int,Z: int] :
% 0.28/0.54        ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 0.28/0.54        = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_right
% 0.28/0.54  thf(fact_2681_max__add__distrib__right,axiom,
% 0.28/0.54      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.28/0.54        ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 0.28/0.54        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_add_distrib_right
% 0.28/0.54  thf(fact_2682_max__diff__distrib__left,axiom,
% 0.28/0.54      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.28/0.54        ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_diff_distrib_left
% 0.28/0.54  thf(fact_2683_max__diff__distrib__left,axiom,
% 0.28/0.54      ! [X: real,Y: real,Z: real] :
% 0.28/0.54        ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_diff_distrib_left
% 0.28/0.54  thf(fact_2684_max__diff__distrib__left,axiom,
% 0.28/0.54      ! [X: rat,Y: rat,Z: rat] :
% 0.28/0.54        ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_diff_distrib_left
% 0.28/0.54  thf(fact_2685_max__diff__distrib__left,axiom,
% 0.28/0.54      ! [X: int,Y: int,Z: int] :
% 0.28/0.54        ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.28/0.54        = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % max_diff_distrib_left
% 0.28/0.54  thf(fact_2686_nat__add__max__left,axiom,
% 0.28/0.54      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.54        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.28/0.54        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_add_max_left
% 0.28/0.54  thf(fact_2687_nat__add__max__right,axiom,
% 0.28/0.54      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.54        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.28/0.54        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_add_max_right
% 0.28/0.54  thf(fact_2688_nat__mult__max__left,axiom,
% 0.28/0.54      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.54        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 0.28/0.54        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_mult_max_left
% 0.28/0.54  thf(fact_2689_nat__mult__max__right,axiom,
% 0.28/0.54      ! [M: nat,N: nat,Q2: nat] :
% 0.28/0.54        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 0.28/0.54        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_mult_max_right
% 0.28/0.54  thf(fact_2690_nat__minus__add__max,axiom,
% 0.28/0.54      ! [N: nat,M: nat] :
% 0.28/0.54        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 0.28/0.54        = ( ord_max_nat @ N @ M ) ) ).
% 0.28/0.54  
% 0.28/0.54  % nat_minus_add_max
% 0.28/0.54  thf(fact_2691_minus__int__code_I1_J,axiom,
% 0.28/0.54      ! [K: int] :
% 0.28/0.54        ( ( minus_minus_int @ K @ zero_zero_int )
% 0.28/0.54        = K ) ).
% 0.28/0.54  
% 0.28/0.54  % minus_int_code(1)
% 0.28/0.54  thf(fact_2692_int__distrib_I3_J,axiom,
% 0.28/0.54      ! [Z1: int,Z22: int,W: int] :
% 0.28/0.54        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 0.28/0.54        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_distrib(3)
% 0.28/0.54  thf(fact_2693_int__distrib_I4_J,axiom,
% 0.28/0.54      ! [W: int,Z1: int,Z22: int] :
% 0.28/0.54        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.28/0.54        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % int_distrib(4)
% 0.28/0.54  thf(fact_2694_option_Odistinct_I1_J,axiom,
% 0.28/0.54      ! [X22: nat] :
% 0.28/0.54        ( none_nat
% 0.28/0.54       != ( some_nat @ X22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.distinct(1)
% 0.28/0.54  thf(fact_2695_option_Odistinct_I1_J,axiom,
% 0.28/0.54      ! [X22: product_prod_nat_nat] :
% 0.28/0.54        ( none_P5556105721700978146at_nat
% 0.28/0.54       != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.distinct(1)
% 0.28/0.54  thf(fact_2696_option_Odistinct_I1_J,axiom,
% 0.28/0.54      ! [X22: num] :
% 0.28/0.54        ( none_num
% 0.28/0.54       != ( some_num @ X22 ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.distinct(1)
% 0.28/0.54  thf(fact_2697_option_OdiscI,axiom,
% 0.28/0.54      ! [Option: option_nat,X22: nat] :
% 0.28/0.54        ( ( Option
% 0.28/0.54          = ( some_nat @ X22 ) )
% 0.28/0.54       => ( Option != none_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.discI
% 0.28/0.54  thf(fact_2698_option_OdiscI,axiom,
% 0.28/0.54      ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 0.28/0.54        ( ( Option
% 0.28/0.54          = ( some_P7363390416028606310at_nat @ X22 ) )
% 0.28/0.54       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.discI
% 0.28/0.54  thf(fact_2699_option_OdiscI,axiom,
% 0.28/0.54      ! [Option: option_num,X22: num] :
% 0.28/0.54        ( ( Option
% 0.28/0.54          = ( some_num @ X22 ) )
% 0.28/0.54       => ( Option != none_num ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.discI
% 0.28/0.54  thf(fact_2700_option_Oexhaust,axiom,
% 0.28/0.54      ! [Y: option_nat] :
% 0.28/0.54        ( ( Y != none_nat )
% 0.28/0.54       => ~ ! [X23: nat] :
% 0.28/0.54              ( Y
% 0.28/0.54             != ( some_nat @ X23 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.exhaust
% 0.28/0.54  thf(fact_2701_option_Oexhaust,axiom,
% 0.28/0.54      ! [Y: option4927543243414619207at_nat] :
% 0.28/0.54        ( ( Y != none_P5556105721700978146at_nat )
% 0.28/0.54       => ~ ! [X23: product_prod_nat_nat] :
% 0.28/0.54              ( Y
% 0.28/0.54             != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.exhaust
% 0.28/0.54  thf(fact_2702_option_Oexhaust,axiom,
% 0.28/0.54      ! [Y: option_num] :
% 0.28/0.54        ( ( Y != none_num )
% 0.28/0.54       => ~ ! [X23: num] :
% 0.28/0.54              ( Y
% 0.28/0.54             != ( some_num @ X23 ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % option.exhaust
% 0.28/0.54  thf(fact_2703_split__option__ex,axiom,
% 0.28/0.54      ( ( ^ [P3: option_nat > $o] :
% 0.28/0.54          ? [X7: option_nat] : ( P3 @ X7 ) )
% 0.28/0.54      = ( ^ [P4: option_nat > $o] :
% 0.28/0.54            ( ( P4 @ none_nat )
% 0.28/0.54            | ? [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_option_ex
% 0.28/0.54  thf(fact_2704_split__option__ex,axiom,
% 0.28/0.54      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.28/0.54          ? [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 0.28/0.54      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.28/0.54            ( ( P4 @ none_P5556105721700978146at_nat )
% 0.28/0.54            | ? [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_option_ex
% 0.28/0.54  thf(fact_2705_split__option__ex,axiom,
% 0.28/0.54      ( ( ^ [P3: option_num > $o] :
% 0.28/0.54          ? [X7: option_num] : ( P3 @ X7 ) )
% 0.28/0.54      = ( ^ [P4: option_num > $o] :
% 0.28/0.54            ( ( P4 @ none_num )
% 0.28/0.54            | ? [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_option_ex
% 0.28/0.54  thf(fact_2706_split__option__all,axiom,
% 0.28/0.54      ( ( ^ [P3: option_nat > $o] :
% 0.28/0.54          ! [X7: option_nat] : ( P3 @ X7 ) )
% 0.28/0.54      = ( ^ [P4: option_nat > $o] :
% 0.28/0.54            ( ( P4 @ none_nat )
% 0.28/0.54            & ! [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 0.28/0.54  
% 0.28/0.54  % split_option_all
% 0.28/0.54  thf(fact_2707_split__option__all,axiom,
% 0.28/0.54      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.28/0.55          ! [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 0.28/0.55      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.28/0.55            ( ( P4 @ none_P5556105721700978146at_nat )
% 0.28/0.55            & ! [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % split_option_all
% 0.28/0.55  thf(fact_2708_split__option__all,axiom,
% 0.28/0.55      ( ( ^ [P3: option_num > $o] :
% 0.28/0.55          ! [X7: option_num] : ( P3 @ X7 ) )
% 0.28/0.55      = ( ^ [P4: option_num > $o] :
% 0.28/0.55            ( ( P4 @ none_num )
% 0.28/0.55            & ! [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % split_option_all
% 0.28/0.55  thf(fact_2709_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 0.28/0.55        ( ( ( X = none_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: nat,B5: nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2710_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.28/0.55        ( ( ( X = none_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: nat,B5: product_prod_nat_nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2711_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 0.28/0.55        ( ( ( X = none_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_num )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: nat,B5: num] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_num @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2712_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 0.28/0.55        ( ( ( X = none_P5556105721700978146at_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: product_prod_nat_nat,B5: nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2713_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.28/0.55        ( ( ( X = none_P5556105721700978146at_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2714_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 0.28/0.55        ( ( ( X = none_P5556105721700978146at_nat )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_num )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: product_prod_nat_nat,B5: num] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_num @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2715_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 0.28/0.55        ( ( ( X = none_num )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: num,B5: nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_num @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2716_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.28/0.55        ( ( ( X = none_num )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: num,B5: product_prod_nat_nat] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_num @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2717_combine__options__cases,axiom,
% 0.28/0.55      ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 0.28/0.55        ( ( ( X = none_num )
% 0.28/0.55         => ( P @ X @ Y ) )
% 0.28/0.55       => ( ( ( Y = none_num )
% 0.28/0.55           => ( P @ X @ Y ) )
% 0.28/0.55         => ( ! [A5: num,B5: num] :
% 0.28/0.55                ( ( X
% 0.28/0.55                  = ( some_num @ A5 ) )
% 0.28/0.55               => ( ( Y
% 0.28/0.55                    = ( some_num @ B5 ) )
% 0.28/0.55                 => ( P @ X @ Y ) ) )
% 0.28/0.55           => ( P @ X @ Y ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % combine_options_cases
% 0.28/0.55  thf(fact_2718_less__eq__int__code_I1_J,axiom,
% 0.28/0.55      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.28/0.55  
% 0.28/0.55  % less_eq_int_code(1)
% 0.28/0.55  thf(fact_2719_less__int__code_I1_J,axiom,
% 0.28/0.55      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.28/0.55  
% 0.28/0.55  % less_int_code(1)
% 0.28/0.55  thf(fact_2720_times__int__code_I1_J,axiom,
% 0.28/0.55      ! [K: int] :
% 0.28/0.55        ( ( times_times_int @ K @ zero_zero_int )
% 0.28/0.55        = zero_zero_int ) ).
% 0.28/0.55  
% 0.28/0.55  % times_int_code(1)
% 0.28/0.55  thf(fact_2721_times__int__code_I2_J,axiom,
% 0.28/0.55      ! [L2: int] :
% 0.28/0.55        ( ( times_times_int @ zero_zero_int @ L2 )
% 0.28/0.55        = zero_zero_int ) ).
% 0.28/0.55  
% 0.28/0.55  % times_int_code(2)
% 0.28/0.55  thf(fact_2722_plus__int__code_I1_J,axiom,
% 0.28/0.55      ! [K: int] :
% 0.28/0.55        ( ( plus_plus_int @ K @ zero_zero_int )
% 0.28/0.55        = K ) ).
% 0.28/0.55  
% 0.28/0.55  % plus_int_code(1)
% 0.28/0.55  thf(fact_2723_plus__int__code_I2_J,axiom,
% 0.28/0.55      ! [L2: int] :
% 0.28/0.55        ( ( plus_plus_int @ zero_zero_int @ L2 )
% 0.28/0.55        = L2 ) ).
% 0.28/0.55  
% 0.28/0.55  % plus_int_code(2)
% 0.28/0.55  thf(fact_2724_int__le__induct,axiom,
% 0.28/0.55      ! [I: int,K: int,P: int > $o] :
% 0.28/0.55        ( ( ord_less_eq_int @ I @ K )
% 0.28/0.55       => ( ( P @ K )
% 0.28/0.55         => ( ! [I4: int] :
% 0.28/0.55                ( ( ord_less_eq_int @ I4 @ K )
% 0.28/0.55               => ( ( P @ I4 )
% 0.28/0.55                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55           => ( P @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_le_induct
% 0.28/0.55  thf(fact_2725_int__less__induct,axiom,
% 0.28/0.55      ! [I: int,K: int,P: int > $o] :
% 0.28/0.55        ( ( ord_less_int @ I @ K )
% 0.28/0.55       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.28/0.55         => ( ! [I4: int] :
% 0.28/0.55                ( ( ord_less_int @ I4 @ K )
% 0.28/0.55               => ( ( P @ I4 )
% 0.28/0.55                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55           => ( P @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_less_induct
% 0.28/0.55  thf(fact_2726_int__distrib_I2_J,axiom,
% 0.28/0.55      ! [W: int,Z1: int,Z22: int] :
% 0.28/0.55        ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.28/0.55        = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_distrib(2)
% 0.28/0.55  thf(fact_2727_int__distrib_I1_J,axiom,
% 0.28/0.55      ! [Z1: int,Z22: int,W: int] :
% 0.28/0.55        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 0.28/0.55        = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_distrib(1)
% 0.28/0.55  thf(fact_2728_option_Osel,axiom,
% 0.28/0.55      ! [X22: nat] :
% 0.28/0.55        ( ( the_nat @ ( some_nat @ X22 ) )
% 0.28/0.55        = X22 ) ).
% 0.28/0.55  
% 0.28/0.55  % option.sel
% 0.28/0.55  thf(fact_2729_option_Osel,axiom,
% 0.28/0.55      ! [X22: product_prod_nat_nat] :
% 0.28/0.55        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.28/0.55        = X22 ) ).
% 0.28/0.55  
% 0.28/0.55  % option.sel
% 0.28/0.55  thf(fact_2730_option_Osel,axiom,
% 0.28/0.55      ! [X22: num] :
% 0.28/0.55        ( ( the_num @ ( some_num @ X22 ) )
% 0.28/0.55        = X22 ) ).
% 0.28/0.55  
% 0.28/0.55  % option.sel
% 0.28/0.55  thf(fact_2731_option_Oexpand,axiom,
% 0.28/0.55      ! [Option: option_nat,Option2: option_nat] :
% 0.28/0.55        ( ( ( Option = none_nat )
% 0.28/0.55          = ( Option2 = none_nat ) )
% 0.28/0.55       => ( ( ( Option != none_nat )
% 0.28/0.55           => ( ( Option2 != none_nat )
% 0.28/0.55             => ( ( the_nat @ Option )
% 0.28/0.55                = ( the_nat @ Option2 ) ) ) )
% 0.28/0.55         => ( Option = Option2 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.expand
% 0.28/0.55  thf(fact_2732_option_Oexpand,axiom,
% 0.28/0.55      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 0.28/0.55        ( ( ( Option = none_P5556105721700978146at_nat )
% 0.28/0.55          = ( Option2 = none_P5556105721700978146at_nat ) )
% 0.28/0.55       => ( ( ( Option != none_P5556105721700978146at_nat )
% 0.28/0.55           => ( ( Option2 != none_P5556105721700978146at_nat )
% 0.28/0.55             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 0.28/0.55                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 0.28/0.55         => ( Option = Option2 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.expand
% 0.28/0.55  thf(fact_2733_option_Oexpand,axiom,
% 0.28/0.55      ! [Option: option_num,Option2: option_num] :
% 0.28/0.55        ( ( ( Option = none_num )
% 0.28/0.55          = ( Option2 = none_num ) )
% 0.28/0.55       => ( ( ( Option != none_num )
% 0.28/0.55           => ( ( Option2 != none_num )
% 0.28/0.55             => ( ( the_num @ Option )
% 0.28/0.55                = ( the_num @ Option2 ) ) ) )
% 0.28/0.55         => ( Option = Option2 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.expand
% 0.28/0.55  thf(fact_2734_invar__vebt_Ointros_I2_J,axiom,
% 0.28/0.55      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.28/0.55        ( ! [X6: vEBT_VEBT] :
% 0.28/0.55            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.55           => ( vEBT_invar_vebt @ X6 @ N ) )
% 0.28/0.55       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.28/0.55         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.28/0.55              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.28/0.55           => ( ( M = N )
% 0.28/0.55             => ( ( Deg
% 0.28/0.55                  = ( plus_plus_nat @ N @ M ) )
% 0.28/0.55               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.28/0.55                 => ( ! [X6: vEBT_VEBT] :
% 0.28/0.55                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.28/0.55                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 0.28/0.55                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % invar_vebt.intros(2)
% 0.28/0.55  thf(fact_2735_zmult__zless__mono2,axiom,
% 0.28/0.55      ! [I: int,J: int,K: int] :
% 0.28/0.55        ( ( ord_less_int @ I @ J )
% 0.28/0.55       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.28/0.55         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % zmult_zless_mono2
% 0.28/0.55  thf(fact_2736_odd__nonzero,axiom,
% 0.28/0.55      ! [Z: int] :
% 0.28/0.55        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.28/0.55       != zero_zero_int ) ).
% 0.28/0.55  
% 0.28/0.55  % odd_nonzero
% 0.28/0.55  thf(fact_2737_int__induct,axiom,
% 0.28/0.55      ! [P: int > $o,K: int,I: int] :
% 0.28/0.55        ( ( P @ K )
% 0.28/0.55       => ( ! [I4: int] :
% 0.28/0.55              ( ( ord_less_eq_int @ K @ I4 )
% 0.28/0.55             => ( ( P @ I4 )
% 0.28/0.55               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55         => ( ! [I4: int] :
% 0.28/0.55                ( ( ord_less_eq_int @ I4 @ K )
% 0.28/0.55               => ( ( P @ I4 )
% 0.28/0.55                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55           => ( P @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_induct
% 0.28/0.55  thf(fact_2738_int__ge__induct,axiom,
% 0.28/0.55      ! [K: int,I: int,P: int > $o] :
% 0.28/0.55        ( ( ord_less_eq_int @ K @ I )
% 0.28/0.55       => ( ( P @ K )
% 0.28/0.55         => ( ! [I4: int] :
% 0.28/0.55                ( ( ord_less_eq_int @ K @ I4 )
% 0.28/0.55               => ( ( P @ I4 )
% 0.28/0.55                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55           => ( P @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_ge_induct
% 0.28/0.55  thf(fact_2739_zless__add1__eq,axiom,
% 0.28/0.55      ! [W: int,Z: int] :
% 0.28/0.55        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.28/0.55        = ( ( ord_less_int @ W @ Z )
% 0.28/0.55          | ( W = Z ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % zless_add1_eq
% 0.28/0.55  thf(fact_2740_int__gr__induct,axiom,
% 0.28/0.55      ! [K: int,I: int,P: int > $o] :
% 0.28/0.55        ( ( ord_less_int @ K @ I )
% 0.28/0.55       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.28/0.55         => ( ! [I4: int] :
% 0.28/0.55                ( ( ord_less_int @ K @ I4 )
% 0.28/0.55               => ( ( P @ I4 )
% 0.28/0.55                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 0.28/0.55           => ( P @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_gr_induct
% 0.28/0.55  thf(fact_2741_option_Oexhaust__sel,axiom,
% 0.28/0.55      ! [Option: option_nat] :
% 0.28/0.55        ( ( Option != none_nat )
% 0.28/0.55       => ( Option
% 0.28/0.55          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.exhaust_sel
% 0.28/0.55  thf(fact_2742_option_Oexhaust__sel,axiom,
% 0.28/0.55      ! [Option: option4927543243414619207at_nat] :
% 0.28/0.55        ( ( Option != none_P5556105721700978146at_nat )
% 0.28/0.55       => ( Option
% 0.28/0.55          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.exhaust_sel
% 0.28/0.55  thf(fact_2743_option_Oexhaust__sel,axiom,
% 0.28/0.55      ! [Option: option_num] :
% 0.28/0.55        ( ( Option != none_num )
% 0.28/0.55       => ( Option
% 0.28/0.55          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % option.exhaust_sel
% 0.28/0.55  thf(fact_2744_int__one__le__iff__zero__less,axiom,
% 0.28/0.55      ! [Z: int] :
% 0.28/0.55        ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.28/0.55        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.28/0.55  
% 0.28/0.55  % int_one_le_iff_zero_less
% 0.28/0.55  thf(fact_2745_pos__zmult__eq__1__iff,axiom,
% 0.28/0.55      ! [M: int,N: int] :
% 0.28/0.55        ( ( ord_less_int @ zero_zero_int @ M )
% 0.28/0.55       => ( ( ( times_times_int @ M @ N )
% 0.28/0.55            = one_one_int )
% 0.28/0.55          = ( ( M = one_one_int )
% 0.28/0.55            & ( N = one_one_int ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % pos_zmult_eq_1_iff
% 0.28/0.55  thf(fact_2746_odd__less__0__iff,axiom,
% 0.28/0.55      ! [Z: int] :
% 0.28/0.55        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.28/0.55        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.28/0.55  
% 0.28/0.55  % odd_less_0_iff
% 0.28/0.55  thf(fact_2747_zless__imp__add1__zle,axiom,
% 0.28/0.55      ! [W: int,Z: int] :
% 0.28/0.55        ( ( ord_less_int @ W @ Z )
% 0.28/0.55       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.28/0.55  
% 0.28/0.55  % zless_imp_add1_zle
% 0.28/0.55  thf(fact_2748_add1__zle__eq,axiom,
% 0.28/0.55      ! [W: int,Z: int] :
% 0.28/0.55        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.28/0.55        = ( ord_less_int @ W @ Z ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add1_zle_eq
% 0.28/0.55  thf(fact_2749_le__imp__0__less,axiom,
% 0.28/0.55      ! [Z: int] :
% 0.28/0.55        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.28/0.55       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % le_imp_0_less
% 0.28/0.55  thf(fact_2750_nested__mint,axiom,
% 0.28/0.55      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 0.28/0.55        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.28/0.55       => ( ( N
% 0.28/0.55            = ( suc @ ( suc @ Va ) ) )
% 0.28/0.55         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 0.28/0.55           => ( ( Ma != Mi )
% 0.28/0.55             => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % nested_mint
% 0.28/0.55  thf(fact_2751_aampt,axiom,
% 0.28/0.55      ( ( ( xa = ma )
% 0.28/0.55       => ( mi
% 0.28/0.55          = ( if_nat
% 0.28/0.55            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 0.28/0.55              = none_nat )
% 0.28/0.55            @ mi
% 0.28/0.55            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) ) ) )
% 0.28/0.55      & ( ( xa != ma )
% 0.28/0.55       => ( mi = ma ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % aampt
% 0.28/0.55  thf(fact_2752_verit__le__mono__div__int,axiom,
% 0.28/0.55      ! [A2: int,B3: int,N: int] :
% 0.28/0.55        ( ( ord_less_int @ A2 @ B3 )
% 0.28/0.55       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.28/0.55         => ( ord_less_eq_int
% 0.28/0.55            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 0.28/0.55              @ ( if_int
% 0.28/0.55                @ ( ( modulo_modulo_int @ B3 @ N )
% 0.28/0.55                  = zero_zero_int )
% 0.28/0.55                @ one_one_int
% 0.28/0.55                @ zero_zero_int ) )
% 0.28/0.55            @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % verit_le_mono_div_int
% 0.28/0.55  thf(fact_2753_buildup__gives__valid,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.55       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % buildup_gives_valid
% 0.28/0.55  thf(fact_2754_verit__le__mono__div,axiom,
% 0.28/0.55      ! [A2: nat,B3: nat,N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ A2 @ B3 )
% 0.28/0.55       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.55         => ( ord_less_eq_nat
% 0.28/0.55            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 0.28/0.55              @ ( if_nat
% 0.28/0.55                @ ( ( modulo_modulo_nat @ B3 @ N )
% 0.28/0.55                  = zero_zero_nat )
% 0.28/0.55                @ one_one_nat
% 0.28/0.55                @ zero_zero_nat ) )
% 0.28/0.55            @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % verit_le_mono_div
% 0.28/0.55  thf(fact_2755_inrange,axiom,
% 0.28/0.55      ! [T: vEBT_VEBT,N: nat] :
% 0.28/0.55        ( ( vEBT_invar_vebt @ T @ N )
% 0.28/0.55       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % inrange
% 0.28/0.55  thf(fact_2756_mul__def,axiom,
% 0.28/0.55      ( vEBT_VEBT_mul
% 0.28/0.55      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mul_def
% 0.28/0.55  thf(fact_2757_add__def,axiom,
% 0.28/0.55      ( vEBT_VEBT_add
% 0.28/0.55      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add_def
% 0.28/0.55  thf(fact_2758_set__bit__0,axiom,
% 0.28/0.55      ! [A: int] :
% 0.28/0.55        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.28/0.55        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % set_bit_0
% 0.28/0.55  thf(fact_2759_set__bit__0,axiom,
% 0.28/0.55      ! [A: nat] :
% 0.28/0.55        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.28/0.55        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % set_bit_0
% 0.28/0.55  thf(fact_2760_even__odd__cases,axiom,
% 0.28/0.55      ! [X: nat] :
% 0.28/0.55        ( ! [N3: nat] :
% 0.28/0.55            ( X
% 0.28/0.55           != ( plus_plus_nat @ N3 @ N3 ) )
% 0.28/0.55       => ~ ! [N3: nat] :
% 0.28/0.55              ( X
% 0.28/0.55             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % even_odd_cases
% 0.28/0.55  thf(fact_2761_set__vebt_H__def,axiom,
% 0.28/0.55      ( vEBT_VEBT_set_vebt
% 0.28/0.55      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % set_vebt'_def
% 0.28/0.55  thf(fact_2762_deg__SUcn__Node,axiom,
% 0.28/0.55      ! [Tree: vEBT_VEBT,N: nat] :
% 0.28/0.55        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 0.28/0.55       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.28/0.55            ( Tree
% 0.28/0.55            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % deg_SUcn_Node
% 0.28/0.55  thf(fact_2763_add__shift,axiom,
% 0.28/0.55      ! [X: nat,Y: nat,Z: nat] :
% 0.28/0.55        ( ( ( plus_plus_nat @ X @ Y )
% 0.28/0.55          = Z )
% 0.28/0.55        = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.28/0.55          = ( some_nat @ Z ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add_shift
% 0.28/0.55  thf(fact_2764_mul__shift,axiom,
% 0.28/0.55      ! [X: nat,Y: nat,Z: nat] :
% 0.28/0.55        ( ( ( times_times_nat @ X @ Y )
% 0.28/0.55          = Z )
% 0.28/0.55        = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.28/0.55          = ( some_nat @ Z ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mul_shift
% 0.28/0.55  thf(fact_2765_verit__eq__simplify_I8_J,axiom,
% 0.28/0.55      ! [X22: num,Y22: num] :
% 0.28/0.55        ( ( ( bit0 @ X22 )
% 0.28/0.55          = ( bit0 @ Y22 ) )
% 0.28/0.55        = ( X22 = Y22 ) ) ).
% 0.28/0.55  
% 0.28/0.55  % verit_eq_simplify(8)
% 0.28/0.55  thf(fact_2766_nat_Oinject,axiom,
% 0.28/0.55      ! [X22: nat,Y22: nat] :
% 0.28/0.55        ( ( ( suc @ X22 )
% 0.28/0.55          = ( suc @ Y22 ) )
% 0.28/0.55        = ( X22 = Y22 ) ) ).
% 0.28/0.55  
% 0.28/0.55  % nat.inject
% 0.28/0.55  thf(fact_2767_old_Onat_Oinject,axiom,
% 0.28/0.55      ! [Nat: nat,Nat2: nat] :
% 0.28/0.55        ( ( ( suc @ Nat )
% 0.28/0.55          = ( suc @ Nat2 ) )
% 0.28/0.55        = ( Nat = Nat2 ) ) ).
% 0.28/0.55  
% 0.28/0.55  % old.nat.inject
% 0.28/0.55  thf(fact_2768_max__enat__simps_I2_J,axiom,
% 0.28/0.55      ! [Q2: extended_enat] :
% 0.28/0.55        ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 0.28/0.55        = Q2 ) ).
% 0.28/0.55  
% 0.28/0.55  % max_enat_simps(2)
% 0.28/0.55  thf(fact_2769_max__enat__simps_I3_J,axiom,
% 0.28/0.55      ! [Q2: extended_enat] :
% 0.28/0.55        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 0.28/0.55        = Q2 ) ).
% 0.28/0.55  
% 0.28/0.55  % max_enat_simps(3)
% 0.28/0.55  thf(fact_2770_Suc__less__eq,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.28/0.55        = ( ord_less_nat @ M @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_less_eq
% 0.28/0.55  thf(fact_2771_Suc__mono,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ M @ N )
% 0.28/0.55       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_mono
% 0.28/0.55  thf(fact_2772_lessI,axiom,
% 0.28/0.55      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lessI
% 0.28/0.55  thf(fact_2773_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: set_nat,L2: set_nat,U: set_nat] :
% 0.28/0.55        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_set_nat @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2774_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: set_int,L2: set_int,U: set_int] :
% 0.28/0.55        ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_set_int @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2775_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: rat,L2: rat,U: rat] :
% 0.28/0.55        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_rat @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2776_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: num,L2: num,U: num] :
% 0.28/0.55        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_num @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2777_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: nat,L2: nat,U: nat] :
% 0.28/0.55        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_nat @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2778_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: int,L2: int,U: int] :
% 0.28/0.55        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_int @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2779_atLeastAtMost__iff,axiom,
% 0.28/0.55      ! [I: real,L2: real,U: real] :
% 0.28/0.55        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 0.28/0.55        = ( ( ord_less_eq_real @ L2 @ I )
% 0.28/0.55          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastAtMost_iff
% 0.28/0.55  thf(fact_2780_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 0.28/0.55        ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 0.28/0.55          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2781_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 0.28/0.55        ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 0.28/0.55          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2782_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: num,H2: num,L3: num,H3: num] :
% 0.28/0.55        ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 0.28/0.55          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2783_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 0.28/0.55        ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 0.28/0.55          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2784_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: int,H2: int,L3: int,H3: int] :
% 0.28/0.55        ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 0.28/0.55          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2785_Icc__eq__Icc,axiom,
% 0.28/0.55      ! [L2: real,H2: real,L3: real,H3: real] :
% 0.28/0.55        ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 0.28/0.55          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.28/0.55        = ( ( ( L2 = L3 )
% 0.28/0.55            & ( H2 = H3 ) )
% 0.28/0.55          | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 0.28/0.55            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Icc_eq_Icc
% 0.28/0.55  thf(fact_2786_Suc__le__mono,axiom,
% 0.28/0.55      ! [N: nat,M: nat] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.28/0.55        = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_le_mono
% 0.28/0.55  thf(fact_2787_add__Suc__right,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.28/0.55        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add_Suc_right
% 0.28/0.55  thf(fact_2788_diff__Suc__Suc,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.28/0.55        = ( minus_minus_nat @ M @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % diff_Suc_Suc
% 0.28/0.55  thf(fact_2789_Suc__diff__diff,axiom,
% 0.28/0.55      ! [M: nat,N: nat,K: nat] :
% 0.28/0.55        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.28/0.55        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_diff_diff
% 0.28/0.55  thf(fact_2790_set__bit__nonnegative__int__iff,axiom,
% 0.28/0.55      ! [N: nat,K: int] :
% 0.28/0.55        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 0.28/0.55        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.28/0.55  
% 0.28/0.55  % set_bit_nonnegative_int_iff
% 0.28/0.55  thf(fact_2791_set__bit__negative__int__iff,axiom,
% 0.28/0.55      ! [N: nat,K: int] :
% 0.28/0.55        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 0.28/0.55        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.28/0.55  
% 0.28/0.55  % set_bit_negative_int_iff
% 0.28/0.55  thf(fact_2792_max__Suc__Suc,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.28/0.55        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_Suc_Suc
% 0.28/0.55  thf(fact_2793_power__0__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.28/0.55        = zero_zero_rat ) ).
% 0.28/0.55  
% 0.28/0.55  % power_0_Suc
% 0.28/0.55  thf(fact_2794_power__0__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.28/0.55        = zero_zero_nat ) ).
% 0.28/0.55  
% 0.28/0.55  % power_0_Suc
% 0.28/0.55  thf(fact_2795_power__0__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 0.28/0.55        = zero_zero_real ) ).
% 0.28/0.55  
% 0.28/0.55  % power_0_Suc
% 0.28/0.55  thf(fact_2796_power__0__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.28/0.55        = zero_zero_int ) ).
% 0.28/0.55  
% 0.28/0.55  % power_0_Suc
% 0.28/0.55  thf(fact_2797_power__0__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 0.28/0.55        = zero_zero_complex ) ).
% 0.28/0.55  
% 0.28/0.55  % power_0_Suc
% 0.28/0.55  thf(fact_2798_power__Suc0__right,axiom,
% 0.28/0.55      ! [A: nat] :
% 0.28/0.55        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = A ) ).
% 0.28/0.55  
% 0.28/0.55  % power_Suc0_right
% 0.28/0.55  thf(fact_2799_power__Suc0__right,axiom,
% 0.28/0.55      ! [A: real] :
% 0.28/0.55        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = A ) ).
% 0.28/0.55  
% 0.28/0.55  % power_Suc0_right
% 0.28/0.55  thf(fact_2800_power__Suc0__right,axiom,
% 0.28/0.55      ! [A: int] :
% 0.28/0.55        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = A ) ).
% 0.28/0.55  
% 0.28/0.55  % power_Suc0_right
% 0.28/0.55  thf(fact_2801_power__Suc0__right,axiom,
% 0.28/0.55      ! [A: complex] :
% 0.28/0.55        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = A ) ).
% 0.28/0.55  
% 0.28/0.55  % power_Suc0_right
% 0.28/0.55  thf(fact_2802_zero__less__Suc,axiom,
% 0.28/0.55      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % zero_less_Suc
% 0.28/0.55  thf(fact_2803_less__Suc0,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = ( N = zero_zero_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % less_Suc0
% 0.28/0.55  thf(fact_2804_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.28/0.55        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_set_int @ C @ A )
% 0.28/0.55            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2805_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.28/0.55        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_rat @ C @ A )
% 0.28/0.55            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2806_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: num,B: num,C: num,D: num] :
% 0.28/0.55        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_num @ C @ A )
% 0.28/0.55            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2807_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.28/0.55        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_nat @ C @ A )
% 0.28/0.55            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2808_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.28/0.55        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_int @ C @ A )
% 0.28/0.55            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2809_atLeastatMost__subset__iff,axiom,
% 0.28/0.55      ! [A: real,B: real,C: real,D: real] :
% 0.28/0.55        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.28/0.55        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.28/0.55          | ( ( ord_less_eq_real @ C @ A )
% 0.28/0.55            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % atLeastatMost_subset_iff
% 0.28/0.55  thf(fact_2810_one__eq__mult__iff,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ( suc @ zero_zero_nat )
% 0.28/0.55          = ( times_times_nat @ M @ N ) )
% 0.28/0.55        = ( ( M
% 0.28/0.55            = ( suc @ zero_zero_nat ) )
% 0.28/0.55          & ( N
% 0.28/0.55            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % one_eq_mult_iff
% 0.28/0.55  thf(fact_2811_mult__eq__1__iff,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ( times_times_nat @ M @ N )
% 0.28/0.55          = ( suc @ zero_zero_nat ) )
% 0.28/0.55        = ( ( M
% 0.28/0.55            = ( suc @ zero_zero_nat ) )
% 0.28/0.55          & ( N
% 0.28/0.55            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_eq_1_iff
% 0.28/0.55  thf(fact_2812_div__by__Suc__0,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = M ) ).
% 0.28/0.55  
% 0.28/0.55  % div_by_Suc_0
% 0.28/0.55  thf(fact_2813_power__Suc__0,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.28/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % power_Suc_0
% 0.28/0.55  thf(fact_2814_nat__power__eq__Suc__0__iff,axiom,
% 0.28/0.55      ! [X: nat,M: nat] :
% 0.28/0.55        ( ( ( power_power_nat @ X @ M )
% 0.28/0.55          = ( suc @ zero_zero_nat ) )
% 0.28/0.55        = ( ( M = zero_zero_nat )
% 0.28/0.55          | ( X
% 0.28/0.55            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % nat_power_eq_Suc_0_iff
% 0.28/0.55  thf(fact_2815_mult__Suc__right,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.28/0.55        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_Suc_right
% 0.28/0.55  thf(fact_2816_diff__Suc__1,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.28/0.55        = N ) ).
% 0.28/0.55  
% 0.28/0.55  % diff_Suc_1
% 0.28/0.55  thf(fact_2817_mod__by__Suc__0,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.28/0.55        = zero_zero_nat ) ).
% 0.28/0.55  
% 0.28/0.55  % mod_by_Suc_0
% 0.28/0.55  thf(fact_2818_Suc__pred,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.55       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.28/0.55          = N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_pred
% 0.28/0.55  thf(fact_2819_one__le__mult__iff,axiom,
% 0.28/0.55      ! [M: nat,N: nat] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.28/0.55        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.28/0.55          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % one_le_mult_iff
% 0.28/0.55  thf(fact_2820_diff__Suc__diff__eq2,axiom,
% 0.28/0.55      ! [K: nat,J: nat,I: nat] :
% 0.28/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.55       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.28/0.55          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % diff_Suc_diff_eq2
% 0.28/0.55  thf(fact_2821_diff__Suc__diff__eq1,axiom,
% 0.28/0.55      ! [K: nat,J: nat,I: nat] :
% 0.28/0.55        ( ( ord_less_eq_nat @ K @ J )
% 0.28/0.55       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.28/0.55          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % diff_Suc_diff_eq1
% 0.28/0.55  thf(fact_2822_Suc__numeral,axiom,
% 0.28/0.55      ! [N: num] :
% 0.28/0.55        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.28/0.55        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_numeral
% 0.28/0.55  thf(fact_2823_Suc__mod__mult__self1,axiom,
% 0.28/0.55      ! [M: nat,K: nat,N: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 0.28/0.55        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_mod_mult_self1
% 0.28/0.55  thf(fact_2824_Suc__mod__mult__self2,axiom,
% 0.28/0.55      ! [M: nat,N: nat,K: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 0.28/0.55        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_mod_mult_self2
% 0.28/0.55  thf(fact_2825_Suc__mod__mult__self3,axiom,
% 0.28/0.55      ! [K: nat,N: nat,M: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 0.28/0.55        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_mod_mult_self3
% 0.28/0.55  thf(fact_2826_Suc__mod__mult__self4,axiom,
% 0.28/0.55      ! [N: nat,K: nat,M: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 0.28/0.55        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_mod_mult_self4
% 0.28/0.55  thf(fact_2827_add__2__eq__Suc_H,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.55        = ( suc @ ( suc @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add_2_eq_Suc'
% 0.28/0.55  thf(fact_2828_add__2__eq__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.28/0.55        = ( suc @ ( suc @ N ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % add_2_eq_Suc
% 0.28/0.55  thf(fact_2829_div2__Suc__Suc,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.55        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % div2_Suc_Suc
% 0.28/0.55  thf(fact_2830_Suc__1,axiom,
% 0.28/0.55      ( ( suc @ one_one_nat )
% 0.28/0.55      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_1
% 0.28/0.55  thf(fact_2831_mod2__Suc__Suc,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.55        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mod2_Suc_Suc
% 0.28/0.55  thf(fact_2832_Suc__diff__1,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.28/0.55       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.28/0.55          = N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_diff_1
% 0.28/0.55  thf(fact_2833_Suc__times__numeral__mod__eq,axiom,
% 0.28/0.55      ! [K: num,N: nat] :
% 0.28/0.55        ( ( ( numeral_numeral_nat @ K )
% 0.28/0.55         != one_one_nat )
% 0.28/0.55       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.28/0.55          = one_one_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_times_numeral_mod_eq
% 0.28/0.55  thf(fact_2834_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.55         != ( suc @ zero_zero_nat ) )
% 0.28/0.55        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.28/0.55          = zero_zero_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % not_mod2_eq_Suc_0_eq_0
% 0.28/0.55  thf(fact_2835_del__x__not__mia,axiom,
% 0.28/0.55      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ( ord_less_nat @ Mi @ X )
% 0.28/0.55          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                  = L2 )
% 0.28/0.55               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                      @ ( vEBT_Node
% 0.28/0.55                        @ ( some_P7363390416028606310at_nat
% 0.28/0.55                          @ ( product_Pair_nat_nat @ Mi
% 0.28/0.55                            @ ( if_nat @ ( X = Ma )
% 0.28/0.55                              @ ( if_nat
% 0.28/0.55                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                                  = none_nat )
% 0.28/0.55                                @ Mi
% 0.28/0.55                                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.28/0.55                              @ Ma ) ) )
% 0.28/0.55                        @ Deg
% 0.28/0.55                        @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_not_mia
% 0.28/0.55  thf(fact_2836_del__x__not__mi__new__node__nil,axiom,
% 0.28/0.55      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.28/0.55        ( ( ( ord_less_nat @ Mi @ X )
% 0.28/0.55          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                  = L2 )
% 0.28/0.55               => ( ( Newnode
% 0.28/0.55                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                   => ( ( Sn
% 0.28/0.55                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                     => ( ( Newlist
% 0.28/0.55                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.55                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                            = ( vEBT_Node
% 0.28/0.55                              @ ( some_P7363390416028606310at_nat
% 0.28/0.55                                @ ( product_Pair_nat_nat @ Mi
% 0.28/0.55                                  @ ( if_nat @ ( X = Ma )
% 0.28/0.55                                    @ ( if_nat
% 0.28/0.55                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 0.28/0.55                                        = none_nat )
% 0.28/0.55                                      @ Mi
% 0.28/0.55                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.28/0.55                                    @ Ma ) ) )
% 0.28/0.55                              @ Deg
% 0.28/0.55                              @ Newlist
% 0.28/0.55                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_not_mi_new_node_nil
% 0.28/0.55  thf(fact_2837_del__x__not__mi,axiom,
% 0.28/0.55      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ( ord_less_nat @ Mi @ X )
% 0.28/0.55          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                  = L2 )
% 0.28/0.55               => ( ( Newnode
% 0.28/0.55                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                 => ( ( Newlist
% 0.28/0.55                      = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.55                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                            = ( vEBT_Node
% 0.28/0.55                              @ ( some_P7363390416028606310at_nat
% 0.28/0.55                                @ ( product_Pair_nat_nat @ Mi
% 0.28/0.55                                  @ ( if_nat @ ( X = Ma )
% 0.28/0.55                                    @ ( if_nat
% 0.28/0.55                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                                        = none_nat )
% 0.28/0.55                                      @ Mi
% 0.28/0.55                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.28/0.55                                    @ Ma ) ) )
% 0.28/0.55                              @ Deg
% 0.28/0.55                              @ Newlist
% 0.28/0.55                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.28/0.55                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_not_mi
% 0.28/0.55  thf(fact_2838_del__x__mia,axiom,
% 0.28/0.55      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ( X = Mi )
% 0.28/0.55          & ( ord_less_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                  @ ( vEBT_Node
% 0.28/0.55                    @ ( some_P7363390416028606310at_nat
% 0.28/0.55                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                        @ ( if_nat
% 0.28/0.55                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                            = Ma )
% 0.28/0.55                          @ ( if_nat
% 0.28/0.55                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                              = none_nat )
% 0.28/0.55                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.28/0.55                          @ Ma ) ) )
% 0.28/0.55                    @ Deg
% 0.28/0.55                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                  @ ( vEBT_Node
% 0.28/0.55                    @ ( some_P7363390416028606310at_nat
% 0.28/0.55                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                        @ ( if_nat
% 0.28/0.55                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                            = Ma )
% 0.28/0.55                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                          @ Ma ) ) )
% 0.28/0.55                    @ Deg
% 0.28/0.55                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                    @ Summary ) )
% 0.28/0.55                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_mia
% 0.28/0.55  thf(fact_2839_del__x__mi__lets__in__minNull,axiom,
% 0.28/0.55      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 0.28/0.55        ( ( ( X = Mi )
% 0.28/0.55          & ( ord_less_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( Xn
% 0.28/0.55                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.28/0.55               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                    = L2 )
% 0.28/0.55                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                   => ( ( Newnode
% 0.28/0.55                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                     => ( ( Newlist
% 0.28/0.55                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.55                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                         => ( ( Sn
% 0.28/0.55                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                              = ( vEBT_Node
% 0.28/0.55                                @ ( some_P7363390416028606310at_nat
% 0.28/0.55                                  @ ( product_Pair_nat_nat @ Xn
% 0.28/0.55                                    @ ( if_nat @ ( Xn = Ma )
% 0.28/0.55                                      @ ( if_nat
% 0.28/0.55                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 0.28/0.55                                          = none_nat )
% 0.28/0.55                                        @ Xn
% 0.28/0.55                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.28/0.55                                      @ Ma ) ) )
% 0.28/0.55                                @ Deg
% 0.28/0.55                                @ Newlist
% 0.28/0.55                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_mi_lets_in_minNull
% 0.28/0.55  thf(fact_2840_del__x__mi__lets__in,axiom,
% 0.28/0.55      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.28/0.55        ( ( ( X = Mi )
% 0.28/0.55          & ( ord_less_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( Xn
% 0.28/0.55                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.28/0.55               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                    = L2 )
% 0.28/0.55                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                   => ( ( Newnode
% 0.28/0.55                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                     => ( ( Newlist
% 0.28/0.55                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 0.28/0.55                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                              = ( vEBT_Node
% 0.28/0.55                                @ ( some_P7363390416028606310at_nat
% 0.28/0.55                                  @ ( product_Pair_nat_nat @ Xn
% 0.28/0.55                                    @ ( if_nat @ ( Xn = Ma )
% 0.28/0.55                                      @ ( if_nat
% 0.28/0.55                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                                          = none_nat )
% 0.28/0.55                                        @ Xn
% 0.28/0.55                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.28/0.55                                      @ Ma ) ) )
% 0.28/0.55                                @ Deg
% 0.28/0.55                                @ Newlist
% 0.28/0.55                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.28/0.55                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.28/0.55                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_mi_lets_in
% 0.28/0.55  thf(fact_2841_del__x__mi,axiom,
% 0.28/0.55      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat] :
% 0.28/0.55        ( ( ( X = Mi )
% 0.28/0.55          & ( ord_less_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                = H2 )
% 0.28/0.55             => ( ( Xn
% 0.28/0.55                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.28/0.55               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.28/0.55                    = L2 )
% 0.28/0.55                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                        @ ( vEBT_Node
% 0.28/0.55                          @ ( some_P7363390416028606310at_nat
% 0.28/0.55                            @ ( product_Pair_nat_nat @ Xn
% 0.28/0.55                              @ ( if_nat @ ( Xn = Ma )
% 0.28/0.55                                @ ( if_nat
% 0.28/0.55                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                                    = none_nat )
% 0.28/0.55                                  @ Xn
% 0.28/0.55                                  @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.28/0.55                                @ Ma ) ) )
% 0.28/0.55                          @ Deg
% 0.28/0.55                          @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 0.28/0.55                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.28/0.55                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_x_mi
% 0.28/0.55  thf(fact_2842_del__in__range,axiom,
% 0.28/0.55      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ( ord_less_eq_nat @ Mi @ X )
% 0.28/0.55          & ( ord_less_eq_nat @ X @ Ma ) )
% 0.28/0.55       => ( ( Mi != Ma )
% 0.28/0.55         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                  @ ( vEBT_Node
% 0.28/0.55                    @ ( some_P7363390416028606310at_nat
% 0.28/0.55                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.28/0.55                        @ ( if_nat
% 0.28/0.55                          @ ( ( ( X = Mi )
% 0.28/0.55                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                                = Ma ) )
% 0.28/0.55                            & ( ( X != Mi )
% 0.28/0.55                             => ( X = Ma ) ) )
% 0.28/0.55                          @ ( if_nat
% 0.28/0.55                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                              = none_nat )
% 0.28/0.55                            @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.28/0.55                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.28/0.55                          @ Ma ) ) )
% 0.28/0.55                    @ Deg
% 0.28/0.55                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                  @ ( vEBT_Node
% 0.28/0.55                    @ ( some_P7363390416028606310at_nat
% 0.28/0.55                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.28/0.55                        @ ( if_nat
% 0.28/0.55                          @ ( ( ( X = Mi )
% 0.28/0.55                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.28/0.55                                = Ma ) )
% 0.28/0.55                            & ( ( X != Mi )
% 0.28/0.55                             => ( X = Ma ) ) )
% 0.28/0.55                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                          @ Ma ) ) )
% 0.28/0.55                    @ Deg
% 0.28/0.55                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                    @ Summary ) )
% 0.28/0.55                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % del_in_range
% 0.28/0.55  thf(fact_2843_pred__less__length__list,axiom,
% 0.28/0.55      ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.28/0.55         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55              = ( if_option_nat
% 0.28/0.55                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                   != none_nat )
% 0.28/0.55                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.28/0.55                @ ( if_option_nat
% 0.28/0.55                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.55                    = none_nat )
% 0.28/0.55                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.28/0.55                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % pred_less_length_list
% 0.28/0.55  thf(fact_2844_pred__lesseq__max,axiom,
% 0.28/0.55      ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55       => ( ( ord_less_eq_nat @ X @ Ma )
% 0.28/0.55         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55              @ ( if_option_nat
% 0.28/0.55                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                   != none_nat )
% 0.28/0.55                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.28/0.55                @ ( if_option_nat
% 0.28/0.55                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.55                    = none_nat )
% 0.28/0.55                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.28/0.55                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.28/0.55              @ none_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % pred_lesseq_max
% 0.28/0.55  thf(fact_2845_succ__greatereq__min,axiom,
% 0.28/0.55      ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.28/0.55         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55              @ ( if_option_nat
% 0.28/0.55                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                   != none_nat )
% 0.28/0.55                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.28/0.55                @ ( if_option_nat
% 0.28/0.55                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.55                    = none_nat )
% 0.28/0.55                  @ none_nat
% 0.28/0.55                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.28/0.55              @ none_nat ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % succ_greatereq_min
% 0.28/0.55  thf(fact_2846_succ__less__length__list,axiom,
% 0.28/0.55      ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.28/0.55        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.28/0.55       => ( ( ord_less_eq_nat @ Mi @ X )
% 0.28/0.55         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.28/0.55           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.28/0.55              = ( if_option_nat
% 0.28/0.55                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.28/0.55                   != none_nat )
% 0.28/0.55                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.28/0.55                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.28/0.55                @ ( if_option_nat
% 0.28/0.55                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.28/0.55                    = none_nat )
% 0.28/0.55                  @ none_nat
% 0.28/0.55                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % succ_less_length_list
% 0.28/0.55  thf(fact_2847_dsimp,axiom,
% 0.28/0.55      ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 0.28/0.55      = ( vEBT_Node
% 0.28/0.55        @ ( some_P7363390416028606310at_nat
% 0.28/0.55          @ ( product_Pair_nat_nat @ mi
% 0.28/0.55            @ ( if_nat @ ( xa = ma )
% 0.28/0.55              @ ( if_nat
% 0.28/0.55                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 0.28/0.55                  = none_nat )
% 0.28/0.55                @ mi
% 0.28/0.55                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) )
% 0.28/0.55              @ ma ) ) )
% 0.28/0.55        @ deg
% 0.28/0.55        @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) )
% 0.28/0.55        @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % dsimp
% 0.28/0.55  thf(fact_2848_mult__commute__abs,axiom,
% 0.28/0.55      ! [C: real] :
% 0.28/0.55        ( ( ^ [X3: real] : ( times_times_real @ X3 @ C ) )
% 0.28/0.55        = ( times_times_real @ C ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_commute_abs
% 0.28/0.55  thf(fact_2849_mult__commute__abs,axiom,
% 0.28/0.55      ! [C: rat] :
% 0.28/0.55        ( ( ^ [X3: rat] : ( times_times_rat @ X3 @ C ) )
% 0.28/0.55        = ( times_times_rat @ C ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_commute_abs
% 0.28/0.55  thf(fact_2850_mult__commute__abs,axiom,
% 0.28/0.55      ! [C: nat] :
% 0.28/0.55        ( ( ^ [X3: nat] : ( times_times_nat @ X3 @ C ) )
% 0.28/0.55        = ( times_times_nat @ C ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_commute_abs
% 0.28/0.55  thf(fact_2851_mult__commute__abs,axiom,
% 0.28/0.55      ! [C: int] :
% 0.28/0.55        ( ( ^ [X3: int] : ( times_times_int @ X3 @ C ) )
% 0.28/0.55        = ( times_times_int @ C ) ) ).
% 0.28/0.55  
% 0.28/0.55  % mult_commute_abs
% 0.28/0.55  thf(fact_2852_Suc__inject,axiom,
% 0.28/0.55      ! [X: nat,Y: nat] :
% 0.28/0.55        ( ( ( suc @ X )
% 0.28/0.55          = ( suc @ Y ) )
% 0.28/0.55       => ( X = Y ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_inject
% 0.28/0.55  thf(fact_2853_n__not__Suc__n,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( N
% 0.28/0.55       != ( suc @ N ) ) ).
% 0.28/0.55  
% 0.28/0.55  % n_not_Suc_n
% 0.28/0.55  thf(fact_2854_max__def__raw,axiom,
% 0.28/0.55      ( ord_ma741700101516333627d_enat
% 0.28/0.55      = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2855_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_Code_integer
% 0.28/0.55      = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2856_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_set_int
% 0.28/0.55      = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2857_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_rat
% 0.28/0.55      = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2858_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_num
% 0.28/0.55      = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2859_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_nat
% 0.28/0.55      = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2860_max__def__raw,axiom,
% 0.28/0.55      ( ord_max_int
% 0.28/0.55      = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % max_def_raw
% 0.28/0.55  thf(fact_2861_lambda__zero,axiom,
% 0.28/0.55      ( ( ^ [H: complex] : zero_zero_complex )
% 0.28/0.55      = ( times_times_complex @ zero_zero_complex ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_zero
% 0.28/0.55  thf(fact_2862_lambda__zero,axiom,
% 0.28/0.55      ( ( ^ [H: real] : zero_zero_real )
% 0.28/0.55      = ( times_times_real @ zero_zero_real ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_zero
% 0.28/0.55  thf(fact_2863_lambda__zero,axiom,
% 0.28/0.55      ( ( ^ [H: rat] : zero_zero_rat )
% 0.28/0.55      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_zero
% 0.28/0.55  thf(fact_2864_lambda__zero,axiom,
% 0.28/0.55      ( ( ^ [H: nat] : zero_zero_nat )
% 0.28/0.55      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_zero
% 0.28/0.55  thf(fact_2865_lambda__zero,axiom,
% 0.28/0.55      ( ( ^ [H: int] : zero_zero_int )
% 0.28/0.55      = ( times_times_int @ zero_zero_int ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_zero
% 0.28/0.55  thf(fact_2866_lambda__one,axiom,
% 0.28/0.55      ( ( ^ [X3: complex] : X3 )
% 0.28/0.55      = ( times_times_complex @ one_one_complex ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_one
% 0.28/0.55  thf(fact_2867_lambda__one,axiom,
% 0.28/0.55      ( ( ^ [X3: real] : X3 )
% 0.28/0.55      = ( times_times_real @ one_one_real ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_one
% 0.28/0.55  thf(fact_2868_lambda__one,axiom,
% 0.28/0.55      ( ( ^ [X3: rat] : X3 )
% 0.28/0.55      = ( times_times_rat @ one_one_rat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_one
% 0.28/0.55  thf(fact_2869_lambda__one,axiom,
% 0.28/0.55      ( ( ^ [X3: nat] : X3 )
% 0.28/0.55      = ( times_times_nat @ one_one_nat ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_one
% 0.28/0.55  thf(fact_2870_lambda__one,axiom,
% 0.28/0.55      ( ( ^ [X3: int] : X3 )
% 0.28/0.55      = ( times_times_int @ one_one_int ) ) ).
% 0.28/0.55  
% 0.28/0.55  % lambda_one
% 0.28/0.55  thf(fact_2871_vebt__buildup_Ocases,axiom,
% 0.28/0.55      ! [X: nat] :
% 0.28/0.55        ( ( X != zero_zero_nat )
% 0.28/0.55       => ( ( X
% 0.28/0.55           != ( suc @ zero_zero_nat ) )
% 0.28/0.55         => ~ ! [Va2: nat] :
% 0.28/0.55                ( X
% 0.28/0.55               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % vebt_buildup.cases
% 0.28/0.55  thf(fact_2872_not0__implies__Suc,axiom,
% 0.28/0.55      ! [N: nat] :
% 0.28/0.55        ( ( N != zero_zero_nat )
% 0.28/0.55       => ? [M4: nat] :
% 0.28/0.55            ( N
% 0.28/0.55            = ( suc @ M4 ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % not0_implies_Suc
% 0.28/0.55  thf(fact_2873_Zero__not__Suc,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( zero_zero_nat
% 0.28/0.55       != ( suc @ M ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Zero_not_Suc
% 0.28/0.55  thf(fact_2874_Zero__neq__Suc,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( zero_zero_nat
% 0.28/0.55       != ( suc @ M ) ) ).
% 0.28/0.55  
% 0.28/0.55  % Zero_neq_Suc
% 0.28/0.55  thf(fact_2875_Suc__neq__Zero,axiom,
% 0.28/0.55      ! [M: nat] :
% 0.28/0.55        ( ( suc @ M )
% 0.28/0.55       != zero_zero_nat ) ).
% 0.28/0.55  
% 0.28/0.55  % Suc_neq_Zero
% 0.28/0.55  thf(fact_2876_zero__induct,axiom,
% 0.28/0.55      ! [P: nat > $o,K: nat] :
% 0.28/0.55        ( ( P @ K )
% 0.28/0.55       => ( ! [N3: nat] :
% 0.28/0.55              ( ( P @ ( suc @ N3 ) )
% 0.28/0.55             => ( P @ N3 ) )
% 0.28/0.55         => ( P @ zero_zero_nat ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % zero_induct
% 0.28/0.55  thf(fact_2877_diff__induct,axiom,
% 0.28/0.55      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.28/0.55        ( ! [X6: nat] : ( P @ X6 @ zero_zero_nat )
% 0.28/0.55       => ( ! [Y5: nat] : ( P @ zero_zero_nat @ ( suc @ Y5 ) )
% 0.28/0.55         => ( ! [X6: nat,Y5: nat] :
% 0.28/0.55                ( ( P @ X6 @ Y5 )
% 0.28/0.55               => ( P @ ( suc @ X6 ) @ ( suc @ Y5 ) ) )
% 0.28/0.55           => ( P @ M @ N ) ) ) ) ).
% 0.28/0.55  
% 0.28/0.55  % diff_induct
% 0.28/0.55  thf(fact_2878_nat__induct,axiom,
% 0.28/0.55      ! [P: nat > $o,N: nat] :
% 0.32/0.55        ( ( P @ zero_zero_nat )
% 0.32/0.55       => ( ! [N3: nat] :
% 0.32/0.55              ( ( P @ N3 )
% 0.32/0.55             => ( P @ ( suc @ N3 ) ) )
% 0.32/0.55         => ( P @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_induct
% 0.32/0.55  thf(fact_2879_old_Onat_Oexhaust,axiom,
% 0.32/0.55      ! [Y: nat] :
% 0.32/0.55        ( ( Y != zero_zero_nat )
% 0.32/0.55       => ~ ! [Nat3: nat] :
% 0.32/0.55              ( Y
% 0.32/0.55             != ( suc @ Nat3 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % old.nat.exhaust
% 0.32/0.55  thf(fact_2880_nat_OdiscI,axiom,
% 0.32/0.55      ! [Nat: nat,X22: nat] :
% 0.32/0.55        ( ( Nat
% 0.32/0.55          = ( suc @ X22 ) )
% 0.32/0.55       => ( Nat != zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat.discI
% 0.32/0.55  thf(fact_2881_old_Onat_Odistinct_I1_J,axiom,
% 0.32/0.55      ! [Nat2: nat] :
% 0.32/0.55        ( zero_zero_nat
% 0.32/0.55       != ( suc @ Nat2 ) ) ).
% 0.32/0.55  
% 0.32/0.55  % old.nat.distinct(1)
% 0.32/0.55  thf(fact_2882_old_Onat_Odistinct_I2_J,axiom,
% 0.32/0.55      ! [Nat2: nat] :
% 0.32/0.55        ( ( suc @ Nat2 )
% 0.32/0.55       != zero_zero_nat ) ).
% 0.32/0.55  
% 0.32/0.55  % old.nat.distinct(2)
% 0.32/0.55  thf(fact_2883_nat_Odistinct_I1_J,axiom,
% 0.32/0.55      ! [X22: nat] :
% 0.32/0.55        ( zero_zero_nat
% 0.32/0.55       != ( suc @ X22 ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat.distinct(1)
% 0.32/0.55  thf(fact_2884_not__less__less__Suc__eq,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.55       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.55          = ( N = M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % not_less_less_Suc_eq
% 0.32/0.55  thf(fact_2885_strict__inc__induct,axiom,
% 0.32/0.55      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.55        ( ( ord_less_nat @ I @ J )
% 0.32/0.55       => ( ! [I4: nat] :
% 0.32/0.55              ( ( J
% 0.32/0.55                = ( suc @ I4 ) )
% 0.32/0.55             => ( P @ I4 ) )
% 0.32/0.55         => ( ! [I4: nat] :
% 0.32/0.55                ( ( ord_less_nat @ I4 @ J )
% 0.32/0.55               => ( ( P @ ( suc @ I4 ) )
% 0.32/0.55                 => ( P @ I4 ) ) )
% 0.32/0.55           => ( P @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % strict_inc_induct
% 0.32/0.55  thf(fact_2886_less__Suc__induct,axiom,
% 0.32/0.55      ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.32/0.55        ( ( ord_less_nat @ I @ J )
% 0.32/0.55       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 0.32/0.55         => ( ! [I4: nat,J2: nat,K3: nat] :
% 0.32/0.55                ( ( ord_less_nat @ I4 @ J2 )
% 0.32/0.55               => ( ( ord_less_nat @ J2 @ K3 )
% 0.32/0.55                 => ( ( P @ I4 @ J2 )
% 0.32/0.55                   => ( ( P @ J2 @ K3 )
% 0.32/0.55                     => ( P @ I4 @ K3 ) ) ) ) )
% 0.32/0.55           => ( P @ I @ J ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_Suc_induct
% 0.32/0.55  thf(fact_2887_less__trans__Suc,axiom,
% 0.32/0.55      ! [I: nat,J: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ I @ J )
% 0.32/0.55       => ( ( ord_less_nat @ J @ K )
% 0.32/0.55         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_trans_Suc
% 0.32/0.55  thf(fact_2888_Suc__less__SucD,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/0.55       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_less_SucD
% 0.32/0.55  thf(fact_2889_less__antisym,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.55       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.55         => ( M = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_antisym
% 0.32/0.55  thf(fact_2890_Suc__less__eq2,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.55        = ( ? [M6: nat] :
% 0.32/0.55              ( ( M
% 0.32/0.55                = ( suc @ M6 ) )
% 0.32/0.55              & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_less_eq2
% 0.32/0.55  thf(fact_2891_All__less__Suc,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ! [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 0.32/0.55             => ( P @ I5 ) ) )
% 0.32/0.55        = ( ( P @ N )
% 0.32/0.55          & ! [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ N )
% 0.32/0.55             => ( P @ I5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % All_less_Suc
% 0.32/0.55  thf(fact_2892_not__less__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.32/0.55        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % not_less_eq
% 0.32/0.55  thf(fact_2893_less__Suc__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( ( ord_less_nat @ M @ N )
% 0.32/0.55          | ( M = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_Suc_eq
% 0.32/0.55  thf(fact_2894_Ex__less__Suc,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ? [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 0.32/0.55              & ( P @ I5 ) ) )
% 0.32/0.55        = ( ( P @ N )
% 0.32/0.55          | ? [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ N )
% 0.32/0.55              & ( P @ I5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Ex_less_Suc
% 0.32/0.55  thf(fact_2895_less__SucI,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ N )
% 0.32/0.55       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_SucI
% 0.32/0.55  thf(fact_2896_less__SucE,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.55       => ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.55         => ( M = N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_SucE
% 0.32/0.55  thf(fact_2897_Suc__lessI,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ N )
% 0.32/0.55       => ( ( ( suc @ M )
% 0.32/0.55           != N )
% 0.32/0.55         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_lessI
% 0.32/0.55  thf(fact_2898_Suc__lessE,axiom,
% 0.32/0.55      ! [I: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.32/0.55       => ~ ! [J2: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I @ J2 )
% 0.32/0.55             => ( K
% 0.32/0.55               != ( suc @ J2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_lessE
% 0.32/0.55  thf(fact_2899_Suc__lessD,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.32/0.55       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_lessD
% 0.32/0.55  thf(fact_2900_Nat_OlessE,axiom,
% 0.32/0.55      ! [I: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ I @ K )
% 0.32/0.55       => ( ( K
% 0.32/0.55           != ( suc @ I ) )
% 0.32/0.55         => ~ ! [J2: nat] :
% 0.32/0.55                ( ( ord_less_nat @ I @ J2 )
% 0.32/0.55               => ( K
% 0.32/0.55                 != ( suc @ J2 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Nat.lessE
% 0.32/0.55  thf(fact_2901_set__vebt__def,axiom,
% 0.32/0.55      ( vEBT_set_vebt
% 0.32/0.55      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % set_vebt_def
% 0.32/0.55  thf(fact_2902_transitive__stepwise__le,axiom,
% 0.32/0.55      ! [M: nat,N: nat,R4: nat > nat > $o] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ! [X6: nat] : ( R4 @ X6 @ X6 )
% 0.32/0.55         => ( ! [X6: nat,Y5: nat,Z5: nat] :
% 0.32/0.55                ( ( R4 @ X6 @ Y5 )
% 0.32/0.55               => ( ( R4 @ Y5 @ Z5 )
% 0.32/0.55                 => ( R4 @ X6 @ Z5 ) ) )
% 0.32/0.55           => ( ! [N3: nat] : ( R4 @ N3 @ ( suc @ N3 ) )
% 0.32/0.55             => ( R4 @ M @ N ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % transitive_stepwise_le
% 0.32/0.55  thf(fact_2903_nat__induct__at__least,axiom,
% 0.32/0.55      ! [M: nat,N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ( P @ M )
% 0.32/0.55         => ( ! [N3: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ M @ N3 )
% 0.32/0.55               => ( ( P @ N3 )
% 0.32/0.55                 => ( P @ ( suc @ N3 ) ) ) )
% 0.32/0.55           => ( P @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_induct_at_least
% 0.32/0.55  thf(fact_2904_full__nat__induct,axiom,
% 0.32/0.55      ! [P: nat > $o,N: nat] :
% 0.32/0.55        ( ! [N3: nat] :
% 0.32/0.55            ( ! [M2: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 0.32/0.55               => ( P @ M2 ) )
% 0.32/0.55           => ( P @ N3 ) )
% 0.32/0.55       => ( P @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % full_nat_induct
% 0.32/0.55  thf(fact_2905_not__less__eq__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.32/0.55        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.32/0.55  
% 0.32/0.55  % not_less_eq_eq
% 0.32/0.55  thf(fact_2906_Suc__n__not__le__n,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_n_not_le_n
% 0.32/0.55  thf(fact_2907_le__Suc__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55          | ( M
% 0.32/0.55            = ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_Suc_eq
% 0.32/0.55  thf(fact_2908_Suc__le__D,axiom,
% 0.32/0.55      ! [N: nat,M7: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
% 0.32/0.55       => ? [M4: nat] :
% 0.32/0.55            ( M7
% 0.32/0.55            = ( suc @ M4 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_le_D
% 0.32/0.55  thf(fact_2909_le__SucI,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_SucI
% 0.32/0.55  thf(fact_2910_le__SucE,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.55       => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.55         => ( M
% 0.32/0.55            = ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_SucE
% 0.32/0.55  thf(fact_2911_Suc__leD,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.55       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_leD
% 0.32/0.55  thf(fact_2912_add__Suc__shift,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.32/0.55        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_Suc_shift
% 0.32/0.55  thf(fact_2913_add__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.32/0.55        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_Suc
% 0.32/0.55  thf(fact_2914_nat__arith_Osuc1,axiom,
% 0.32/0.55      ! [A2: nat,K: nat,A: nat] :
% 0.32/0.55        ( ( A2
% 0.32/0.55          = ( plus_plus_nat @ K @ A ) )
% 0.32/0.55       => ( ( suc @ A2 )
% 0.32/0.55          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_arith.suc1
% 0.32/0.55  thf(fact_2915_zero__induct__lemma,axiom,
% 0.32/0.55      ! [P: nat > $o,K: nat,I: nat] :
% 0.32/0.55        ( ( P @ K )
% 0.32/0.55       => ( ! [N3: nat] :
% 0.32/0.55              ( ( P @ ( suc @ N3 ) )
% 0.32/0.55             => ( P @ N3 ) )
% 0.32/0.55         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % zero_induct_lemma
% 0.32/0.55  thf(fact_2916_Suc__mult__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.32/0.55          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.55        = ( M = N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_mult_cancel1
% 0.32/0.55  thf(fact_2917_numeral__code_I2_J,axiom,
% 0.32/0.55      ! [N: num] :
% 0.32/0.55        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.32/0.55        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_code(2)
% 0.32/0.55  thf(fact_2918_numeral__code_I2_J,axiom,
% 0.32/0.55      ! [N: num] :
% 0.32/0.55        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.32/0.55        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_code(2)
% 0.32/0.55  thf(fact_2919_numeral__code_I2_J,axiom,
% 0.32/0.55      ! [N: num] :
% 0.32/0.55        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.32/0.55        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_code(2)
% 0.32/0.55  thf(fact_2920_numeral__code_I2_J,axiom,
% 0.32/0.55      ! [N: num] :
% 0.32/0.55        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.32/0.55        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_code(2)
% 0.32/0.55  thf(fact_2921_numeral__code_I2_J,axiom,
% 0.32/0.55      ! [N: num] :
% 0.32/0.55        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.32/0.55        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_code(2)
% 0.32/0.55  thf(fact_2922_mod__Suc__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 0.32/0.55        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mod_Suc_eq
% 0.32/0.55  thf(fact_2923_mod__Suc__Suc__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 0.32/0.55        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mod_Suc_Suc_eq
% 0.32/0.55  thf(fact_2924_set__bit__greater__eq,axiom,
% 0.32/0.55      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 0.32/0.55  
% 0.32/0.55  % set_bit_greater_eq
% 0.32/0.55  thf(fact_2925_power__numeral__even,axiom,
% 0.32/0.55      ! [Z: complex,W: num] :
% 0.32/0.55        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.32/0.55        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_numeral_even
% 0.32/0.55  thf(fact_2926_power__numeral__even,axiom,
% 0.32/0.55      ! [Z: real,W: num] :
% 0.32/0.55        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.32/0.55        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_numeral_even
% 0.32/0.55  thf(fact_2927_power__numeral__even,axiom,
% 0.32/0.55      ! [Z: rat,W: num] :
% 0.32/0.55        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.32/0.55        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_numeral_even
% 0.32/0.55  thf(fact_2928_power__numeral__even,axiom,
% 0.32/0.55      ! [Z: nat,W: num] :
% 0.32/0.55        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.32/0.55        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_numeral_even
% 0.32/0.55  thf(fact_2929_power__numeral__even,axiom,
% 0.32/0.55      ! [Z: int,W: num] :
% 0.32/0.55        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.32/0.55        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_numeral_even
% 0.32/0.55  thf(fact_2930_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 0.32/0.55        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_set_int @ C @ A )
% 0.32/0.55              & ( ord_less_eq_set_int @ B @ D )
% 0.32/0.55              & ( ( ord_less_set_int @ C @ A )
% 0.32/0.55                | ( ord_less_set_int @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2931_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.55        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_rat @ C @ A )
% 0.32/0.55              & ( ord_less_eq_rat @ B @ D )
% 0.32/0.55              & ( ( ord_less_rat @ C @ A )
% 0.32/0.55                | ( ord_less_rat @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2932_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: num,B: num,C: num,D: num] :
% 0.32/0.55        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_num @ C @ A )
% 0.32/0.55              & ( ord_less_eq_num @ B @ D )
% 0.32/0.55              & ( ( ord_less_num @ C @ A )
% 0.32/0.55                | ( ord_less_num @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2933_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.55        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.55              & ( ord_less_eq_nat @ B @ D )
% 0.32/0.55              & ( ( ord_less_nat @ C @ A )
% 0.32/0.55                | ( ord_less_nat @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2934_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.55        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_int @ C @ A )
% 0.32/0.55              & ( ord_less_eq_int @ B @ D )
% 0.32/0.55              & ( ( ord_less_int @ C @ A )
% 0.32/0.55                | ( ord_less_int @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2935_atLeastatMost__psubset__iff,axiom,
% 0.32/0.55      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.55        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 0.32/0.55        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.32/0.55            | ( ( ord_less_eq_real @ C @ A )
% 0.32/0.55              & ( ord_less_eq_real @ B @ D )
% 0.32/0.55              & ( ( ord_less_real @ C @ A )
% 0.32/0.55                | ( ord_less_real @ B @ D ) ) ) )
% 0.32/0.55          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % atLeastatMost_psubset_iff
% 0.32/0.55  thf(fact_2936_ex__nat__less,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ? [M3: nat] :
% 0.32/0.55              ( ( ord_less_eq_nat @ M3 @ N )
% 0.32/0.55              & ( P @ M3 ) ) )
% 0.32/0.55        = ( ? [X3: nat] :
% 0.32/0.55              ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.55              & ( P @ X3 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ex_nat_less
% 0.32/0.55  thf(fact_2937_all__nat__less,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ! [M3: nat] :
% 0.32/0.55              ( ( ord_less_eq_nat @ M3 @ N )
% 0.32/0.55             => ( P @ M3 ) ) )
% 0.32/0.55        = ( ! [X3: nat] :
% 0.32/0.55              ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.55             => ( P @ X3 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % all_nat_less
% 0.32/0.55  thf(fact_2938_lift__Suc__mono__less__iff,axiom,
% 0.32/0.55      ! [F: nat > real,N: nat,M: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.55          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less_iff
% 0.32/0.55  thf(fact_2939_lift__Suc__mono__less__iff,axiom,
% 0.32/0.55      ! [F: nat > rat,N: nat,M: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.55          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less_iff
% 0.32/0.55  thf(fact_2940_lift__Suc__mono__less__iff,axiom,
% 0.32/0.55      ! [F: nat > num,N: nat,M: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.55          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less_iff
% 0.32/0.55  thf(fact_2941_lift__Suc__mono__less__iff,axiom,
% 0.32/0.55      ! [F: nat > nat,N: nat,M: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.55          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less_iff
% 0.32/0.55  thf(fact_2942_lift__Suc__mono__less__iff,axiom,
% 0.32/0.55      ! [F: nat > int,N: nat,M: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.32/0.55          = ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less_iff
% 0.32/0.55  thf(fact_2943_lift__Suc__mono__less,axiom,
% 0.32/0.55      ! [F: nat > real,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less
% 0.32/0.55  thf(fact_2944_lift__Suc__mono__less,axiom,
% 0.32/0.55      ! [F: nat > rat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less
% 0.32/0.55  thf(fact_2945_lift__Suc__mono__less,axiom,
% 0.32/0.55      ! [F: nat > num,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less
% 0.32/0.55  thf(fact_2946_lift__Suc__mono__less,axiom,
% 0.32/0.55      ! [F: nat > nat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less
% 0.32/0.55  thf(fact_2947_lift__Suc__mono__less,axiom,
% 0.32/0.55      ! [F: nat > int,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_less
% 0.32/0.55  thf(fact_2948_power__Suc,axiom,
% 0.32/0.55      ! [A: complex,N: nat] :
% 0.32/0.55        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc
% 0.32/0.55  thf(fact_2949_power__Suc,axiom,
% 0.32/0.55      ! [A: real,N: nat] :
% 0.32/0.55        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc
% 0.32/0.55  thf(fact_2950_power__Suc,axiom,
% 0.32/0.55      ! [A: rat,N: nat] :
% 0.32/0.55        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc
% 0.32/0.55  thf(fact_2951_power__Suc,axiom,
% 0.32/0.55      ! [A: nat,N: nat] :
% 0.32/0.55        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc
% 0.32/0.55  thf(fact_2952_power__Suc,axiom,
% 0.32/0.55      ! [A: int,N: nat] :
% 0.32/0.55        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc
% 0.32/0.55  thf(fact_2953_power__Suc2,axiom,
% 0.32/0.55      ! [A: complex,N: nat] :
% 0.32/0.55        ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc2
% 0.32/0.55  thf(fact_2954_power__Suc2,axiom,
% 0.32/0.55      ! [A: real,N: nat] :
% 0.32/0.55        ( ( power_power_real @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc2
% 0.32/0.55  thf(fact_2955_power__Suc2,axiom,
% 0.32/0.55      ! [A: rat,N: nat] :
% 0.32/0.55        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc2
% 0.32/0.55  thf(fact_2956_power__Suc2,axiom,
% 0.32/0.55      ! [A: nat,N: nat] :
% 0.32/0.55        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc2
% 0.32/0.55  thf(fact_2957_power__Suc2,axiom,
% 0.32/0.55      ! [A: int,N: nat] :
% 0.32/0.55        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.32/0.55        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_Suc2
% 0.32/0.55  thf(fact_2958_lift__Suc__antimono__le,axiom,
% 0.32/0.55      ! [F: nat > set_int,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_antimono_le
% 0.32/0.55  thf(fact_2959_lift__Suc__antimono__le,axiom,
% 0.32/0.55      ! [F: nat > rat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_antimono_le
% 0.32/0.55  thf(fact_2960_lift__Suc__antimono__le,axiom,
% 0.32/0.55      ! [F: nat > num,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_antimono_le
% 0.32/0.55  thf(fact_2961_lift__Suc__antimono__le,axiom,
% 0.32/0.55      ! [F: nat > nat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_antimono_le
% 0.32/0.55  thf(fact_2962_lift__Suc__antimono__le,axiom,
% 0.32/0.55      ! [F: nat > int,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_antimono_le
% 0.32/0.55  thf(fact_2963_lift__Suc__mono__le,axiom,
% 0.32/0.55      ! [F: nat > set_int,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_le
% 0.32/0.55  thf(fact_2964_lift__Suc__mono__le,axiom,
% 0.32/0.55      ! [F: nat > rat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_le
% 0.32/0.55  thf(fact_2965_lift__Suc__mono__le,axiom,
% 0.32/0.55      ! [F: nat > num,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_le
% 0.32/0.55  thf(fact_2966_lift__Suc__mono__le,axiom,
% 0.32/0.55      ! [F: nat > nat,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_le
% 0.32/0.55  thf(fact_2967_lift__Suc__mono__le,axiom,
% 0.32/0.55      ! [F: nat > int,N: nat,N5: nat] :
% 0.32/0.55        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ N @ N5 )
% 0.32/0.55         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % lift_Suc_mono_le
% 0.32/0.55  thf(fact_2968_less__Suc__eq__0__disj,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( ( M = zero_zero_nat )
% 0.32/0.55          | ? [J3: nat] :
% 0.32/0.55              ( ( M
% 0.32/0.55                = ( suc @ J3 ) )
% 0.32/0.55              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_Suc_eq_0_disj
% 0.32/0.55  thf(fact_2969_gr0__implies__Suc,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ? [M4: nat] :
% 0.32/0.55            ( N
% 0.32/0.55            = ( suc @ M4 ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % gr0_implies_Suc
% 0.32/0.55  thf(fact_2970_All__less__Suc2,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ! [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 0.32/0.55             => ( P @ I5 ) ) )
% 0.32/0.55        = ( ( P @ zero_zero_nat )
% 0.32/0.55          & ! [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ N )
% 0.32/0.55             => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % All_less_Suc2
% 0.32/0.55  thf(fact_2971_gr0__conv__Suc,axiom,
% 0.32/0.55      ! [N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55        = ( ? [M3: nat] :
% 0.32/0.55              ( N
% 0.32/0.55              = ( suc @ M3 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % gr0_conv_Suc
% 0.32/0.55  thf(fact_2972_Ex__less__Suc2,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ? [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 0.32/0.55              & ( P @ I5 ) ) )
% 0.32/0.55        = ( ( P @ zero_zero_nat )
% 0.32/0.55          | ? [I5: nat] :
% 0.32/0.55              ( ( ord_less_nat @ I5 @ N )
% 0.32/0.55              & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Ex_less_Suc2
% 0.32/0.55  thf(fact_2973_Suc__leI,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ N )
% 0.32/0.55       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_leI
% 0.32/0.55  thf(fact_2974_Suc__le__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.55        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_le_eq
% 0.32/0.55  thf(fact_2975_dec__induct,axiom,
% 0.32/0.55      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( P @ I )
% 0.32/0.55         => ( ! [N3: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ I @ N3 )
% 0.32/0.55               => ( ( ord_less_nat @ N3 @ J )
% 0.32/0.55                 => ( ( P @ N3 )
% 0.32/0.55                   => ( P @ ( suc @ N3 ) ) ) ) )
% 0.32/0.55           => ( P @ J ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % dec_induct
% 0.32/0.55  thf(fact_2976_inc__induct,axiom,
% 0.32/0.55      ! [I: nat,J: nat,P: nat > $o] :
% 0.32/0.55        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.55       => ( ( P @ J )
% 0.32/0.55         => ( ! [N3: nat] :
% 0.32/0.55                ( ( ord_less_eq_nat @ I @ N3 )
% 0.32/0.55               => ( ( ord_less_nat @ N3 @ J )
% 0.32/0.55                 => ( ( P @ ( suc @ N3 ) )
% 0.32/0.55                   => ( P @ N3 ) ) ) )
% 0.32/0.55           => ( P @ I ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % inc_induct
% 0.32/0.55  thf(fact_2977_Suc__le__lessD,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.55       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_le_lessD
% 0.32/0.55  thf(fact_2978_le__less__Suc__eq,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.55          = ( N = M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_less_Suc_eq
% 0.32/0.55  thf(fact_2979_less__Suc__eq__le,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_Suc_eq_le
% 0.32/0.55  thf(fact_2980_less__eq__Suc__le,axiom,
% 0.32/0.55      ( ord_less_nat
% 0.32/0.55      = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_eq_Suc_le
% 0.32/0.55  thf(fact_2981_le__imp__less__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.55       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % le_imp_less_Suc
% 0.32/0.55  thf(fact_2982_add__is__1,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.55          = ( suc @ zero_zero_nat ) )
% 0.32/0.55        = ( ( ( M
% 0.32/0.55              = ( suc @ zero_zero_nat ) )
% 0.32/0.55            & ( N = zero_zero_nat ) )
% 0.32/0.55          | ( ( M = zero_zero_nat )
% 0.32/0.55            & ( N
% 0.32/0.55              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % add_is_1
% 0.32/0.55  thf(fact_2983_one__is__add,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ( suc @ zero_zero_nat )
% 0.32/0.55          = ( plus_plus_nat @ M @ N ) )
% 0.32/0.55        = ( ( ( M
% 0.32/0.55              = ( suc @ zero_zero_nat ) )
% 0.32/0.55            & ( N = zero_zero_nat ) )
% 0.32/0.55          | ( ( M = zero_zero_nat )
% 0.32/0.55            & ( N
% 0.32/0.55              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % one_is_add
% 0.32/0.55  thf(fact_2984_option_Osize_I4_J,axiom,
% 0.32/0.55      ! [X22: nat] :
% 0.32/0.55        ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 0.32/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(4)
% 0.32/0.55  thf(fact_2985_option_Osize_I4_J,axiom,
% 0.32/0.55      ! [X22: product_prod_nat_nat] :
% 0.32/0.55        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.32/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(4)
% 0.32/0.55  thf(fact_2986_option_Osize_I4_J,axiom,
% 0.32/0.55      ! [X22: num] :
% 0.32/0.55        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 0.32/0.55        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(4)
% 0.32/0.55  thf(fact_2987_less__natE,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ N )
% 0.32/0.55       => ~ ! [Q3: nat] :
% 0.32/0.55              ( N
% 0.32/0.55             != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_natE
% 0.32/0.55  thf(fact_2988_less__add__Suc1,axiom,
% 0.32/0.55      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_add_Suc1
% 0.32/0.55  thf(fact_2989_less__add__Suc2,axiom,
% 0.32/0.55      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_add_Suc2
% 0.32/0.55  thf(fact_2990_less__iff__Suc__add,axiom,
% 0.32/0.55      ( ord_less_nat
% 0.32/0.55      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.55          ? [K2: nat] :
% 0.32/0.55            ( N2
% 0.32/0.55            = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_iff_Suc_add
% 0.32/0.55  thf(fact_2991_less__imp__Suc__add,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ M @ N )
% 0.32/0.55       => ? [K3: nat] :
% 0.32/0.55            ( N
% 0.32/0.55            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % less_imp_Suc_add
% 0.32/0.55  thf(fact_2992_option_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_option_nat @ none_nat )
% 0.32/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(3)
% 0.32/0.55  thf(fact_2993_option_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.32/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(3)
% 0.32/0.55  thf(fact_2994_option_Osize_I3_J,axiom,
% 0.32/0.55      ( ( size_size_option_num @ none_num )
% 0.32/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % option.size(3)
% 0.32/0.55  thf(fact_2995_diff__less__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_less_Suc
% 0.32/0.55  thf(fact_2996_Suc__diff__Suc,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ N @ M )
% 0.32/0.55       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.32/0.55          = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_diff_Suc
% 0.32/0.55  thf(fact_2997_Suc__mult__less__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.55        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_mult_less_cancel1
% 0.32/0.55  thf(fact_2998_Suc__diff__le,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.55       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.32/0.55          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_diff_le
% 0.32/0.55  thf(fact_2999_Suc__mult__le__cancel1,axiom,
% 0.32/0.55      ! [K: nat,M: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.32/0.55        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_mult_le_cancel1
% 0.32/0.55  thf(fact_3000_One__nat__def,axiom,
% 0.32/0.55      ( one_one_nat
% 0.32/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % One_nat_def
% 0.32/0.55  thf(fact_3001_Suc__div__le__mono,axiom,
% 0.32/0.55      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_div_le_mono
% 0.32/0.55  thf(fact_3002_mult__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.32/0.55        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mult_Suc
% 0.32/0.55  thf(fact_3003_Suc__eq__plus1,axiom,
% 0.32/0.55      ( suc
% 0.32/0.55      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_eq_plus1
% 0.32/0.55  thf(fact_3004_plus__1__eq__Suc,axiom,
% 0.32/0.55      ( ( plus_plus_nat @ one_one_nat )
% 0.32/0.55      = suc ) ).
% 0.32/0.55  
% 0.32/0.55  % plus_1_eq_Suc
% 0.32/0.55  thf(fact_3005_Suc__eq__plus1__left,axiom,
% 0.32/0.55      ( suc
% 0.32/0.55      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % Suc_eq_plus1_left
% 0.32/0.55  thf(fact_3006_diff__Suc__eq__diff__pred,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.32/0.55        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_Suc_eq_diff_pred
% 0.32/0.55  thf(fact_3007_mod__Suc,axiom,
% 0.32/0.55      ! [M: nat,N: nat] :
% 0.32/0.55        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.55            = N )
% 0.32/0.55         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.32/0.55            = zero_zero_nat ) )
% 0.32/0.55        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.55           != N )
% 0.32/0.55         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.32/0.55            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mod_Suc
% 0.32/0.55  thf(fact_3008_mod__induct,axiom,
% 0.32/0.55      ! [P: nat > $o,N: nat,P5: nat,M: nat] :
% 0.32/0.55        ( ( P @ N )
% 0.32/0.55       => ( ( ord_less_nat @ N @ P5 )
% 0.32/0.55         => ( ( ord_less_nat @ M @ P5 )
% 0.32/0.55           => ( ! [N3: nat] :
% 0.32/0.55                  ( ( ord_less_nat @ N3 @ P5 )
% 0.32/0.55                 => ( ( P @ N3 )
% 0.32/0.55                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 0.32/0.55             => ( P @ M ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % mod_induct
% 0.32/0.55  thf(fact_3009_mod__Suc__le__divisor,axiom,
% 0.32/0.55      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 0.32/0.55  
% 0.32/0.55  % mod_Suc_le_divisor
% 0.32/0.55  thf(fact_3010_power__inject__base,axiom,
% 0.32/0.55      ! [A: real,N: nat,B: real] :
% 0.32/0.55        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 0.32/0.55          = ( power_power_real @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.55         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.32/0.55           => ( A = B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_inject_base
% 0.32/0.55  thf(fact_3011_power__inject__base,axiom,
% 0.32/0.55      ! [A: rat,N: nat,B: rat] :
% 0.32/0.55        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.32/0.55          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.55         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55           => ( A = B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_inject_base
% 0.32/0.55  thf(fact_3012_power__inject__base,axiom,
% 0.32/0.55      ! [A: nat,N: nat,B: nat] :
% 0.32/0.55        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.32/0.55          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.55         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55           => ( A = B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_inject_base
% 0.32/0.55  thf(fact_3013_power__inject__base,axiom,
% 0.32/0.55      ! [A: int,N: nat,B: int] :
% 0.32/0.55        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.32/0.55          = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.55         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55           => ( A = B ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_inject_base
% 0.32/0.55  thf(fact_3014_power__le__imp__le__base,axiom,
% 0.32/0.55      ! [A: real,N: nat,B: real] :
% 0.32/0.55        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.32/0.55         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_le_imp_le_base
% 0.32/0.55  thf(fact_3015_power__le__imp__le__base,axiom,
% 0.32/0.55      ! [A: rat,N: nat,B: rat] :
% 0.32/0.55        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.55         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_le_imp_le_base
% 0.32/0.55  thf(fact_3016_power__le__imp__le__base,axiom,
% 0.32/0.55      ! [A: nat,N: nat,B: nat] :
% 0.32/0.55        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.32/0.55         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_le_imp_le_base
% 0.32/0.55  thf(fact_3017_power__le__imp__le__base,axiom,
% 0.32/0.55      ! [A: int,N: nat,B: int] :
% 0.32/0.55        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.32/0.55       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.55         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_le_imp_le_base
% 0.32/0.55  thf(fact_3018_power__gt1,axiom,
% 0.32/0.55      ! [A: real,N: nat] :
% 0.32/0.55        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.55       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_gt1
% 0.32/0.55  thf(fact_3019_power__gt1,axiom,
% 0.32/0.55      ! [A: rat,N: nat] :
% 0.32/0.55        ( ( ord_less_rat @ one_one_rat @ A )
% 0.32/0.55       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_gt1
% 0.32/0.55  thf(fact_3020_power__gt1,axiom,
% 0.32/0.55      ! [A: nat,N: nat] :
% 0.32/0.55        ( ( ord_less_nat @ one_one_nat @ A )
% 0.32/0.55       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_gt1
% 0.32/0.55  thf(fact_3021_power__gt1,axiom,
% 0.32/0.55      ! [A: int,N: nat] :
% 0.32/0.55        ( ( ord_less_int @ one_one_int @ A )
% 0.32/0.55       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_gt1
% 0.32/0.55  thf(fact_3022_numeral__1__eq__Suc__0,axiom,
% 0.32/0.55      ( ( numeral_numeral_nat @ one )
% 0.32/0.55      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.55  
% 0.32/0.55  % numeral_1_eq_Suc_0
% 0.32/0.55  thf(fact_3023_ex__least__nat__less,axiom,
% 0.32/0.55      ! [P: nat > $o,N: nat] :
% 0.32/0.55        ( ( P @ N )
% 0.32/0.55       => ( ~ ( P @ zero_zero_nat )
% 0.32/0.55         => ? [K3: nat] :
% 0.32/0.55              ( ( ord_less_nat @ K3 @ N )
% 0.32/0.55              & ! [I2: nat] :
% 0.32/0.55                  ( ( ord_less_eq_nat @ I2 @ K3 )
% 0.32/0.55                 => ~ ( P @ I2 ) )
% 0.32/0.55              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % ex_least_nat_less
% 0.32/0.55  thf(fact_3024_verit__la__disequality,axiom,
% 0.32/0.55      ! [A: rat,B: rat] :
% 0.32/0.55        ( ( A = B )
% 0.32/0.55        | ~ ( ord_less_eq_rat @ A @ B )
% 0.32/0.55        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_la_disequality
% 0.32/0.55  thf(fact_3025_verit__la__disequality,axiom,
% 0.32/0.55      ! [A: num,B: num] :
% 0.32/0.55        ( ( A = B )
% 0.32/0.55        | ~ ( ord_less_eq_num @ A @ B )
% 0.32/0.55        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_la_disequality
% 0.32/0.55  thf(fact_3026_verit__la__disequality,axiom,
% 0.32/0.55      ! [A: nat,B: nat] :
% 0.32/0.55        ( ( A = B )
% 0.32/0.55        | ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.55        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_la_disequality
% 0.32/0.55  thf(fact_3027_verit__la__disequality,axiom,
% 0.32/0.55      ! [A: int,B: int] :
% 0.32/0.55        ( ( A = B )
% 0.32/0.55        | ~ ( ord_less_eq_int @ A @ B )
% 0.32/0.55        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_la_disequality
% 0.32/0.55  thf(fact_3028_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.55      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(2)
% 0.32/0.55  thf(fact_3029_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.55      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(2)
% 0.32/0.55  thf(fact_3030_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.55      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(2)
% 0.32/0.55  thf(fact_3031_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.55      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(2)
% 0.32/0.55  thf(fact_3032_verit__comp__simplify1_I2_J,axiom,
% 0.32/0.55      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(2)
% 0.32/0.55  thf(fact_3033_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.55      ! [A: real] :
% 0.32/0.55        ~ ( ord_less_real @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(1)
% 0.32/0.55  thf(fact_3034_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.55      ! [A: rat] :
% 0.32/0.55        ~ ( ord_less_rat @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(1)
% 0.32/0.55  thf(fact_3035_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.55      ! [A: num] :
% 0.32/0.55        ~ ( ord_less_num @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(1)
% 0.32/0.55  thf(fact_3036_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.55      ! [A: nat] :
% 0.32/0.55        ~ ( ord_less_nat @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(1)
% 0.32/0.55  thf(fact_3037_verit__comp__simplify1_I1_J,axiom,
% 0.32/0.55      ! [A: int] :
% 0.32/0.55        ~ ( ord_less_int @ A @ A ) ).
% 0.32/0.55  
% 0.32/0.55  % verit_comp_simplify1(1)
% 0.32/0.55  thf(fact_3038_diff__Suc__less,axiom,
% 0.32/0.55      ! [N: nat,I: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 0.32/0.55  
% 0.32/0.55  % diff_Suc_less
% 0.32/0.55  thf(fact_3039_n__less__n__mult__m,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % n_less_n_mult_m
% 0.32/0.55  thf(fact_3040_n__less__m__mult__n,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % n_less_m_mult_n
% 0.32/0.55  thf(fact_3041_one__less__mult,axiom,
% 0.32/0.55      ! [N: nat,M: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.55       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.55         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % one_less_mult
% 0.32/0.55  thf(fact_3042_nat__induct__non__zero,axiom,
% 0.32/0.55      ! [N: nat,P: nat > $o] :
% 0.32/0.55        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.55       => ( ( P @ one_one_nat )
% 0.32/0.55         => ( ! [N3: nat] :
% 0.32/0.55                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.55               => ( ( P @ N3 )
% 0.32/0.55                 => ( P @ ( suc @ N3 ) ) ) )
% 0.32/0.55           => ( P @ N ) ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % nat_induct_non_zero
% 0.32/0.55  thf(fact_3043_power__gt__expt,axiom,
% 0.32/0.55      ! [N: nat,K: nat] :
% 0.32/0.55        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.55       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 0.32/0.55  
% 0.32/0.55  % power_gt_expt
% 0.32/0.55  thf(fact_3044_realpow__pos__nth2,axiom,
% 0.32/0.55      ! [A: real,N: nat] :
% 0.32/0.56        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.56       => ? [R2: real] :
% 0.32/0.56            ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.32/0.56            & ( ( power_power_real @ R2 @ ( suc @ N ) )
% 0.32/0.56              = A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % realpow_pos_nth2
% 0.32/0.56  thf(fact_3045_nat__one__le__power,axiom,
% 0.32/0.56      ! [I: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 0.32/0.56       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_one_le_power
% 0.32/0.56  thf(fact_3046_verit__la__generic,axiom,
% 0.32/0.56      ! [A: int,X: int] :
% 0.32/0.56        ( ( ord_less_eq_int @ A @ X )
% 0.32/0.56        | ( A = X )
% 0.32/0.56        | ( ord_less_eq_int @ X @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_la_generic
% 0.32/0.56  thf(fact_3047_power__Suc__le__self,axiom,
% 0.32/0.56      ! [A: real,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.56       => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.32/0.56         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_le_self
% 0.32/0.56  thf(fact_3048_power__Suc__le__self,axiom,
% 0.32/0.56      ! [A: rat,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.32/0.56         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_le_self
% 0.32/0.56  thf(fact_3049_power__Suc__le__self,axiom,
% 0.32/0.56      ! [A: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.32/0.56       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.32/0.56         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_le_self
% 0.32/0.56  thf(fact_3050_power__Suc__le__self,axiom,
% 0.32/0.56      ! [A: int,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.32/0.56         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_le_self
% 0.32/0.56  thf(fact_3051_power__Suc__less__one,axiom,
% 0.32/0.56      ! [A: real,N: nat] :
% 0.32/0.56        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.56       => ( ( ord_less_real @ A @ one_one_real )
% 0.32/0.56         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_less_one
% 0.32/0.56  thf(fact_3052_power__Suc__less__one,axiom,
% 0.32/0.56      ! [A: rat,N: nat] :
% 0.32/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.56       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.32/0.56         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_less_one
% 0.32/0.56  thf(fact_3053_power__Suc__less__one,axiom,
% 0.32/0.56      ! [A: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.32/0.56       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.32/0.56         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_less_one
% 0.32/0.56  thf(fact_3054_power__Suc__less__one,axiom,
% 0.32/0.56      ! [A: int,N: nat] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.56       => ( ( ord_less_int @ A @ one_one_int )
% 0.32/0.56         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_Suc_less_one
% 0.32/0.56  thf(fact_3055_numeral__2__eq__2,axiom,
% 0.32/0.56      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.32/0.56      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % numeral_2_eq_2
% 0.32/0.56  thf(fact_3056_double__not__eq__Suc__double,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.32/0.56       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % double_not_eq_Suc_double
% 0.32/0.56  thf(fact_3057_Suc__double__not__eq__double,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.32/0.56       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_double_not_eq_double
% 0.32/0.56  thf(fact_3058_div__if,axiom,
% 0.32/0.56      ( divide_divide_nat
% 0.32/0.56      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.56            ( if_nat
% 0.32/0.56            @ ( ( ord_less_nat @ M3 @ N2 )
% 0.32/0.56              | ( N2 = zero_zero_nat ) )
% 0.32/0.56            @ zero_zero_nat
% 0.32/0.56            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_if
% 0.32/0.56  thf(fact_3059_div__geq,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_geq
% 0.32/0.56  thf(fact_3060_Suc__diff__eq__diff__pred,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.32/0.56          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_diff_eq_diff_pred
% 0.32/0.56  thf(fact_3061_Suc__pred_H,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( N
% 0.32/0.56          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_pred'
% 0.32/0.56  thf(fact_3062_div__nat__eqI,axiom,
% 0.32/0.56      ! [N: nat,Q2: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 0.32/0.56       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = Q2 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_nat_eqI
% 0.32/0.56  thf(fact_3063_add__eq__if,axiom,
% 0.32/0.56      ( plus_plus_nat
% 0.32/0.56      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % add_eq_if
% 0.32/0.56  thf(fact_3064_Suc__nat__number__of__add,axiom,
% 0.32/0.56      ! [V: num,N: nat] :
% 0.32/0.56        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.32/0.56        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_nat_number_of_add
% 0.32/0.56  thf(fact_3065_set__bit__Suc,axiom,
% 0.32/0.56      ! [N: nat,A: code_integer] :
% 0.32/0.56        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 0.32/0.56        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % set_bit_Suc
% 0.32/0.56  thf(fact_3066_set__bit__Suc,axiom,
% 0.32/0.56      ! [N: nat,A: int] :
% 0.32/0.56        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 0.32/0.56        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % set_bit_Suc
% 0.32/0.56  thf(fact_3067_set__bit__Suc,axiom,
% 0.32/0.56      ! [N: nat,A: nat] :
% 0.32/0.56        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 0.32/0.56        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % set_bit_Suc
% 0.32/0.56  thf(fact_3068_num_Osize_I5_J,axiom,
% 0.32/0.56      ! [X22: num] :
% 0.32/0.56        ( ( size_size_num @ ( bit0 @ X22 ) )
% 0.32/0.56        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % num.size(5)
% 0.32/0.56  thf(fact_3069_less__2__cases__iff,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.56        = ( ( N = zero_zero_nat )
% 0.32/0.56          | ( N
% 0.32/0.56            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_2_cases_iff
% 0.32/0.56  thf(fact_3070_less__2__cases,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.56       => ( ( N = zero_zero_nat )
% 0.32/0.56          | ( N
% 0.32/0.56            = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % less_2_cases
% 0.32/0.56  thf(fact_3071_le__div__geq,axiom,
% 0.32/0.56      ! [N: nat,M: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.56         => ( ( divide_divide_nat @ M @ N )
% 0.32/0.56            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % le_div_geq
% 0.32/0.56  thf(fact_3072_split__div_H,axiom,
% 0.32/0.56      ! [P: nat > $o,M: nat,N: nat] :
% 0.32/0.56        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.56        = ( ( ( N = zero_zero_nat )
% 0.32/0.56            & ( P @ zero_zero_nat ) )
% 0.32/0.56          | ? [Q5: nat] :
% 0.32/0.56              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 0.32/0.56              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 0.32/0.56              & ( P @ Q5 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % split_div'
% 0.32/0.56  thf(fact_3073_Suc__times__mod__eq,axiom,
% 0.32/0.56      ! [M: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.32/0.56       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.32/0.56          = one_one_nat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_times_mod_eq
% 0.32/0.56  thf(fact_3074_power__odd__eq,axiom,
% 0.32/0.56      ! [A: complex,N: nat] :
% 0.32/0.56        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.56        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_odd_eq
% 0.32/0.56  thf(fact_3075_power__odd__eq,axiom,
% 0.32/0.56      ! [A: real,N: nat] :
% 0.32/0.56        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.56        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_odd_eq
% 0.32/0.56  thf(fact_3076_power__odd__eq,axiom,
% 0.32/0.56      ! [A: rat,N: nat] :
% 0.32/0.56        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.56        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_odd_eq
% 0.32/0.56  thf(fact_3077_power__odd__eq,axiom,
% 0.32/0.56      ! [A: nat,N: nat] :
% 0.32/0.56        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.56        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_odd_eq
% 0.32/0.56  thf(fact_3078_power__odd__eq,axiom,
% 0.32/0.56      ! [A: int,N: nat] :
% 0.32/0.56        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.56        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % power_odd_eq
% 0.32/0.56  thf(fact_3079_nat__bit__induct,axiom,
% 0.32/0.56      ! [P: nat > $o,N: nat] :
% 0.32/0.56        ( ( P @ zero_zero_nat )
% 0.32/0.56       => ( ! [N3: nat] :
% 0.32/0.56              ( ( P @ N3 )
% 0.32/0.56             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.56               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.32/0.56         => ( ! [N3: nat] :
% 0.32/0.56                ( ( P @ N3 )
% 0.32/0.56               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.32/0.56           => ( P @ N ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % nat_bit_induct
% 0.32/0.56  thf(fact_3080_Suc__n__div__2__gt__zero,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % Suc_n_div_2_gt_zero
% 0.32/0.56  thf(fact_3081_div__2__gt__zero,axiom,
% 0.32/0.56      ! [N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.56       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_2_gt_zero
% 0.32/0.56  thf(fact_3082_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.56      ! [B4: real,A4: real] :
% 0.32/0.56        ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 0.32/0.56        = ( ord_less_real @ A4 @ B4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_comp_simplify1(3)
% 0.32/0.56  thf(fact_3083_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.56      ! [B4: rat,A4: rat] :
% 0.32/0.56        ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 0.32/0.56        = ( ord_less_rat @ A4 @ B4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_comp_simplify1(3)
% 0.32/0.56  thf(fact_3084_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.56      ! [B4: num,A4: num] :
% 0.32/0.56        ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 0.32/0.56        = ( ord_less_num @ A4 @ B4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_comp_simplify1(3)
% 0.32/0.56  thf(fact_3085_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.56      ! [B4: nat,A4: nat] :
% 0.32/0.56        ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.32/0.56        = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_comp_simplify1(3)
% 0.32/0.56  thf(fact_3086_verit__comp__simplify1_I3_J,axiom,
% 0.32/0.56      ! [B4: int,A4: int] :
% 0.32/0.56        ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 0.32/0.56        = ( ord_less_int @ A4 @ B4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_comp_simplify1(3)
% 0.32/0.56  thf(fact_3087_verit__sum__simplify,axiom,
% 0.32/0.56      ! [A: complex] :
% 0.32/0.56        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_sum_simplify
% 0.32/0.56  thf(fact_3088_verit__sum__simplify,axiom,
% 0.32/0.56      ! [A: real] :
% 0.32/0.56        ( ( plus_plus_real @ A @ zero_zero_real )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_sum_simplify
% 0.32/0.56  thf(fact_3089_verit__sum__simplify,axiom,
% 0.32/0.56      ! [A: rat] :
% 0.32/0.56        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_sum_simplify
% 0.32/0.56  thf(fact_3090_verit__sum__simplify,axiom,
% 0.32/0.56      ! [A: nat] :
% 0.32/0.56        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_sum_simplify
% 0.32/0.56  thf(fact_3091_verit__sum__simplify,axiom,
% 0.32/0.56      ! [A: int] :
% 0.32/0.56        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.32/0.56        = A ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_sum_simplify
% 0.32/0.56  thf(fact_3092_verit__eq__simplify_I10_J,axiom,
% 0.32/0.56      ! [X22: num] :
% 0.32/0.56        ( one
% 0.32/0.56       != ( bit0 @ X22 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % verit_eq_simplify(10)
% 0.32/0.56  thf(fact_3093_odd__0__le__power__imp__0__le,axiom,
% 0.32/0.56      ! [A: real,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.56       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_0_le_power_imp_0_le
% 0.32/0.56  thf(fact_3094_odd__0__le__power__imp__0__le,axiom,
% 0.32/0.56      ! [A: rat,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.56       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_0_le_power_imp_0_le
% 0.32/0.56  thf(fact_3095_odd__0__le__power__imp__0__le,axiom,
% 0.32/0.56      ! [A: int,N: nat] :
% 0.32/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.56       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_0_le_power_imp_0_le
% 0.32/0.56  thf(fact_3096_odd__power__less__zero,axiom,
% 0.32/0.56      ! [A: real,N: nat] :
% 0.32/0.56        ( ( ord_less_real @ A @ zero_zero_real )
% 0.32/0.56       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_power_less_zero
% 0.32/0.56  thf(fact_3097_odd__power__less__zero,axiom,
% 0.32/0.56      ! [A: rat,N: nat] :
% 0.32/0.56        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.56       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_power_less_zero
% 0.32/0.56  thf(fact_3098_odd__power__less__zero,axiom,
% 0.32/0.56      ! [A: int,N: nat] :
% 0.32/0.56        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.56       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 0.32/0.56  
% 0.32/0.56  % odd_power_less_zero
% 0.32/0.56  thf(fact_3099_int__power__div__base,axiom,
% 0.32/0.56      ! [M: nat,K: int] :
% 0.32/0.56        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.56         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.32/0.56            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % int_power_div_base
% 0.32/0.56  thf(fact_3100_invar__vebt_Ointros_I3_J,axiom,
% 0.32/0.56      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.32/0.56        ( ! [X6: vEBT_VEBT] :
% 0.32/0.56            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.56           => ( vEBT_invar_vebt @ X6 @ N ) )
% 0.32/0.56       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.32/0.56         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.32/0.56              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.32/0.56           => ( ( M
% 0.32/0.56                = ( suc @ N ) )
% 0.32/0.56             => ( ( Deg
% 0.32/0.56                  = ( plus_plus_nat @ N @ M ) )
% 0.32/0.56               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.32/0.56                 => ( ! [X6: vEBT_VEBT] :
% 0.32/0.56                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.56                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 0.32/0.56                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % invar_vebt.intros(3)
% 0.32/0.56  thf(fact_3101_div__less__mono,axiom,
% 0.32/0.56      ! [A2: nat,B3: nat,N: nat] :
% 0.32/0.56        ( ( ord_less_nat @ A2 @ B3 )
% 0.32/0.56       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.56         => ( ( ( modulo_modulo_nat @ A2 @ N )
% 0.32/0.56              = zero_zero_nat )
% 0.32/0.56           => ( ( ( modulo_modulo_nat @ B3 @ N )
% 0.32/0.56                = zero_zero_nat )
% 0.32/0.56             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_less_mono
% 0.32/0.56  thf(fact_3102_div__mod__decomp,axiom,
% 0.32/0.56      ! [A2: nat,N: nat] :
% 0.32/0.56        ( A2
% 0.32/0.56        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mod_decomp
% 0.32/0.56  thf(fact_3103_zdiv__mono__strict,axiom,
% 0.32/0.56      ! [A2: int,B3: int,N: int] :
% 0.32/0.56        ( ( ord_less_int @ A2 @ B3 )
% 0.32/0.56       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.56         => ( ( ( modulo_modulo_int @ A2 @ N )
% 0.32/0.56              = zero_zero_int )
% 0.32/0.56           => ( ( ( modulo_modulo_int @ B3 @ N )
% 0.32/0.56                = zero_zero_int )
% 0.32/0.56             => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % zdiv_mono_strict
% 0.32/0.56  thf(fact_3104_div__mod__decomp__int,axiom,
% 0.32/0.56      ! [A2: int,N: int] :
% 0.32/0.56        ( A2
% 0.32/0.56        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % div_mod_decomp_int
% 0.32/0.56  thf(fact_3105_invar__vebt_Ointros_I5_J,axiom,
% 0.32/0.56      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.32/0.56        ( ! [X6: vEBT_VEBT] :
% 0.32/0.56            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.56           => ( vEBT_invar_vebt @ X6 @ N ) )
% 0.32/0.56       => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.32/0.56         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.32/0.56              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.32/0.56           => ( ( M
% 0.32/0.56                = ( suc @ N ) )
% 0.32/0.56             => ( ( Deg
% 0.32/0.56                  = ( plus_plus_nat @ N @ M ) )
% 0.32/0.56               => ( ! [I4: nat] :
% 0.32/0.56                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.32/0.56                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 0.32/0.56                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 0.32/0.56                 => ( ( ( Mi = Ma )
% 0.32/0.56                     => ! [X6: vEBT_VEBT] :
% 0.32/0.56                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.56                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 0.32/0.56                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.32/0.56                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.32/0.56                       => ( ( ( Mi != Ma )
% 0.32/0.56                           => ! [I4: nat] :
% 0.32/0.56                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.32/0.56                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.32/0.56                                      = I4 )
% 0.32/0.56                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.32/0.56                                  & ! [X6: nat] :
% 0.32/0.56                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 0.32/0.56                                          = I4 )
% 0.32/0.56                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 0.32/0.56                                     => ( ( ord_less_nat @ Mi @ X6 )
% 0.32/0.56                                        & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 0.32/0.56                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % invar_vebt.intros(5)
% 0.32/0.56  thf(fact_3106_vebt__delete_Osimps_I7_J,axiom,
% 0.32/0.56      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.32/0.56        ( ( ( ( ord_less_nat @ X @ Mi )
% 0.32/0.56            | ( ord_less_nat @ Ma @ X ) )
% 0.32/0.56         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 0.32/0.56        & ( ~ ( ( ord_less_nat @ X @ Mi )
% 0.32/0.56              | ( ord_less_nat @ Ma @ X ) )
% 0.32/0.56         => ( ( ( ( X = Mi )
% 0.32/0.56                & ( X = Ma ) )
% 0.32/0.56             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 0.32/0.56            & ( ~ ( ( X = Mi )
% 0.32/0.56                  & ( X = Ma ) )
% 0.32/0.56             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.56                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                    @ ( vEBT_Node
% 0.32/0.56                      @ ( some_P7363390416028606310at_nat
% 0.32/0.56                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.32/0.56                          @ ( if_nat
% 0.32/0.56                            @ ( ( ( X = Mi )
% 0.32/0.56                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.32/0.56                                  = Ma ) )
% 0.32/0.56                              & ( ( X != Mi )
% 0.32/0.56                               => ( X = Ma ) ) )
% 0.32/0.56                            @ ( if_nat
% 0.32/0.56                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                = none_nat )
% 0.32/0.56                              @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.32/0.56                              @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56                            @ Ma ) ) )
% 0.32/0.56                      @ ( suc @ ( suc @ Va ) )
% 0.32/0.56                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                    @ ( vEBT_Node
% 0.32/0.56                      @ ( some_P7363390416028606310at_nat
% 0.32/0.56                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.32/0.56                          @ ( if_nat
% 0.32/0.56                            @ ( ( ( X = Mi )
% 0.32/0.56                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.32/0.56                                  = Ma ) )
% 0.32/0.56                              & ( ( X != Mi )
% 0.32/0.56                               => ( X = Ma ) ) )
% 0.32/0.56                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                            @ Ma ) ) )
% 0.32/0.56                      @ ( suc @ ( suc @ Va ) )
% 0.32/0.56                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                      @ Summary ) )
% 0.32/0.56                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(7)
% 0.32/0.56  thf(fact_3107_vebt__pred_Osimps_I7_J,axiom,
% 0.32/0.56      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.32/0.56        ( ( ( ord_less_nat @ Ma @ X )
% 0.32/0.56         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56            = ( some_nat @ Ma ) ) )
% 0.32/0.56        & ( ~ ( ord_less_nat @ Ma @ X )
% 0.32/0.56         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.56              @ ( if_option_nat
% 0.32/0.56                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                   != none_nat )
% 0.32/0.56                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                @ ( if_option_nat
% 0.32/0.56                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.56                    = none_nat )
% 0.32/0.56                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.32/0.56                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56              @ none_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(7)
% 0.32/0.56  thf(fact_3108_vebt__succ_Osimps_I6_J,axiom,
% 0.32/0.56      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.32/0.56        ( ( ( ord_less_nat @ X @ Mi )
% 0.32/0.56         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56            = ( some_nat @ Mi ) ) )
% 0.32/0.56        & ( ~ ( ord_less_nat @ X @ Mi )
% 0.32/0.56         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.56              @ ( if_option_nat
% 0.32/0.56                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                   != none_nat )
% 0.32/0.56                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                @ ( if_option_nat
% 0.32/0.56                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.56                    = none_nat )
% 0.32/0.56                  @ none_nat
% 0.32/0.56                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56              @ none_nat ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(6)
% 0.32/0.56  thf(fact_3109_vebt__insert_Osimps_I5_J,axiom,
% 0.32/0.56      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56        = ( if_VEBT_VEBT
% 0.32/0.56          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.56            & ~ ( ( X = Mi )
% 0.32/0.56                | ( X = Ma ) ) )
% 0.32/0.56          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.32/0.56          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.simps(5)
% 0.32/0.56  thf(fact_3110_vebt__member_Osimps_I5_J,axiom,
% 0.32/0.56      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56        = ( ( X != Mi )
% 0.32/0.56         => ( ( X != Ma )
% 0.32/0.56           => ( ~ ( ord_less_nat @ X @ Mi )
% 0.32/0.56              & ( ~ ( ord_less_nat @ X @ Mi )
% 0.32/0.56               => ( ~ ( ord_less_nat @ Ma @ X )
% 0.32/0.56                  & ( ~ ( ord_less_nat @ Ma @ X )
% 0.32/0.56                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.56                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.simps(5)
% 0.32/0.56  thf(fact_3111_vebt__insert_Osimps_I4_J,axiom,
% 0.32/0.56      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 0.32/0.56        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.simps(4)
% 0.32/0.56  thf(fact_3112_vebt__pred_Osimps_I6_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.32/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(6)
% 0.32/0.56  thf(fact_3113_vebt__succ_Osimps_I5_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.32/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(5)
% 0.32/0.56  thf(fact_3114_vebt__delete_Osimps_I6_J,axiom,
% 0.32/0.56      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 0.32/0.56        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(6)
% 0.32/0.56  thf(fact_3115_vebt__insert_Osimps_I2_J,axiom,
% 0.32/0.56      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 0.32/0.56        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.simps(2)
% 0.32/0.56  thf(fact_3116_vebt__delete_Osimps_I4_J,axiom,
% 0.32/0.56      ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu )
% 0.32/0.56        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(4)
% 0.32/0.56  thf(fact_3117_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 0.32/0.56      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.32/0.56        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.simps(5)
% 0.32/0.56  thf(fact_3118_vebt__member_Osimps_I2_J,axiom,
% 0.32/0.56      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 0.32/0.56        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.simps(2)
% 0.32/0.56  thf(fact_3119_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 0.32/0.56      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.simps(4)
% 0.32/0.56  thf(fact_3120_is__pred__in__set__def,axiom,
% 0.32/0.56      ( vEBT_is_pred_in_set
% 0.32/0.56      = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 0.32/0.56            ( ( member_nat @ Y3 @ Xs2 )
% 0.32/0.56            & ( ord_less_nat @ Y3 @ X3 )
% 0.32/0.56            & ! [Z3: nat] :
% 0.32/0.56                ( ( member_nat @ Z3 @ Xs2 )
% 0.32/0.56               => ( ( ord_less_nat @ Z3 @ X3 )
% 0.32/0.56                 => ( ord_less_eq_nat @ Z3 @ Y3 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % is_pred_in_set_def
% 0.32/0.56  thf(fact_3121_is__succ__in__set__def,axiom,
% 0.32/0.56      ( vEBT_is_succ_in_set
% 0.32/0.56      = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 0.32/0.56            ( ( member_nat @ Y3 @ Xs2 )
% 0.32/0.56            & ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.56            & ! [Z3: nat] :
% 0.32/0.56                ( ( member_nat @ Z3 @ Xs2 )
% 0.32/0.56               => ( ( ord_less_nat @ X3 @ Z3 )
% 0.32/0.56                 => ( ord_less_eq_nat @ Y3 @ Z3 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % is_succ_in_set_def
% 0.32/0.56  thf(fact_3122_vebt__insert_Osimps_I3_J,axiom,
% 0.32/0.56      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 0.32/0.56        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.simps(3)
% 0.32/0.56  thf(fact_3123_vebt__member_Osimps_I3_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.32/0.56        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.simps(3)
% 0.32/0.56  thf(fact_3124_vebt__succ_Osimps_I3_J,axiom,
% 0.32/0.56      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 0.32/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(3)
% 0.32/0.56  thf(fact_3125_vebt__pred_Osimps_I4_J,axiom,
% 0.32/0.56      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 0.32/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(4)
% 0.32/0.56  thf(fact_3126_vebt__member_Osimps_I4_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.32/0.56        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.simps(4)
% 0.32/0.56  thf(fact_3127_vebt__delete_Osimps_I5_J,axiom,
% 0.32/0.56      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 0.32/0.56        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(5)
% 0.32/0.56  thf(fact_3128_vebt__succ_Osimps_I4_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.32/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(4)
% 0.32/0.56  thf(fact_3129_vebt__pred_Osimps_I5_J,axiom,
% 0.32/0.56      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.32/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(5)
% 0.32/0.56  thf(fact_3130_vebt__pred_Oelims,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.32/0.56        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.32/0.56          = Y )
% 0.32/0.56       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.32/0.56                ( X
% 0.32/0.56                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.56           => ( ( Xa2 = zero_zero_nat )
% 0.32/0.56             => ( Y != none_nat ) ) )
% 0.32/0.56         => ( ! [A5: $o] :
% 0.32/0.56                ( ? [Uw2: $o] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 0.32/0.56               => ( ( Xa2
% 0.32/0.56                    = ( suc @ zero_zero_nat ) )
% 0.32/0.56                 => ~ ( ( A5
% 0.32/0.56                       => ( Y
% 0.32/0.56                          = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.56                      & ( ~ A5
% 0.32/0.56                       => ( Y = none_nat ) ) ) ) )
% 0.32/0.56           => ( ! [A5: $o,B5: $o] :
% 0.32/0.56                  ( ( X
% 0.32/0.56                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56                 => ( ? [Va2: nat] :
% 0.32/0.56                        ( Xa2
% 0.32/0.56                        = ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.56                   => ~ ( ( B5
% 0.32/0.56                         => ( Y
% 0.32/0.56                            = ( some_nat @ one_one_nat ) ) )
% 0.32/0.56                        & ( ~ B5
% 0.32/0.56                         => ( ( A5
% 0.32/0.56                             => ( Y
% 0.32/0.56                                = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.56                            & ( ~ A5
% 0.32/0.56                             => ( Y = none_nat ) ) ) ) ) ) )
% 0.32/0.56             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.32/0.56                      ( X
% 0.32/0.56                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.32/0.56                 => ( Y != none_nat ) )
% 0.32/0.56               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.32/0.56                        ( X
% 0.32/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.32/0.56                   => ( Y != none_nat ) )
% 0.32/0.56                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.32/0.56                          ( X
% 0.32/0.56                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.32/0.56                     => ( Y != none_nat ) )
% 0.32/0.56                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.56                          ( ( X
% 0.32/0.56                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                               => ( Y
% 0.32/0.56                                  = ( some_nat @ Ma2 ) ) )
% 0.32/0.56                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                               => ( Y
% 0.32/0.56                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                    @ ( if_option_nat
% 0.32/0.56                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                         != none_nat )
% 0.32/0.56                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                      @ ( if_option_nat
% 0.32/0.56                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.56                                          = none_nat )
% 0.32/0.56                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.32/0.56                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.elims
% 0.32/0.56  thf(fact_3131_vebt__succ_Oelims,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.32/0.56        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.32/0.56          = Y )
% 0.32/0.56       => ( ! [Uu2: $o,B5: $o] :
% 0.32/0.56              ( ( X
% 0.32/0.56                = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 0.32/0.56             => ( ( Xa2 = zero_zero_nat )
% 0.32/0.56               => ~ ( ( B5
% 0.32/0.56                     => ( Y
% 0.32/0.56                        = ( some_nat @ one_one_nat ) ) )
% 0.32/0.56                    & ( ~ B5
% 0.32/0.56                     => ( Y = none_nat ) ) ) ) )
% 0.32/0.56         => ( ( ? [Uv2: $o,Uw2: $o] :
% 0.32/0.56                  ( X
% 0.32/0.56                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.32/0.56             => ( ? [N3: nat] :
% 0.32/0.56                    ( Xa2
% 0.32/0.56                    = ( suc @ N3 ) )
% 0.32/0.56               => ( Y != none_nat ) ) )
% 0.32/0.56           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.56               => ( Y != none_nat ) )
% 0.32/0.56             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.32/0.56                      ( X
% 0.32/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.32/0.56                 => ( Y != none_nat ) )
% 0.32/0.56               => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.32/0.56                        ( X
% 0.32/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.32/0.56                   => ( Y != none_nat ) )
% 0.32/0.56                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.56                        ( ( X
% 0.32/0.56                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                             => ( Y
% 0.32/0.56                                = ( some_nat @ Mi2 ) ) )
% 0.32/0.56                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                             => ( Y
% 0.32/0.56                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                  @ ( if_option_nat
% 0.32/0.56                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                       != none_nat )
% 0.32/0.56                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                                    @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                    @ ( if_option_nat
% 0.32/0.56                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.56                                        = none_nat )
% 0.32/0.56                                      @ none_nat
% 0.32/0.56                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.elims
% 0.32/0.56  thf(fact_3132_vebt__delete_Oelims,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.32/0.56        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.32/0.56          = Y )
% 0.32/0.56       => ( ! [A5: $o,B5: $o] :
% 0.32/0.56              ( ( X
% 0.32/0.56                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56             => ( ( Xa2 = zero_zero_nat )
% 0.32/0.56               => ( Y
% 0.32/0.56                 != ( vEBT_Leaf @ $false @ B5 ) ) ) )
% 0.32/0.56         => ( ! [A5: $o] :
% 0.32/0.56                ( ? [B5: $o] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56               => ( ( Xa2
% 0.32/0.56                    = ( suc @ zero_zero_nat ) )
% 0.32/0.56                 => ( Y
% 0.32/0.56                   != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 0.32/0.56           => ( ! [A5: $o,B5: $o] :
% 0.32/0.56                  ( ( X
% 0.32/0.56                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56                 => ( ? [N3: nat] :
% 0.32/0.56                        ( Xa2
% 0.32/0.56                        = ( suc @ ( suc @ N3 ) ) )
% 0.32/0.56                   => ( Y
% 0.32/0.56                     != ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 0.32/0.56             => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.56                    ( ( X
% 0.32/0.56                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.56                   => ( Y
% 0.32/0.56                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 0.32/0.56               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.32/0.56                      ( ( X
% 0.32/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.32/0.56                     => ( Y
% 0.32/0.56                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 0.32/0.56                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.32/0.56                        ( ( X
% 0.32/0.56                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.32/0.56                       => ( Y
% 0.32/0.56                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 0.32/0.56                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.56                          ( ( X
% 0.32/0.56                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56                         => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.32/0.56                               => ( Y
% 0.32/0.56                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.56                              & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.32/0.56                               => ( ( ( ( Xa2 = Mi2 )
% 0.32/0.56                                      & ( Xa2 = Ma2 ) )
% 0.32/0.56                                   => ( Y
% 0.32/0.56                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.56                                  & ( ~ ( ( Xa2 = Mi2 )
% 0.32/0.56                                        & ( Xa2 = Ma2 ) )
% 0.32/0.56                                   => ( Y
% 0.32/0.56                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                          @ ( vEBT_Node
% 0.32/0.56                                            @ ( some_P7363390416028606310at_nat
% 0.32/0.56                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.56                                                @ ( if_nat
% 0.32/0.56                                                  @ ( ( ( Xa2 = Mi2 )
% 0.32/0.56                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.32/0.56                                                        = Ma2 ) )
% 0.32/0.56                                                    & ( ( Xa2 != Mi2 )
% 0.32/0.56                                                     => ( Xa2 = Ma2 ) ) )
% 0.32/0.56                                                  @ ( if_nat
% 0.32/0.56                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                                      = none_nat )
% 0.32/0.56                                                    @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.56                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.56                                                  @ Ma2 ) ) )
% 0.32/0.56                                            @ ( suc @ ( suc @ Va2 ) )
% 0.32/0.56                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                          @ ( vEBT_Node
% 0.32/0.56                                            @ ( some_P7363390416028606310at_nat
% 0.32/0.56                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.56                                                @ ( if_nat
% 0.32/0.56                                                  @ ( ( ( Xa2 = Mi2 )
% 0.32/0.56                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.32/0.56                                                        = Ma2 ) )
% 0.32/0.56                                                    & ( ( Xa2 != Mi2 )
% 0.32/0.56                                                     => ( Xa2 = Ma2 ) ) )
% 0.32/0.56                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.56                                                  @ Ma2 ) ) )
% 0.32/0.56                                            @ ( suc @ ( suc @ Va2 ) )
% 0.32/0.56                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                            @ Summary2 ) )
% 0.32/0.56                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.elims
% 0.32/0.56  thf(fact_3133_cppi,axiom,
% 0.32/0.56      ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56             => ( ( P @ X6 )
% 0.32/0.56                = ( P6 @ X6 ) ) )
% 0.32/0.56         => ( ! [X6: int] :
% 0.32/0.56                ( ! [Xa: int] :
% 0.32/0.56                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                   => ! [Xb: int] :
% 0.32/0.56                        ( ( member_int @ Xb @ A2 )
% 0.32/0.56                       => ( X6
% 0.32/0.56                         != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56               => ( ( P @ X6 )
% 0.32/0.56                 => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56           => ( ! [X6: int,K3: int] :
% 0.32/0.56                  ( ( P6 @ X6 )
% 0.32/0.56                  = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56             => ( ( ? [X2: int] : ( P @ X2 ) )
% 0.32/0.56                = ( ? [X3: int] :
% 0.32/0.56                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                      & ( P6 @ X3 ) )
% 0.32/0.56                  | ? [X3: int] :
% 0.32/0.56                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                      & ? [Y3: int] :
% 0.32/0.56                          ( ( member_int @ Y3 @ A2 )
% 0.32/0.56                          & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % cppi
% 0.32/0.56  thf(fact_3134_cpmi,axiom,
% 0.32/0.56      ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56             => ( ( P @ X6 )
% 0.32/0.56                = ( P6 @ X6 ) ) )
% 0.32/0.56         => ( ! [X6: int] :
% 0.32/0.56                ( ! [Xa: int] :
% 0.32/0.56                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                   => ! [Xb: int] :
% 0.32/0.56                        ( ( member_int @ Xb @ B3 )
% 0.32/0.56                       => ( X6
% 0.32/0.56                         != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56               => ( ( P @ X6 )
% 0.32/0.56                 => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56           => ( ! [X6: int,K3: int] :
% 0.32/0.56                  ( ( P6 @ X6 )
% 0.32/0.56                  = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56             => ( ( ? [X2: int] : ( P @ X2 ) )
% 0.32/0.56                = ( ? [X3: int] :
% 0.32/0.56                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                      & ( P6 @ X3 ) )
% 0.32/0.56                  | ? [X3: int] :
% 0.32/0.56                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                      & ? [Y3: int] :
% 0.32/0.56                          ( ( member_int @ Y3 @ B3 )
% 0.32/0.56                          & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % cpmi
% 0.32/0.56  thf(fact_3135_bset_I6_J,axiom,
% 0.32/0.56      ! [D4: int,B3: set_int,T: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ! [X4: int] :
% 0.32/0.56            ( ! [Xa3: int] :
% 0.32/0.56                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb2: int] :
% 0.32/0.56                    ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                   => ( X4
% 0.32/0.56                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56           => ( ( ord_less_eq_int @ X4 @ T )
% 0.32/0.56             => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(6)
% 0.32/0.56  thf(fact_3136_bset_I8_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,B3: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ord_less_eq_int @ T @ X4 )
% 0.32/0.56               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(8)
% 0.32/0.56  thf(fact_3137_Leaf__0__not,axiom,
% 0.32/0.56      ! [A: $o,B: $o] :
% 0.32/0.56        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % Leaf_0_not
% 0.32/0.56  thf(fact_3138_deg__1__Leafy,axiom,
% 0.32/0.56      ! [T: vEBT_VEBT,N: nat] :
% 0.32/0.56        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.56       => ( ( N = one_one_nat )
% 0.32/0.56         => ? [A5: $o,B5: $o] :
% 0.32/0.56              ( T
% 0.32/0.56              = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % deg_1_Leafy
% 0.32/0.56  thf(fact_3139_deg__1__Leaf,axiom,
% 0.32/0.56      ! [T: vEBT_VEBT] :
% 0.32/0.56        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.32/0.56       => ? [A5: $o,B5: $o] :
% 0.32/0.56            ( T
% 0.32/0.56            = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % deg_1_Leaf
% 0.32/0.56  thf(fact_3140_deg1Leaf,axiom,
% 0.32/0.56      ! [T: vEBT_VEBT] :
% 0.32/0.56        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.32/0.56        = ( ? [A3: $o,B2: $o] :
% 0.32/0.56              ( T
% 0.32/0.56              = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % deg1Leaf
% 0.32/0.56  thf(fact_3141_VEBT_Osize_I4_J,axiom,
% 0.32/0.56      ! [X21: $o,X222: $o] :
% 0.32/0.56        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.32/0.56        = zero_zero_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT.size(4)
% 0.32/0.56  thf(fact_3142_VEBT_Oexhaust,axiom,
% 0.32/0.56      ! [Y: vEBT_VEBT] :
% 0.32/0.56        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 0.32/0.56            ( Y
% 0.32/0.56           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 0.32/0.56       => ~ ! [X212: $o,X223: $o] :
% 0.32/0.56              ( Y
% 0.32/0.56             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT.exhaust
% 0.32/0.56  thf(fact_3143_VEBT_Odistinct_I1_J,axiom,
% 0.32/0.56      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 0.32/0.56        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.32/0.56       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT.distinct(1)
% 0.32/0.56  thf(fact_3144_VEBT__internal_Ovalid_H_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 0.32/0.56       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.valid'.cases
% 0.32/0.56  thf(fact_3145_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 0.32/0.56      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.simps(1)
% 0.32/0.56  thf(fact_3146_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 0.32/0.56      ! [Uv: $o] :
% 0.32/0.56        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.simps(2)
% 0.32/0.56  thf(fact_3147_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 0.32/0.56      ! [Uu: $o] :
% 0.32/0.56        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.simps(3)
% 0.32/0.56  thf(fact_3148_vebt__delete_Osimps_I3_J,axiom,
% 0.32/0.56      ! [A: $o,B: $o,N: nat] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.32/0.56        = ( vEBT_Leaf @ A @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(3)
% 0.32/0.56  thf(fact_3149_vebt__delete_Osimps_I1_J,axiom,
% 0.32/0.56      ! [A: $o,B: $o] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.32/0.56        = ( vEBT_Leaf @ $false @ B ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(1)
% 0.32/0.56  thf(fact_3150_vebt__buildup_Osimps_I1_J,axiom,
% 0.32/0.56      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.32/0.56      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_buildup.simps(1)
% 0.32/0.56  thf(fact_3151_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [A5: $o,B5: $o,X6: nat] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 0.32/0.56       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 0.32/0.56         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X6 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.naive_member.cases
% 0.32/0.56  thf(fact_3152_invar__vebt_Ointros_I1_J,axiom,
% 0.32/0.56      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.32/0.56  
% 0.32/0.56  % invar_vebt.intros(1)
% 0.32/0.56  thf(fact_3153_vebt__delete_Osimps_I2_J,axiom,
% 0.32/0.56      ! [A: $o,B: $o] :
% 0.32/0.56        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.56        = ( vEBT_Leaf @ A @ $false ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.simps(2)
% 0.32/0.56  thf(fact_3154_VEBT__internal_OminNull_Ocases,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT] :
% 0.32/0.56        ( ( X
% 0.32/0.56         != ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.56       => ( ! [Uv2: $o] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.32/0.56         => ( ! [Uu2: $o] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.32/0.56           => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.32/0.56             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.cases
% 0.32/0.56  thf(fact_3155_vebt__member_Osimps_I1_J,axiom,
% 0.32/0.56      ! [A: $o,B: $o,X: nat] :
% 0.32/0.56        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.32/0.56        = ( ( ( X = zero_zero_nat )
% 0.32/0.56           => A )
% 0.32/0.56          & ( ( X != zero_zero_nat )
% 0.32/0.56           => ( ( ( X = one_one_nat )
% 0.32/0.56               => B )
% 0.32/0.56              & ( X = one_one_nat ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.simps(1)
% 0.32/0.56  thf(fact_3156_vebt__buildup_Osimps_I2_J,axiom,
% 0.32/0.56      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.32/0.56      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_buildup.simps(2)
% 0.32/0.56  thf(fact_3157_vebt__insert_Osimps_I1_J,axiom,
% 0.32/0.56      ! [X: nat,A: $o,B: $o] :
% 0.32/0.56        ( ( ( X = zero_zero_nat )
% 0.32/0.56         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.32/0.56            = ( vEBT_Leaf @ $true @ B ) ) )
% 0.32/0.56        & ( ( X != zero_zero_nat )
% 0.32/0.56         => ( ( ( X = one_one_nat )
% 0.32/0.56             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.32/0.56                = ( vEBT_Leaf @ A @ $true ) ) )
% 0.32/0.56            & ( ( X != one_one_nat )
% 0.32/0.56             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.32/0.56                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.simps(1)
% 0.32/0.56  thf(fact_3158_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT] :
% 0.32/0.56        ( ~ ( vEBT_VEBT_minNull @ X )
% 0.32/0.56       => ( ! [Uv2: $o] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.32/0.56         => ( ! [Uu2: $o] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.32/0.56           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.elims(3)
% 0.32/0.56  thf(fact_3159_pinf_I1_J,axiom,
% 0.32/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.32/0.56        ( ? [Z4: real] :
% 0.32/0.56          ! [X6: real] :
% 0.32/0.56            ( ( ord_less_real @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: real] :
% 0.32/0.56            ! [X6: real] :
% 0.32/0.56              ( ( ord_less_real @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: real] :
% 0.32/0.56            ! [X4: real] :
% 0.32/0.56              ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(1)
% 0.32/0.56  thf(fact_3160_pinf_I1_J,axiom,
% 0.32/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.32/0.56        ( ? [Z4: rat] :
% 0.32/0.56          ! [X6: rat] :
% 0.32/0.56            ( ( ord_less_rat @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: rat] :
% 0.32/0.56            ! [X6: rat] :
% 0.32/0.56              ( ( ord_less_rat @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: rat] :
% 0.32/0.56            ! [X4: rat] :
% 0.32/0.56              ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(1)
% 0.32/0.56  thf(fact_3161_pinf_I1_J,axiom,
% 0.32/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.32/0.56        ( ? [Z4: num] :
% 0.32/0.56          ! [X6: num] :
% 0.32/0.56            ( ( ord_less_num @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: num] :
% 0.32/0.56            ! [X6: num] :
% 0.32/0.56              ( ( ord_less_num @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: num] :
% 0.32/0.56            ! [X4: num] :
% 0.32/0.56              ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(1)
% 0.32/0.56  thf(fact_3162_pinf_I1_J,axiom,
% 0.32/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.32/0.56        ( ? [Z4: nat] :
% 0.32/0.56          ! [X6: nat] :
% 0.32/0.56            ( ( ord_less_nat @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: nat] :
% 0.32/0.56            ! [X6: nat] :
% 0.32/0.56              ( ( ord_less_nat @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: nat] :
% 0.32/0.56            ! [X4: nat] :
% 0.32/0.56              ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(1)
% 0.32/0.56  thf(fact_3163_pinf_I1_J,axiom,
% 0.32/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.32/0.56        ( ? [Z4: int] :
% 0.32/0.56          ! [X6: int] :
% 0.32/0.56            ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: int] :
% 0.32/0.56            ! [X4: int] :
% 0.32/0.56              ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(1)
% 0.32/0.56  thf(fact_3164_pinf_I2_J,axiom,
% 0.32/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.32/0.56        ( ? [Z4: real] :
% 0.32/0.56          ! [X6: real] :
% 0.32/0.56            ( ( ord_less_real @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: real] :
% 0.32/0.56            ! [X6: real] :
% 0.32/0.56              ( ( ord_less_real @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: real] :
% 0.32/0.56            ! [X4: real] :
% 0.32/0.56              ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(2)
% 0.32/0.56  thf(fact_3165_pinf_I2_J,axiom,
% 0.32/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.32/0.56        ( ? [Z4: rat] :
% 0.32/0.56          ! [X6: rat] :
% 0.32/0.56            ( ( ord_less_rat @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: rat] :
% 0.32/0.56            ! [X6: rat] :
% 0.32/0.56              ( ( ord_less_rat @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: rat] :
% 0.32/0.56            ! [X4: rat] :
% 0.32/0.56              ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(2)
% 0.32/0.56  thf(fact_3166_pinf_I2_J,axiom,
% 0.32/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.32/0.56        ( ? [Z4: num] :
% 0.32/0.56          ! [X6: num] :
% 0.32/0.56            ( ( ord_less_num @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: num] :
% 0.32/0.56            ! [X6: num] :
% 0.32/0.56              ( ( ord_less_num @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: num] :
% 0.32/0.56            ! [X4: num] :
% 0.32/0.56              ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(2)
% 0.32/0.56  thf(fact_3167_pinf_I2_J,axiom,
% 0.32/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.32/0.56        ( ? [Z4: nat] :
% 0.32/0.56          ! [X6: nat] :
% 0.32/0.56            ( ( ord_less_nat @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: nat] :
% 0.32/0.56            ! [X6: nat] :
% 0.32/0.56              ( ( ord_less_nat @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: nat] :
% 0.32/0.56            ! [X4: nat] :
% 0.32/0.56              ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(2)
% 0.32/0.56  thf(fact_3168_pinf_I2_J,axiom,
% 0.32/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.32/0.56        ( ? [Z4: int] :
% 0.32/0.56          ! [X6: int] :
% 0.32/0.56            ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: int] :
% 0.32/0.56            ! [X4: int] :
% 0.32/0.56              ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(2)
% 0.32/0.56  thf(fact_3169_pinf_I3_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(3)
% 0.32/0.56  thf(fact_3170_pinf_I3_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(3)
% 0.32/0.56  thf(fact_3171_pinf_I3_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(3)
% 0.32/0.56  thf(fact_3172_pinf_I3_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(3)
% 0.32/0.56  thf(fact_3173_pinf_I3_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(3)
% 0.32/0.56  thf(fact_3174_pinf_I4_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(4)
% 0.32/0.56  thf(fact_3175_pinf_I4_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(4)
% 0.32/0.56  thf(fact_3176_pinf_I4_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(4)
% 0.32/0.56  thf(fact_3177_pinf_I4_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(4)
% 0.32/0.56  thf(fact_3178_pinf_I4_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(4)
% 0.32/0.56  thf(fact_3179_pinf_I5_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_real @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(5)
% 0.32/0.56  thf(fact_3180_pinf_I5_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(5)
% 0.32/0.56  thf(fact_3181_pinf_I5_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_num @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(5)
% 0.32/0.56  thf(fact_3182_pinf_I5_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(5)
% 0.32/0.56  thf(fact_3183_pinf_I5_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_int @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(5)
% 0.32/0.56  thf(fact_3184_pinf_I7_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_real @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(7)
% 0.32/0.56  thf(fact_3185_pinf_I7_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_rat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(7)
% 0.32/0.56  thf(fact_3186_pinf_I7_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_num @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(7)
% 0.32/0.56  thf(fact_3187_pinf_I7_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_nat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(7)
% 0.32/0.56  thf(fact_3188_pinf_I7_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_int @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(7)
% 0.32/0.56  thf(fact_3189_minf_I1_J,axiom,
% 0.32/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.32/0.56        ( ? [Z4: real] :
% 0.32/0.56          ! [X6: real] :
% 0.32/0.56            ( ( ord_less_real @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: real] :
% 0.32/0.56            ! [X6: real] :
% 0.32/0.56              ( ( ord_less_real @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: real] :
% 0.32/0.56            ! [X4: real] :
% 0.32/0.56              ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(1)
% 0.32/0.56  thf(fact_3190_minf_I1_J,axiom,
% 0.32/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.32/0.56        ( ? [Z4: rat] :
% 0.32/0.56          ! [X6: rat] :
% 0.32/0.56            ( ( ord_less_rat @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: rat] :
% 0.32/0.56            ! [X6: rat] :
% 0.32/0.56              ( ( ord_less_rat @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: rat] :
% 0.32/0.56            ! [X4: rat] :
% 0.32/0.56              ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(1)
% 0.32/0.56  thf(fact_3191_minf_I1_J,axiom,
% 0.32/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.32/0.56        ( ? [Z4: num] :
% 0.32/0.56          ! [X6: num] :
% 0.32/0.56            ( ( ord_less_num @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: num] :
% 0.32/0.56            ! [X6: num] :
% 0.32/0.56              ( ( ord_less_num @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: num] :
% 0.32/0.56            ! [X4: num] :
% 0.32/0.56              ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(1)
% 0.32/0.56  thf(fact_3192_minf_I1_J,axiom,
% 0.32/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.32/0.56        ( ? [Z4: nat] :
% 0.32/0.56          ! [X6: nat] :
% 0.32/0.56            ( ( ord_less_nat @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: nat] :
% 0.32/0.56            ! [X6: nat] :
% 0.32/0.56              ( ( ord_less_nat @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: nat] :
% 0.32/0.56            ! [X4: nat] :
% 0.32/0.56              ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(1)
% 0.32/0.56  thf(fact_3193_minf_I1_J,axiom,
% 0.32/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.32/0.56        ( ? [Z4: int] :
% 0.32/0.56          ! [X6: int] :
% 0.32/0.56            ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: int] :
% 0.32/0.56            ! [X4: int] :
% 0.32/0.56              ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(1)
% 0.32/0.56  thf(fact_3194_minf_I2_J,axiom,
% 0.32/0.56      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 0.32/0.56        ( ? [Z4: real] :
% 0.32/0.56          ! [X6: real] :
% 0.32/0.56            ( ( ord_less_real @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: real] :
% 0.32/0.56            ! [X6: real] :
% 0.32/0.56              ( ( ord_less_real @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: real] :
% 0.32/0.56            ! [X4: real] :
% 0.32/0.56              ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(2)
% 0.32/0.56  thf(fact_3195_minf_I2_J,axiom,
% 0.32/0.56      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 0.32/0.56        ( ? [Z4: rat] :
% 0.32/0.56          ! [X6: rat] :
% 0.32/0.56            ( ( ord_less_rat @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: rat] :
% 0.32/0.56            ! [X6: rat] :
% 0.32/0.56              ( ( ord_less_rat @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: rat] :
% 0.32/0.56            ! [X4: rat] :
% 0.32/0.56              ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(2)
% 0.32/0.56  thf(fact_3196_minf_I2_J,axiom,
% 0.32/0.56      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 0.32/0.56        ( ? [Z4: num] :
% 0.32/0.56          ! [X6: num] :
% 0.32/0.56            ( ( ord_less_num @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: num] :
% 0.32/0.56            ! [X6: num] :
% 0.32/0.56              ( ( ord_less_num @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: num] :
% 0.32/0.56            ! [X4: num] :
% 0.32/0.56              ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(2)
% 0.32/0.56  thf(fact_3197_minf_I2_J,axiom,
% 0.32/0.56      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 0.32/0.56        ( ? [Z4: nat] :
% 0.32/0.56          ! [X6: nat] :
% 0.32/0.56            ( ( ord_less_nat @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: nat] :
% 0.32/0.56            ! [X6: nat] :
% 0.32/0.56              ( ( ord_less_nat @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: nat] :
% 0.32/0.56            ! [X4: nat] :
% 0.32/0.56              ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(2)
% 0.32/0.56  thf(fact_3198_minf_I2_J,axiom,
% 0.32/0.56      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 0.32/0.56        ( ? [Z4: int] :
% 0.32/0.56          ! [X6: int] :
% 0.32/0.56            ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56              = ( P6 @ X6 ) ) )
% 0.32/0.56       => ( ? [Z4: int] :
% 0.32/0.56            ! [X6: int] :
% 0.32/0.56              ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56                = ( Q6 @ X6 ) ) )
% 0.32/0.56         => ? [Z5: int] :
% 0.32/0.56            ! [X4: int] :
% 0.32/0.56              ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56                = ( ( P6 @ X4 )
% 0.32/0.56                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(2)
% 0.32/0.56  thf(fact_3199_minf_I3_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(3)
% 0.32/0.56  thf(fact_3200_minf_I3_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(3)
% 0.32/0.56  thf(fact_3201_minf_I3_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(3)
% 0.32/0.56  thf(fact_3202_minf_I3_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(3)
% 0.32/0.56  thf(fact_3203_minf_I3_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(3)
% 0.32/0.56  thf(fact_3204_minf_I4_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(4)
% 0.32/0.56  thf(fact_3205_minf_I4_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(4)
% 0.32/0.56  thf(fact_3206_minf_I4_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(4)
% 0.32/0.56  thf(fact_3207_minf_I4_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(4)
% 0.32/0.56  thf(fact_3208_minf_I4_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ( X4 != T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(4)
% 0.32/0.56  thf(fact_3209_minf_I5_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_real @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(5)
% 0.32/0.56  thf(fact_3210_minf_I5_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_rat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(5)
% 0.32/0.56  thf(fact_3211_minf_I5_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_num @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(5)
% 0.32/0.56  thf(fact_3212_minf_I5_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_nat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(5)
% 0.32/0.56  thf(fact_3213_minf_I5_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_int @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(5)
% 0.32/0.56  thf(fact_3214_minf_I7_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_real @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(7)
% 0.32/0.56  thf(fact_3215_minf_I7_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(7)
% 0.32/0.56  thf(fact_3216_minf_I7_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_num @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(7)
% 0.32/0.56  thf(fact_3217_minf_I7_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(7)
% 0.32/0.56  thf(fact_3218_minf_I7_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_int @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(7)
% 0.32/0.56  thf(fact_3219_vebt__succ_Osimps_I2_J,axiom,
% 0.32/0.56      ! [Uv: $o,Uw: $o,N: nat] :
% 0.32/0.56        ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(2)
% 0.32/0.56  thf(fact_3220_vebt__pred_Osimps_I1_J,axiom,
% 0.32/0.56      ! [Uu: $o,Uv: $o] :
% 0.32/0.56        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 0.32/0.56        = none_nat ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(1)
% 0.32/0.56  thf(fact_3221_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT] :
% 0.32/0.56        ( ( vEBT_VEBT_minNull @ X )
% 0.32/0.56       => ( ( X
% 0.32/0.56           != ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.56         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.elims(2)
% 0.32/0.56  thf(fact_3222_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Y: $o] :
% 0.32/0.56        ( ( ( vEBT_VEBT_minNull @ X )
% 0.32/0.56          = Y )
% 0.32/0.56       => ( ( ( X
% 0.32/0.56              = ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.56           => ~ Y )
% 0.32/0.56         => ( ( ? [Uv2: $o] :
% 0.32/0.56                  ( X
% 0.32/0.56                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.32/0.56             => Y )
% 0.32/0.56           => ( ( ? [Uu2: $o] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.32/0.56               => Y )
% 0.32/0.56             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.56                      ( X
% 0.32/0.56                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.32/0.56                 => ~ Y )
% 0.32/0.56               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.56                        ( X
% 0.32/0.56                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.32/0.56                   => Y ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.minNull.elims(1)
% 0.32/0.56  thf(fact_3223_vebt__pred_Osimps_I2_J,axiom,
% 0.32/0.56      ! [A: $o,Uw: $o] :
% 0.32/0.56        ( ( A
% 0.32/0.56         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.56            = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.56        & ( ~ A
% 0.32/0.56         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.56            = none_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(2)
% 0.32/0.56  thf(fact_3224_vebt__succ_Osimps_I1_J,axiom,
% 0.32/0.56      ! [B: $o,Uu: $o] :
% 0.32/0.56        ( ( B
% 0.32/0.56         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.32/0.56            = ( some_nat @ one_one_nat ) ) )
% 0.32/0.56        & ( ~ B
% 0.32/0.56         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.32/0.56            = none_nat ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.simps(1)
% 0.32/0.56  thf(fact_3225_VEBT__internal_Omembermima_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 0.32/0.56       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 0.32/0.56         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X6 ) )
% 0.32/0.56           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X6 ) )
% 0.32/0.56             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X6 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % VEBT_internal.membermima.cases
% 0.32/0.56  thf(fact_3226_vebt__pred_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 0.32/0.56       => ( ! [A5: $o,Uw2: $o] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 0.32/0.56         => ( ! [A5: $o,B5: $o,Va2: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 0.32/0.56           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 0.32/0.56             => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 0.32/0.56               => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.32/0.56                      ( X
% 0.32/0.56                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 0.32/0.56                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                        ( X
% 0.32/0.56                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.cases
% 0.32/0.56  thf(fact_3227_vebt__succ_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [Uu2: $o,B5: $o] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 0.32/0.56       => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 0.32/0.56         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 0.32/0.56           => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 0.32/0.56             => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 0.32/0.56               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                      ( X
% 0.32/0.56                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_succ.cases
% 0.32/0.56  thf(fact_3228_vebt__delete_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [A5: $o,B5: $o] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) )
% 0.32/0.56       => ( ! [A5: $o,B5: $o] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) )
% 0.32/0.56         => ( ! [A5: $o,B5: $o,N3: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 0.32/0.56           => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu2 ) )
% 0.32/0.56             => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X6 ) )
% 0.32/0.56               => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                      ( X
% 0.32/0.56                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X6 ) )
% 0.32/0.56                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                        ( X
% 0.32/0.56                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_delete.cases
% 0.32/0.56  thf(fact_3229_vebt__insert_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [A5: $o,B5: $o,X6: nat] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 0.32/0.56       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X6 ) )
% 0.32/0.56         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X6 ) )
% 0.32/0.56           => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) )
% 0.32/0.56             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_insert.cases
% 0.32/0.56  thf(fact_3230_vebt__member_Ocases,axiom,
% 0.32/0.56      ! [X: produc9072475918466114483BT_nat] :
% 0.32/0.56        ( ! [A5: $o,B5: $o,X6: nat] :
% 0.32/0.56            ( X
% 0.32/0.56           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 0.32/0.56       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X6: nat] :
% 0.32/0.56              ( X
% 0.32/0.56             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X6 ) )
% 0.32/0.56         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X6 ) )
% 0.32/0.56           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X6 ) )
% 0.32/0.56             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.cases
% 0.32/0.56  thf(fact_3231_vebt__pred_Osimps_I3_J,axiom,
% 0.32/0.56      ! [B: $o,A: $o,Va: nat] :
% 0.32/0.56        ( ( B
% 0.32/0.56         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.56            = ( some_nat @ one_one_nat ) ) )
% 0.32/0.56        & ( ~ B
% 0.32/0.56         => ( ( A
% 0.32/0.56             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.56                = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.56            & ( ~ A
% 0.32/0.56             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.56                = none_nat ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_pred.simps(3)
% 0.32/0.56  thf(fact_3232_pinf_I6_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(6)
% 0.32/0.56  thf(fact_3233_pinf_I6_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(6)
% 0.32/0.56  thf(fact_3234_pinf_I6_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(6)
% 0.32/0.56  thf(fact_3235_pinf_I6_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(6)
% 0.32/0.56  thf(fact_3236_pinf_I6_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(6)
% 0.32/0.56  thf(fact_3237_pinf_I8_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_eq_real @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(8)
% 0.32/0.56  thf(fact_3238_pinf_I8_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(8)
% 0.32/0.56  thf(fact_3239_pinf_I8_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_eq_num @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(8)
% 0.32/0.56  thf(fact_3240_pinf_I8_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(8)
% 0.32/0.56  thf(fact_3241_pinf_I8_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.56       => ( ord_less_eq_int @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % pinf(8)
% 0.32/0.56  thf(fact_3242_minf_I6_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_eq_real @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(6)
% 0.32/0.56  thf(fact_3243_minf_I6_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(6)
% 0.32/0.56  thf(fact_3244_minf_I6_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_eq_num @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(6)
% 0.32/0.56  thf(fact_3245_minf_I6_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(6)
% 0.32/0.56  thf(fact_3246_minf_I6_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ( ord_less_eq_int @ X4 @ T ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(6)
% 0.32/0.56  thf(fact_3247_minf_I8_J,axiom,
% 0.32/0.56      ! [T: real] :
% 0.32/0.56      ? [Z5: real] :
% 0.32/0.56      ! [X4: real] :
% 0.32/0.56        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(8)
% 0.32/0.56  thf(fact_3248_minf_I8_J,axiom,
% 0.32/0.56      ! [T: rat] :
% 0.32/0.56      ? [Z5: rat] :
% 0.32/0.56      ! [X4: rat] :
% 0.32/0.56        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(8)
% 0.32/0.56  thf(fact_3249_minf_I8_J,axiom,
% 0.32/0.56      ! [T: num] :
% 0.32/0.56      ? [Z5: num] :
% 0.32/0.56      ! [X4: num] :
% 0.32/0.56        ( ( ord_less_num @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(8)
% 0.32/0.56  thf(fact_3250_minf_I8_J,axiom,
% 0.32/0.56      ! [T: nat] :
% 0.32/0.56      ? [Z5: nat] :
% 0.32/0.56      ! [X4: nat] :
% 0.32/0.56        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(8)
% 0.32/0.56  thf(fact_3251_minf_I8_J,axiom,
% 0.32/0.56      ! [T: int] :
% 0.32/0.56      ? [Z5: int] :
% 0.32/0.56      ! [X4: int] :
% 0.32/0.56        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.56       => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minf(8)
% 0.32/0.56  thf(fact_3252_inf__period_I1_J,axiom,
% 0.32/0.56      ! [P: real > $o,D4: real,Q: real > $o] :
% 0.32/0.56        ( ! [X6: real,K3: real] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: real,K3: real] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: real,K4: real] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                & ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 0.32/0.56                & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(1)
% 0.32/0.56  thf(fact_3253_inf__period_I1_J,axiom,
% 0.32/0.56      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 0.32/0.56        ( ! [X6: rat,K3: rat] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: rat,K3: rat] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: rat,K4: rat] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                & ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 0.32/0.56                & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(1)
% 0.32/0.56  thf(fact_3254_inf__period_I1_J,axiom,
% 0.32/0.56      ! [P: int > $o,D4: int,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int,K3: int] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int,K3: int] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int,K4: int] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                & ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 0.32/0.56                & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(1)
% 0.32/0.56  thf(fact_3255_inf__period_I2_J,axiom,
% 0.32/0.56      ! [P: real > $o,D4: real,Q: real > $o] :
% 0.32/0.56        ( ! [X6: real,K3: real] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: real,K3: real] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: real,K4: real] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                | ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 0.32/0.56                | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(2)
% 0.32/0.56  thf(fact_3256_inf__period_I2_J,axiom,
% 0.32/0.56      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 0.32/0.56        ( ! [X6: rat,K3: rat] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: rat,K3: rat] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: rat,K4: rat] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                | ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 0.32/0.56                | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(2)
% 0.32/0.56  thf(fact_3257_inf__period_I2_J,axiom,
% 0.32/0.56      ! [P: int > $o,D4: int,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int,K3: int] :
% 0.32/0.56            ( ( P @ X6 )
% 0.32/0.56            = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int,K3: int] :
% 0.32/0.56              ( ( Q @ X6 )
% 0.32/0.56              = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int,K4: int] :
% 0.32/0.56              ( ( ( P @ X4 )
% 0.32/0.56                | ( Q @ X4 ) )
% 0.32/0.56              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 0.32/0.56                | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % inf_period(2)
% 0.32/0.56  thf(fact_3258_conj__le__cong,axiom,
% 0.32/0.56      ! [X: int,X5: int,P: $o,P6: $o] :
% 0.32/0.56        ( ( X = X5 )
% 0.32/0.56       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.32/0.56           => ( P = P6 ) )
% 0.32/0.56         => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.56              & P )
% 0.32/0.56            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.32/0.56              & P6 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % conj_le_cong
% 0.32/0.56  thf(fact_3259_imp__le__cong,axiom,
% 0.32/0.56      ! [X: int,X5: int,P: $o,P6: $o] :
% 0.32/0.56        ( ( X = X5 )
% 0.32/0.56       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.32/0.56           => ( P = P6 ) )
% 0.32/0.56         => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.56             => P )
% 0.32/0.56            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.32/0.56             => P6 ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % imp_le_cong
% 0.32/0.56  thf(fact_3260_bset_I1_J,axiom,
% 0.32/0.56      ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int] :
% 0.32/0.56            ( ! [Xa: int] :
% 0.32/0.56                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb: int] :
% 0.32/0.56                    ( ( member_int @ Xb @ B3 )
% 0.32/0.56                   => ( X6
% 0.32/0.56                     != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ! [Xa: int] :
% 0.32/0.56                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb: int] :
% 0.32/0.56                      ( ( member_int @ Xb @ B3 )
% 0.32/0.56                     => ( X6
% 0.32/0.56                       != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56               => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56               => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 0.32/0.56                  & ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(1)
% 0.32/0.56  thf(fact_3261_bset_I2_J,axiom,
% 0.32/0.56      ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int] :
% 0.32/0.56            ( ! [Xa: int] :
% 0.32/0.56                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb: int] :
% 0.32/0.56                    ( ( member_int @ Xb @ B3 )
% 0.32/0.56                   => ( X6
% 0.32/0.56                     != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ! [Xa: int] :
% 0.32/0.56                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb: int] :
% 0.32/0.56                      ( ( member_int @ Xb @ B3 )
% 0.32/0.56                     => ( X6
% 0.32/0.56                       != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56               => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56               => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 0.32/0.56                  | ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(2)
% 0.32/0.56  thf(fact_3262_aset_I1_J,axiom,
% 0.32/0.56      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int] :
% 0.32/0.56            ( ! [Xa: int] :
% 0.32/0.56                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb: int] :
% 0.32/0.56                    ( ( member_int @ Xb @ A2 )
% 0.32/0.56                   => ( X6
% 0.32/0.56                     != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ! [Xa: int] :
% 0.32/0.56                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb: int] :
% 0.32/0.56                      ( ( member_int @ Xb @ A2 )
% 0.32/0.56                     => ( X6
% 0.32/0.56                       != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56               => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  & ( Q @ X4 ) )
% 0.32/0.56               => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 0.32/0.56                  & ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(1)
% 0.32/0.56  thf(fact_3263_aset_I2_J,axiom,
% 0.32/0.56      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 0.32/0.56        ( ! [X6: int] :
% 0.32/0.56            ( ! [Xa: int] :
% 0.32/0.56                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb: int] :
% 0.32/0.56                    ( ( member_int @ Xb @ A2 )
% 0.32/0.56                   => ( X6
% 0.32/0.56                     != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56           => ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ! [Xa: int] :
% 0.32/0.56                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb: int] :
% 0.32/0.56                      ( ( member_int @ Xb @ A2 )
% 0.32/0.56                     => ( X6
% 0.32/0.56                       != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 0.32/0.56             => ( ( Q @ X6 )
% 0.32/0.56               => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ( P @ X4 )
% 0.32/0.56                  | ( Q @ X4 ) )
% 0.32/0.56               => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 0.32/0.56                  | ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(2)
% 0.32/0.56  thf(fact_3264_plusinfinity,axiom,
% 0.32/0.56      ! [D: int,P6: int > $o,P: int > $o] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ! [X6: int,K3: int] :
% 0.32/0.56              ( ( P6 @ X6 )
% 0.32/0.56              = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.32/0.56         => ( ? [Z4: int] :
% 0.32/0.56              ! [X6: int] :
% 0.32/0.56                ( ( ord_less_int @ Z4 @ X6 )
% 0.32/0.56               => ( ( P @ X6 )
% 0.32/0.56                  = ( P6 @ X6 ) ) )
% 0.32/0.56           => ( ? [X_12: int] : ( P6 @ X_12 )
% 0.32/0.56             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % plusinfinity
% 0.32/0.56  thf(fact_3265_minusinfinity,axiom,
% 0.32/0.56      ! [D: int,P1: int > $o,P: int > $o] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ! [X6: int,K3: int] :
% 0.32/0.56              ( ( P1 @ X6 )
% 0.32/0.56              = ( P1 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.32/0.56         => ( ? [Z4: int] :
% 0.32/0.56              ! [X6: int] :
% 0.32/0.56                ( ( ord_less_int @ X6 @ Z4 )
% 0.32/0.56               => ( ( P @ X6 )
% 0.32/0.56                  = ( P1 @ X6 ) ) )
% 0.32/0.56           => ( ? [X_12: int] : ( P1 @ X_12 )
% 0.32/0.56             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % minusinfinity
% 0.32/0.56  thf(fact_3266_vebt__member_Oelims_I2_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.56        ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.56       => ( ! [A5: $o,B5: $o] :
% 0.32/0.56              ( ( X
% 0.32/0.56                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.56                   => A5 )
% 0.32/0.56                  & ( ( Xa2 != zero_zero_nat )
% 0.32/0.56                   => ( ( ( Xa2 = one_one_nat )
% 0.32/0.56                       => B5 )
% 0.32/0.56                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.56         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.56                ( ? [Summary2: vEBT_VEBT] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56               => ~ ( ( Xa2 != Mi2 )
% 0.32/0.56                   => ( ( Xa2 != Ma2 )
% 0.32/0.56                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.elims(2)
% 0.32/0.56  thf(fact_3267_vebt__member_Oelims_I3_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.56        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.56       => ( ! [A5: $o,B5: $o] :
% 0.32/0.56              ( ( X
% 0.32/0.56                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56             => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.56                 => A5 )
% 0.32/0.56                & ( ( Xa2 != zero_zero_nat )
% 0.32/0.56                 => ( ( ( Xa2 = one_one_nat )
% 0.32/0.56                     => B5 )
% 0.32/0.56                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.56         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.56                ( X
% 0.32/0.56               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.56           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.56                  ( X
% 0.32/0.56                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.32/0.56             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.56                    ( X
% 0.32/0.56                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.32/0.56               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.56                      ( ? [Summary2: vEBT_VEBT] :
% 0.32/0.56                          ( X
% 0.32/0.56                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56                     => ( ( Xa2 != Mi2 )
% 0.32/0.56                       => ( ( Xa2 != Ma2 )
% 0.32/0.56                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.elims(3)
% 0.32/0.56  thf(fact_3268_vebt__member_Oelims_I1_J,axiom,
% 0.32/0.56      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.56        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.56          = Y )
% 0.32/0.56       => ( ! [A5: $o,B5: $o] :
% 0.32/0.56              ( ( X
% 0.32/0.56                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.56             => ( Y
% 0.32/0.56                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.56                       => A5 )
% 0.32/0.56                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.56                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.56                           => B5 )
% 0.32/0.56                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.32/0.56         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.56                  ( X
% 0.32/0.56                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.56             => Y )
% 0.32/0.56           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.56                    ( X
% 0.32/0.56                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.32/0.56               => Y )
% 0.32/0.56             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.56                      ( X
% 0.32/0.56                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.32/0.56                 => Y )
% 0.32/0.56               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.56                      ( ? [Summary2: vEBT_VEBT] :
% 0.32/0.56                          ( X
% 0.32/0.56                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.56                     => ( Y
% 0.32/0.56                        = ( ~ ( ( Xa2 != Mi2 )
% 0.32/0.56                             => ( ( Xa2 != Ma2 )
% 0.32/0.56                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.56                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.56                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.56                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.56                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % vebt_member.elims(1)
% 0.32/0.56  thf(fact_3269_incr__mult__lemma,axiom,
% 0.32/0.56      ! [D: int,P: int > $o,K: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( plus_plus_int @ X6 @ D ) ) )
% 0.32/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.56           => ! [X4: int] :
% 0.32/0.56                ( ( P @ X4 )
% 0.32/0.56               => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % incr_mult_lemma
% 0.32/0.56  thf(fact_3270_decr__mult__lemma,axiom,
% 0.32/0.56      ! [D: int,P: int > $o,K: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ! [X6: int] :
% 0.32/0.56              ( ( P @ X6 )
% 0.32/0.56             => ( P @ ( minus_minus_int @ X6 @ D ) ) )
% 0.32/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.56           => ! [X4: int] :
% 0.32/0.56                ( ( P @ X4 )
% 0.32/0.56               => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % decr_mult_lemma
% 0.32/0.56  thf(fact_3271_periodic__finite__ex,axiom,
% 0.32/0.56      ! [D: int,P: int > $o] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.56       => ( ! [X6: int,K3: int] :
% 0.32/0.56              ( ( P @ X6 )
% 0.32/0.56              = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 0.32/0.56         => ( ( ? [X2: int] : ( P @ X2 ) )
% 0.32/0.56            = ( ? [X3: int] :
% 0.32/0.56                  ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.32/0.56                  & ( P @ X3 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % periodic_finite_ex
% 0.32/0.56  thf(fact_3272_aset_I7_J,axiom,
% 0.32/0.56      ! [D4: int,A2: set_int,T: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ! [X4: int] :
% 0.32/0.56            ( ! [Xa3: int] :
% 0.32/0.56                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb2: int] :
% 0.32/0.56                    ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                   => ( X4
% 0.32/0.56                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56           => ( ( ord_less_int @ T @ X4 )
% 0.32/0.56             => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(7)
% 0.32/0.56  thf(fact_3273_aset_I5_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,A2: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ T @ A2 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ord_less_int @ X4 @ T )
% 0.32/0.56               => ( ord_less_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(5)
% 0.32/0.56  thf(fact_3274_aset_I4_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,A2: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ T @ A2 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( X4 != T )
% 0.32/0.56               => ( ( plus_plus_int @ X4 @ D4 )
% 0.32/0.56                 != T ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(4)
% 0.32/0.56  thf(fact_3275_aset_I3_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,A2: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( X4 = T )
% 0.32/0.56               => ( ( plus_plus_int @ X4 @ D4 )
% 0.32/0.56                  = T ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % aset(3)
% 0.32/0.56  thf(fact_3276_bset_I7_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,B3: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ T @ B3 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56                 => ! [Xb2: int] :
% 0.32/0.56                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                     => ( X4
% 0.32/0.56                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56             => ( ( ord_less_int @ T @ X4 )
% 0.32/0.56               => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(7)
% 0.32/0.56  thf(fact_3277_bset_I5_J,axiom,
% 0.32/0.56      ! [D4: int,B3: set_int,T: int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ! [X4: int] :
% 0.32/0.56            ( ! [Xa3: int] :
% 0.32/0.56                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.56               => ! [Xb2: int] :
% 0.32/0.56                    ( ( member_int @ Xb2 @ B3 )
% 0.32/0.56                   => ( X4
% 0.32/0.56                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.56           => ( ( ord_less_int @ X4 @ T )
% 0.32/0.56             => ( ord_less_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 0.32/0.56  
% 0.32/0.56  % bset(5)
% 0.32/0.56  thf(fact_3278_bset_I4_J,axiom,
% 0.32/0.56      ! [D4: int,T: int,B3: set_int] :
% 0.32/0.56        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.56       => ( ( member_int @ T @ B3 )
% 0.32/0.56         => ! [X4: int] :
% 0.32/0.56              ( ! [Xa3: int] :
% 0.32/0.56                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.57                 => ! [Xb2: int] :
% 0.32/0.57                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.57                     => ( X4
% 0.32/0.57                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.57             => ( ( X4 != T )
% 0.32/0.57               => ( ( minus_minus_int @ X4 @ D4 )
% 0.32/0.57                 != T ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % bset(4)
% 0.32/0.57  thf(fact_3279_bset_I3_J,axiom,
% 0.32/0.57      ! [D4: int,T: int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.57       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 0.32/0.57         => ! [X4: int] :
% 0.32/0.57              ( ! [Xa3: int] :
% 0.32/0.57                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.57                 => ! [Xb2: int] :
% 0.32/0.57                      ( ( member_int @ Xb2 @ B3 )
% 0.32/0.57                     => ( X4
% 0.32/0.57                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.57             => ( ( X4 = T )
% 0.32/0.57               => ( ( minus_minus_int @ X4 @ D4 )
% 0.32/0.57                  = T ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % bset(3)
% 0.32/0.57  thf(fact_3280_invar__vebt_Osimps,axiom,
% 0.32/0.57      ( vEBT_invar_vebt
% 0.32/0.57      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 0.32/0.57            ( ( ? [A3: $o,B2: $o] :
% 0.32/0.57                  ( A1
% 0.32/0.57                  = ( vEBT_Leaf @ A3 @ B2 ) )
% 0.32/0.57              & ( A22
% 0.32/0.57                = ( suc @ zero_zero_nat ) ) )
% 0.32/0.57            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 0.32/0.57                ( ( A1
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 0.32/0.57                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 0.32/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.32/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.32/0.57                & ( A22
% 0.32/0.57                  = ( plus_plus_nat @ N2 @ N2 ) )
% 0.32/0.57                & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.57            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 0.32/0.57                ( ( A1
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 0.32/0.57                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 0.32/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.32/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.32/0.57                & ( A22
% 0.32/0.57                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 0.32/0.57                & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.57            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.32/0.57                ( ( A1
% 0.32/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 0.32/0.57                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 0.32/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.32/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.32/0.57                & ( A22
% 0.32/0.57                  = ( plus_plus_nat @ N2 @ N2 ) )
% 0.32/0.57                & ! [I5: nat] :
% 0.32/0.57                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.32/0.57                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 0.32/0.57                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 0.32/0.57                & ( ( Mi3 = Ma3 )
% 0.32/0.57                 => ! [X3: vEBT_VEBT] :
% 0.32/0.57                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.57                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.57                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.32/0.57                & ( ( Mi3 != Ma3 )
% 0.32/0.57                 => ! [I5: nat] :
% 0.32/0.57                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 0.32/0.57                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 0.32/0.57                            = I5 )
% 0.32/0.57                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 0.32/0.57                        & ! [X3: nat] :
% 0.32/0.57                            ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 0.32/0.57                                = I5 )
% 0.32/0.57                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 0.32/0.57                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.57                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 0.32/0.57            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.32/0.57                ( ( A1
% 0.32/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 0.32/0.57                & ! [X3: vEBT_VEBT] :
% 0.32/0.57                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 0.32/0.57                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 0.32/0.57                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.32/0.57                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.32/0.57                & ( A22
% 0.32/0.57                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 0.32/0.57                & ! [I5: nat] :
% 0.32/0.57                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.32/0.57                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 0.32/0.57                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 0.32/0.57                & ( ( Mi3 = Ma3 )
% 0.32/0.57                 => ! [X3: vEBT_VEBT] :
% 0.32/0.57                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.32/0.57                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.57                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.57                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 0.32/0.57                & ( ( Mi3 != Ma3 )
% 0.32/0.57                 => ! [I5: nat] :
% 0.32/0.57                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 0.32/0.57                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 0.32/0.57                            = I5 )
% 0.32/0.57                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 0.32/0.57                        & ! [X3: nat] :
% 0.32/0.57                            ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 0.32/0.57                                = I5 )
% 0.32/0.57                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 0.32/0.57                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.57                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % invar_vebt.simps
% 0.32/0.57  thf(fact_3281_invar__vebt_Ocases,axiom,
% 0.32/0.57      ! [A12: vEBT_VEBT,A23: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 0.32/0.57       => ( ( ? [A5: $o,B5: $o] :
% 0.32/0.57                ( A12
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57           => ( A23
% 0.32/0.57             != ( suc @ zero_zero_nat ) ) )
% 0.32/0.57         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.32/0.57                ( ( A12
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57               => ( ( A23 = Deg2 )
% 0.32/0.57                 => ( ! [X4: vEBT_VEBT] :
% 0.32/0.57                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                       => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 0.32/0.57                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.32/0.57                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.57                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                       => ( ( M4 = N3 )
% 0.32/0.57                         => ( ( Deg2
% 0.32/0.57                              = ( plus_plus_nat @ N3 @ M4 ) )
% 0.32/0.57                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.32/0.57                             => ~ ! [X4: vEBT_VEBT] :
% 0.32/0.57                                    ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.32/0.57           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 0.32/0.57                  ( ( A12
% 0.32/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57                 => ( ( A23 = Deg2 )
% 0.32/0.57                   => ( ! [X4: vEBT_VEBT] :
% 0.32/0.57                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                         => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 0.32/0.57                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.32/0.57                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.57                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                         => ( ( M4
% 0.32/0.57                              = ( suc @ N3 ) )
% 0.32/0.57                           => ( ( Deg2
% 0.32/0.57                                = ( plus_plus_nat @ N3 @ M4 ) )
% 0.32/0.57                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.32/0.57                               => ~ ! [X4: vEBT_VEBT] :
% 0.32/0.57                                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.32/0.57             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.32/0.57                    ( ( A12
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57                   => ( ( A23 = Deg2 )
% 0.32/0.57                     => ( ! [X4: vEBT_VEBT] :
% 0.32/0.57                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                           => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 0.32/0.57                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.32/0.57                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.57                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                           => ( ( M4 = N3 )
% 0.32/0.57                             => ( ( Deg2
% 0.32/0.57                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 0.32/0.57                               => ( ! [I2: nat] :
% 0.32/0.57                                      ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 0.32/0.57                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 0.32/0.57                                 => ( ( ( Mi2 = Ma2 )
% 0.32/0.57                                     => ! [X4: vEBT_VEBT] :
% 0.32/0.57                                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 0.32/0.57                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.32/0.57                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.57                                       => ~ ( ( Mi2 != Ma2 )
% 0.32/0.57                                           => ! [I2: nat] :
% 0.32/0.57                                                ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.32/0.57                                                      = I2 )
% 0.32/0.57                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.32/0.57                                                  & ! [X4: nat] :
% 0.32/0.57                                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 0.32/0.57                                                          = I2 )
% 0.32/0.57                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 0.32/0.57                                                     => ( ( ord_less_nat @ Mi2 @ X4 )
% 0.32/0.57                                                        & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.57               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.32/0.57                      ( ( A12
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57                     => ( ( A23 = Deg2 )
% 0.32/0.57                       => ( ! [X4: vEBT_VEBT] :
% 0.32/0.57                              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                             => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 0.32/0.57                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 0.32/0.57                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.57                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                             => ( ( M4
% 0.32/0.57                                  = ( suc @ N3 ) )
% 0.32/0.57                               => ( ( Deg2
% 0.32/0.57                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 0.32/0.57                                 => ( ! [I2: nat] :
% 0.32/0.57                                        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                                       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 0.32/0.57                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 0.32/0.57                                   => ( ( ( Mi2 = Ma2 )
% 0.32/0.57                                       => ! [X4: vEBT_VEBT] :
% 0.32/0.57                                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.57                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 0.32/0.57                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.32/0.57                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.57                                         => ~ ( ( Mi2 != Ma2 )
% 0.32/0.57                                             => ! [I2: nat] :
% 0.32/0.57                                                  ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 0.32/0.57                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.32/0.57                                                        = I2 )
% 0.32/0.57                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.32/0.57                                                    & ! [X4: nat] :
% 0.32/0.57                                                        ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 0.32/0.57                                                            = I2 )
% 0.32/0.57                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 0.32/0.57                                                       => ( ( ord_less_nat @ Mi2 @ X4 )
% 0.32/0.57                                                          & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % invar_vebt.cases
% 0.32/0.57  thf(fact_3282_vebt__insert_Oelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.32/0.57        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                   => ( Y
% 0.32/0.57                      = ( vEBT_Leaf @ $true @ B5 ) ) )
% 0.32/0.57                  & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                   => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                       => ( Y
% 0.32/0.57                          = ( vEBT_Leaf @ A5 @ $true ) ) )
% 0.32/0.57                      & ( ( Xa2 != one_one_nat )
% 0.32/0.57                       => ( Y
% 0.32/0.57                          = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 0.32/0.57         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.32/0.57               => ( Y
% 0.32/0.57                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 0.32/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.32/0.57                 => ( Y
% 0.32/0.57                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 0.32/0.57             => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                   => ( Y
% 0.32/0.57                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.57               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                     => ( Y
% 0.32/0.57                       != ( if_VEBT_VEBT
% 0.32/0.57                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                            & ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                                | ( Xa2 = Ma2 ) ) )
% 0.32/0.57                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.32/0.57                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_insert.elims
% 0.32/0.57  thf(fact_3283_aset_I8_J,axiom,
% 0.32/0.57      ! [D4: int,A2: set_int,T: int] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.57       => ! [X4: int] :
% 0.32/0.57            ( ! [Xa3: int] :
% 0.32/0.57                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.57               => ! [Xb2: int] :
% 0.32/0.57                    ( ( member_int @ Xb2 @ A2 )
% 0.32/0.57                   => ( X4
% 0.32/0.57                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.57           => ( ( ord_less_eq_int @ T @ X4 )
% 0.32/0.57             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % aset(8)
% 0.32/0.57  thf(fact_3284_aset_I6_J,axiom,
% 0.32/0.57      ! [D4: int,T: int,A2: set_int] :
% 0.32/0.57        ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.32/0.57       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 0.32/0.57         => ! [X4: int] :
% 0.32/0.57              ( ! [Xa3: int] :
% 0.32/0.57                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.57                 => ! [Xb2: int] :
% 0.32/0.57                      ( ( member_int @ Xb2 @ A2 )
% 0.32/0.57                     => ( X4
% 0.32/0.57                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.57             => ( ( ord_less_eq_int @ X4 @ T )
% 0.32/0.57               => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % aset(6)
% 0.32/0.57  thf(fact_3285_vebt__mint_Oelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Y: option_nat] :
% 0.32/0.57        ( ( ( vEBT_vebt_mint @ X )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ~ ( ( A5
% 0.32/0.57                   => ( Y
% 0.32/0.57                      = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57                  & ( ~ A5
% 0.32/0.57                   => ( ( B5
% 0.32/0.57                       => ( Y
% 0.32/0.57                          = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57                      & ( ~ B5
% 0.32/0.57                       => ( Y = none_nat ) ) ) ) ) )
% 0.32/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( X
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.57             => ( Y != none_nat ) )
% 0.32/0.57           => ~ ! [Mi2: nat] :
% 0.32/0.57                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.57                 => ( Y
% 0.32/0.57                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_mint.elims
% 0.32/0.57  thf(fact_3286_vebt__maxt_Oelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Y: option_nat] :
% 0.32/0.57        ( ( ( vEBT_vebt_maxt @ X )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ~ ( ( B5
% 0.32/0.57                   => ( Y
% 0.32/0.57                      = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57                  & ( ~ B5
% 0.32/0.57                   => ( ( A5
% 0.32/0.57                       => ( Y
% 0.32/0.57                          = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57                      & ( ~ A5
% 0.32/0.57                       => ( Y = none_nat ) ) ) ) ) )
% 0.32/0.57         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( X
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.57             => ( Y != none_nat ) )
% 0.32/0.57           => ~ ! [Mi2: nat,Ma2: nat] :
% 0.32/0.57                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.57                 => ( Y
% 0.32/0.57                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_maxt.elims
% 0.32/0.57  thf(fact_3287_vebt__mint_Osimps_I1_J,axiom,
% 0.32/0.57      ! [A: $o,B: $o] :
% 0.32/0.57        ( ( A
% 0.32/0.57         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57            = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57        & ( ~ A
% 0.32/0.57         => ( ( B
% 0.32/0.57             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57                = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57            & ( ~ B
% 0.32/0.57             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57                = none_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_mint.simps(1)
% 0.32/0.57  thf(fact_3288_vebt__maxt_Osimps_I1_J,axiom,
% 0.32/0.57      ! [B: $o,A: $o] :
% 0.32/0.57        ( ( B
% 0.32/0.57         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57            = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57        & ( ~ B
% 0.32/0.57         => ( ( A
% 0.32/0.57             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57                = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57            & ( ~ A
% 0.32/0.57             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.32/0.57                = none_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_maxt.simps(1)
% 0.32/0.57  thf(fact_3289_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.57        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.32/0.57                ( X
% 0.32/0.57                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.57           => Y )
% 0.32/0.57         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.57                  ( X
% 0.32/0.57                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.32/0.57             => Y )
% 0.32/0.57           => ( ! [Mi2: nat,Ma2: nat] :
% 0.32/0.57                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.57                 => ( Y
% 0.32/0.57                    = ( ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                          | ( Xa2 = Ma2 ) ) ) ) )
% 0.32/0.57             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                    ( ? [Vc2: vEBT_VEBT] :
% 0.32/0.57                        ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.57                   => ( Y
% 0.32/0.57                      = ( ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                            | ( Xa2 = Ma2 )
% 0.32/0.57                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 0.32/0.57               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                      ( ? [Vd2: vEBT_VEBT] :
% 0.32/0.57                          ( X
% 0.32/0.57                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.57                     => ( Y
% 0.32/0.57                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.elims(1)
% 0.32/0.57  thf(fact_3290_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.57       => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.57         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.32/0.57           => ( ! [Mi2: nat,Ma2: nat] :
% 0.32/0.57                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.57                 => ( ( Xa2 = Mi2 )
% 0.32/0.57                    | ( Xa2 = Ma2 ) ) )
% 0.32/0.57             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                    ( ? [Vc2: vEBT_VEBT] :
% 0.32/0.57                        ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.57                   => ( ( Xa2 = Mi2 )
% 0.32/0.57                      | ( Xa2 = Ma2 )
% 0.32/0.57                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.32/0.57               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                      ( ? [Vd2: vEBT_VEBT] :
% 0.32/0.57                          ( X
% 0.32/0.57                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.57                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.elims(3)
% 0.32/0.57  thf(fact_3291_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.57        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ( Y
% 0.32/0.57                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                       => A5 )
% 0.32/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                           => B5 )
% 0.32/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.32/0.57         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( X
% 0.32/0.57                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.32/0.57             => Y )
% 0.32/0.57           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                  ( ? [S3: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57                 => ( Y
% 0.32/0.57                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.elims(1)
% 0.32/0.57  thf(fact_3292_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                   => A5 )
% 0.32/0.57                  & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                   => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                       => B5 )
% 0.32/0.57                      & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.57         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                ( ? [S3: vEBT_VEBT] :
% 0.32/0.57                    ( X
% 0.32/0.57                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.elims(2)
% 0.32/0.57  thf(fact_3293_buildup__nothing__in__min__max,axiom,
% 0.32/0.57      ! [N: nat,X: nat] :
% 0.32/0.57        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.32/0.57  
% 0.32/0.57  % buildup_nothing_in_min_max
% 0.32/0.57  thf(fact_3294_buildup__nothing__in__leaf,axiom,
% 0.32/0.57      ! [N: nat,X: nat] :
% 0.32/0.57        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.32/0.57  
% 0.32/0.57  % buildup_nothing_in_leaf
% 0.32/0.57  thf(fact_3295_both__member__options__def,axiom,
% 0.32/0.57      ( vEBT_V8194947554948674370ptions
% 0.32/0.57      = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 0.32/0.57            ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 0.32/0.57            | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % both_member_options_def
% 0.32/0.57  thf(fact_3296_member__valid__both__member__options,axiom,
% 0.32/0.57      ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ Tree @ N )
% 0.32/0.57       => ( ( vEBT_vebt_member @ Tree @ X )
% 0.32/0.57         => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 0.32/0.57            | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % member_valid_both_member_options
% 0.32/0.57  thf(fact_3297_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.32/0.57        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.simps(2)
% 0.32/0.57  thf(fact_3298_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 0.32/0.57        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.simps(2)
% 0.32/0.57  thf(fact_3299_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.32/0.57      ! [A: $o,B: $o,X: nat] :
% 0.32/0.57        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.32/0.57        = ( ( ( X = zero_zero_nat )
% 0.32/0.57           => A )
% 0.32/0.57          & ( ( X != zero_zero_nat )
% 0.32/0.57           => ( ( ( X = one_one_nat )
% 0.32/0.57               => B )
% 0.32/0.57              & ( X = one_one_nat ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.simps(1)
% 0.32/0.57  thf(fact_3300_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.32/0.57      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 0.32/0.57        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 0.32/0.57        = ( ( X = Mi )
% 0.32/0.57          | ( X = Ma ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.simps(3)
% 0.32/0.57  thf(fact_3301_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc8306885398267862888on_nat] :
% 0.32/0.57        ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 0.32/0.57         => ~ ! [F2: nat > nat > nat,A5: nat,B5: nat] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.cases
% 0.32/0.57  thf(fact_3302_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc5542196010084753463at_nat] :
% 0.32/0.57        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 0.32/0.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.cases
% 0.32/0.57  thf(fact_3303_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc1193250871479095198on_num] :
% 0.32/0.57        ( ! [Uu2: num > num > num,Uv2: option_num] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: num > num > num,V2: num] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 0.32/0.57         => ~ ! [F2: num > num > num,A5: num,B5: num] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.cases
% 0.32/0.57  thf(fact_3304_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc2233624965454879586on_nat] :
% 0.32/0.57        ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 0.32/0.57         => ~ ! [F2: nat > nat > $o,X6: nat,Y5: nat] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X6 ) @ ( some_nat @ Y5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_comp_shift.cases
% 0.32/0.57  thf(fact_3305_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc5491161045314408544at_nat] :
% 0.32/0.57        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 0.32/0.57         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X6: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X6 ) @ ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_comp_shift.cases
% 0.32/0.57  thf(fact_3306_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.32/0.57      ! [X: produc7036089656553540234on_num] :
% 0.32/0.57        ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.32/0.57       => ( ! [Uw2: num > num > $o,V2: num] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 0.32/0.57         => ~ ! [F2: num > num > $o,X6: num,Y5: num] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X6 ) @ ( some_num @ Y5 ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_comp_shift.cases
% 0.32/0.57  thf(fact_3307_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.32/0.57      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.32/0.57        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 0.32/0.57        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(3)
% 0.32/0.57  thf(fact_3308_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.32/0.57      ! [F: num > num > num,A: num,B: num] :
% 0.32/0.57        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 0.32/0.57        = ( some_num @ ( F @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(3)
% 0.32/0.57  thf(fact_3309_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.32/0.57      ! [F: nat > nat > nat,A: nat,B: nat] :
% 0.32/0.57        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 0.32/0.57        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(3)
% 0.32/0.57  thf(fact_3310_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.32/0.57      ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 0.32/0.57        ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 0.32/0.57        = none_P5556105721700978146at_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(1)
% 0.32/0.57  thf(fact_3311_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.32/0.57      ! [Uu: num > num > num,Uv: option_num] :
% 0.32/0.57        ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 0.32/0.57        = none_num ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(1)
% 0.32/0.57  thf(fact_3312_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 0.32/0.57      ! [Uu: nat > nat > nat,Uv: option_nat] :
% 0.32/0.57        ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 0.32/0.57        = none_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(1)
% 0.32/0.57  thf(fact_3313_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 0.32/0.57        ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 0.32/0.57        = none_P5556105721700978146at_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(2)
% 0.32/0.57  thf(fact_3314_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uw: num > num > num,V: num] :
% 0.32/0.57        ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 0.32/0.57        = none_num ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(2)
% 0.32/0.57  thf(fact_3315_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uw: nat > nat > nat,V: nat] :
% 0.32/0.57        ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 0.32/0.57        = none_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.simps(2)
% 0.32/0.57  thf(fact_3316_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.32/0.57      ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb3: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 0.32/0.57        ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb3 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 0.32/0.57           => ( Y != none_P5556105721700978146at_nat ) )
% 0.32/0.57         => ( ( ? [V2: product_prod_nat_nat] :
% 0.32/0.57                  ( Xa2
% 0.32/0.57                  = ( some_P7363390416028606310at_nat @ V2 ) )
% 0.32/0.57             => ( ( Xb3 = none_P5556105721700978146at_nat )
% 0.32/0.57               => ( Y != none_P5556105721700978146at_nat ) ) )
% 0.32/0.57           => ~ ! [A5: product_prod_nat_nat] :
% 0.32/0.57                  ( ( Xa2
% 0.32/0.57                    = ( some_P7363390416028606310at_nat @ A5 ) )
% 0.32/0.57                 => ! [B5: product_prod_nat_nat] :
% 0.32/0.57                      ( ( Xb3
% 0.32/0.57                        = ( some_P7363390416028606310at_nat @ B5 ) )
% 0.32/0.57                     => ( Y
% 0.32/0.57                       != ( some_P7363390416028606310at_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.elims
% 0.32/0.57  thf(fact_3317_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.32/0.57      ! [X: num > num > num,Xa2: option_num,Xb3: option_num,Y: option_num] :
% 0.32/0.57        ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb3 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( ( Xa2 = none_num )
% 0.32/0.57           => ( Y != none_num ) )
% 0.32/0.57         => ( ( ? [V2: num] :
% 0.32/0.57                  ( Xa2
% 0.32/0.57                  = ( some_num @ V2 ) )
% 0.32/0.57             => ( ( Xb3 = none_num )
% 0.32/0.57               => ( Y != none_num ) ) )
% 0.32/0.57           => ~ ! [A5: num] :
% 0.32/0.57                  ( ( Xa2
% 0.32/0.57                    = ( some_num @ A5 ) )
% 0.32/0.57                 => ! [B5: num] :
% 0.32/0.57                      ( ( Xb3
% 0.32/0.57                        = ( some_num @ B5 ) )
% 0.32/0.57                     => ( Y
% 0.32/0.57                       != ( some_num @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.elims
% 0.32/0.57  thf(fact_3318_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.32/0.57      ! [X: nat > nat > nat,Xa2: option_nat,Xb3: option_nat,Y: option_nat] :
% 0.32/0.57        ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb3 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( ( Xa2 = none_nat )
% 0.32/0.57           => ( Y != none_nat ) )
% 0.32/0.57         => ( ( ? [V2: nat] :
% 0.32/0.57                  ( Xa2
% 0.32/0.57                  = ( some_nat @ V2 ) )
% 0.32/0.57             => ( ( Xb3 = none_nat )
% 0.32/0.57               => ( Y != none_nat ) ) )
% 0.32/0.57           => ~ ! [A5: nat] :
% 0.32/0.57                  ( ( Xa2
% 0.32/0.57                    = ( some_nat @ A5 ) )
% 0.32/0.57                 => ! [B5: nat] :
% 0.32/0.57                      ( ( Xb3
% 0.32/0.57                        = ( some_nat @ B5 ) )
% 0.32/0.57                     => ( Y
% 0.32/0.57                       != ( some_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.option_shift.elims
% 0.32/0.57  thf(fact_3319_vebt__maxt_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.32/0.57        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.32/0.57        = none_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_maxt.simps(2)
% 0.32/0.57  thf(fact_3320_vebt__mint_Osimps_I2_J,axiom,
% 0.32/0.57      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.32/0.57        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.32/0.57        = none_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_mint.simps(2)
% 0.32/0.57  thf(fact_3321_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.32/0.57      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 0.32/0.57        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 0.32/0.57        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.57           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.simps(5)
% 0.32/0.57  thf(fact_3322_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.32/0.57      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.32/0.57        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X )
% 0.32/0.57        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.57           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.simps(3)
% 0.32/0.57  thf(fact_3323_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.32/0.57      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.32/0.57        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 0.32/0.57        = ( ( X = Mi )
% 0.32/0.57          | ( X = Ma )
% 0.32/0.57          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.32/0.57             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57            & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.simps(4)
% 0.32/0.57  thf(fact_3324_vebt__mint_Ocases,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT] :
% 0.32/0.57        ( ! [A5: $o,B5: $o] :
% 0.32/0.57            ( X
% 0.32/0.57           != ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57              ( X
% 0.32/0.57             != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.57         => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_mint.cases
% 0.32/0.57  thf(fact_3325_vebt__maxt_Osimps_I3_J,axiom,
% 0.32/0.57      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.32/0.57        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.32/0.57        = ( some_nat @ Ma ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_maxt.simps(3)
% 0.32/0.57  thf(fact_3326_vebt__mint_Osimps_I3_J,axiom,
% 0.32/0.57      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.32/0.57        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 0.32/0.57        = ( some_nat @ Mi ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_mint.simps(3)
% 0.32/0.57  thf(fact_3327_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.57       => ( ! [Mi2: nat,Ma2: nat] :
% 0.32/0.57              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.57                  ( X
% 0.32/0.57                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.57             => ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                  | ( Xa2 = Ma2 ) ) )
% 0.32/0.57         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                ( ? [Vc2: vEBT_VEBT] :
% 0.32/0.57                    ( X
% 0.32/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.57               => ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                    | ( Xa2 = Ma2 )
% 0.32/0.57                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.32/0.57           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                  ( ? [Vd2: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.57                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.membermima.elims(2)
% 0.32/0.57  thf(fact_3328_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57       => ( ! [A5: $o,B5: $o] :
% 0.32/0.57              ( ( X
% 0.32/0.57                = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57             => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                 => A5 )
% 0.32/0.57                & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                 => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                     => B5 )
% 0.32/0.57                    & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.57         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                ( X
% 0.32/0.57               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.32/0.57           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 0.32/0.57                  ( ? [S3: vEBT_VEBT] :
% 0.32/0.57                      ( X
% 0.32/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.elims(3)
% 0.32/0.57  thf(fact_3329_succ__empty,axiom,
% 0.32/0.57      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.57       => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.32/0.57            = none_nat )
% 0.32/0.57          = ( ( collect_nat
% 0.32/0.57              @ ^ [Y3: nat] :
% 0.32/0.57                  ( ( vEBT_vebt_member @ T @ Y3 )
% 0.32/0.57                  & ( ord_less_nat @ X @ Y3 ) ) )
% 0.32/0.57            = bot_bot_set_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % succ_empty
% 0.32/0.57  thf(fact_3330_pred__empty,axiom,
% 0.32/0.57      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.57       => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.32/0.57            = none_nat )
% 0.32/0.57          = ( ( collect_nat
% 0.32/0.57              @ ^ [Y3: nat] :
% 0.32/0.57                  ( ( vEBT_vebt_member @ T @ Y3 )
% 0.32/0.57                  & ( ord_less_nat @ Y3 @ X ) ) )
% 0.32/0.57            = bot_bot_set_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % pred_empty
% 0.32/0.57  thf(fact_3331_vebt__succ_Opelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.32/0.57        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [Uu2: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 0.32/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                 => ( ( ( B5
% 0.32/0.57                       => ( Y
% 0.32/0.57                          = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57                      & ( ~ B5
% 0.32/0.57                       => ( Y = none_nat ) ) )
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 0.32/0.57           => ( ! [Uv2: $o,Uw2: $o] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 0.32/0.57                 => ! [N3: nat] :
% 0.32/0.57                      ( ( Xa2
% 0.32/0.57                        = ( suc @ N3 ) )
% 0.32/0.57                     => ( ( Y = none_nat )
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 0.32/0.57             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.57                   => ( ( Y = none_nat )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.32/0.57               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 0.32/0.57                     => ( ( Y = none_nat )
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 0.32/0.57                 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 0.32/0.57                       => ( ( Y = none_nat )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 0.32/0.57                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                          ( ( X
% 0.32/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                               => ( Y
% 0.32/0.57                                  = ( some_nat @ Mi2 ) ) )
% 0.32/0.57                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                               => ( Y
% 0.32/0.57                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                    @ ( if_option_nat
% 0.32/0.57                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                         != none_nat )
% 0.32/0.57                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.57                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                      @ ( if_option_nat
% 0.32/0.57                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.57                                          = none_nat )
% 0.32/0.57                                        @ none_nat
% 0.32/0.57                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.57                                    @ none_nat ) ) ) )
% 0.32/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_succ.pelims
% 0.32/0.57  thf(fact_3332_psubsetI,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( A2 != B3 )
% 0.32/0.57         => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubsetI
% 0.32/0.57  thf(fact_3333_vebt__pred_Opelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.32/0.57        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                 => ( ( Y = none_nat )
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 0.32/0.57           => ( ! [A5: $o,Uw2: $o] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 0.32/0.57                 => ( ( Xa2
% 0.32/0.57                      = ( suc @ zero_zero_nat ) )
% 0.32/0.57                   => ( ( ( A5
% 0.32/0.57                         => ( Y
% 0.32/0.57                            = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57                        & ( ~ A5
% 0.32/0.57                         => ( Y = none_nat ) ) )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.32/0.57             => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57                   => ! [Va2: nat] :
% 0.32/0.57                        ( ( Xa2
% 0.32/0.57                          = ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.57                       => ( ( ( B5
% 0.32/0.57                             => ( Y
% 0.32/0.57                                = ( some_nat @ one_one_nat ) ) )
% 0.32/0.57                            & ( ~ B5
% 0.32/0.57                             => ( ( A5
% 0.32/0.57                                 => ( Y
% 0.32/0.57                                    = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.57                                & ( ~ A5
% 0.32/0.57                                 => ( Y = none_nat ) ) ) ) )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 0.32/0.57               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 0.32/0.57                     => ( ( Y = none_nat )
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.32/0.57                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 0.32/0.57                       => ( ( Y = none_nat )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 0.32/0.57                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 0.32/0.57                          ( ( X
% 0.32/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 0.32/0.57                         => ( ( Y = none_nat )
% 0.32/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 0.32/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                            ( ( X
% 0.32/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                 => ( Y
% 0.32/0.57                                    = ( some_nat @ Ma2 ) ) )
% 0.32/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                 => ( Y
% 0.32/0.57                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                      @ ( if_option_nat
% 0.32/0.57                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                           != none_nat )
% 0.32/0.57                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.57                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                        @ ( if_option_nat
% 0.32/0.57                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.57                                            = none_nat )
% 0.32/0.57                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.32/0.57                                          @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.57                                      @ none_nat ) ) ) )
% 0.32/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_pred.pelims
% 0.32/0.57  thf(fact_3334_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.32/0.57       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3335_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.57       => ( ( ord_max_Code_integer @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3336_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: real,A: real] :
% 0.32/0.57        ( ( ord_less_real @ B @ A )
% 0.32/0.57       => ( ( ord_max_real @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3337_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_rat @ B @ A )
% 0.32/0.57       => ( ( ord_max_rat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3338_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: num,A: num] :
% 0.32/0.57        ( ( ord_less_num @ B @ A )
% 0.32/0.57       => ( ( ord_max_num @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3339_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_nat @ B @ A )
% 0.32/0.57       => ( ( ord_max_nat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3340_max_Oabsorb3,axiom,
% 0.32/0.57      ! [B: int,A: int] :
% 0.32/0.57        ( ( ord_less_int @ B @ A )
% 0.32/0.57       => ( ( ord_max_int @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb3
% 0.32/0.57  thf(fact_3341_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ A @ B )
% 0.32/0.57       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3342_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.57       => ( ( ord_max_Code_integer @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3343_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: real,B: real] :
% 0.32/0.57        ( ( ord_less_real @ A @ B )
% 0.32/0.57       => ( ( ord_max_real @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3344_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: rat,B: rat] :
% 0.32/0.57        ( ( ord_less_rat @ A @ B )
% 0.32/0.57       => ( ( ord_max_rat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3345_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: num,B: num] :
% 0.32/0.57        ( ( ord_less_num @ A @ B )
% 0.32/0.57       => ( ( ord_max_num @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3346_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_nat @ A @ B )
% 0.32/0.57       => ( ( ord_max_nat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3347_max_Oabsorb4,axiom,
% 0.32/0.57      ! [A: int,B: int] :
% 0.32/0.57        ( ( ord_less_int @ A @ B )
% 0.32/0.57       => ( ( ord_max_int @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb4
% 0.32/0.57  thf(fact_3348_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 0.32/0.57          & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3349_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 0.32/0.57          & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3350_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: real,Y: real,Z: real] :
% 0.32/0.57        ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_less_real @ X @ Z )
% 0.32/0.57          & ( ord_less_real @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3351_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.57        ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_less_rat @ X @ Z )
% 0.32/0.57          & ( ord_less_rat @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3352_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: num,Y: num,Z: num] :
% 0.32/0.57        ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_less_num @ X @ Z )
% 0.32/0.57          & ( ord_less_num @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3353_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.57        ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_less_nat @ X @ Z )
% 0.32/0.57          & ( ord_less_nat @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3354_max__less__iff__conj,axiom,
% 0.32/0.57      ! [X: int,Y: int,Z: int] :
% 0.32/0.57        ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.32/0.57        = ( ( ord_less_int @ X @ Z )
% 0.32/0.57          & ( ord_less_int @ Y @ Z ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max_less_iff_conj
% 0.32/0.57  thf(fact_3355_buildup__gives__empty,axiom,
% 0.32/0.57      ! [N: nat] :
% 0.32/0.57        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 0.32/0.57        = bot_bot_set_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % buildup_gives_empty
% 0.32/0.57  thf(fact_3356_Diff__empty,axiom,
% 0.32/0.57      ! [A2: set_int] :
% 0.32/0.57        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 0.32/0.57        = A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_empty
% 0.32/0.57  thf(fact_3357_Diff__empty,axiom,
% 0.32/0.57      ! [A2: set_real] :
% 0.32/0.57        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 0.32/0.57        = A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_empty
% 0.32/0.57  thf(fact_3358_Diff__empty,axiom,
% 0.32/0.57      ! [A2: set_nat] :
% 0.32/0.57        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 0.32/0.57        = A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_empty
% 0.32/0.57  thf(fact_3359_empty__Diff,axiom,
% 0.32/0.57      ! [A2: set_int] :
% 0.32/0.57        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 0.32/0.57        = bot_bot_set_int ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_Diff
% 0.32/0.57  thf(fact_3360_empty__Diff,axiom,
% 0.32/0.57      ! [A2: set_real] :
% 0.32/0.57        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 0.32/0.57        = bot_bot_set_real ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_Diff
% 0.32/0.57  thf(fact_3361_empty__Diff,axiom,
% 0.32/0.57      ! [A2: set_nat] :
% 0.32/0.57        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 0.32/0.57        = bot_bot_set_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_Diff
% 0.32/0.57  thf(fact_3362_Diff__cancel,axiom,
% 0.32/0.57      ! [A2: set_int] :
% 0.32/0.57        ( ( minus_minus_set_int @ A2 @ A2 )
% 0.32/0.57        = bot_bot_set_int ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_cancel
% 0.32/0.57  thf(fact_3363_Diff__cancel,axiom,
% 0.32/0.57      ! [A2: set_real] :
% 0.32/0.57        ( ( minus_minus_set_real @ A2 @ A2 )
% 0.32/0.57        = bot_bot_set_real ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_cancel
% 0.32/0.57  thf(fact_3364_Diff__cancel,axiom,
% 0.32/0.57      ! [A2: set_nat] :
% 0.32/0.57        ( ( minus_minus_set_nat @ A2 @ A2 )
% 0.32/0.57        = bot_bot_set_nat ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_cancel
% 0.32/0.57  thf(fact_3365_subset__antisym,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.57         => ( A2 = B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_antisym
% 0.32/0.57  thf(fact_3366_subsetI,axiom,
% 0.32/0.57      ! [A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ! [X6: complex] :
% 0.32/0.57            ( ( member_complex @ X6 @ A2 )
% 0.32/0.57           => ( member_complex @ X6 @ B3 ) )
% 0.32/0.57       => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetI
% 0.32/0.57  thf(fact_3367_subsetI,axiom,
% 0.32/0.57      ! [A2: set_real,B3: set_real] :
% 0.32/0.57        ( ! [X6: real] :
% 0.32/0.57            ( ( member_real @ X6 @ A2 )
% 0.32/0.57           => ( member_real @ X6 @ B3 ) )
% 0.32/0.57       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetI
% 0.32/0.57  thf(fact_3368_subsetI,axiom,
% 0.32/0.57      ! [A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ! [X6: set_nat] :
% 0.32/0.57            ( ( member_set_nat @ X6 @ A2 )
% 0.32/0.57           => ( member_set_nat @ X6 @ B3 ) )
% 0.32/0.57       => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetI
% 0.32/0.57  thf(fact_3369_subsetI,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ! [X6: nat] :
% 0.32/0.57            ( ( member_nat @ X6 @ A2 )
% 0.32/0.57           => ( member_nat @ X6 @ B3 ) )
% 0.32/0.57       => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetI
% 0.32/0.57  thf(fact_3370_subsetI,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ! [X6: int] :
% 0.32/0.57            ( ( member_int @ X6 @ A2 )
% 0.32/0.57           => ( member_int @ X6 @ B3 ) )
% 0.32/0.57       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetI
% 0.32/0.57  thf(fact_3371_maxt__corr__help__empty,axiom,
% 0.32/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.57       => ( ( ( vEBT_vebt_maxt @ T )
% 0.32/0.57            = none_nat )
% 0.32/0.57         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.32/0.57            = bot_bot_set_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % maxt_corr_help_empty
% 0.32/0.57  thf(fact_3372_mint__corr__help__empty,axiom,
% 0.32/0.57      ! [T: vEBT_VEBT,N: nat] :
% 0.32/0.57        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.57       => ( ( ( vEBT_vebt_mint @ T )
% 0.32/0.57            = none_nat )
% 0.32/0.57         => ( ( vEBT_VEBT_set_vebt @ T )
% 0.32/0.57            = bot_bot_set_nat ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % mint_corr_help_empty
% 0.32/0.57  thf(fact_3373_Diff__eq__empty__iff,axiom,
% 0.32/0.57      ! [A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( ( minus_minus_set_real @ A2 @ B3 )
% 0.32/0.57          = bot_bot_set_real )
% 0.32/0.57        = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_eq_empty_iff
% 0.32/0.57  thf(fact_3374_Diff__eq__empty__iff,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 0.32/0.57          = bot_bot_set_nat )
% 0.32/0.57        = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_eq_empty_iff
% 0.32/0.57  thf(fact_3375_Diff__eq__empty__iff,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ( minus_minus_set_int @ A2 @ B3 )
% 0.32/0.57          = bot_bot_set_int )
% 0.32/0.57        = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_eq_empty_iff
% 0.32/0.57  thf(fact_3376_empty__subsetI,axiom,
% 0.32/0.57      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_subsetI
% 0.32/0.57  thf(fact_3377_empty__subsetI,axiom,
% 0.32/0.57      ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_subsetI
% 0.32/0.57  thf(fact_3378_empty__subsetI,axiom,
% 0.32/0.57      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % empty_subsetI
% 0.32/0.57  thf(fact_3379_subset__empty,axiom,
% 0.32/0.57      ! [A2: set_nat] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 0.32/0.57        = ( A2 = bot_bot_set_nat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_empty
% 0.32/0.57  thf(fact_3380_subset__empty,axiom,
% 0.32/0.57      ! [A2: set_real] :
% 0.32/0.57        ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 0.32/0.57        = ( A2 = bot_bot_set_real ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_empty
% 0.32/0.57  thf(fact_3381_subset__empty,axiom,
% 0.32/0.57      ! [A2: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 0.32/0.57        = ( A2 = bot_bot_set_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_empty
% 0.32/0.57  thf(fact_3382_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.32/0.57          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3383_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.57          & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3384_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: rat,C: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.57          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3385_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: num,C: num,A: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_less_eq_num @ B @ A )
% 0.32/0.57          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3386_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: nat,C: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.57          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3387_max_Obounded__iff,axiom,
% 0.32/0.57      ! [B: int,C: int,A: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.32/0.57        = ( ( ord_less_eq_int @ B @ A )
% 0.32/0.57          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.bounded_iff
% 0.32/0.57  thf(fact_3388_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 0.32/0.57       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3389_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.57       => ( ( ord_max_Code_integer @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3390_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: rat,B: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.57       => ( ( ord_max_rat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3391_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: num,B: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.57       => ( ( ord_max_num @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3392_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.57       => ( ( ord_max_nat @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3393_max_Oabsorb2,axiom,
% 0.32/0.57      ! [A: int,B: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.57       => ( ( ord_max_int @ A @ B )
% 0.32/0.57          = B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb2
% 0.32/0.57  thf(fact_3394_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.32/0.57       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3395_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.57       => ( ( ord_max_Code_integer @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3396_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.57       => ( ( ord_max_rat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3397_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: num,A: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.57       => ( ( ord_max_num @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3398_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.57       => ( ( ord_max_nat @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3399_max_Oabsorb1,axiom,
% 0.32/0.57      ! [B: int,A: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.57       => ( ( ord_max_int @ A @ B )
% 0.32/0.57          = A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb1
% 0.32/0.57  thf(fact_3400_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: set_int,B: set_int] :
% 0.32/0.57        ( ( bot_bot_set_set_int
% 0.32/0.57          = ( set_or370866239135849197et_int @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3401_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: rat,B: rat] :
% 0.32/0.57        ( ( bot_bot_set_rat
% 0.32/0.57          = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3402_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: num,B: num] :
% 0.32/0.57        ( ( bot_bot_set_num
% 0.32/0.57          = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3403_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: nat,B: nat] :
% 0.32/0.57        ( ( bot_bot_set_nat
% 0.32/0.57          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3404_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: int,B: int] :
% 0.32/0.57        ( ( bot_bot_set_int
% 0.32/0.57          = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3405_atLeastatMost__empty__iff2,axiom,
% 0.32/0.57      ! [A: real,B: real] :
% 0.32/0.57        ( ( bot_bot_set_real
% 0.32/0.57          = ( set_or1222579329274155063t_real @ A @ B ) )
% 0.32/0.57        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff2
% 0.32/0.57  thf(fact_3406_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: set_int,B: set_int] :
% 0.32/0.57        ( ( ( set_or370866239135849197et_int @ A @ B )
% 0.32/0.57          = bot_bot_set_set_int )
% 0.32/0.57        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3407_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: rat,B: rat] :
% 0.32/0.57        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.32/0.57          = bot_bot_set_rat )
% 0.32/0.57        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3408_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: num,B: num] :
% 0.32/0.57        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.32/0.57          = bot_bot_set_num )
% 0.32/0.57        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3409_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: nat,B: nat] :
% 0.32/0.57        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.32/0.57          = bot_bot_set_nat )
% 0.32/0.57        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3410_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: int,B: int] :
% 0.32/0.57        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.32/0.57          = bot_bot_set_int )
% 0.32/0.57        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3411_atLeastatMost__empty__iff,axiom,
% 0.32/0.57      ! [A: real,B: real] :
% 0.32/0.57        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.32/0.57          = bot_bot_set_real )
% 0.32/0.57        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty_iff
% 0.32/0.57  thf(fact_3412_atLeastatMost__empty,axiom,
% 0.32/0.57      ! [B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_rat @ B @ A )
% 0.32/0.57       => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.32/0.57          = bot_bot_set_rat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty
% 0.32/0.57  thf(fact_3413_atLeastatMost__empty,axiom,
% 0.32/0.57      ! [B: num,A: num] :
% 0.32/0.57        ( ( ord_less_num @ B @ A )
% 0.32/0.57       => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.32/0.57          = bot_bot_set_num ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty
% 0.32/0.57  thf(fact_3414_atLeastatMost__empty,axiom,
% 0.32/0.57      ! [B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_nat @ B @ A )
% 0.32/0.57       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.32/0.57          = bot_bot_set_nat ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty
% 0.32/0.57  thf(fact_3415_atLeastatMost__empty,axiom,
% 0.32/0.57      ! [B: int,A: int] :
% 0.32/0.57        ( ( ord_less_int @ B @ A )
% 0.32/0.57       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.32/0.57          = bot_bot_set_int ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty
% 0.32/0.57  thf(fact_3416_atLeastatMost__empty,axiom,
% 0.32/0.57      ! [B: real,A: real] :
% 0.32/0.57        ( ( ord_less_real @ B @ A )
% 0.32/0.57       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.32/0.57          = bot_bot_set_real ) ) ).
% 0.32/0.57  
% 0.32/0.57  % atLeastatMost_empty
% 0.32/0.57  thf(fact_3417_double__diff,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 0.32/0.57         => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.32/0.57            = A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % double_diff
% 0.32/0.57  thf(fact_3418_double__diff,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.32/0.57         => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 0.32/0.57            = A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % double_diff
% 0.32/0.57  thf(fact_3419_Diff__subset,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_subset
% 0.32/0.57  thf(fact_3420_Diff__subset,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_subset
% 0.32/0.57  thf(fact_3421_Diff__mono,axiom,
% 0.32/0.57      ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.32/0.57       => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 0.32/0.57         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_mono
% 0.32/0.57  thf(fact_3422_Diff__mono,axiom,
% 0.32/0.57      ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 0.32/0.57       => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 0.32/0.57         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_mono
% 0.32/0.57  thf(fact_3423_Collect__mono__iff,axiom,
% 0.32/0.57      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 0.32/0.57        ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 0.32/0.57        = ( ! [X3: product_prod_int_int] :
% 0.32/0.57              ( ( P @ X3 )
% 0.32/0.57             => ( Q @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono_iff
% 0.32/0.57  thf(fact_3424_Collect__mono__iff,axiom,
% 0.32/0.57      ! [P: complex > $o,Q: complex > $o] :
% 0.32/0.57        ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 0.32/0.57        = ( ! [X3: complex] :
% 0.32/0.57              ( ( P @ X3 )
% 0.32/0.57             => ( Q @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono_iff
% 0.32/0.57  thf(fact_3425_Collect__mono__iff,axiom,
% 0.32/0.57      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.32/0.57        ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 0.32/0.57        = ( ! [X3: set_nat] :
% 0.32/0.57              ( ( P @ X3 )
% 0.32/0.57             => ( Q @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono_iff
% 0.32/0.57  thf(fact_3426_Collect__mono__iff,axiom,
% 0.32/0.57      ! [P: nat > $o,Q: nat > $o] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 0.32/0.57        = ( ! [X3: nat] :
% 0.32/0.57              ( ( P @ X3 )
% 0.32/0.57             => ( Q @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono_iff
% 0.32/0.57  thf(fact_3427_Collect__mono__iff,axiom,
% 0.32/0.57      ! [P: int > $o,Q: int > $o] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 0.32/0.57        = ( ! [X3: int] :
% 0.32/0.57              ( ( P @ X3 )
% 0.32/0.57             => ( Q @ X3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono_iff
% 0.32/0.57  thf(fact_3428_set__eq__subset,axiom,
% 0.32/0.57      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.32/0.57            & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_eq_subset
% 0.32/0.57  thf(fact_3429_subset__trans,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.32/0.57         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_trans
% 0.32/0.57  thf(fact_3430_Collect__mono,axiom,
% 0.32/0.57      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 0.32/0.57        ( ! [X6: product_prod_int_int] :
% 0.32/0.57            ( ( P @ X6 )
% 0.32/0.57           => ( Q @ X6 ) )
% 0.32/0.57       => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono
% 0.32/0.57  thf(fact_3431_Collect__mono,axiom,
% 0.32/0.57      ! [P: complex > $o,Q: complex > $o] :
% 0.32/0.57        ( ! [X6: complex] :
% 0.32/0.57            ( ( P @ X6 )
% 0.32/0.57           => ( Q @ X6 ) )
% 0.32/0.57       => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono
% 0.32/0.57  thf(fact_3432_Collect__mono,axiom,
% 0.32/0.57      ! [P: set_nat > $o,Q: set_nat > $o] :
% 0.32/0.57        ( ! [X6: set_nat] :
% 0.32/0.57            ( ( P @ X6 )
% 0.32/0.57           => ( Q @ X6 ) )
% 0.32/0.57       => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono
% 0.32/0.57  thf(fact_3433_Collect__mono,axiom,
% 0.32/0.57      ! [P: nat > $o,Q: nat > $o] :
% 0.32/0.57        ( ! [X6: nat] :
% 0.32/0.57            ( ( P @ X6 )
% 0.32/0.57           => ( Q @ X6 ) )
% 0.32/0.57       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono
% 0.32/0.57  thf(fact_3434_Collect__mono,axiom,
% 0.32/0.57      ! [P: int > $o,Q: int > $o] :
% 0.32/0.57        ( ! [X6: int] :
% 0.32/0.57            ( ( P @ X6 )
% 0.32/0.57           => ( Q @ X6 ) )
% 0.32/0.57       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_mono
% 0.32/0.57  thf(fact_3435_subset__refl,axiom,
% 0.32/0.57      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_refl
% 0.32/0.57  thf(fact_3436_subset__iff,axiom,
% 0.32/0.57      ( ord_le211207098394363844omplex
% 0.32/0.57      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.32/0.57          ! [T2: complex] :
% 0.32/0.57            ( ( member_complex @ T2 @ A6 )
% 0.32/0.57           => ( member_complex @ T2 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff
% 0.32/0.57  thf(fact_3437_subset__iff,axiom,
% 0.32/0.57      ( ord_less_eq_set_real
% 0.32/0.57      = ( ^ [A6: set_real,B6: set_real] :
% 0.32/0.57          ! [T2: real] :
% 0.32/0.57            ( ( member_real @ T2 @ A6 )
% 0.32/0.57           => ( member_real @ T2 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff
% 0.32/0.57  thf(fact_3438_subset__iff,axiom,
% 0.32/0.57      ( ord_le6893508408891458716et_nat
% 0.32/0.57      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.32/0.57          ! [T2: set_nat] :
% 0.32/0.57            ( ( member_set_nat @ T2 @ A6 )
% 0.32/0.57           => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff
% 0.32/0.57  thf(fact_3439_subset__iff,axiom,
% 0.32/0.57      ( ord_less_eq_set_nat
% 0.32/0.57      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.32/0.57          ! [T2: nat] :
% 0.32/0.57            ( ( member_nat @ T2 @ A6 )
% 0.32/0.57           => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff
% 0.32/0.57  thf(fact_3440_subset__iff,axiom,
% 0.32/0.57      ( ord_less_eq_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57          ! [T2: int] :
% 0.32/0.57            ( ( member_int @ T2 @ A6 )
% 0.32/0.57           => ( member_int @ T2 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff
% 0.32/0.57  thf(fact_3441_equalityD2,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( A2 = B3 )
% 0.32/0.57       => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % equalityD2
% 0.32/0.57  thf(fact_3442_equalityD1,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( A2 = B3 )
% 0.32/0.57       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % equalityD1
% 0.32/0.57  thf(fact_3443_subset__eq,axiom,
% 0.32/0.57      ( ord_le211207098394363844omplex
% 0.32/0.57      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.32/0.57          ! [X3: complex] :
% 0.32/0.57            ( ( member_complex @ X3 @ A6 )
% 0.32/0.57           => ( member_complex @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_eq
% 0.32/0.57  thf(fact_3444_subset__eq,axiom,
% 0.32/0.57      ( ord_less_eq_set_real
% 0.32/0.57      = ( ^ [A6: set_real,B6: set_real] :
% 0.32/0.57          ! [X3: real] :
% 0.32/0.57            ( ( member_real @ X3 @ A6 )
% 0.32/0.57           => ( member_real @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_eq
% 0.32/0.57  thf(fact_3445_subset__eq,axiom,
% 0.32/0.57      ( ord_le6893508408891458716et_nat
% 0.32/0.57      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.32/0.57          ! [X3: set_nat] :
% 0.32/0.57            ( ( member_set_nat @ X3 @ A6 )
% 0.32/0.57           => ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_eq
% 0.32/0.57  thf(fact_3446_subset__eq,axiom,
% 0.32/0.57      ( ord_less_eq_set_nat
% 0.32/0.57      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.32/0.57          ! [X3: nat] :
% 0.32/0.57            ( ( member_nat @ X3 @ A6 )
% 0.32/0.57           => ( member_nat @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_eq
% 0.32/0.57  thf(fact_3447_subset__eq,axiom,
% 0.32/0.57      ( ord_less_eq_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57          ! [X3: int] :
% 0.32/0.57            ( ( member_int @ X3 @ A6 )
% 0.32/0.57           => ( member_int @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_eq
% 0.32/0.57  thf(fact_3448_equalityE,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( A2 = B3 )
% 0.32/0.57       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57           => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % equalityE
% 0.32/0.57  thf(fact_3449_subsetD,axiom,
% 0.32/0.57      ! [A2: set_complex,B3: set_complex,C: complex] :
% 0.32/0.57        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.57       => ( ( member_complex @ C @ A2 )
% 0.32/0.57         => ( member_complex @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetD
% 0.32/0.57  thf(fact_3450_subsetD,axiom,
% 0.32/0.57      ! [A2: set_real,B3: set_real,C: real] :
% 0.32/0.57        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.57       => ( ( member_real @ C @ A2 )
% 0.32/0.57         => ( member_real @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetD
% 0.32/0.57  thf(fact_3451_subsetD,axiom,
% 0.32/0.57      ! [A2: set_set_nat,B3: set_set_nat,C: set_nat] :
% 0.32/0.57        ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 0.32/0.57       => ( ( member_set_nat @ C @ A2 )
% 0.32/0.57         => ( member_set_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetD
% 0.32/0.57  thf(fact_3452_subsetD,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat,C: nat] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.57       => ( ( member_nat @ C @ A2 )
% 0.32/0.57         => ( member_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetD
% 0.32/0.57  thf(fact_3453_subsetD,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,C: int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( member_int @ C @ A2 )
% 0.32/0.57         => ( member_int @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subsetD
% 0.32/0.57  thf(fact_3454_in__mono,axiom,
% 0.32/0.57      ! [A2: set_complex,B3: set_complex,X: complex] :
% 0.32/0.57        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.57       => ( ( member_complex @ X @ A2 )
% 0.32/0.57         => ( member_complex @ X @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % in_mono
% 0.32/0.57  thf(fact_3455_in__mono,axiom,
% 0.32/0.57      ! [A2: set_real,B3: set_real,X: real] :
% 0.32/0.57        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.57       => ( ( member_real @ X @ A2 )
% 0.32/0.57         => ( member_real @ X @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % in_mono
% 0.32/0.57  thf(fact_3456_in__mono,axiom,
% 0.32/0.57      ! [A2: set_set_nat,B3: set_set_nat,X: set_nat] :
% 0.32/0.57        ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 0.32/0.57       => ( ( member_set_nat @ X @ A2 )
% 0.32/0.57         => ( member_set_nat @ X @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % in_mono
% 0.32/0.57  thf(fact_3457_in__mono,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat,X: nat] :
% 0.32/0.57        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.57       => ( ( member_nat @ X @ A2 )
% 0.32/0.57         => ( member_nat @ X @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % in_mono
% 0.32/0.57  thf(fact_3458_in__mono,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,X: int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( member_int @ X @ A2 )
% 0.32/0.57         => ( member_int @ X @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % in_mono
% 0.32/0.57  thf(fact_3459_psubset__imp__ex__mem,axiom,
% 0.32/0.57      ! [A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( ord_less_set_complex @ A2 @ B3 )
% 0.32/0.57       => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_ex_mem
% 0.32/0.57  thf(fact_3460_psubset__imp__ex__mem,axiom,
% 0.32/0.57      ! [A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( ord_less_set_real @ A2 @ B3 )
% 0.32/0.57       => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_ex_mem
% 0.32/0.57  thf(fact_3461_psubset__imp__ex__mem,axiom,
% 0.32/0.57      ! [A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( ord_less_set_set_nat @ A2 @ B3 )
% 0.32/0.57       => ? [B5: set_nat] : ( member_set_nat @ B5 @ ( minus_2163939370556025621et_nat @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_ex_mem
% 0.32/0.57  thf(fact_3462_psubset__imp__ex__mem,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_set_int @ A2 @ B3 )
% 0.32/0.57       => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_ex_mem
% 0.32/0.57  thf(fact_3463_psubset__imp__ex__mem,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( ord_less_set_nat @ A2 @ B3 )
% 0.32/0.57       => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_ex_mem
% 0.32/0.57  thf(fact_3464_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_real,P: real > $o] :
% 0.32/0.57        ( ord_less_eq_set_real
% 0.32/0.57        @ ( collect_real
% 0.32/0.57          @ ^ [X3: real] :
% 0.32/0.57              ( ( member_real @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3465_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 0.32/0.57        ( ord_le2843351958646193337nt_int
% 0.32/0.57        @ ( collec213857154873943460nt_int
% 0.32/0.57          @ ^ [X3: product_prod_int_int] :
% 0.32/0.57              ( ( member5262025264175285858nt_int @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3466_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_complex,P: complex > $o] :
% 0.32/0.57        ( ord_le211207098394363844omplex
% 0.32/0.57        @ ( collect_complex
% 0.32/0.57          @ ^ [X3: complex] :
% 0.32/0.57              ( ( member_complex @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3467_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_set_nat,P: set_nat > $o] :
% 0.32/0.57        ( ord_le6893508408891458716et_nat
% 0.32/0.57        @ ( collect_set_nat
% 0.32/0.57          @ ^ [X3: set_nat] :
% 0.32/0.57              ( ( member_set_nat @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3468_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_nat,P: nat > $o] :
% 0.32/0.57        ( ord_less_eq_set_nat
% 0.32/0.57        @ ( collect_nat
% 0.32/0.57          @ ^ [X3: nat] :
% 0.32/0.57              ( ( member_nat @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3469_Collect__subset,axiom,
% 0.32/0.57      ! [A2: set_int,P: int > $o] :
% 0.32/0.57        ( ord_less_eq_set_int
% 0.32/0.57        @ ( collect_int
% 0.32/0.57          @ ^ [X3: int] :
% 0.32/0.57              ( ( member_int @ X3 @ A2 )
% 0.32/0.57              & ( P @ X3 ) ) )
% 0.32/0.57        @ A2 ) ).
% 0.32/0.57  
% 0.32/0.57  % Collect_subset
% 0.32/0.57  thf(fact_3470_less__eq__set__def,axiom,
% 0.32/0.57      ( ord_le211207098394363844omplex
% 0.32/0.57      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.32/0.57            ( ord_le4573692005234683329plex_o
% 0.32/0.57            @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 0.32/0.57            @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_eq_set_def
% 0.32/0.57  thf(fact_3471_less__eq__set__def,axiom,
% 0.32/0.57      ( ord_less_eq_set_real
% 0.32/0.57      = ( ^ [A6: set_real,B6: set_real] :
% 0.32/0.57            ( ord_less_eq_real_o
% 0.32/0.57            @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 0.32/0.57            @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_eq_set_def
% 0.32/0.57  thf(fact_3472_less__eq__set__def,axiom,
% 0.32/0.57      ( ord_le6893508408891458716et_nat
% 0.32/0.57      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.32/0.57            ( ord_le3964352015994296041_nat_o
% 0.32/0.57            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 0.32/0.57            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_eq_set_def
% 0.32/0.57  thf(fact_3473_less__eq__set__def,axiom,
% 0.32/0.57      ( ord_less_eq_set_nat
% 0.32/0.57      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.32/0.57            ( ord_less_eq_nat_o
% 0.32/0.57            @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 0.32/0.57            @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_eq_set_def
% 0.32/0.57  thf(fact_3474_less__eq__set__def,axiom,
% 0.32/0.57      ( ord_less_eq_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( ord_less_eq_int_o
% 0.32/0.57            @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 0.32/0.57            @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_eq_set_def
% 0.32/0.57  thf(fact_3475_max_Omono,axiom,
% 0.32/0.57      ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.32/0.57       => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 0.32/0.57         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3476_max_Omono,axiom,
% 0.32/0.57      ! [C: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ D @ B )
% 0.32/0.57         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3477_max_Omono,axiom,
% 0.32/0.57      ! [C: rat,A: rat,D: rat,B: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ C @ A )
% 0.32/0.57       => ( ( ord_less_eq_rat @ D @ B )
% 0.32/0.57         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3478_max_Omono,axiom,
% 0.32/0.57      ! [C: num,A: num,D: num,B: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ C @ A )
% 0.32/0.57       => ( ( ord_less_eq_num @ D @ B )
% 0.32/0.57         => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3479_max_Omono,axiom,
% 0.32/0.57      ! [C: nat,A: nat,D: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.57       => ( ( ord_less_eq_nat @ D @ B )
% 0.32/0.57         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3480_max_Omono,axiom,
% 0.32/0.57      ! [C: int,A: int,D: int,B: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ C @ A )
% 0.32/0.57       => ( ( ord_less_eq_int @ D @ B )
% 0.32/0.57         => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.mono
% 0.32/0.57  thf(fact_3481_max_OorderE,axiom,
% 0.32/0.57      ! [B: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3482_max_OorderE,axiom,
% 0.32/0.57      ! [B: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3483_max_OorderE,axiom,
% 0.32/0.57      ! [B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_max_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3484_max_OorderE,axiom,
% 0.32/0.57      ! [B: num,A: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_max_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3485_max_OorderE,axiom,
% 0.32/0.57      ! [B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_max_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3486_max_OorderE,axiom,
% 0.32/0.57      ! [B: int,A: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.57       => ( A
% 0.32/0.57          = ( ord_max_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderE
% 0.32/0.57  thf(fact_3487_max_OorderI,axiom,
% 0.32/0.57      ! [A: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 0.32/0.57       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3488_max_OorderI,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_max_Code_integer @ A @ B ) )
% 0.32/0.57       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3489_max_OorderI,axiom,
% 0.32/0.57      ! [A: rat,B: rat] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_max_rat @ A @ B ) )
% 0.32/0.57       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3490_max_OorderI,axiom,
% 0.32/0.57      ! [A: num,B: num] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_max_num @ A @ B ) )
% 0.32/0.57       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3491_max_OorderI,axiom,
% 0.32/0.57      ! [A: nat,B: nat] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_max_nat @ A @ B ) )
% 0.32/0.57       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3492_max_OorderI,axiom,
% 0.32/0.57      ! [A: int,B: int] :
% 0.32/0.57        ( ( A
% 0.32/0.57          = ( ord_max_int @ A @ B ) )
% 0.32/0.57       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.orderI
% 0.32/0.57  thf(fact_3493_max_OboundedE,axiom,
% 0.32/0.57      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.32/0.57           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3494_max_OboundedE,axiom,
% 0.32/0.57      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.57           => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3495_max_OboundedE,axiom,
% 0.32/0.57      ! [B: rat,C: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.57           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3496_max_OboundedE,axiom,
% 0.32/0.57      ! [B: num,C: num,A: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_eq_num @ B @ A )
% 0.32/0.57           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3497_max_OboundedE,axiom,
% 0.32/0.57      ! [B: nat,C: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.57           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3498_max_OboundedE,axiom,
% 0.32/0.57      ! [B: int,C: int,A: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_eq_int @ B @ A )
% 0.32/0.57           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedE
% 0.32/0.57  thf(fact_3499_max_OboundedI,axiom,
% 0.32/0.57      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 0.32/0.57       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.32/0.57         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3500_max_OboundedI,axiom,
% 0.32/0.57      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.32/0.57       => ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.32/0.57         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3501_max_OboundedI,axiom,
% 0.32/0.57      ! [B: rat,A: rat,C: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.57       => ( ( ord_less_eq_rat @ C @ A )
% 0.32/0.57         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3502_max_OboundedI,axiom,
% 0.32/0.57      ! [B: num,A: num,C: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.57       => ( ( ord_less_eq_num @ C @ A )
% 0.32/0.57         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3503_max_OboundedI,axiom,
% 0.32/0.57      ! [B: nat,A: nat,C: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.57       => ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.57         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3504_max_OboundedI,axiom,
% 0.32/0.57      ! [B: int,A: int,C: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.57       => ( ( ord_less_eq_int @ C @ A )
% 0.32/0.57         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.boundedI
% 0.32/0.57  thf(fact_3505_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_le2932123472753598470d_enat
% 0.32/0.57      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3506_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_le3102999989581377725nteger
% 0.32/0.57      = ( ^ [B2: code_integer,A3: code_integer] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_max_Code_integer @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3507_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_less_eq_rat
% 0.32/0.57      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3508_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_less_eq_num
% 0.32/0.57      = ( ^ [B2: num,A3: num] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3509_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_less_eq_nat
% 0.32/0.57      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3510_max_Oorder__iff,axiom,
% 0.32/0.57      ( ord_less_eq_int
% 0.32/0.57      = ( ^ [B2: int,A3: int] :
% 0.32/0.57            ( A3
% 0.32/0.57            = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.order_iff
% 0.32/0.57  thf(fact_3511_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3512_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3513_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3514_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3515_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3516_max_Ocobounded1,axiom,
% 0.32/0.57      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded1
% 0.32/0.57  thf(fact_3517_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3518_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3519_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3520_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3521_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3522_max_Ocobounded2,axiom,
% 0.32/0.57      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.cobounded2
% 0.32/0.57  thf(fact_3523_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 0.32/0.57          | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3524_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 0.32/0.57        = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 0.32/0.57          | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3525_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_eq_rat @ Z @ X )
% 0.32/0.57          | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3526_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: num,X: num,Y: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_eq_num @ Z @ X )
% 0.32/0.57          | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3527_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_eq_nat @ Z @ X )
% 0.32/0.57          | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3528_le__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: int,X: int,Y: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_eq_int @ Z @ X )
% 0.32/0.57          | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % le_max_iff_disj
% 0.32/0.57  thf(fact_3529_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_le2932123472753598470d_enat
% 0.32/0.57      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 0.32/0.57            ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3530_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_le3102999989581377725nteger
% 0.32/0.57      = ( ^ [B2: code_integer,A3: code_integer] :
% 0.32/0.57            ( ( ord_max_Code_integer @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3531_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_less_eq_rat
% 0.32/0.57      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.57            ( ( ord_max_rat @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3532_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_less_eq_num
% 0.32/0.57      = ( ^ [B2: num,A3: num] :
% 0.32/0.57            ( ( ord_max_num @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3533_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_less_eq_nat
% 0.32/0.57      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.57            ( ( ord_max_nat @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3534_max_Oabsorb__iff1,axiom,
% 0.32/0.57      ( ord_less_eq_int
% 0.32/0.57      = ( ^ [B2: int,A3: int] :
% 0.32/0.57            ( ( ord_max_int @ A3 @ B2 )
% 0.32/0.57            = A3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff1
% 0.32/0.57  thf(fact_3535_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_le2932123472753598470d_enat
% 0.32/0.57      = ( ^ [A3: extended_enat,B2: extended_enat] :
% 0.32/0.57            ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3536_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_le3102999989581377725nteger
% 0.32/0.57      = ( ^ [A3: code_integer,B2: code_integer] :
% 0.32/0.57            ( ( ord_max_Code_integer @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3537_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_less_eq_rat
% 0.32/0.57      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.57            ( ( ord_max_rat @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3538_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_less_eq_num
% 0.32/0.57      = ( ^ [A3: num,B2: num] :
% 0.32/0.57            ( ( ord_max_num @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3539_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_less_eq_nat
% 0.32/0.57      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.57            ( ( ord_max_nat @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3540_max_Oabsorb__iff2,axiom,
% 0.32/0.57      ( ord_less_eq_int
% 0.32/0.57      = ( ^ [A3: int,B2: int] :
% 0.32/0.57            ( ( ord_max_int @ A3 @ B2 )
% 0.32/0.57            = B2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.absorb_iff2
% 0.32/0.57  thf(fact_3541_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 0.32/0.57       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3542_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ C @ A )
% 0.32/0.57       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3543_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: rat,A: rat,B: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ C @ A )
% 0.32/0.57       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3544_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: num,A: num,B: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ C @ A )
% 0.32/0.57       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3545_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: nat,A: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.57       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3546_max_OcoboundedI1,axiom,
% 0.32/0.57      ! [C: int,A: int,B: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ C @ A )
% 0.32/0.57       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI1
% 0.32/0.57  thf(fact_3547_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 0.32/0.57       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3548_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.32/0.57       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3549_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: rat,B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.57       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3550_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: num,B: num,A: num] :
% 0.32/0.57        ( ( ord_less_eq_num @ C @ B )
% 0.32/0.57       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3551_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: nat,B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.57       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3552_max_OcoboundedI2,axiom,
% 0.32/0.57      ! [C: int,B: int,A: int] :
% 0.32/0.57        ( ( ord_less_eq_int @ C @ B )
% 0.32/0.57       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.coboundedI2
% 0.32/0.57  thf(fact_3553_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 0.32/0.57          | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3554_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 0.32/0.57        = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 0.32/0.57          | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3555_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: real,X: real,Y: real] :
% 0.32/0.57        ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_real @ Z @ X )
% 0.32/0.57          | ( ord_less_real @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3556_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.57        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_rat @ Z @ X )
% 0.32/0.57          | ( ord_less_rat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3557_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: num,X: num,Y: num] :
% 0.32/0.57        ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_num @ Z @ X )
% 0.32/0.57          | ( ord_less_num @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3558_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.57        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_nat @ Z @ X )
% 0.32/0.57          | ( ord_less_nat @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3559_less__max__iff__disj,axiom,
% 0.32/0.57      ! [Z: int,X: int,Y: int] :
% 0.32/0.57        ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 0.32/0.57        = ( ( ord_less_int @ Z @ X )
% 0.32/0.57          | ( ord_less_int @ Z @ Y ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % less_max_iff_disj
% 0.32/0.57  thf(fact_3560_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 0.32/0.57           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3561_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.32/0.57           => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3562_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: real,C: real,A: real] :
% 0.32/0.57        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_real @ B @ A )
% 0.32/0.57           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3563_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: rat,C: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_rat @ B @ A )
% 0.32/0.57           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3564_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: num,C: num,A: num] :
% 0.32/0.57        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_num @ B @ A )
% 0.32/0.57           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3565_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: nat,C: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_nat @ B @ A )
% 0.32/0.57           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3566_max_Ostrict__boundedE,axiom,
% 0.32/0.57      ! [B: int,C: int,A: int] :
% 0.32/0.57        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 0.32/0.57       => ~ ( ( ord_less_int @ B @ A )
% 0.32/0.57           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_boundedE
% 0.32/0.57  thf(fact_3567_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_le72135733267957522d_enat
% 0.32/0.57      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3568_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_le6747313008572928689nteger
% 0.32/0.57      = ( ^ [B2: code_integer,A3: code_integer] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_Code_integer @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3569_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_less_real
% 0.32/0.57      = ( ^ [B2: real,A3: real] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_real @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3570_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_less_rat
% 0.32/0.57      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_rat @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3571_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_less_num
% 0.32/0.57      = ( ^ [B2: num,A3: num] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_num @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3572_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_less_nat
% 0.32/0.57      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_nat @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3573_max_Ostrict__order__iff,axiom,
% 0.32/0.57      ( ord_less_int
% 0.32/0.57      = ( ^ [B2: int,A3: int] :
% 0.32/0.57            ( ( A3
% 0.32/0.57              = ( ord_max_int @ A3 @ B2 ) )
% 0.32/0.57            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_order_iff
% 0.32/0.57  thf(fact_3574_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ C @ A )
% 0.32/0.57       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3575_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ C @ A )
% 0.32/0.57       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3576_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: real,A: real,B: real] :
% 0.32/0.57        ( ( ord_less_real @ C @ A )
% 0.32/0.57       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3577_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: rat,A: rat,B: rat] :
% 0.32/0.57        ( ( ord_less_rat @ C @ A )
% 0.32/0.57       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3578_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: num,A: num,B: num] :
% 0.32/0.57        ( ( ord_less_num @ C @ A )
% 0.32/0.57       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3579_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: nat,A: nat,B: nat] :
% 0.32/0.57        ( ( ord_less_nat @ C @ A )
% 0.32/0.57       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3580_max_Ostrict__coboundedI1,axiom,
% 0.32/0.57      ! [C: int,A: int,B: int] :
% 0.32/0.57        ( ( ord_less_int @ C @ A )
% 0.32/0.57       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI1
% 0.32/0.57  thf(fact_3581_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 0.32/0.57        ( ( ord_le72135733267957522d_enat @ C @ B )
% 0.32/0.57       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3582_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.57        ( ( ord_le6747313008572928689nteger @ C @ B )
% 0.32/0.57       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3583_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: real,B: real,A: real] :
% 0.32/0.57        ( ( ord_less_real @ C @ B )
% 0.32/0.57       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3584_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: rat,B: rat,A: rat] :
% 0.32/0.57        ( ( ord_less_rat @ C @ B )
% 0.32/0.57       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3585_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: num,B: num,A: num] :
% 0.32/0.57        ( ( ord_less_num @ C @ B )
% 0.32/0.57       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3586_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: nat,B: nat,A: nat] :
% 0.32/0.57        ( ( ord_less_nat @ C @ B )
% 0.32/0.57       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3587_max_Ostrict__coboundedI2,axiom,
% 0.32/0.57      ! [C: int,B: int,A: int] :
% 0.32/0.57        ( ( ord_less_int @ C @ B )
% 0.32/0.57       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % max.strict_coboundedI2
% 0.32/0.57  thf(fact_3588_psubsetE,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_set_int @ A2 @ B3 )
% 0.32/0.57       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57           => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubsetE
% 0.32/0.57  thf(fact_3589_psubset__eq,axiom,
% 0.32/0.57      ( ord_less_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.32/0.57            & ( A6 != B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_eq
% 0.32/0.57  thf(fact_3590_psubset__imp__subset,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( ord_less_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_imp_subset
% 0.32/0.57  thf(fact_3591_psubset__subset__trans,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.32/0.57        ( ( ord_less_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 0.32/0.57         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % psubset_subset_trans
% 0.32/0.57  thf(fact_3592_subset__not__subset__eq,axiom,
% 0.32/0.57      ( ord_less_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.32/0.57            & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_not_subset_eq
% 0.32/0.57  thf(fact_3593_subset__psubset__trans,axiom,
% 0.32/0.57      ! [A2: set_int,B3: set_int,C4: set_int] :
% 0.32/0.57        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.57       => ( ( ord_less_set_int @ B3 @ C4 )
% 0.32/0.57         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_psubset_trans
% 0.32/0.57  thf(fact_3594_subset__iff__psubset__eq,axiom,
% 0.32/0.57      ( ord_less_eq_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( ( ord_less_set_int @ A6 @ B6 )
% 0.32/0.57            | ( A6 = B6 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % subset_iff_psubset_eq
% 0.32/0.57  thf(fact_3595_vebt__delete_Opelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.32/0.57        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                 => ( ( Y
% 0.32/0.57                      = ( vEBT_Leaf @ $false @ B5 ) )
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 0.32/0.57           => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57                 => ( ( Xa2
% 0.32/0.57                      = ( suc @ zero_zero_nat ) )
% 0.32/0.57                   => ( ( Y
% 0.32/0.57                        = ( vEBT_Leaf @ A5 @ $false ) )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.32/0.57             => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57                   => ! [N3: nat] :
% 0.32/0.57                        ( ( Xa2
% 0.32/0.57                          = ( suc @ ( suc @ N3 ) ) )
% 0.32/0.57                       => ( ( Y
% 0.32/0.57                            = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 0.32/0.57               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57                     => ( ( Y
% 0.32/0.57                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 0.32/0.57                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.32/0.57                       => ( ( Y
% 0.32/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 0.32/0.57                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.32/0.57                          ( ( X
% 0.32/0.57                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.32/0.57                         => ( ( Y
% 0.32/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.32/0.57                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 0.32/0.57                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                            ( ( X
% 0.32/0.57                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                           => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.32/0.57                                 => ( Y
% 0.32/0.57                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.57                                & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.32/0.57                                 => ( ( ( ( Xa2 = Mi2 )
% 0.32/0.57                                        & ( Xa2 = Ma2 ) )
% 0.32/0.57                                     => ( Y
% 0.32/0.57                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.57                                    & ( ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                                          & ( Xa2 = Ma2 ) )
% 0.32/0.57                                     => ( Y
% 0.32/0.57                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                            @ ( vEBT_Node
% 0.32/0.57                                              @ ( some_P7363390416028606310at_nat
% 0.32/0.57                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.57                                                  @ ( if_nat
% 0.32/0.57                                                    @ ( ( ( Xa2 = Mi2 )
% 0.32/0.57                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.32/0.57                                                          = Ma2 ) )
% 0.32/0.57                                                      & ( ( Xa2 != Mi2 )
% 0.32/0.57                                                       => ( Xa2 = Ma2 ) ) )
% 0.32/0.57                                                    @ ( if_nat
% 0.32/0.57                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                                        = none_nat )
% 0.32/0.57                                                      @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.57                                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.57                                                    @ Ma2 ) ) )
% 0.32/0.57                                              @ ( suc @ ( suc @ Va2 ) )
% 0.32/0.57                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                            @ ( vEBT_Node
% 0.32/0.57                                              @ ( some_P7363390416028606310at_nat
% 0.32/0.57                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.32/0.57                                                  @ ( if_nat
% 0.32/0.57                                                    @ ( ( ( Xa2 = Mi2 )
% 0.32/0.57                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.32/0.57                                                          = Ma2 ) )
% 0.32/0.57                                                      & ( ( Xa2 != Mi2 )
% 0.32/0.57                                                       => ( Xa2 = Ma2 ) ) )
% 0.32/0.57                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.32/0.57                                                    @ Ma2 ) ) )
% 0.32/0.57                                              @ ( suc @ ( suc @ Va2 ) )
% 0.32/0.57                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                              @ Summary2 ) )
% 0.32/0.57                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 0.32/0.57                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_delete.pelims
% 0.32/0.57  thf(fact_3596_vebt__insert_Opelims,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.32/0.57        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                     => ( Y
% 0.32/0.57                        = ( vEBT_Leaf @ $true @ B5 ) ) )
% 0.32/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                         => ( Y
% 0.32/0.57                            = ( vEBT_Leaf @ A5 @ $true ) ) )
% 0.32/0.57                        & ( ( Xa2 != one_one_nat )
% 0.32/0.57                         => ( Y
% 0.32/0.57                            = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 0.32/0.57           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.32/0.57                 => ( ( Y
% 0.32/0.57                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 0.32/0.57             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.32/0.57                   => ( ( Y
% 0.32/0.57                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 0.32/0.57               => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                     => ( ( Y
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 0.32/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                       => ( ( Y
% 0.32/0.57                            = ( if_VEBT_VEBT
% 0.32/0.57                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                & ~ ( ( Xa2 = Mi2 )
% 0.32/0.57                                    | ( Xa2 = Ma2 ) ) )
% 0.32/0.57                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.32/0.57                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_insert.pelims
% 0.32/0.57  thf(fact_3597_vebt__member_Opelims_I3_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 0.32/0.57                 => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                     => A5 )
% 0.32/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                         => B5 )
% 0.32/0.57                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.32/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.32/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 0.32/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 0.32/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.32/0.57                         => ( ( Xa2 != Mi2 )
% 0.32/0.57                           => ( ( Xa2 != Ma2 )
% 0.32/0.57                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_member.pelims(3)
% 0.32/0.57  thf(fact_3598_vebt__member_Opelims_I1_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.57        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( Y
% 0.32/0.57                    = ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                       => A5 )
% 0.32/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                           => B5 )
% 0.32/0.57                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 0.32/0.57           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.57                 => ( ~ Y
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.32/0.57             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 0.32/0.57                   => ( ~ Y
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 0.32/0.57               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.57                      ( ( X
% 0.32/0.57                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.32/0.57                     => ( ~ Y
% 0.32/0.57                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.32/0.57                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                        ( ( X
% 0.32/0.57                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                       => ( ( Y
% 0.32/0.57                            = ( ( Xa2 != Mi2 )
% 0.32/0.57                             => ( ( Xa2 != Ma2 )
% 0.32/0.57                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 0.32/0.57                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_member.pelims(1)
% 0.32/0.57  thf(fact_3599_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 0.32/0.57                 => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                     => A5 )
% 0.32/0.57                    & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                     => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                         => B5 )
% 0.32/0.57                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.32/0.57           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 0.32/0.57             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 0.32/0.57                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.pelims(3)
% 0.32/0.57  thf(fact_3600_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 0.32/0.57                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                       => A5 )
% 0.32/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                           => B5 )
% 0.32/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.32/0.57           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 0.32/0.57                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.pelims(2)
% 0.32/0.57  thf(fact_3601_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.57        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( Y
% 0.32/0.57                    = ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                       => A5 )
% 0.32/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                           => B5 )
% 0.32/0.57                          & ( Xa2 = one_one_nat ) ) ) ) )
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 0.32/0.57           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 0.32/0.57                 => ( ~ Y
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 0.32/0.57             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 0.32/0.57                    ( ( X
% 0.32/0.57                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 0.32/0.57                   => ( ( Y
% 0.32/0.57                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.32/0.57                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % VEBT_internal.naive_member.pelims(1)
% 0.32/0.57  thf(fact_3602_vebt__member_Opelims_I2_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.57        ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [A5: $o,B5: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.57               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 0.32/0.57                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.57                       => A5 )
% 0.32/0.57                      & ( ( Xa2 != zero_zero_nat )
% 0.32/0.57                       => ( ( ( Xa2 = one_one_nat )
% 0.32/0.57                           => B5 )
% 0.32/0.57                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.32/0.57           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 0.32/0.57                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.32/0.57                   => ~ ( ( Xa2 != Mi2 )
% 0.32/0.57                       => ( ( Xa2 != Ma2 )
% 0.32/0.57                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.32/0.57                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.32/0.57                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.57                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.57                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % vebt_member.pelims(2)
% 0.32/0.57  thf(fact_3603_DiffI,axiom,
% 0.32/0.57      ! [C: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( member_complex @ C @ A2 )
% 0.32/0.57       => ( ~ ( member_complex @ C @ B3 )
% 0.32/0.57         => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffI
% 0.32/0.57  thf(fact_3604_DiffI,axiom,
% 0.32/0.57      ! [C: real,A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( member_real @ C @ A2 )
% 0.32/0.57       => ( ~ ( member_real @ C @ B3 )
% 0.32/0.57         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffI
% 0.32/0.57  thf(fact_3605_DiffI,axiom,
% 0.32/0.57      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( member_set_nat @ C @ A2 )
% 0.32/0.57       => ( ~ ( member_set_nat @ C @ B3 )
% 0.32/0.57         => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffI
% 0.32/0.57  thf(fact_3606_DiffI,axiom,
% 0.32/0.57      ! [C: int,A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( member_int @ C @ A2 )
% 0.32/0.57       => ( ~ ( member_int @ C @ B3 )
% 0.32/0.57         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffI
% 0.32/0.57  thf(fact_3607_DiffI,axiom,
% 0.32/0.57      ! [C: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( member_nat @ C @ A2 )
% 0.32/0.57       => ( ~ ( member_nat @ C @ B3 )
% 0.32/0.57         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffI
% 0.32/0.57  thf(fact_3608_Diff__iff,axiom,
% 0.32/0.57      ! [C: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.57        = ( ( member_complex @ C @ A2 )
% 0.32/0.57          & ~ ( member_complex @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_iff
% 0.32/0.57  thf(fact_3609_Diff__iff,axiom,
% 0.32/0.57      ! [C: real,A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 0.32/0.57        = ( ( member_real @ C @ A2 )
% 0.32/0.57          & ~ ( member_real @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_iff
% 0.32/0.57  thf(fact_3610_Diff__iff,axiom,
% 0.32/0.57      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 0.32/0.57        = ( ( member_set_nat @ C @ A2 )
% 0.32/0.57          & ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_iff
% 0.32/0.57  thf(fact_3611_Diff__iff,axiom,
% 0.32/0.57      ! [C: int,A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.57        = ( ( member_int @ C @ A2 )
% 0.32/0.57          & ~ ( member_int @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_iff
% 0.32/0.57  thf(fact_3612_Diff__iff,axiom,
% 0.32/0.57      ! [C: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.57        = ( ( member_nat @ C @ A2 )
% 0.32/0.57          & ~ ( member_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_iff
% 0.32/0.57  thf(fact_3613_Diff__idemp,axiom,
% 0.32/0.57      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ B3 )
% 0.32/0.57        = ( minus_minus_set_nat @ A2 @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % Diff_idemp
% 0.32/0.57  thf(fact_3614_DiffE,axiom,
% 0.32/0.57      ! [C: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( ( member_complex @ C @ A2 )
% 0.32/0.57           => ( member_complex @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffE
% 0.32/0.57  thf(fact_3615_DiffE,axiom,
% 0.32/0.57      ! [C: real,A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( ( member_real @ C @ A2 )
% 0.32/0.57           => ( member_real @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffE
% 0.32/0.57  thf(fact_3616_DiffE,axiom,
% 0.32/0.57      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( ( member_set_nat @ C @ A2 )
% 0.32/0.57           => ( member_set_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffE
% 0.32/0.57  thf(fact_3617_DiffE,axiom,
% 0.32/0.57      ! [C: int,A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( ( member_int @ C @ A2 )
% 0.32/0.57           => ( member_int @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffE
% 0.32/0.57  thf(fact_3618_DiffE,axiom,
% 0.32/0.57      ! [C: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( ( member_nat @ C @ A2 )
% 0.32/0.57           => ( member_nat @ C @ B3 ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffE
% 0.32/0.57  thf(fact_3619_DiffD1,axiom,
% 0.32/0.57      ! [C: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.57       => ( member_complex @ C @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD1
% 0.32/0.57  thf(fact_3620_DiffD1,axiom,
% 0.32/0.57      ! [C: real,A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 0.32/0.57       => ( member_real @ C @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD1
% 0.32/0.57  thf(fact_3621_DiffD1,axiom,
% 0.32/0.57      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 0.32/0.57       => ( member_set_nat @ C @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD1
% 0.32/0.57  thf(fact_3622_DiffD1,axiom,
% 0.32/0.57      ! [C: int,A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.57       => ( member_int @ C @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD1
% 0.32/0.57  thf(fact_3623_DiffD1,axiom,
% 0.32/0.57      ! [C: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.57       => ( member_nat @ C @ A2 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD1
% 0.32/0.57  thf(fact_3624_DiffD2,axiom,
% 0.32/0.57      ! [C: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.57        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( member_complex @ C @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD2
% 0.32/0.57  thf(fact_3625_DiffD2,axiom,
% 0.32/0.57      ! [C: real,A2: set_real,B3: set_real] :
% 0.32/0.57        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( member_real @ C @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD2
% 0.32/0.57  thf(fact_3626_DiffD2,axiom,
% 0.32/0.57      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.57        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( member_set_nat @ C @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD2
% 0.32/0.57  thf(fact_3627_DiffD2,axiom,
% 0.32/0.57      ! [C: int,A2: set_int,B3: set_int] :
% 0.32/0.57        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( member_int @ C @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD2
% 0.32/0.57  thf(fact_3628_DiffD2,axiom,
% 0.32/0.57      ! [C: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.57        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.57       => ~ ( member_nat @ C @ B3 ) ) ).
% 0.32/0.57  
% 0.32/0.57  % DiffD2
% 0.32/0.57  thf(fact_3629_minus__set__def,axiom,
% 0.32/0.57      ( minus_minus_set_real
% 0.32/0.57      = ( ^ [A6: set_real,B6: set_real] :
% 0.32/0.57            ( collect_real
% 0.32/0.57            @ ( minus_minus_real_o
% 0.32/0.57              @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3630_minus__set__def,axiom,
% 0.32/0.57      ( minus_1052850069191792384nt_int
% 0.32/0.57      = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 0.32/0.57            ( collec213857154873943460nt_int
% 0.32/0.57            @ ( minus_711738161318947805_int_o
% 0.32/0.57              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3631_minus__set__def,axiom,
% 0.32/0.57      ( minus_811609699411566653omplex
% 0.32/0.57      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.32/0.57            ( collect_complex
% 0.32/0.57            @ ( minus_8727706125548526216plex_o
% 0.32/0.57              @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3632_minus__set__def,axiom,
% 0.32/0.57      ( minus_2163939370556025621et_nat
% 0.32/0.57      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.32/0.57            ( collect_set_nat
% 0.32/0.57            @ ( minus_6910147592129066416_nat_o
% 0.32/0.57              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3633_minus__set__def,axiom,
% 0.32/0.57      ( minus_minus_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( collect_int
% 0.32/0.57            @ ( minus_minus_int_o
% 0.32/0.57              @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3634_minus__set__def,axiom,
% 0.32/0.57      ( minus_minus_set_nat
% 0.32/0.57      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.32/0.57            ( collect_nat
% 0.32/0.57            @ ( minus_minus_nat_o
% 0.32/0.57              @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 0.32/0.57              @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % minus_set_def
% 0.32/0.57  thf(fact_3635_set__diff__eq,axiom,
% 0.32/0.57      ( minus_minus_set_real
% 0.32/0.57      = ( ^ [A6: set_real,B6: set_real] :
% 0.32/0.57            ( collect_real
% 0.32/0.57            @ ^ [X3: real] :
% 0.32/0.57                ( ( member_real @ X3 @ A6 )
% 0.32/0.57                & ~ ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3636_set__diff__eq,axiom,
% 0.32/0.57      ( minus_1052850069191792384nt_int
% 0.32/0.57      = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 0.32/0.57            ( collec213857154873943460nt_int
% 0.32/0.57            @ ^ [X3: product_prod_int_int] :
% 0.32/0.57                ( ( member5262025264175285858nt_int @ X3 @ A6 )
% 0.32/0.57                & ~ ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3637_set__diff__eq,axiom,
% 0.32/0.57      ( minus_811609699411566653omplex
% 0.32/0.57      = ( ^ [A6: set_complex,B6: set_complex] :
% 0.32/0.57            ( collect_complex
% 0.32/0.57            @ ^ [X3: complex] :
% 0.32/0.57                ( ( member_complex @ X3 @ A6 )
% 0.32/0.57                & ~ ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3638_set__diff__eq,axiom,
% 0.32/0.57      ( minus_2163939370556025621et_nat
% 0.32/0.57      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.32/0.57            ( collect_set_nat
% 0.32/0.57            @ ^ [X3: set_nat] :
% 0.32/0.57                ( ( member_set_nat @ X3 @ A6 )
% 0.32/0.57                & ~ ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3639_set__diff__eq,axiom,
% 0.32/0.57      ( minus_minus_set_int
% 0.32/0.57      = ( ^ [A6: set_int,B6: set_int] :
% 0.32/0.57            ( collect_int
% 0.32/0.57            @ ^ [X3: int] :
% 0.32/0.57                ( ( member_int @ X3 @ A6 )
% 0.32/0.57                & ~ ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3640_set__diff__eq,axiom,
% 0.32/0.57      ( minus_minus_set_nat
% 0.32/0.57      = ( ^ [A6: set_nat,B6: set_nat] :
% 0.32/0.57            ( collect_nat
% 0.32/0.57            @ ^ [X3: nat] :
% 0.32/0.57                ( ( member_nat @ X3 @ A6 )
% 0.32/0.57                & ~ ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 0.32/0.57  
% 0.32/0.57  % set_diff_eq
% 0.32/0.57  thf(fact_3641_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.32/0.57      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.57        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.57          = Y )
% 0.32/0.57       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.57         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.57                ( ( X
% 0.32/0.57                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.57               => ( ~ Y
% 0.32/0.57                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.32/0.57           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.57                  ( ( X
% 0.32/0.57                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.32/0.57                 => ( ~ Y
% 0.32/0.57                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 0.32/0.57             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.58                    ( ( X
% 0.32/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.58                   => ( ( Y
% 0.32/0.58                        = ( ( Xa2 = Mi2 )
% 0.32/0.58                          | ( Xa2 = Ma2 ) ) )
% 0.32/0.58                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 0.32/0.58               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.58                      ( ( X
% 0.32/0.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.58                     => ( ( Y
% 0.32/0.58                          = ( ( Xa2 = Mi2 )
% 0.32/0.58                            | ( Xa2 = Ma2 )
% 0.32/0.58                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 0.32/0.58                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 0.32/0.58                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.32/0.58                        ( ( X
% 0.32/0.58                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.58                       => ( ( Y
% 0.32/0.58                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 0.32/0.58                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % VEBT_internal.membermima.pelims(1)
% 0.32/0.58  thf(fact_3642_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.32/0.58      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.58        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.58       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.58         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.58                ( ( X
% 0.32/0.58                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.58               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 0.32/0.58           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.58                  ( ( X
% 0.32/0.58                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 0.32/0.58                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 0.32/0.58             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.58                    ( ( X
% 0.32/0.58                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.58                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.32/0.58                     => ( ( Xa2 = Mi2 )
% 0.32/0.58                        | ( Xa2 = Ma2 ) ) ) )
% 0.32/0.58               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.58                      ( ( X
% 0.32/0.58                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.58                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 0.32/0.58                       => ( ( Xa2 = Mi2 )
% 0.32/0.58                          | ( Xa2 = Ma2 )
% 0.32/0.58                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.32/0.58                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.32/0.58                        ( ( X
% 0.32/0.58                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.58                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 0.32/0.58                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % VEBT_internal.membermima.pelims(3)
% 0.32/0.58  thf(fact_3643_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.32/0.58      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.58        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.32/0.58       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.58         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.32/0.58                ( ( X
% 0.32/0.58                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.32/0.58               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.32/0.58                 => ~ ( ( Xa2 = Mi2 )
% 0.32/0.58                      | ( Xa2 = Ma2 ) ) ) )
% 0.32/0.58           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.58                  ( ( X
% 0.32/0.58                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 0.32/0.58                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 0.32/0.58                   => ~ ( ( Xa2 = Mi2 )
% 0.32/0.58                        | ( Xa2 = Ma2 )
% 0.32/0.58                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 0.32/0.58             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 0.32/0.58                    ( ( X
% 0.32/0.58                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 0.32/0.58                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 0.32/0.58                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.32/0.58                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.58                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % VEBT_internal.membermima.pelims(2)
% 0.32/0.58  thf(fact_3644_unset__bit__0,axiom,
% 0.32/0.58      ! [A: int] :
% 0.32/0.58        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.32/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_0
% 0.32/0.58  thf(fact_3645_unset__bit__0,axiom,
% 0.32/0.58      ! [A: nat] :
% 0.32/0.58        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.32/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_0
% 0.32/0.58  thf(fact_3646_unset__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: code_integer] :
% 0.32/0.58        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_Suc
% 0.32/0.58  thf(fact_3647_unset__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: int] :
% 0.32/0.58        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_Suc
% 0.32/0.58  thf(fact_3648_unset__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: nat] :
% 0.32/0.58        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_Suc
% 0.32/0.58  thf(fact_3649_flip__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: code_integer] :
% 0.32/0.58        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % flip_bit_Suc
% 0.32/0.58  thf(fact_3650_flip__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: int] :
% 0.32/0.58        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % flip_bit_Suc
% 0.32/0.58  thf(fact_3651_flip__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,A: nat] :
% 0.32/0.58        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 0.32/0.58        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % flip_bit_Suc
% 0.32/0.58  thf(fact_3652_Bolzano,axiom,
% 0.32/0.58      ! [A: real,B: real,P: real > real > $o] :
% 0.32/0.58        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.58       => ( ! [A5: real,B5: real,C2: real] :
% 0.32/0.58              ( ( P @ A5 @ B5 )
% 0.32/0.58             => ( ( P @ B5 @ C2 )
% 0.32/0.58               => ( ( ord_less_eq_real @ A5 @ B5 )
% 0.32/0.58                 => ( ( ord_less_eq_real @ B5 @ C2 )
% 0.32/0.58                   => ( P @ A5 @ C2 ) ) ) ) )
% 0.32/0.58         => ( ! [X6: real] :
% 0.32/0.58                ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.58               => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.58                 => ? [D5: real] :
% 0.32/0.58                      ( ( ord_less_real @ zero_zero_real @ D5 )
% 0.32/0.58                      & ! [A5: real,B5: real] :
% 0.32/0.58                          ( ( ( ord_less_eq_real @ A5 @ X6 )
% 0.32/0.58                            & ( ord_less_eq_real @ X6 @ B5 )
% 0.32/0.58                            & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 0.32/0.58                         => ( P @ A5 @ B5 ) ) ) ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Bolzano
% 0.32/0.58  thf(fact_3653_unset__bit__nonnegative__int__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 0.32/0.58        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_nonnegative_int_iff
% 0.32/0.58  thf(fact_3654_flip__bit__nonnegative__int__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 0.32/0.58        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.58  
% 0.32/0.58  % flip_bit_nonnegative_int_iff
% 0.32/0.58  thf(fact_3655_unset__bit__negative__int__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int] :
% 0.32/0.58        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 0.32/0.58        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_negative_int_iff
% 0.32/0.58  thf(fact_3656_flip__bit__negative__int__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int] :
% 0.32/0.58        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 0.32/0.58        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.58  
% 0.32/0.58  % flip_bit_negative_int_iff
% 0.32/0.58  thf(fact_3657_unset__bit__less__eq,axiom,
% 0.32/0.58      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 0.32/0.58  
% 0.32/0.58  % unset_bit_less_eq
% 0.32/0.58  thf(fact_3658_mult__le__cancel__iff1,axiom,
% 0.32/0.58      ! [Z: real,X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff1
% 0.32/0.58  thf(fact_3659_mult__le__cancel__iff1,axiom,
% 0.32/0.58      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff1
% 0.32/0.58  thf(fact_3660_mult__le__cancel__iff1,axiom,
% 0.32/0.58      ! [Z: int,X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.58       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff1
% 0.32/0.58  thf(fact_3661_mult__le__cancel__iff2,axiom,
% 0.32/0.58      ! [Z: real,X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 0.32/0.58          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff2
% 0.32/0.58  thf(fact_3662_mult__le__cancel__iff2,axiom,
% 0.32/0.58      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 0.32/0.58          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff2
% 0.32/0.58  thf(fact_3663_mult__le__cancel__iff2,axiom,
% 0.32/0.58      ! [Z: int,X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.58       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 0.32/0.58          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_le_cancel_iff2
% 0.32/0.58  thf(fact_3664_divides__aux__eq,axiom,
% 0.32/0.58      ! [Q2: nat,R: nat] :
% 0.32/0.58        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 0.32/0.58        = ( R = zero_zero_nat ) ) ).
% 0.32/0.58  
% 0.32/0.58  % divides_aux_eq
% 0.32/0.58  thf(fact_3665_divides__aux__eq,axiom,
% 0.32/0.58      ! [Q2: int,R: int] :
% 0.32/0.58        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58        = ( R = zero_zero_int ) ) ).
% 0.32/0.58  
% 0.32/0.58  % divides_aux_eq
% 0.32/0.58  thf(fact_3666_neg__eucl__rel__int__mult__2,axiom,
% 0.32/0.58      ! [B: int,A: int,Q2: int,R: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.32/0.58       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % neg_eucl_rel_int_mult_2
% 0.32/0.58  thf(fact_3667_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3668_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3669_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3670_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3671_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3672_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_o,Ys: list_o] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3673_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_o,Ys: list_nat] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3674_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_o,Ys: list_int] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3675_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3676_product__nth,axiom,
% 0.32/0.58      ! [N: nat,Xs: list_nat,Ys: list_o] :
% 0.32/0.58        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 0.32/0.58       => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys ) @ N )
% 0.32/0.58          = ( product_Pair_nat_o @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % product_nth
% 0.32/0.58  thf(fact_3677_obtain__set__succ,axiom,
% 0.32/0.58      ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Z )
% 0.32/0.58       => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 0.32/0.58         => ( ( finite_finite_nat @ B3 )
% 0.32/0.58           => ( ( A2 = B3 )
% 0.32/0.58             => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % obtain_set_succ
% 0.32/0.58  thf(fact_3678_obtain__set__pred,axiom,
% 0.32/0.58      ! [Z: nat,X: nat,A2: set_nat] :
% 0.32/0.58        ( ( ord_less_nat @ Z @ X )
% 0.32/0.58       => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 0.32/0.58         => ( ( finite_finite_nat @ A2 )
% 0.32/0.58           => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % obtain_set_pred
% 0.32/0.58  thf(fact_3679_set__vebt__finite,axiom,
% 0.32/0.58      ! [T: vEBT_VEBT,N: nat] :
% 0.32/0.58        ( ( vEBT_invar_vebt @ T @ N )
% 0.32/0.58       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % set_vebt_finite
% 0.32/0.58  thf(fact_3680_pred__none__empty,axiom,
% 0.32/0.58      ! [Xs: set_nat,A: nat] :
% 0.32/0.58        ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 0.32/0.58       => ( ( finite_finite_nat @ Xs )
% 0.32/0.58         => ~ ? [X4: nat] :
% 0.32/0.58                ( ( member_nat @ X4 @ Xs )
% 0.32/0.58                & ( ord_less_nat @ X4 @ A ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % pred_none_empty
% 0.32/0.58  thf(fact_3681_succ__none__empty,axiom,
% 0.32/0.58      ! [Xs: set_nat,A: nat] :
% 0.32/0.58        ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 0.32/0.58       => ( ( finite_finite_nat @ Xs )
% 0.32/0.58         => ~ ? [X4: nat] :
% 0.32/0.58                ( ( member_nat @ X4 @ Xs )
% 0.32/0.58                & ( ord_less_nat @ A @ X4 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % succ_none_empty
% 0.32/0.58  thf(fact_3682_List_Ofinite__set,axiom,
% 0.32/0.58      ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 0.32/0.58  
% 0.32/0.58  % List.finite_set
% 0.32/0.58  thf(fact_3683_List_Ofinite__set,axiom,
% 0.32/0.58      ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 0.32/0.58  
% 0.32/0.58  % List.finite_set
% 0.32/0.58  thf(fact_3684_List_Ofinite__set,axiom,
% 0.32/0.58      ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 0.32/0.58  
% 0.32/0.58  % List.finite_set
% 0.32/0.58  thf(fact_3685_List_Ofinite__set,axiom,
% 0.32/0.58      ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 0.32/0.58  
% 0.32/0.58  % List.finite_set
% 0.32/0.58  thf(fact_3686_finite__atLeastAtMost,axiom,
% 0.32/0.58      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_atLeastAtMost
% 0.32/0.58  thf(fact_3687_infinite__Icc__iff,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.32/0.58        = ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_Icc_iff
% 0.32/0.58  thf(fact_3688_infinite__Icc__iff,axiom,
% 0.32/0.58      ! [A: real,B: real] :
% 0.32/0.58        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 0.32/0.58        = ( ord_less_real @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_Icc_iff
% 0.32/0.58  thf(fact_3689_length__product,axiom,
% 0.32/0.58      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3690_length__product,axiom,
% 0.32/0.58      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.32/0.58        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3691_length__product,axiom,
% 0.32/0.58      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.32/0.58        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3692_length__product,axiom,
% 0.32/0.58      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.32/0.58        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3693_length__product,axiom,
% 0.32/0.58      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3694_length__product,axiom,
% 0.32/0.58      ! [Xs: list_o,Ys: list_o] :
% 0.32/0.58        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3695_length__product,axiom,
% 0.32/0.58      ! [Xs: list_o,Ys: list_nat] :
% 0.32/0.58        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3696_length__product,axiom,
% 0.32/0.58      ! [Xs: list_o,Ys: list_int] :
% 0.32/0.58        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3697_length__product,axiom,
% 0.32/0.58      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 0.32/0.58        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3698_length__product,axiom,
% 0.32/0.58      ! [Xs: list_nat,Ys: list_o] :
% 0.32/0.58        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 0.32/0.58        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % length_product
% 0.32/0.58  thf(fact_3699_unique__remainder,axiom,
% 0.32/0.58      ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 0.32/0.58        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.32/0.58         => ( R = R3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unique_remainder
% 0.32/0.58  thf(fact_3700_unique__quotient,axiom,
% 0.32/0.58      ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 0.32/0.58        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.32/0.58         => ( Q2 = Q4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % unique_quotient
% 0.32/0.58  thf(fact_3701_bounded__nat__set__is__finite,axiom,
% 0.32/0.58      ! [N4: set_nat,N: nat] :
% 0.32/0.58        ( ! [X6: nat] :
% 0.32/0.58            ( ( member_nat @ X6 @ N4 )
% 0.32/0.58           => ( ord_less_nat @ X6 @ N ) )
% 0.32/0.58       => ( finite_finite_nat @ N4 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % bounded_nat_set_is_finite
% 0.32/0.58  thf(fact_3702_finite__nat__set__iff__bounded,axiom,
% 0.32/0.58      ( finite_finite_nat
% 0.32/0.58      = ( ^ [N6: set_nat] :
% 0.32/0.58          ? [M3: nat] :
% 0.32/0.58          ! [X3: nat] :
% 0.32/0.58            ( ( member_nat @ X3 @ N6 )
% 0.32/0.58           => ( ord_less_nat @ X3 @ M3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_nat_set_iff_bounded
% 0.32/0.58  thf(fact_3703_finite__nat__set__iff__bounded__le,axiom,
% 0.32/0.58      ( finite_finite_nat
% 0.32/0.58      = ( ^ [N6: set_nat] :
% 0.32/0.58          ? [M3: nat] :
% 0.32/0.58          ! [X3: nat] :
% 0.32/0.58            ( ( member_nat @ X3 @ N6 )
% 0.32/0.58           => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_nat_set_iff_bounded_le
% 0.32/0.58  thf(fact_3704_finite__list,axiom,
% 0.32/0.58      ! [A2: set_VEBT_VEBT] :
% 0.32/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.32/0.58       => ? [Xs3: list_VEBT_VEBT] :
% 0.32/0.58            ( ( set_VEBT_VEBT2 @ Xs3 )
% 0.32/0.58            = A2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_list
% 0.32/0.58  thf(fact_3705_finite__list,axiom,
% 0.32/0.58      ! [A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ? [Xs3: list_nat] :
% 0.32/0.58            ( ( set_nat2 @ Xs3 )
% 0.32/0.58            = A2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_list
% 0.32/0.58  thf(fact_3706_finite__list,axiom,
% 0.32/0.58      ! [A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ? [Xs3: list_int] :
% 0.32/0.58            ( ( set_int2 @ Xs3 )
% 0.32/0.58            = A2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_list
% 0.32/0.58  thf(fact_3707_finite__list,axiom,
% 0.32/0.58      ! [A2: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.58       => ? [Xs3: list_complex] :
% 0.32/0.58            ( ( set_complex2 @ Xs3 )
% 0.32/0.58            = A2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_list
% 0.32/0.58  thf(fact_3708_finite__M__bounded__by__nat,axiom,
% 0.32/0.58      ! [P: nat > $o,I: nat] :
% 0.32/0.58        ( finite_finite_nat
% 0.32/0.58        @ ( collect_nat
% 0.32/0.58          @ ^ [K2: nat] :
% 0.32/0.58              ( ( P @ K2 )
% 0.32/0.58              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_M_bounded_by_nat
% 0.32/0.58  thf(fact_3709_finite__less__ub,axiom,
% 0.32/0.58      ! [F: nat > nat,U: nat] :
% 0.32/0.58        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 0.32/0.58       => ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_less_ub
% 0.32/0.58  thf(fact_3710_finite__lists__length__eq,axiom,
% 0.32/0.58      ! [A2: set_complex,N: nat] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.58       => ( finite8712137658972009173omplex
% 0.32/0.58          @ ( collect_list_complex
% 0.32/0.58            @ ^ [Xs2: list_complex] :
% 0.32/0.58                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.32/0.58                  = N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_eq
% 0.32/0.58  thf(fact_3711_finite__lists__length__eq,axiom,
% 0.32/0.58      ! [A2: set_VEBT_VEBT,N: nat] :
% 0.32/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.32/0.58       => ( finite3004134309566078307T_VEBT
% 0.32/0.58          @ ( collec5608196760682091941T_VEBT
% 0.32/0.58            @ ^ [Xs2: list_VEBT_VEBT] :
% 0.32/0.58                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.32/0.58                  = N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_eq
% 0.32/0.58  thf(fact_3712_finite__lists__length__eq,axiom,
% 0.32/0.58      ! [A2: set_o,N: nat] :
% 0.32/0.58        ( ( finite_finite_o @ A2 )
% 0.32/0.58       => ( finite_finite_list_o
% 0.32/0.58          @ ( collect_list_o
% 0.32/0.58            @ ^ [Xs2: list_o] :
% 0.32/0.58                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ( size_size_list_o @ Xs2 )
% 0.32/0.58                  = N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_eq
% 0.32/0.58  thf(fact_3713_finite__lists__length__eq,axiom,
% 0.32/0.58      ! [A2: set_nat,N: nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( finite8100373058378681591st_nat
% 0.32/0.58          @ ( collect_list_nat
% 0.32/0.58            @ ^ [Xs2: list_nat] :
% 0.32/0.58                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ( size_size_list_nat @ Xs2 )
% 0.32/0.58                  = N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_eq
% 0.32/0.58  thf(fact_3714_finite__lists__length__eq,axiom,
% 0.32/0.58      ! [A2: set_int,N: nat] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( finite3922522038869484883st_int
% 0.32/0.58          @ ( collect_list_int
% 0.32/0.58            @ ^ [Xs2: list_int] :
% 0.32/0.58                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ( size_size_list_int @ Xs2 )
% 0.32/0.58                  = N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_eq
% 0.32/0.58  thf(fact_3715_eucl__rel__int__by0,axiom,
% 0.32/0.58      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.32/0.58  
% 0.32/0.58  % eucl_rel_int_by0
% 0.32/0.58  thf(fact_3716_div__int__unique,axiom,
% 0.32/0.58      ! [K: int,L2: int,Q2: int,R: int] :
% 0.32/0.58        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58       => ( ( divide_divide_int @ K @ L2 )
% 0.32/0.58          = Q2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % div_int_unique
% 0.32/0.58  thf(fact_3717_mod__int__unique,axiom,
% 0.32/0.58      ! [K: int,L2: int,Q2: int,R: int] :
% 0.32/0.58        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58       => ( ( modulo_modulo_int @ K @ L2 )
% 0.32/0.58          = R ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mod_int_unique
% 0.32/0.58  thf(fact_3718_ex__min__if__finite,axiom,
% 0.32/0.58      ! [S2: set_real] :
% 0.32/0.58        ( ( finite_finite_real @ S2 )
% 0.32/0.58       => ( ( S2 != bot_bot_set_real )
% 0.32/0.58         => ? [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ S2 )
% 0.32/0.58              & ~ ? [Xa: real] :
% 0.32/0.58                    ( ( member_real @ Xa @ S2 )
% 0.32/0.58                    & ( ord_less_real @ Xa @ X6 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ex_min_if_finite
% 0.32/0.58  thf(fact_3719_ex__min__if__finite,axiom,
% 0.32/0.58      ! [S2: set_rat] :
% 0.32/0.58        ( ( finite_finite_rat @ S2 )
% 0.32/0.58       => ( ( S2 != bot_bot_set_rat )
% 0.32/0.58         => ? [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ S2 )
% 0.32/0.58              & ~ ? [Xa: rat] :
% 0.32/0.58                    ( ( member_rat @ Xa @ S2 )
% 0.32/0.58                    & ( ord_less_rat @ Xa @ X6 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ex_min_if_finite
% 0.32/0.58  thf(fact_3720_ex__min__if__finite,axiom,
% 0.32/0.58      ! [S2: set_num] :
% 0.32/0.58        ( ( finite_finite_num @ S2 )
% 0.32/0.58       => ( ( S2 != bot_bot_set_num )
% 0.32/0.58         => ? [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ S2 )
% 0.32/0.58              & ~ ? [Xa: num] :
% 0.32/0.58                    ( ( member_num @ Xa @ S2 )
% 0.32/0.58                    & ( ord_less_num @ Xa @ X6 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ex_min_if_finite
% 0.32/0.58  thf(fact_3721_ex__min__if__finite,axiom,
% 0.32/0.58      ! [S2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ S2 )
% 0.32/0.58       => ( ( S2 != bot_bot_set_nat )
% 0.32/0.58         => ? [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ S2 )
% 0.32/0.58              & ~ ? [Xa: nat] :
% 0.32/0.58                    ( ( member_nat @ Xa @ S2 )
% 0.32/0.58                    & ( ord_less_nat @ Xa @ X6 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ex_min_if_finite
% 0.32/0.58  thf(fact_3722_ex__min__if__finite,axiom,
% 0.32/0.58      ! [S2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ S2 )
% 0.32/0.58       => ( ( S2 != bot_bot_set_int )
% 0.32/0.58         => ? [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ S2 )
% 0.32/0.58              & ~ ? [Xa: int] :
% 0.32/0.58                    ( ( member_int @ Xa @ S2 )
% 0.32/0.58                    & ( ord_less_int @ Xa @ X6 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ex_min_if_finite
% 0.32/0.58  thf(fact_3723_infinite__growing,axiom,
% 0.32/0.58      ! [X8: set_real] :
% 0.32/0.58        ( ( X8 != bot_bot_set_real )
% 0.32/0.58       => ( ! [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ X8 )
% 0.32/0.58             => ? [Xa: real] :
% 0.32/0.58                  ( ( member_real @ Xa @ X8 )
% 0.32/0.58                  & ( ord_less_real @ X6 @ Xa ) ) )
% 0.32/0.58         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_growing
% 0.32/0.58  thf(fact_3724_infinite__growing,axiom,
% 0.32/0.58      ! [X8: set_rat] :
% 0.32/0.58        ( ( X8 != bot_bot_set_rat )
% 0.32/0.58       => ( ! [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ X8 )
% 0.32/0.58             => ? [Xa: rat] :
% 0.32/0.58                  ( ( member_rat @ Xa @ X8 )
% 0.32/0.58                  & ( ord_less_rat @ X6 @ Xa ) ) )
% 0.32/0.58         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_growing
% 0.32/0.58  thf(fact_3725_infinite__growing,axiom,
% 0.32/0.58      ! [X8: set_num] :
% 0.32/0.58        ( ( X8 != bot_bot_set_num )
% 0.32/0.58       => ( ! [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ X8 )
% 0.32/0.58             => ? [Xa: num] :
% 0.32/0.58                  ( ( member_num @ Xa @ X8 )
% 0.32/0.58                  & ( ord_less_num @ X6 @ Xa ) ) )
% 0.32/0.58         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_growing
% 0.32/0.58  thf(fact_3726_infinite__growing,axiom,
% 0.32/0.58      ! [X8: set_nat] :
% 0.32/0.58        ( ( X8 != bot_bot_set_nat )
% 0.32/0.58       => ( ! [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ X8 )
% 0.32/0.58             => ? [Xa: nat] :
% 0.32/0.58                  ( ( member_nat @ Xa @ X8 )
% 0.32/0.58                  & ( ord_less_nat @ X6 @ Xa ) ) )
% 0.32/0.58         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_growing
% 0.32/0.58  thf(fact_3727_infinite__growing,axiom,
% 0.32/0.58      ! [X8: set_int] :
% 0.32/0.58        ( ( X8 != bot_bot_set_int )
% 0.32/0.58       => ( ! [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ X8 )
% 0.32/0.58             => ? [Xa: int] :
% 0.32/0.58                  ( ( member_int @ Xa @ X8 )
% 0.32/0.58                  & ( ord_less_int @ X6 @ Xa ) ) )
% 0.32/0.58         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_growing
% 0.32/0.58  thf(fact_3728_infinite__Icc,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_Icc
% 0.32/0.58  thf(fact_3729_infinite__Icc,axiom,
% 0.32/0.58      ! [A: real,B: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_Icc
% 0.32/0.58  thf(fact_3730_finite__lists__length__le,axiom,
% 0.32/0.58      ! [A2: set_complex,N: nat] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.58       => ( finite8712137658972009173omplex
% 0.32/0.58          @ ( collect_list_complex
% 0.32/0.58            @ ^ [Xs2: list_complex] :
% 0.32/0.58                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_le
% 0.32/0.58  thf(fact_3731_finite__lists__length__le,axiom,
% 0.32/0.58      ! [A2: set_VEBT_VEBT,N: nat] :
% 0.32/0.58        ( ( finite5795047828879050333T_VEBT @ A2 )
% 0.32/0.58       => ( finite3004134309566078307T_VEBT
% 0.32/0.58          @ ( collec5608196760682091941T_VEBT
% 0.32/0.58            @ ^ [Xs2: list_VEBT_VEBT] :
% 0.32/0.58                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_le
% 0.32/0.58  thf(fact_3732_finite__lists__length__le,axiom,
% 0.32/0.58      ! [A2: set_o,N: nat] :
% 0.32/0.58        ( ( finite_finite_o @ A2 )
% 0.32/0.58       => ( finite_finite_list_o
% 0.32/0.58          @ ( collect_list_o
% 0.32/0.58            @ ^ [Xs2: list_o] :
% 0.32/0.58                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_le
% 0.32/0.58  thf(fact_3733_finite__lists__length__le,axiom,
% 0.32/0.58      ! [A2: set_nat,N: nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( finite8100373058378681591st_nat
% 0.32/0.58          @ ( collect_list_nat
% 0.32/0.58            @ ^ [Xs2: list_nat] :
% 0.32/0.58                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_le
% 0.32/0.58  thf(fact_3734_finite__lists__length__le,axiom,
% 0.32/0.58      ! [A2: set_int,N: nat] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( finite3922522038869484883st_int
% 0.32/0.58          @ ( collect_list_int
% 0.32/0.58            @ ^ [Xs2: list_int] :
% 0.32/0.58                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 0.32/0.58                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_lists_length_le
% 0.32/0.58  thf(fact_3735_eucl__rel__int__dividesI,axiom,
% 0.32/0.58      ! [L2: int,K: int,Q2: int] :
% 0.32/0.58        ( ( L2 != zero_zero_int )
% 0.32/0.58       => ( ( K
% 0.32/0.58            = ( times_times_int @ Q2 @ L2 ) )
% 0.32/0.58         => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % eucl_rel_int_dividesI
% 0.32/0.58  thf(fact_3736_eucl__rel__int,axiom,
% 0.32/0.58      ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % eucl_rel_int
% 0.32/0.58  thf(fact_3737_subset__eq__atLeast0__atMost__finite,axiom,
% 0.32/0.58      ! [N4: set_nat,N: nat] :
% 0.32/0.58        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.58       => ( finite_finite_nat @ N4 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % subset_eq_atLeast0_atMost_finite
% 0.32/0.58  thf(fact_3738_eucl__rel__int__iff,axiom,
% 0.32/0.58      ! [K: int,L2: int,Q2: int,R: int] :
% 0.32/0.58        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58        = ( ( K
% 0.32/0.58            = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 0.32/0.58          & ( ( ord_less_int @ zero_zero_int @ L2 )
% 0.32/0.58           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.32/0.58              & ( ord_less_int @ R @ L2 ) ) )
% 0.32/0.58          & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 0.32/0.58           => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.32/0.58               => ( ( ord_less_int @ L2 @ R )
% 0.32/0.58                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 0.32/0.58              & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 0.32/0.58               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % eucl_rel_int_iff
% 0.32/0.58  thf(fact_3739_mult__less__iff1,axiom,
% 0.32/0.58      ! [Z: real,X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.58       => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_real @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_less_iff1
% 0.32/0.58  thf(fact_3740_mult__less__iff1,axiom,
% 0.32/0.58      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.32/0.58       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_rat @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_less_iff1
% 0.32/0.58  thf(fact_3741_mult__less__iff1,axiom,
% 0.32/0.58      ! [Z: int,X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.58       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.32/0.58          = ( ord_less_int @ X @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % mult_less_iff1
% 0.32/0.58  thf(fact_3742_pos__eucl__rel__int__mult__2,axiom,
% 0.32/0.58      ! [B: int,A: int,Q2: int,R: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.58         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % pos_eucl_rel_int_mult_2
% 0.32/0.58  thf(fact_3743_finite__Collect__le__nat,axiom,
% 0.32/0.58      ! [K: nat] :
% 0.32/0.58        ( finite_finite_nat
% 0.32/0.58        @ ( collect_nat
% 0.32/0.58          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Collect_le_nat
% 0.32/0.58  thf(fact_3744_finite__Collect__less__nat,axiom,
% 0.32/0.58      ! [K: nat] :
% 0.32/0.58        ( finite_finite_nat
% 0.32/0.58        @ ( collect_nat
% 0.32/0.58          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Collect_less_nat
% 0.32/0.58  thf(fact_3745_finite__Collect__subsets,axiom,
% 0.32/0.58      ! [A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( finite1152437895449049373et_nat
% 0.32/0.58          @ ( collect_set_nat
% 0.32/0.58            @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Collect_subsets
% 0.32/0.58  thf(fact_3746_finite__Collect__subsets,axiom,
% 0.32/0.58      ! [A2: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.58       => ( finite6551019134538273531omplex
% 0.32/0.58          @ ( collect_set_complex
% 0.32/0.58            @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Collect_subsets
% 0.32/0.58  thf(fact_3747_finite__Collect__subsets,axiom,
% 0.32/0.58      ! [A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( finite6197958912794628473et_int
% 0.32/0.58          @ ( collect_set_int
% 0.32/0.58            @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Collect_subsets
% 0.32/0.58  thf(fact_3748_finite__roots__unity,axiom,
% 0.32/0.58      ! [N: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.32/0.58       => ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [Z3: real] :
% 0.32/0.58                ( ( power_power_real @ Z3 @ N )
% 0.32/0.58                = one_one_real ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_roots_unity
% 0.32/0.58  thf(fact_3749_finite__roots__unity,axiom,
% 0.32/0.58      ! [N: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.32/0.58       => ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [Z3: complex] :
% 0.32/0.58                ( ( power_power_complex @ Z3 @ N )
% 0.32/0.58                = one_one_complex ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_roots_unity
% 0.32/0.58  thf(fact_3750_finite__Diff2,axiom,
% 0.32/0.58      ! [B3: set_int,A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ B3 )
% 0.32/0.58       => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.58          = ( finite_finite_int @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff2
% 0.32/0.58  thf(fact_3751_finite__Diff2,axiom,
% 0.32/0.58      ! [B3: set_complex,A2: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.58       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.58          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff2
% 0.32/0.58  thf(fact_3752_finite__Diff2,axiom,
% 0.32/0.58      ! [B3: set_nat,A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ B3 )
% 0.32/0.58       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.58          = ( finite_finite_nat @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff2
% 0.32/0.58  thf(fact_3753_finite__Diff,axiom,
% 0.32/0.58      ! [A2: set_int,B3: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff
% 0.32/0.58  thf(fact_3754_finite__Diff,axiom,
% 0.32/0.58      ! [A2: set_complex,B3: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.58       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff
% 0.32/0.58  thf(fact_3755_finite__Diff,axiom,
% 0.32/0.58      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_Diff
% 0.32/0.58  thf(fact_3756_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > complex,Y: real > complex] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3757_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3758_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_int,X: int > complex,Y: int > complex] :
% 0.32/0.58        ( ( finite_finite_int
% 0.32/0.58          @ ( collect_int
% 0.32/0.58            @ ^ [I5: int] :
% 0.32/0.58                ( ( member_int @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3759_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [I5: complex] :
% 0.32/0.58                ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_complex ) ) ) )
% 0.32/0.58       => ( ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_complex ) ) ) )
% 0.32/0.58         => ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3760_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > real,Y: real > real] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_real ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3761_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_real ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3762_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_int,X: int > real,Y: int > real] :
% 0.32/0.58        ( ( finite_finite_int
% 0.32/0.58          @ ( collect_int
% 0.32/0.58            @ ^ [I5: int] :
% 0.32/0.58                ( ( member_int @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_real ) ) ) )
% 0.32/0.58         => ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3763_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 0.32/0.58        ( ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [I5: complex] :
% 0.32/0.58                ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_real ) ) ) )
% 0.32/0.58       => ( ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_real ) ) ) )
% 0.32/0.58         => ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3764_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > rat,Y: real > rat] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_rat ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_rat ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_rat ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3765_prod_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != one_one_rat ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != one_one_rat ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != one_one_rat ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.finite_Collect_op
% 0.32/0.58  thf(fact_3766_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > complex,Y: real > complex] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3767_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3768_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_int,X: int > complex,Y: int > complex] :
% 0.32/0.58        ( ( finite_finite_int
% 0.32/0.58          @ ( collect_int
% 0.32/0.58            @ ^ [I5: int] :
% 0.32/0.58                ( ( member_int @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_complex ) ) ) )
% 0.32/0.58       => ( ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_complex ) ) ) )
% 0.32/0.58         => ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3769_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [I5: complex] :
% 0.32/0.58                ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_complex ) ) ) )
% 0.32/0.58       => ( ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_complex ) ) ) )
% 0.32/0.58         => ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_complex ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3770_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > real,Y: real > real] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_real ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3771_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_real ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3772_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_int,X: int > real,Y: int > real] :
% 0.32/0.58        ( ( finite_finite_int
% 0.32/0.58          @ ( collect_int
% 0.32/0.58            @ ^ [I5: int] :
% 0.32/0.58                ( ( member_int @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_real ) ) ) )
% 0.32/0.58       => ( ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_real ) ) ) )
% 0.32/0.58         => ( finite_finite_int
% 0.32/0.58            @ ( collect_int
% 0.32/0.58              @ ^ [I5: int] :
% 0.32/0.58                  ( ( member_int @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3773_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 0.32/0.58        ( ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [I5: complex] :
% 0.32/0.58                ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_real ) ) ) )
% 0.32/0.58       => ( ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_real ) ) ) )
% 0.32/0.58         => ( finite3207457112153483333omplex
% 0.32/0.58            @ ( collect_complex
% 0.32/0.58              @ ^ [I5: complex] :
% 0.32/0.58                  ( ( member_complex @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3774_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_real,X: real > rat,Y: real > rat] :
% 0.32/0.58        ( ( finite_finite_real
% 0.32/0.58          @ ( collect_real
% 0.32/0.58            @ ^ [I5: real] :
% 0.32/0.58                ( ( member_real @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_rat ) ) ) )
% 0.32/0.58       => ( ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_rat ) ) ) )
% 0.32/0.58         => ( finite_finite_real
% 0.32/0.58            @ ( collect_real
% 0.32/0.58              @ ^ [I5: real] :
% 0.32/0.58                  ( ( member_real @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3775_sum_Ofinite__Collect__op,axiom,
% 0.32/0.58      ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 0.32/0.58        ( ( finite_finite_nat
% 0.32/0.58          @ ( collect_nat
% 0.32/0.58            @ ^ [I5: nat] :
% 0.32/0.58                ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                & ( ( X @ I5 )
% 0.32/0.58                 != zero_zero_rat ) ) ) )
% 0.32/0.58       => ( ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( Y @ I5 )
% 0.32/0.58                   != zero_zero_rat ) ) ) )
% 0.32/0.58         => ( finite_finite_nat
% 0.32/0.58            @ ( collect_nat
% 0.32/0.58              @ ^ [I5: nat] :
% 0.32/0.58                  ( ( member_nat @ I5 @ I6 )
% 0.32/0.58                  & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 0.32/0.58                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % sum.finite_Collect_op
% 0.32/0.58  thf(fact_3776_finite__atLeastAtMost__int,axiom,
% 0.32/0.58      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_atLeastAtMost_int
% 0.32/0.58  thf(fact_3777_finite__interval__int1,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( finite_finite_int
% 0.32/0.58        @ ( collect_int
% 0.32/0.58          @ ^ [I5: int] :
% 0.32/0.58              ( ( ord_less_eq_int @ A @ I5 )
% 0.32/0.58              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_interval_int1
% 0.32/0.58  thf(fact_3778_finite__interval__int3,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( finite_finite_int
% 0.32/0.58        @ ( collect_int
% 0.32/0.58          @ ^ [I5: int] :
% 0.32/0.58              ( ( ord_less_int @ A @ I5 )
% 0.32/0.58              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_interval_int3
% 0.32/0.58  thf(fact_3779_finite__interval__int2,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( finite_finite_int
% 0.32/0.58        @ ( collect_int
% 0.32/0.58          @ ^ [I5: int] :
% 0.32/0.58              ( ( ord_less_eq_int @ A @ I5 )
% 0.32/0.58              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_interval_int2
% 0.32/0.58  thf(fact_3780_finite__maxlen,axiom,
% 0.32/0.58      ! [M5: set_list_VEBT_VEBT] :
% 0.32/0.58        ( ( finite3004134309566078307T_VEBT @ M5 )
% 0.32/0.58       => ? [N3: nat] :
% 0.32/0.58          ! [X4: list_VEBT_VEBT] :
% 0.32/0.58            ( ( member2936631157270082147T_VEBT @ X4 @ M5 )
% 0.32/0.58           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X4 ) @ N3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_maxlen
% 0.32/0.58  thf(fact_3781_finite__maxlen,axiom,
% 0.32/0.58      ! [M5: set_list_o] :
% 0.32/0.58        ( ( finite_finite_list_o @ M5 )
% 0.32/0.58       => ? [N3: nat] :
% 0.32/0.58          ! [X4: list_o] :
% 0.32/0.58            ( ( member_list_o @ X4 @ M5 )
% 0.32/0.58           => ( ord_less_nat @ ( size_size_list_o @ X4 ) @ N3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_maxlen
% 0.32/0.58  thf(fact_3782_finite__maxlen,axiom,
% 0.32/0.58      ! [M5: set_list_nat] :
% 0.32/0.58        ( ( finite8100373058378681591st_nat @ M5 )
% 0.32/0.58       => ? [N3: nat] :
% 0.32/0.58          ! [X4: list_nat] :
% 0.32/0.58            ( ( member_list_nat @ X4 @ M5 )
% 0.32/0.58           => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_maxlen
% 0.32/0.58  thf(fact_3783_finite__maxlen,axiom,
% 0.32/0.58      ! [M5: set_list_int] :
% 0.32/0.58        ( ( finite3922522038869484883st_int @ M5 )
% 0.32/0.58       => ? [N3: nat] :
% 0.32/0.58          ! [X4: list_int] :
% 0.32/0.58            ( ( member_list_int @ X4 @ M5 )
% 0.32/0.58           => ( ord_less_nat @ ( size_size_list_int @ X4 ) @ N3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_maxlen
% 0.32/0.58  thf(fact_3784_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_real,A: real] :
% 0.32/0.58        ( ( finite_finite_real @ A2 )
% 0.32/0.58       => ( ( member_real @ A @ A2 )
% 0.32/0.58         => ? [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_real @ A @ X6 )
% 0.32/0.58              & ! [Xa: real] :
% 0.32/0.58                  ( ( member_real @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_real @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3785_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_set_nat,A: set_nat] :
% 0.32/0.58        ( ( finite1152437895449049373et_nat @ A2 )
% 0.32/0.58       => ( ( member_set_nat @ A @ A2 )
% 0.32/0.58         => ? [X6: set_nat] :
% 0.32/0.58              ( ( member_set_nat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_set_nat @ A @ X6 )
% 0.32/0.58              & ! [Xa: set_nat] :
% 0.32/0.58                  ( ( member_set_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_nat @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3786_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_set_int,A: set_int] :
% 0.32/0.58        ( ( finite6197958912794628473et_int @ A2 )
% 0.32/0.58       => ( ( member_set_int @ A @ A2 )
% 0.32/0.58         => ? [X6: set_int] :
% 0.32/0.58              ( ( member_set_int @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_set_int @ A @ X6 )
% 0.32/0.58              & ! [Xa: set_int] :
% 0.32/0.58                  ( ( member_set_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3787_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_rat,A: rat] :
% 0.32/0.58        ( ( finite_finite_rat @ A2 )
% 0.32/0.58       => ( ( member_rat @ A @ A2 )
% 0.32/0.58         => ? [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_rat @ A @ X6 )
% 0.32/0.58              & ! [Xa: rat] :
% 0.32/0.58                  ( ( member_rat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3788_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_num,A: num] :
% 0.32/0.58        ( ( finite_finite_num @ A2 )
% 0.32/0.58       => ( ( member_num @ A @ A2 )
% 0.32/0.58         => ? [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_num @ A @ X6 )
% 0.32/0.58              & ! [Xa: num] :
% 0.32/0.58                  ( ( member_num @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_num @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3789_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_nat,A: nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( ( member_nat @ A @ A2 )
% 0.32/0.58         => ? [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_nat @ A @ X6 )
% 0.32/0.58              & ! [Xa: nat] :
% 0.32/0.58                  ( ( member_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3790_finite__has__maximal2,axiom,
% 0.32/0.58      ! [A2: set_int,A: int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( ( member_int @ A @ A2 )
% 0.32/0.58         => ? [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_int @ A @ X6 )
% 0.32/0.58              & ! [Xa: int] :
% 0.32/0.58                  ( ( member_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_int @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal2
% 0.32/0.58  thf(fact_3791_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_real,A: real] :
% 0.32/0.58        ( ( finite_finite_real @ A2 )
% 0.32/0.58       => ( ( member_real @ A @ A2 )
% 0.32/0.58         => ? [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_real @ X6 @ A )
% 0.32/0.58              & ! [Xa: real] :
% 0.32/0.58                  ( ( member_real @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_real @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3792_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_set_nat,A: set_nat] :
% 0.32/0.58        ( ( finite1152437895449049373et_nat @ A2 )
% 0.32/0.58       => ( ( member_set_nat @ A @ A2 )
% 0.32/0.58         => ? [X6: set_nat] :
% 0.32/0.58              ( ( member_set_nat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_set_nat @ X6 @ A )
% 0.32/0.58              & ! [Xa: set_nat] :
% 0.32/0.58                  ( ( member_set_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_nat @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3793_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_set_int,A: set_int] :
% 0.32/0.58        ( ( finite6197958912794628473et_int @ A2 )
% 0.32/0.58       => ( ( member_set_int @ A @ A2 )
% 0.32/0.58         => ? [X6: set_int] :
% 0.32/0.58              ( ( member_set_int @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_set_int @ X6 @ A )
% 0.32/0.58              & ! [Xa: set_int] :
% 0.32/0.58                  ( ( member_set_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3794_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_rat,A: rat] :
% 0.32/0.58        ( ( finite_finite_rat @ A2 )
% 0.32/0.58       => ( ( member_rat @ A @ A2 )
% 0.32/0.58         => ? [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_rat @ X6 @ A )
% 0.32/0.58              & ! [Xa: rat] :
% 0.32/0.58                  ( ( member_rat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3795_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_num,A: num] :
% 0.32/0.58        ( ( finite_finite_num @ A2 )
% 0.32/0.58       => ( ( member_num @ A @ A2 )
% 0.32/0.58         => ? [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_num @ X6 @ A )
% 0.32/0.58              & ! [Xa: num] :
% 0.32/0.58                  ( ( member_num @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_num @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3796_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_nat,A: nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( ( member_nat @ A @ A2 )
% 0.32/0.58         => ? [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_nat @ X6 @ A )
% 0.32/0.58              & ! [Xa: nat] :
% 0.32/0.58                  ( ( member_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3797_finite__has__minimal2,axiom,
% 0.32/0.58      ! [A2: set_int,A: int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( ( member_int @ A @ A2 )
% 0.32/0.58         => ? [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ A2 )
% 0.32/0.58              & ( ord_less_eq_int @ X6 @ A )
% 0.32/0.58              & ! [Xa: int] :
% 0.32/0.58                  ( ( member_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_int @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal2
% 0.32/0.58  thf(fact_3798_finite__subset,axiom,
% 0.32/0.58      ! [A2: set_nat,B3: set_nat] :
% 0.32/0.58        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.58       => ( ( finite_finite_nat @ B3 )
% 0.32/0.58         => ( finite_finite_nat @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_subset
% 0.32/0.58  thf(fact_3799_finite__subset,axiom,
% 0.32/0.58      ! [A2: set_complex,B3: set_complex] :
% 0.32/0.58        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.58       => ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.58         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_subset
% 0.32/0.58  thf(fact_3800_finite__subset,axiom,
% 0.32/0.58      ! [A2: set_int,B3: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.58       => ( ( finite_finite_int @ B3 )
% 0.32/0.58         => ( finite_finite_int @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_subset
% 0.32/0.58  thf(fact_3801_infinite__super,axiom,
% 0.32/0.58      ! [S2: set_nat,T3: set_nat] :
% 0.32/0.58        ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.58       => ( ~ ( finite_finite_nat @ S2 )
% 0.32/0.58         => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_super
% 0.32/0.58  thf(fact_3802_infinite__super,axiom,
% 0.32/0.58      ! [S2: set_complex,T3: set_complex] :
% 0.32/0.58        ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.58       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.32/0.58         => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_super
% 0.32/0.58  thf(fact_3803_infinite__super,axiom,
% 0.32/0.58      ! [S2: set_int,T3: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.58       => ( ~ ( finite_finite_int @ S2 )
% 0.32/0.58         => ~ ( finite_finite_int @ T3 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % infinite_super
% 0.32/0.58  thf(fact_3804_rev__finite__subset,axiom,
% 0.32/0.58      ! [B3: set_nat,A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ B3 )
% 0.32/0.58       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.58         => ( finite_finite_nat @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % rev_finite_subset
% 0.32/0.58  thf(fact_3805_rev__finite__subset,axiom,
% 0.32/0.58      ! [B3: set_complex,A2: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.58       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.58         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % rev_finite_subset
% 0.32/0.58  thf(fact_3806_rev__finite__subset,axiom,
% 0.32/0.58      ! [B3: set_int,A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ B3 )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.58         => ( finite_finite_int @ A2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % rev_finite_subset
% 0.32/0.58  thf(fact_3807_Diff__infinite__finite,axiom,
% 0.32/0.58      ! [T3: set_int,S2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ T3 )
% 0.32/0.58       => ( ~ ( finite_finite_int @ S2 )
% 0.32/0.58         => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Diff_infinite_finite
% 0.32/0.58  thf(fact_3808_Diff__infinite__finite,axiom,
% 0.32/0.58      ! [T3: set_complex,S2: set_complex] :
% 0.32/0.58        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.58       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.32/0.58         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Diff_infinite_finite
% 0.32/0.58  thf(fact_3809_Diff__infinite__finite,axiom,
% 0.32/0.58      ! [T3: set_nat,S2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ T3 )
% 0.32/0.58       => ( ~ ( finite_finite_nat @ S2 )
% 0.32/0.58         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Diff_infinite_finite
% 0.32/0.58  thf(fact_3810_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_real] :
% 0.32/0.58        ( ( finite_finite_real @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_real )
% 0.32/0.58         => ? [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: real] :
% 0.32/0.58                  ( ( member_real @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_real @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3811_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_set_int] :
% 0.32/0.58        ( ( finite6197958912794628473et_int @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_set_int )
% 0.32/0.58         => ? [X6: set_int] :
% 0.32/0.58              ( ( member_set_int @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: set_int] :
% 0.32/0.58                  ( ( member_set_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3812_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_rat] :
% 0.32/0.58        ( ( finite_finite_rat @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_rat )
% 0.32/0.58         => ? [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: rat] :
% 0.32/0.58                  ( ( member_rat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3813_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_num] :
% 0.32/0.58        ( ( finite_finite_num @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_num )
% 0.32/0.58         => ? [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: num] :
% 0.32/0.58                  ( ( member_num @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_num @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3814_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_nat )
% 0.32/0.58         => ? [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: nat] :
% 0.32/0.58                  ( ( member_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3815_finite__has__minimal,axiom,
% 0.32/0.58      ! [A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_int )
% 0.32/0.58         => ? [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: int] :
% 0.32/0.58                  ( ( member_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_int @ Xa @ X6 )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_minimal
% 0.32/0.58  thf(fact_3816_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_real] :
% 0.32/0.58        ( ( finite_finite_real @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_real )
% 0.32/0.58         => ? [X6: real] :
% 0.32/0.58              ( ( member_real @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: real] :
% 0.32/0.58                  ( ( member_real @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_real @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3817_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_set_int] :
% 0.32/0.58        ( ( finite6197958912794628473et_int @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_set_int )
% 0.32/0.58         => ? [X6: set_int] :
% 0.32/0.58              ( ( member_set_int @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: set_int] :
% 0.32/0.58                  ( ( member_set_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3818_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_rat] :
% 0.32/0.58        ( ( finite_finite_rat @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_rat )
% 0.32/0.58         => ? [X6: rat] :
% 0.32/0.58              ( ( member_rat @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: rat] :
% 0.32/0.58                  ( ( member_rat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3819_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_num] :
% 0.32/0.58        ( ( finite_finite_num @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_num )
% 0.32/0.58         => ? [X6: num] :
% 0.32/0.58              ( ( member_num @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: num] :
% 0.32/0.58                  ( ( member_num @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_num @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3820_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_nat] :
% 0.32/0.58        ( ( finite_finite_nat @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_nat )
% 0.32/0.58         => ? [X6: nat] :
% 0.32/0.58              ( ( member_nat @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: nat] :
% 0.32/0.58                  ( ( member_nat @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3821_finite__has__maximal,axiom,
% 0.32/0.58      ! [A2: set_int] :
% 0.32/0.58        ( ( finite_finite_int @ A2 )
% 0.32/0.58       => ( ( A2 != bot_bot_set_int )
% 0.32/0.58         => ? [X6: int] :
% 0.32/0.58              ( ( member_int @ X6 @ A2 )
% 0.32/0.58              & ! [Xa: int] :
% 0.32/0.58                  ( ( member_int @ Xa @ A2 )
% 0.32/0.58                 => ( ( ord_less_eq_int @ X6 @ Xa )
% 0.32/0.58                   => ( X6 = Xa ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_has_maximal
% 0.32/0.58  thf(fact_3822_arcosh__1,axiom,
% 0.32/0.58      ( ( arcosh_real @ one_one_real )
% 0.32/0.58      = zero_zero_real ) ).
% 0.32/0.58  
% 0.32/0.58  % arcosh_1
% 0.32/0.58  thf(fact_3823_finite__nth__roots,axiom,
% 0.32/0.58      ! [N: nat,C: complex] :
% 0.32/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.58       => ( finite3207457112153483333omplex
% 0.32/0.58          @ ( collect_complex
% 0.32/0.58            @ ^ [Z3: complex] :
% 0.32/0.58                ( ( power_power_complex @ Z3 @ N )
% 0.32/0.58                = C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % finite_nth_roots
% 0.32/0.58  thf(fact_3824_artanh__0,axiom,
% 0.32/0.58      ( ( artanh_real @ zero_zero_real )
% 0.32/0.58      = zero_zero_real ) ).
% 0.32/0.58  
% 0.32/0.58  % artanh_0
% 0.32/0.58  thf(fact_3825_arsinh__0,axiom,
% 0.32/0.58      ( ( arsinh_real @ zero_zero_real )
% 0.32/0.58      = zero_zero_real ) ).
% 0.32/0.58  
% 0.32/0.58  % arsinh_0
% 0.32/0.58  thf(fact_3826_prod_Oinject,axiom,
% 0.32/0.58      ! [X1: int,X22: int,Y1: int,Y22: int] :
% 0.32/0.58        ( ( ( product_Pair_int_int @ X1 @ X22 )
% 0.32/0.58          = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 0.32/0.58        = ( ( X1 = Y1 )
% 0.32/0.58          & ( X22 = Y22 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.inject
% 0.32/0.58  thf(fact_3827_prod_Oinject,axiom,
% 0.32/0.58      ! [X1: code_integer > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc6137756002093451184nteger @ X1 @ X22 )
% 0.32/0.58          = ( produc6137756002093451184nteger @ Y1 @ Y22 ) )
% 0.32/0.58        = ( ( X1 = Y1 )
% 0.32/0.58          & ( X22 = Y22 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.inject
% 0.32/0.58  thf(fact_3828_prod_Oinject,axiom,
% 0.32/0.58      ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 0.32/0.58          = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 0.32/0.58        = ( ( X1 = Y1 )
% 0.32/0.58          & ( X22 = Y22 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.inject
% 0.32/0.58  thf(fact_3829_prod_Oinject,axiom,
% 0.32/0.58      ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 0.32/0.58          = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 0.32/0.58        = ( ( X1 = Y1 )
% 0.32/0.58          & ( X22 = Y22 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.inject
% 0.32/0.58  thf(fact_3830_prod_Oinject,axiom,
% 0.32/0.58      ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 0.32/0.58          = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 0.32/0.58        = ( ( X1 = Y1 )
% 0.32/0.58          & ( X22 = Y22 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod.inject
% 0.32/0.58  thf(fact_3831_old_Oprod_Oinject,axiom,
% 0.32/0.58      ! [A: int,B: int,A4: int,B4: int] :
% 0.32/0.58        ( ( ( product_Pair_int_int @ A @ B )
% 0.32/0.58          = ( product_Pair_int_int @ A4 @ B4 ) )
% 0.32/0.58        = ( ( A = A4 )
% 0.32/0.58          & ( B = B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.inject
% 0.32/0.58  thf(fact_3832_old_Oprod_Oinject,axiom,
% 0.32/0.58      ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc6137756002093451184nteger @ A @ B )
% 0.32/0.58          = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 0.32/0.58        = ( ( A = A4 )
% 0.32/0.58          & ( B = B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.inject
% 0.32/0.58  thf(fact_3833_old_Oprod_Oinject,axiom,
% 0.32/0.58      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.32/0.58          = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 0.32/0.58        = ( ( A = A4 )
% 0.32/0.58          & ( B = B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.inject
% 0.32/0.58  thf(fact_3834_old_Oprod_Oinject,axiom,
% 0.32/0.58      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.32/0.58          = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 0.32/0.58        = ( ( A = A4 )
% 0.32/0.58          & ( B = B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.inject
% 0.32/0.58  thf(fact_3835_old_Oprod_Oinject,axiom,
% 0.32/0.58      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.32/0.58          = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 0.32/0.58        = ( ( A = A4 )
% 0.32/0.58          & ( B = B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.inject
% 0.32/0.58  thf(fact_3836_old_Oprod_Oexhaust,axiom,
% 0.32/0.58      ! [Y: product_prod_int_int] :
% 0.32/0.58        ~ ! [A5: int,B5: int] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( product_Pair_int_int @ A5 @ B5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.exhaust
% 0.32/0.58  thf(fact_3837_old_Oprod_Oexhaust,axiom,
% 0.32/0.58      ! [Y: produc8763457246119570046nteger] :
% 0.32/0.58        ~ ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc6137756002093451184nteger @ A5 @ B5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.exhaust
% 0.32/0.58  thf(fact_3838_old_Oprod_Oexhaust,axiom,
% 0.32/0.58      ! [Y: produc1908205239877642774nteger] :
% 0.32/0.58        ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc8603105652947943368nteger @ A5 @ B5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.exhaust
% 0.32/0.58  thf(fact_3839_old_Oprod_Oexhaust,axiom,
% 0.32/0.58      ! [Y: produc2285326912895808259nt_int] :
% 0.32/0.58        ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc5700946648718959541nt_int @ A5 @ B5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.exhaust
% 0.32/0.58  thf(fact_3840_old_Oprod_Oexhaust,axiom,
% 0.32/0.58      ! [Y: produc7773217078559923341nt_int] :
% 0.32/0.58        ~ ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc4305682042979456191nt_int @ A5 @ B5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % old.prod.exhaust
% 0.32/0.58  thf(fact_3841_surj__pair,axiom,
% 0.32/0.58      ! [P5: product_prod_int_int] :
% 0.32/0.58      ? [X6: int,Y5: int] :
% 0.32/0.58        ( P5
% 0.32/0.58        = ( product_Pair_int_int @ X6 @ Y5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % surj_pair
% 0.32/0.58  thf(fact_3842_surj__pair,axiom,
% 0.32/0.58      ! [P5: produc8763457246119570046nteger] :
% 0.32/0.58      ? [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.58        ( P5
% 0.32/0.58        = ( produc6137756002093451184nteger @ X6 @ Y5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % surj_pair
% 0.32/0.58  thf(fact_3843_surj__pair,axiom,
% 0.32/0.58      ! [P5: produc1908205239877642774nteger] :
% 0.32/0.58      ? [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.58        ( P5
% 0.32/0.58        = ( produc8603105652947943368nteger @ X6 @ Y5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % surj_pair
% 0.32/0.58  thf(fact_3844_surj__pair,axiom,
% 0.32/0.58      ! [P5: produc2285326912895808259nt_int] :
% 0.32/0.58      ? [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.32/0.58        ( P5
% 0.32/0.58        = ( produc5700946648718959541nt_int @ X6 @ Y5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % surj_pair
% 0.32/0.58  thf(fact_3845_surj__pair,axiom,
% 0.32/0.58      ! [P5: produc7773217078559923341nt_int] :
% 0.32/0.58      ? [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.32/0.58        ( P5
% 0.32/0.58        = ( produc4305682042979456191nt_int @ X6 @ Y5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % surj_pair
% 0.32/0.58  thf(fact_3846_prod__cases,axiom,
% 0.32/0.58      ! [P: product_prod_int_int > $o,P5: product_prod_int_int] :
% 0.32/0.58        ( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.58       => ( P @ P5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases
% 0.32/0.58  thf(fact_3847_prod__cases,axiom,
% 0.32/0.58      ! [P: produc8763457246119570046nteger > $o,P5: produc8763457246119570046nteger] :
% 0.32/0.58        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.58       => ( P @ P5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases
% 0.32/0.58  thf(fact_3848_prod__cases,axiom,
% 0.32/0.58      ! [P: produc1908205239877642774nteger > $o,P5: produc1908205239877642774nteger] :
% 0.32/0.58        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 0.32/0.58       => ( P @ P5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases
% 0.32/0.58  thf(fact_3849_prod__cases,axiom,
% 0.32/0.58      ! [P: produc2285326912895808259nt_int > $o,P5: produc2285326912895808259nt_int] :
% 0.32/0.58        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 0.32/0.58       => ( P @ P5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases
% 0.32/0.58  thf(fact_3850_prod__cases,axiom,
% 0.32/0.58      ! [P: produc7773217078559923341nt_int > $o,P5: produc7773217078559923341nt_int] :
% 0.32/0.58        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 0.32/0.58       => ( P @ P5 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases
% 0.32/0.58  thf(fact_3851_Pair__inject,axiom,
% 0.32/0.58      ! [A: int,B: int,A4: int,B4: int] :
% 0.32/0.58        ( ( ( product_Pair_int_int @ A @ B )
% 0.32/0.58          = ( product_Pair_int_int @ A4 @ B4 ) )
% 0.32/0.58       => ~ ( ( A = A4 )
% 0.32/0.58           => ( B != B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Pair_inject
% 0.32/0.58  thf(fact_3852_Pair__inject,axiom,
% 0.32/0.58      ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc6137756002093451184nteger @ A @ B )
% 0.32/0.58          = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 0.32/0.58       => ~ ( ( A = A4 )
% 0.32/0.58           => ( B != B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Pair_inject
% 0.32/0.58  thf(fact_3853_Pair__inject,axiom,
% 0.32/0.58      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 0.32/0.58        ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.32/0.58          = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 0.32/0.58       => ~ ( ( A = A4 )
% 0.32/0.58           => ( B != B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Pair_inject
% 0.32/0.58  thf(fact_3854_Pair__inject,axiom,
% 0.32/0.58      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.32/0.58          = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 0.32/0.58       => ~ ( ( A = A4 )
% 0.32/0.58           => ( B != B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Pair_inject
% 0.32/0.58  thf(fact_3855_Pair__inject,axiom,
% 0.32/0.58      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 0.32/0.58        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.32/0.58          = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 0.32/0.58       => ~ ( ( A = A4 )
% 0.32/0.58           => ( B != B4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Pair_inject
% 0.32/0.58  thf(fact_3856_prod__cases3,axiom,
% 0.32/0.58      ! [Y: produc8763457246119570046nteger] :
% 0.32/0.58        ~ ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases3
% 0.32/0.58  thf(fact_3857_prod__cases3,axiom,
% 0.32/0.58      ! [Y: produc1908205239877642774nteger] :
% 0.32/0.58        ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases3
% 0.32/0.58  thf(fact_3858_prod__cases3,axiom,
% 0.32/0.58      ! [Y: produc2285326912895808259nt_int] :
% 0.32/0.58        ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases3
% 0.32/0.58  thf(fact_3859_prod__cases3,axiom,
% 0.32/0.58      ! [Y: produc7773217078559923341nt_int] :
% 0.32/0.58        ~ ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] :
% 0.32/0.58            ( Y
% 0.32/0.58           != ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_cases3
% 0.32/0.58  thf(fact_3860_prod__induct3,axiom,
% 0.32/0.58      ! [P: produc8763457246119570046nteger > $o,X: produc8763457246119570046nteger] :
% 0.32/0.58        ( ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 0.32/0.58       => ( P @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_induct3
% 0.32/0.58  thf(fact_3861_prod__induct3,axiom,
% 0.32/0.58      ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 0.32/0.58        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 0.32/0.58       => ( P @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_induct3
% 0.32/0.58  thf(fact_3862_prod__induct3,axiom,
% 0.32/0.58      ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 0.32/0.58        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 0.32/0.58       => ( P @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_induct3
% 0.32/0.58  thf(fact_3863_prod__induct3,axiom,
% 0.32/0.58      ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 0.32/0.58        ( ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 0.32/0.58       => ( P @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % prod_induct3
% 0.32/0.58  thf(fact_3864_artanh__def,axiom,
% 0.32/0.58      ( artanh_real
% 0.32/0.58      = ( ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % artanh_def
% 0.32/0.58  thf(fact_3865_gcd__nat__induct,axiom,
% 0.32/0.58      ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.32/0.58        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 0.32/0.58       => ( ! [M4: nat,N3: nat] :
% 0.32/0.58              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.58             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 0.32/0.58               => ( P @ M4 @ N3 ) ) )
% 0.32/0.58         => ( P @ M @ N ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % gcd_nat_induct
% 0.32/0.58  thf(fact_3866_concat__bit__Suc,axiom,
% 0.32/0.58      ! [N: nat,K: int,L2: int] :
% 0.32/0.58        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 0.32/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % concat_bit_Suc
% 0.32/0.58  thf(fact_3867_dual__order_Orefl,axiom,
% 0.32/0.58      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.refl
% 0.32/0.58  thf(fact_3868_dual__order_Orefl,axiom,
% 0.32/0.58      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.refl
% 0.32/0.58  thf(fact_3869_dual__order_Orefl,axiom,
% 0.32/0.58      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.refl
% 0.32/0.58  thf(fact_3870_dual__order_Orefl,axiom,
% 0.32/0.58      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.refl
% 0.32/0.58  thf(fact_3871_dual__order_Orefl,axiom,
% 0.32/0.58      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.refl
% 0.32/0.58  thf(fact_3872_order__refl,axiom,
% 0.32/0.58      ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_refl
% 0.32/0.58  thf(fact_3873_order__refl,axiom,
% 0.32/0.58      ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_refl
% 0.32/0.58  thf(fact_3874_order__refl,axiom,
% 0.32/0.58      ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_refl
% 0.32/0.58  thf(fact_3875_order__refl,axiom,
% 0.32/0.58      ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_refl
% 0.32/0.58  thf(fact_3876_order__refl,axiom,
% 0.32/0.58      ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_refl
% 0.32/0.58  thf(fact_3877_ln__less__cancel__iff,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 0.32/0.58            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_less_cancel_iff
% 0.32/0.58  thf(fact_3878_ln__inj__iff,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ( ( ln_ln_real @ X )
% 0.32/0.58              = ( ln_ln_real @ Y ) )
% 0.32/0.58            = ( X = Y ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_inj_iff
% 0.32/0.58  thf(fact_3879_concat__bit__0,axiom,
% 0.32/0.58      ! [K: int,L2: int] :
% 0.32/0.58        ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 0.32/0.58        = L2 ) ).
% 0.32/0.58  
% 0.32/0.58  % concat_bit_0
% 0.32/0.58  thf(fact_3880_ln__le__cancel__iff,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 0.32/0.58            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_le_cancel_iff
% 0.32/0.58  thf(fact_3881_ln__less__zero__iff,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.32/0.58          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_less_zero_iff
% 0.32/0.58  thf(fact_3882_ln__gt__zero__iff,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.32/0.58          = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_gt_zero_iff
% 0.32/0.58  thf(fact_3883_ln__eq__zero__iff,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ( ln_ln_real @ X )
% 0.32/0.58            = zero_zero_real )
% 0.32/0.58          = ( X = one_one_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_eq_zero_iff
% 0.32/0.58  thf(fact_3884_ln__one,axiom,
% 0.32/0.58      ( ( ln_ln_real @ one_one_real )
% 0.32/0.58      = zero_zero_real ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_one
% 0.32/0.58  thf(fact_3885_concat__bit__nonnegative__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int,L2: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 0.32/0.58        = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % concat_bit_nonnegative_iff
% 0.32/0.58  thf(fact_3886_concat__bit__negative__iff,axiom,
% 0.32/0.58      ! [N: nat,K: int,L2: int] :
% 0.32/0.58        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 0.32/0.58        = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 0.32/0.58  
% 0.32/0.58  % concat_bit_negative_iff
% 0.32/0.58  thf(fact_3887_ln__le__zero__iff,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.32/0.58          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_le_zero_iff
% 0.32/0.58  thf(fact_3888_ln__ge__zero__iff,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.32/0.58          = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_ge_zero_iff
% 0.32/0.58  thf(fact_3889_concat__bit__assoc,axiom,
% 0.32/0.58      ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 0.32/0.58        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 0.32/0.58        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 0.32/0.58  
% 0.32/0.58  % concat_bit_assoc
% 0.32/0.58  thf(fact_3890_ln__less__self,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_less_self
% 0.32/0.58  thf(fact_3891_ln__bound,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_bound
% 0.32/0.58  thf(fact_3892_ln__gt__zero__imp__gt__one,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58         => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_gt_zero_imp_gt_one
% 0.32/0.58  thf(fact_3893_ln__less__zero,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.58         => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_less_zero
% 0.32/0.58  thf(fact_3894_ln__gt__zero,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.58       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_gt_zero
% 0.32/0.58  thf(fact_3895_ln__ge__zero,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.58       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_ge_zero
% 0.32/0.58  thf(fact_3896_order__antisym__conv,axiom,
% 0.32/0.58      ! [Y: set_int,X: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ Y @ X )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym_conv
% 0.32/0.58  thf(fact_3897_order__antisym__conv,axiom,
% 0.32/0.58      ! [Y: rat,X: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ Y @ X )
% 0.32/0.58       => ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym_conv
% 0.32/0.58  thf(fact_3898_order__antisym__conv,axiom,
% 0.32/0.58      ! [Y: num,X: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ Y @ X )
% 0.32/0.58       => ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym_conv
% 0.32/0.58  thf(fact_3899_order__antisym__conv,axiom,
% 0.32/0.58      ! [Y: nat,X: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.58       => ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym_conv
% 0.32/0.58  thf(fact_3900_order__antisym__conv,axiom,
% 0.32/0.58      ! [Y: int,X: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ Y @ X )
% 0.32/0.58       => ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym_conv
% 0.32/0.58  thf(fact_3901_linorder__le__cases,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_cases
% 0.32/0.58  thf(fact_3902_linorder__le__cases,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ~ ( ord_less_eq_num @ X @ Y )
% 0.32/0.58       => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_cases
% 0.32/0.58  thf(fact_3903_linorder__le__cases,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_cases
% 0.32/0.58  thf(fact_3904_linorder__le__cases,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ~ ( ord_less_eq_int @ X @ Y )
% 0.32/0.58       => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_cases
% 0.32/0.58  thf(fact_3905_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3906_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3907_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3908_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3909_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3910_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3911_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3912_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3913_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3914_ord__le__eq__subst,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_subst
% 0.32/0.58  thf(fact_3915_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3916_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3917_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3918_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3919_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3920_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3921_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3922_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: int,F: num > int,B: num,C: num] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3923_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3924_ord__eq__le__subst,axiom,
% 0.32/0.58      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_subst
% 0.32/0.58  thf(fact_3925_linorder__linear,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58        | ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_linear
% 0.32/0.58  thf(fact_3926_linorder__linear,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58        | ( ord_less_eq_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_linear
% 0.32/0.58  thf(fact_3927_linorder__linear,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58        | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_linear
% 0.32/0.58  thf(fact_3928_linorder__linear,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58        | ( ord_less_eq_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_linear
% 0.32/0.58  thf(fact_3929_order__eq__refl,axiom,
% 0.32/0.58      ! [X: set_int,Y: set_int] :
% 0.32/0.58        ( ( X = Y )
% 0.32/0.58       => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_eq_refl
% 0.32/0.58  thf(fact_3930_order__eq__refl,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( X = Y )
% 0.32/0.58       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_eq_refl
% 0.32/0.58  thf(fact_3931_order__eq__refl,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( X = Y )
% 0.32/0.58       => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_eq_refl
% 0.32/0.58  thf(fact_3932_order__eq__refl,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( X = Y )
% 0.32/0.58       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_eq_refl
% 0.32/0.58  thf(fact_3933_order__eq__refl,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( X = Y )
% 0.32/0.58       => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_eq_refl
% 0.32/0.58  thf(fact_3934_order__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3935_order__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3936_order__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3937_order__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3938_order__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3939_order__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3940_order__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3941_order__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3942_order__subst2,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3943_order__subst2,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst2
% 0.32/0.58  thf(fact_3944_order__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3945_order__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3946_order__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3947_order__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_eq_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3948_order__subst1,axiom,
% 0.32/0.58      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3949_order__subst1,axiom,
% 0.32/0.58      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3950_order__subst1,axiom,
% 0.32/0.58      ! [A: num,F: nat > num,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3951_order__subst1,axiom,
% 0.32/0.58      ! [A: num,F: int > num,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_eq_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3952_order__subst1,axiom,
% 0.32/0.58      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3953_order__subst1,axiom,
% 0.32/0.58      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_subst1
% 0.32/0.58  thf(fact_3954_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: set_int,B2: set_int] :
% 0.32/0.58            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.32/0.58            & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Orderings.order_eq_iff
% 0.32/0.58  thf(fact_3955_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.58            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.32/0.58            & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Orderings.order_eq_iff
% 0.32/0.58  thf(fact_3956_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: num,B2: num] :
% 0.32/0.58            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.32/0.58            & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Orderings.order_eq_iff
% 0.32/0.58  thf(fact_3957_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.58            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.32/0.58            & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Orderings.order_eq_iff
% 0.32/0.58  thf(fact_3958_Orderings_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: int,B2: int] :
% 0.32/0.58            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.32/0.58            & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % Orderings.order_eq_iff
% 0.32/0.58  thf(fact_3959_antisym,axiom,
% 0.32/0.58      ! [A: set_int,B: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ B @ A )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym
% 0.32/0.58  thf(fact_3960_antisym,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym
% 0.32/0.58  thf(fact_3961_antisym,axiom,
% 0.32/0.58      ! [A: num,B: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ A )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym
% 0.32/0.58  thf(fact_3962_antisym,axiom,
% 0.32/0.58      ! [A: nat,B: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym
% 0.32/0.58  thf(fact_3963_antisym,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_int @ B @ A )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym
% 0.32/0.58  thf(fact_3964_dual__order_Otrans,axiom,
% 0.32/0.58      ! [B: set_int,A: set_int,C: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ C @ B )
% 0.32/0.58         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.trans
% 0.32/0.58  thf(fact_3965_dual__order_Otrans,axiom,
% 0.32/0.58      ! [B: rat,A: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.58         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.trans
% 0.32/0.58  thf(fact_3966_dual__order_Otrans,axiom,
% 0.32/0.58      ! [B: num,A: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_num @ C @ B )
% 0.32/0.58         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.trans
% 0.32/0.58  thf(fact_3967_dual__order_Otrans,axiom,
% 0.32/0.58      ! [B: nat,A: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.58         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.trans
% 0.32/0.58  thf(fact_3968_dual__order_Otrans,axiom,
% 0.32/0.58      ! [B: int,A: int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_int @ C @ B )
% 0.32/0.58         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.trans
% 0.32/0.58  thf(fact_3969_dual__order_Oantisym,axiom,
% 0.32/0.58      ! [B: set_int,A: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.antisym
% 0.32/0.58  thf(fact_3970_dual__order_Oantisym,axiom,
% 0.32/0.58      ! [B: rat,A: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.antisym
% 0.32/0.58  thf(fact_3971_dual__order_Oantisym,axiom,
% 0.32/0.58      ! [B: num,A: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.antisym
% 0.32/0.58  thf(fact_3972_dual__order_Oantisym,axiom,
% 0.32/0.58      ! [B: nat,A: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.antisym
% 0.32/0.58  thf(fact_3973_dual__order_Oantisym,axiom,
% 0.32/0.58      ! [B: int,A: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.58       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.58         => ( A = B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.antisym
% 0.32/0.58  thf(fact_3974_dual__order_Oeq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: set_int,B2: set_int] :
% 0.32/0.58            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.32/0.58            & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.eq_iff
% 0.32/0.58  thf(fact_3975_dual__order_Oeq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.58            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.32/0.58            & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.eq_iff
% 0.32/0.58  thf(fact_3976_dual__order_Oeq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: num,B2: num] :
% 0.32/0.58            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.32/0.58            & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.eq_iff
% 0.32/0.58  thf(fact_3977_dual__order_Oeq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.58            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.32/0.58            & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.eq_iff
% 0.32/0.58  thf(fact_3978_dual__order_Oeq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [A3: int,B2: int] :
% 0.32/0.58            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.32/0.58            & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.eq_iff
% 0.32/0.58  thf(fact_3979_linorder__wlog,axiom,
% 0.32/0.58      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.32/0.58        ( ! [A5: rat,B5: rat] :
% 0.32/0.58            ( ( ord_less_eq_rat @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: rat,B5: rat] :
% 0.32/0.58              ( ( P @ B5 @ A5 )
% 0.32/0.58             => ( P @ A5 @ B5 ) )
% 0.32/0.58         => ( P @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_wlog
% 0.32/0.58  thf(fact_3980_linorder__wlog,axiom,
% 0.32/0.58      ! [P: num > num > $o,A: num,B: num] :
% 0.32/0.58        ( ! [A5: num,B5: num] :
% 0.32/0.58            ( ( ord_less_eq_num @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: num,B5: num] :
% 0.32/0.58              ( ( P @ B5 @ A5 )
% 0.32/0.58             => ( P @ A5 @ B5 ) )
% 0.32/0.58         => ( P @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_wlog
% 0.32/0.58  thf(fact_3981_linorder__wlog,axiom,
% 0.32/0.58      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.58        ( ! [A5: nat,B5: nat] :
% 0.32/0.58            ( ( ord_less_eq_nat @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: nat,B5: nat] :
% 0.32/0.58              ( ( P @ B5 @ A5 )
% 0.32/0.58             => ( P @ A5 @ B5 ) )
% 0.32/0.58         => ( P @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_wlog
% 0.32/0.58  thf(fact_3982_linorder__wlog,axiom,
% 0.32/0.58      ! [P: int > int > $o,A: int,B: int] :
% 0.32/0.58        ( ! [A5: int,B5: int] :
% 0.32/0.58            ( ( ord_less_eq_int @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: int,B5: int] :
% 0.32/0.58              ( ( P @ B5 @ A5 )
% 0.32/0.58             => ( P @ A5 @ B5 ) )
% 0.32/0.58         => ( P @ A @ B ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_wlog
% 0.32/0.58  thf(fact_3983_order__trans,axiom,
% 0.32/0.58      ! [X: set_int,Y: set_int,Z: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.32/0.58         => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_trans
% 0.32/0.58  thf(fact_3984_order__trans,axiom,
% 0.32/0.58      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.32/0.58         => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_trans
% 0.32/0.58  thf(fact_3985_order__trans,axiom,
% 0.32/0.58      ! [X: num,Y: num,Z: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_num @ Y @ Z )
% 0.32/0.58         => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_trans
% 0.32/0.58  thf(fact_3986_order__trans,axiom,
% 0.32/0.58      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.32/0.58         => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_trans
% 0.32/0.58  thf(fact_3987_order__trans,axiom,
% 0.32/0.58      ! [X: int,Y: int,Z: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_int @ Y @ Z )
% 0.32/0.58         => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_trans
% 0.32/0.58  thf(fact_3988_order_Otrans,axiom,
% 0.32/0.58      ! [A: set_int,B: set_int,C: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ B @ C )
% 0.32/0.58         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.trans
% 0.32/0.58  thf(fact_3989_order_Otrans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.trans
% 0.32/0.58  thf(fact_3990_order_Otrans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.trans
% 0.32/0.58  thf(fact_3991_order_Otrans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.trans
% 0.32/0.58  thf(fact_3992_order_Otrans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.58         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.trans
% 0.32/0.58  thf(fact_3993_order__antisym,axiom,
% 0.32/0.58      ! [X: set_int,Y: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ Y @ X )
% 0.32/0.58         => ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym
% 0.32/0.58  thf(fact_3994_order__antisym,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_rat @ Y @ X )
% 0.32/0.58         => ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym
% 0.32/0.58  thf(fact_3995_order__antisym,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_num @ Y @ X )
% 0.32/0.58         => ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym
% 0.32/0.58  thf(fact_3996_order__antisym,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.58         => ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym
% 0.32/0.58  thf(fact_3997_order__antisym,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_eq_int @ Y @ X )
% 0.32/0.58         => ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_antisym
% 0.32/0.58  thf(fact_3998_ord__le__eq__trans,axiom,
% 0.32/0.58      ! [A: set_int,B: set_int,C: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_trans
% 0.32/0.58  thf(fact_3999_ord__le__eq__trans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_trans
% 0.32/0.58  thf(fact_4000_ord__le__eq__trans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_trans
% 0.32/0.58  thf(fact_4001_ord__le__eq__trans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_trans
% 0.32/0.58  thf(fact_4002_ord__le__eq__trans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_le_eq_trans
% 0.32/0.58  thf(fact_4003_ord__eq__le__trans,axiom,
% 0.32/0.58      ! [A: set_int,B: set_int,C: set_int] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_eq_set_int @ B @ C )
% 0.32/0.58         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_trans
% 0.32/0.58  thf(fact_4004_ord__eq__le__trans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_trans
% 0.32/0.58  thf(fact_4005_ord__eq__le__trans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.58         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_trans
% 0.32/0.58  thf(fact_4006_ord__eq__le__trans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.58         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_trans
% 0.32/0.58  thf(fact_4007_ord__eq__le__trans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.58         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_le_trans
% 0.32/0.58  thf(fact_4008_order__class_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [X3: set_int,Y3: set_int] :
% 0.32/0.58            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 0.32/0.58            & ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_class.order_eq_iff
% 0.32/0.58  thf(fact_4009_order__class_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [X3: rat,Y3: rat] :
% 0.32/0.58            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.32/0.58            & ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_class.order_eq_iff
% 0.32/0.58  thf(fact_4010_order__class_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [X3: num,Y3: num] :
% 0.32/0.58            ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.32/0.58            & ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_class.order_eq_iff
% 0.32/0.58  thf(fact_4011_order__class_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.58            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.32/0.58            & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_class.order_eq_iff
% 0.32/0.58  thf(fact_4012_order__class_Oorder__eq__iff,axiom,
% 0.32/0.58      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.32/0.58      = ( ^ [X3: int,Y3: int] :
% 0.32/0.58            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.32/0.58            & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_class.order_eq_iff
% 0.32/0.58  thf(fact_4013_le__cases3,axiom,
% 0.32/0.58      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.58        ( ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 0.32/0.58       => ( ( ( ord_less_eq_rat @ Y @ X )
% 0.32/0.58           => ~ ( ord_less_eq_rat @ X @ Z ) )
% 0.32/0.58         => ( ( ( ord_less_eq_rat @ X @ Z )
% 0.32/0.58             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 0.32/0.58           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 0.32/0.58               => ~ ( ord_less_eq_rat @ Y @ X ) )
% 0.32/0.58             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 0.32/0.58                 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 0.32/0.58               => ~ ( ( ord_less_eq_rat @ Z @ X )
% 0.32/0.58                   => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % le_cases3
% 0.32/0.58  thf(fact_4014_le__cases3,axiom,
% 0.32/0.58      ! [X: num,Y: num,Z: num] :
% 0.32/0.58        ( ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58         => ~ ( ord_less_eq_num @ Y @ Z ) )
% 0.32/0.58       => ( ( ( ord_less_eq_num @ Y @ X )
% 0.32/0.58           => ~ ( ord_less_eq_num @ X @ Z ) )
% 0.32/0.58         => ( ( ( ord_less_eq_num @ X @ Z )
% 0.32/0.58             => ~ ( ord_less_eq_num @ Z @ Y ) )
% 0.32/0.58           => ( ( ( ord_less_eq_num @ Z @ Y )
% 0.32/0.58               => ~ ( ord_less_eq_num @ Y @ X ) )
% 0.32/0.58             => ( ( ( ord_less_eq_num @ Y @ Z )
% 0.32/0.58                 => ~ ( ord_less_eq_num @ Z @ X ) )
% 0.32/0.58               => ~ ( ( ord_less_eq_num @ Z @ X )
% 0.32/0.58                   => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % le_cases3
% 0.32/0.58  thf(fact_4015_le__cases3,axiom,
% 0.32/0.58      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.58        ( ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.32/0.58       => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.58           => ~ ( ord_less_eq_nat @ X @ Z ) )
% 0.32/0.58         => ( ( ( ord_less_eq_nat @ X @ Z )
% 0.32/0.58             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.32/0.58           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.32/0.58               => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.32/0.58             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.32/0.58                 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 0.32/0.58               => ~ ( ( ord_less_eq_nat @ Z @ X )
% 0.32/0.58                   => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % le_cases3
% 0.32/0.58  thf(fact_4016_le__cases3,axiom,
% 0.32/0.58      ! [X: int,Y: int,Z: int] :
% 0.32/0.58        ( ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 0.32/0.58       => ( ( ( ord_less_eq_int @ Y @ X )
% 0.32/0.58           => ~ ( ord_less_eq_int @ X @ Z ) )
% 0.32/0.58         => ( ( ( ord_less_eq_int @ X @ Z )
% 0.32/0.58             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 0.32/0.58           => ( ( ( ord_less_eq_int @ Z @ Y )
% 0.32/0.58               => ~ ( ord_less_eq_int @ Y @ X ) )
% 0.32/0.58             => ( ( ( ord_less_eq_int @ Y @ Z )
% 0.32/0.58                 => ~ ( ord_less_eq_int @ Z @ X ) )
% 0.32/0.58               => ~ ( ( ord_less_eq_int @ Z @ X )
% 0.32/0.58                   => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % le_cases3
% 0.32/0.58  thf(fact_4017_nle__le,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.32/0.58        = ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.58          & ( B != A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % nle_le
% 0.32/0.58  thf(fact_4018_nle__le,axiom,
% 0.32/0.58      ! [A: num,B: num] :
% 0.32/0.58        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.32/0.58        = ( ( ord_less_eq_num @ B @ A )
% 0.32/0.58          & ( B != A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % nle_le
% 0.32/0.58  thf(fact_4019_nle__le,axiom,
% 0.32/0.58      ! [A: nat,B: nat] :
% 0.32/0.58        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.32/0.58        = ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.58          & ( B != A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % nle_le
% 0.32/0.58  thf(fact_4020_nle__le,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.32/0.58        = ( ( ord_less_eq_int @ B @ A )
% 0.32/0.58          & ( B != A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % nle_le
% 0.32/0.58  thf(fact_4021_order__less__imp__not__less,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_less
% 0.32/0.58  thf(fact_4022_order__less__imp__not__less,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_less
% 0.32/0.58  thf(fact_4023_order__less__imp__not__less,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_less
% 0.32/0.58  thf(fact_4024_order__less__imp__not__less,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_less
% 0.32/0.58  thf(fact_4025_order__less__imp__not__less,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_less
% 0.32/0.58  thf(fact_4026_order__less__imp__not__eq2,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( Y != X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq2
% 0.32/0.58  thf(fact_4027_order__less__imp__not__eq2,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( Y != X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq2
% 0.32/0.58  thf(fact_4028_order__less__imp__not__eq2,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( Y != X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq2
% 0.32/0.58  thf(fact_4029_order__less__imp__not__eq2,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( Y != X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq2
% 0.32/0.58  thf(fact_4030_order__less__imp__not__eq2,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( Y != X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq2
% 0.32/0.58  thf(fact_4031_order__less__imp__not__eq,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq
% 0.32/0.58  thf(fact_4032_order__less__imp__not__eq,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq
% 0.32/0.58  thf(fact_4033_order__less__imp__not__eq,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq
% 0.32/0.58  thf(fact_4034_order__less__imp__not__eq,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq
% 0.32/0.58  thf(fact_4035_order__less__imp__not__eq,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_not_eq
% 0.32/0.58  thf(fact_4036_linorder__less__linear,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58        | ( X = Y )
% 0.32/0.58        | ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_linear
% 0.32/0.58  thf(fact_4037_linorder__less__linear,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58        | ( X = Y )
% 0.32/0.58        | ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_linear
% 0.32/0.58  thf(fact_4038_linorder__less__linear,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58        | ( X = Y )
% 0.32/0.58        | ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_linear
% 0.32/0.58  thf(fact_4039_linorder__less__linear,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58        | ( X = Y )
% 0.32/0.58        | ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_linear
% 0.32/0.58  thf(fact_4040_linorder__less__linear,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58        | ( X = Y )
% 0.32/0.58        | ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_linear
% 0.32/0.58  thf(fact_4041_order__less__imp__triv,axiom,
% 0.32/0.58      ! [X: real,Y: real,P: $o] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( ( ord_less_real @ Y @ X )
% 0.32/0.58         => P ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_triv
% 0.32/0.58  thf(fact_4042_order__less__imp__triv,axiom,
% 0.32/0.58      ! [X: rat,Y: rat,P: $o] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_rat @ Y @ X )
% 0.32/0.58         => P ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_triv
% 0.32/0.58  thf(fact_4043_order__less__imp__triv,axiom,
% 0.32/0.58      ! [X: num,Y: num,P: $o] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( ( ord_less_num @ Y @ X )
% 0.32/0.58         => P ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_triv
% 0.32/0.58  thf(fact_4044_order__less__imp__triv,axiom,
% 0.32/0.58      ! [X: nat,Y: nat,P: $o] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_nat @ Y @ X )
% 0.32/0.58         => P ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_triv
% 0.32/0.58  thf(fact_4045_order__less__imp__triv,axiom,
% 0.32/0.58      ! [X: int,Y: int,P: $o] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_int @ Y @ X )
% 0.32/0.58         => P ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_imp_triv
% 0.32/0.58  thf(fact_4046_order__less__not__sym,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_not_sym
% 0.32/0.58  thf(fact_4047_order__less__not__sym,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_not_sym
% 0.32/0.58  thf(fact_4048_order__less__not__sym,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_not_sym
% 0.32/0.58  thf(fact_4049_order__less__not__sym,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_not_sym
% 0.32/0.58  thf(fact_4050_order__less__not__sym,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_not_sym
% 0.32/0.58  thf(fact_4051_order__less__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4052_order__less__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4053_order__less__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > num,C: num] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4054_order__less__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4055_order__less__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > int,C: int] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4056_order__less__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4057_order__less__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4058_order__less__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4059_order__less__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4060_order__less__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst2
% 0.32/0.58  thf(fact_4061_order__less__subst1,axiom,
% 0.32/0.58      ! [A: real,F: real > real,B: real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4062_order__less__subst1,axiom,
% 0.32/0.58      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4063_order__less__subst1,axiom,
% 0.32/0.58      ! [A: real,F: num > real,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4064_order__less__subst1,axiom,
% 0.32/0.58      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4065_order__less__subst1,axiom,
% 0.32/0.58      ! [A: real,F: int > real,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_int @ B @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4066_order__less__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4067_order__less__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4068_order__less__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_num @ B @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4069_order__less__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_nat @ B @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4070_order__less__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_int @ B @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_subst1
% 0.32/0.58  thf(fact_4071_order__less__irrefl,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ~ ( ord_less_real @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_irrefl
% 0.32/0.58  thf(fact_4072_order__less__irrefl,axiom,
% 0.32/0.58      ! [X: rat] :
% 0.32/0.58        ~ ( ord_less_rat @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_irrefl
% 0.32/0.58  thf(fact_4073_order__less__irrefl,axiom,
% 0.32/0.58      ! [X: num] :
% 0.32/0.58        ~ ( ord_less_num @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_irrefl
% 0.32/0.58  thf(fact_4074_order__less__irrefl,axiom,
% 0.32/0.58      ! [X: nat] :
% 0.32/0.58        ~ ( ord_less_nat @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_irrefl
% 0.32/0.58  thf(fact_4075_order__less__irrefl,axiom,
% 0.32/0.58      ! [X: int] :
% 0.32/0.58        ~ ( ord_less_int @ X @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_irrefl
% 0.32/0.58  thf(fact_4076_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4077_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4078_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > num,C: num] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4079_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4080_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > int,C: int] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4081_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4082_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4083_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4084_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4085_ord__less__eq__subst,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ( F @ B )
% 0.32/0.58            = C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_subst
% 0.32/0.58  thf(fact_4086_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: real,F: real > real,B: real,C: real] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4087_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4088_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: num,F: real > num,B: real,C: real] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4089_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: nat,F: real > nat,B: real,C: real] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4090_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: int,F: real > int,B: real,C: real] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4091_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4092_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4093_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4094_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4095_ord__eq__less__subst,axiom,
% 0.32/0.58      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.58        ( ( A
% 0.32/0.58          = ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_subst
% 0.32/0.58  thf(fact_4096_order__less__trans,axiom,
% 0.32/0.58      ! [X: real,Y: real,Z: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( ( ord_less_real @ Y @ Z )
% 0.32/0.58         => ( ord_less_real @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_trans
% 0.32/0.58  thf(fact_4097_order__less__trans,axiom,
% 0.32/0.58      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_rat @ Y @ Z )
% 0.32/0.58         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_trans
% 0.32/0.58  thf(fact_4098_order__less__trans,axiom,
% 0.32/0.58      ! [X: num,Y: num,Z: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( ( ord_less_num @ Y @ Z )
% 0.32/0.58         => ( ord_less_num @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_trans
% 0.32/0.58  thf(fact_4099_order__less__trans,axiom,
% 0.32/0.58      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_nat @ Y @ Z )
% 0.32/0.58         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_trans
% 0.32/0.58  thf(fact_4100_order__less__trans,axiom,
% 0.32/0.58      ! [X: int,Y: int,Z: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_int @ Y @ Z )
% 0.32/0.58         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_trans
% 0.32/0.58  thf(fact_4101_order__less__asym_H,axiom,
% 0.32/0.58      ! [A: real,B: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym'
% 0.32/0.58  thf(fact_4102_order__less__asym_H,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym'
% 0.32/0.58  thf(fact_4103_order__less__asym_H,axiom,
% 0.32/0.58      ! [A: num,B: num] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym'
% 0.32/0.58  thf(fact_4104_order__less__asym_H,axiom,
% 0.32/0.58      ! [A: nat,B: nat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym'
% 0.32/0.58  thf(fact_4105_order__less__asym_H,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym'
% 0.32/0.58  thf(fact_4106_linorder__neq__iff,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58        = ( ( ord_less_real @ X @ Y )
% 0.32/0.58          | ( ord_less_real @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neq_iff
% 0.32/0.58  thf(fact_4107_linorder__neq__iff,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58        = ( ( ord_less_rat @ X @ Y )
% 0.32/0.58          | ( ord_less_rat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neq_iff
% 0.32/0.58  thf(fact_4108_linorder__neq__iff,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58        = ( ( ord_less_num @ X @ Y )
% 0.32/0.58          | ( ord_less_num @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neq_iff
% 0.32/0.58  thf(fact_4109_linorder__neq__iff,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58        = ( ( ord_less_nat @ X @ Y )
% 0.32/0.58          | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neq_iff
% 0.32/0.58  thf(fact_4110_linorder__neq__iff,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58        = ( ( ord_less_int @ X @ Y )
% 0.32/0.58          | ( ord_less_int @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neq_iff
% 0.32/0.58  thf(fact_4111_order__less__asym,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym
% 0.32/0.58  thf(fact_4112_order__less__asym,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym
% 0.32/0.58  thf(fact_4113_order__less__asym,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym
% 0.32/0.58  thf(fact_4114_order__less__asym,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym
% 0.32/0.58  thf(fact_4115_order__less__asym,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_asym
% 0.32/0.58  thf(fact_4116_linorder__neqE,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58       => ( ~ ( ord_less_real @ X @ Y )
% 0.32/0.58         => ( ord_less_real @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neqE
% 0.32/0.58  thf(fact_4117_linorder__neqE,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58       => ( ~ ( ord_less_rat @ X @ Y )
% 0.32/0.58         => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neqE
% 0.32/0.58  thf(fact_4118_linorder__neqE,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58       => ( ~ ( ord_less_num @ X @ Y )
% 0.32/0.58         => ( ord_less_num @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neqE
% 0.32/0.58  thf(fact_4119_linorder__neqE,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58       => ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.58         => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neqE
% 0.32/0.58  thf(fact_4120_linorder__neqE,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( X != Y )
% 0.32/0.58       => ( ~ ( ord_less_int @ X @ Y )
% 0.32/0.58         => ( ord_less_int @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_neqE
% 0.32/0.58  thf(fact_4121_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [B: real,A: real] :
% 0.32/0.58        ( ( ord_less_real @ B @ A )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4122_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [B: rat,A: rat] :
% 0.32/0.58        ( ( ord_less_rat @ B @ A )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4123_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [B: num,A: num] :
% 0.32/0.58        ( ( ord_less_num @ B @ A )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4124_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [B: nat,A: nat] :
% 0.32/0.58        ( ( ord_less_nat @ B @ A )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4125_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [B: int,A: int] :
% 0.32/0.58        ( ( ord_less_int @ B @ A )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4126_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [A: real,B: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4127_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4128_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [A: num,B: num] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4129_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [A: nat,B: nat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4130_order_Ostrict__implies__not__eq,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ( A != B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_implies_not_eq
% 0.32/0.58  thf(fact_4131_dual__order_Ostrict__trans,axiom,
% 0.32/0.58      ! [B: real,A: real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ B @ A )
% 0.32/0.58       => ( ( ord_less_real @ C @ B )
% 0.32/0.58         => ( ord_less_real @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_trans
% 0.32/0.58  thf(fact_4132_dual__order_Ostrict__trans,axiom,
% 0.32/0.58      ! [B: rat,A: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ B @ A )
% 0.32/0.58       => ( ( ord_less_rat @ C @ B )
% 0.32/0.58         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_trans
% 0.32/0.58  thf(fact_4133_dual__order_Ostrict__trans,axiom,
% 0.32/0.58      ! [B: num,A: num,C: num] :
% 0.32/0.58        ( ( ord_less_num @ B @ A )
% 0.32/0.58       => ( ( ord_less_num @ C @ B )
% 0.32/0.58         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_trans
% 0.32/0.58  thf(fact_4134_dual__order_Ostrict__trans,axiom,
% 0.32/0.58      ! [B: nat,A: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_nat @ B @ A )
% 0.32/0.58       => ( ( ord_less_nat @ C @ B )
% 0.32/0.58         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_trans
% 0.32/0.58  thf(fact_4135_dual__order_Ostrict__trans,axiom,
% 0.32/0.58      ! [B: int,A: int,C: int] :
% 0.32/0.58        ( ( ord_less_int @ B @ A )
% 0.32/0.58       => ( ( ord_less_int @ C @ B )
% 0.32/0.58         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.strict_trans
% 0.32/0.58  thf(fact_4136_not__less__iff__gr__or__eq,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.32/0.58        = ( ( ord_less_real @ Y @ X )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % not_less_iff_gr_or_eq
% 0.32/0.58  thf(fact_4137_not__less__iff__gr__or__eq,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.32/0.58        = ( ( ord_less_rat @ Y @ X )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % not_less_iff_gr_or_eq
% 0.32/0.58  thf(fact_4138_not__less__iff__gr__or__eq,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.32/0.58        = ( ( ord_less_num @ Y @ X )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % not_less_iff_gr_or_eq
% 0.32/0.58  thf(fact_4139_not__less__iff__gr__or__eq,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.32/0.58        = ( ( ord_less_nat @ Y @ X )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % not_less_iff_gr_or_eq
% 0.32/0.58  thf(fact_4140_not__less__iff__gr__or__eq,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.32/0.58        = ( ( ord_less_int @ Y @ X )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % not_less_iff_gr_or_eq
% 0.32/0.58  thf(fact_4141_order_Ostrict__trans,axiom,
% 0.32/0.58      ! [A: real,B: real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ord_less_real @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_trans
% 0.32/0.58  thf(fact_4142_order_Ostrict__trans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_trans
% 0.32/0.58  thf(fact_4143_order_Ostrict__trans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_num @ B @ C )
% 0.32/0.58         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_trans
% 0.32/0.58  thf(fact_4144_order_Ostrict__trans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_nat @ B @ C )
% 0.32/0.58         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_trans
% 0.32/0.58  thf(fact_4145_order_Ostrict__trans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_int @ B @ C )
% 0.32/0.58         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.strict_trans
% 0.32/0.58  thf(fact_4146_linorder__less__wlog,axiom,
% 0.32/0.58      ! [P: real > real > $o,A: real,B: real] :
% 0.32/0.58        ( ! [A5: real,B5: real] :
% 0.32/0.58            ( ( ord_less_real @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 0.32/0.58         => ( ! [A5: real,B5: real] :
% 0.32/0.58                ( ( P @ B5 @ A5 )
% 0.32/0.58               => ( P @ A5 @ B5 ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_wlog
% 0.32/0.58  thf(fact_4147_linorder__less__wlog,axiom,
% 0.32/0.58      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.32/0.58        ( ! [A5: rat,B5: rat] :
% 0.32/0.58            ( ( ord_less_rat @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 0.32/0.58         => ( ! [A5: rat,B5: rat] :
% 0.32/0.58                ( ( P @ B5 @ A5 )
% 0.32/0.58               => ( P @ A5 @ B5 ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_wlog
% 0.32/0.58  thf(fact_4148_linorder__less__wlog,axiom,
% 0.32/0.58      ! [P: num > num > $o,A: num,B: num] :
% 0.32/0.58        ( ! [A5: num,B5: num] :
% 0.32/0.58            ( ( ord_less_num @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 0.32/0.58         => ( ! [A5: num,B5: num] :
% 0.32/0.58                ( ( P @ B5 @ A5 )
% 0.32/0.58               => ( P @ A5 @ B5 ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_wlog
% 0.32/0.58  thf(fact_4149_linorder__less__wlog,axiom,
% 0.32/0.58      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.58        ( ! [A5: nat,B5: nat] :
% 0.32/0.58            ( ( ord_less_nat @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 0.32/0.58         => ( ! [A5: nat,B5: nat] :
% 0.32/0.58                ( ( P @ B5 @ A5 )
% 0.32/0.58               => ( P @ A5 @ B5 ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_wlog
% 0.32/0.58  thf(fact_4150_linorder__less__wlog,axiom,
% 0.32/0.58      ! [P: int > int > $o,A: int,B: int] :
% 0.32/0.58        ( ! [A5: int,B5: int] :
% 0.32/0.58            ( ( ord_less_int @ A5 @ B5 )
% 0.32/0.58           => ( P @ A5 @ B5 ) )
% 0.32/0.58       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 0.32/0.58         => ( ! [A5: int,B5: int] :
% 0.32/0.58                ( ( P @ B5 @ A5 )
% 0.32/0.58               => ( P @ A5 @ B5 ) )
% 0.32/0.58           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_less_wlog
% 0.32/0.58  thf(fact_4151_exists__least__iff,axiom,
% 0.32/0.58      ( ( ^ [P3: nat > $o] :
% 0.32/0.58          ? [X7: nat] : ( P3 @ X7 ) )
% 0.32/0.58      = ( ^ [P4: nat > $o] :
% 0.32/0.58          ? [N2: nat] :
% 0.32/0.58            ( ( P4 @ N2 )
% 0.32/0.58            & ! [M3: nat] :
% 0.32/0.58                ( ( ord_less_nat @ M3 @ N2 )
% 0.32/0.58               => ~ ( P4 @ M3 ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % exists_least_iff
% 0.32/0.58  thf(fact_4152_dual__order_Oirrefl,axiom,
% 0.32/0.58      ! [A: real] :
% 0.32/0.58        ~ ( ord_less_real @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.irrefl
% 0.32/0.58  thf(fact_4153_dual__order_Oirrefl,axiom,
% 0.32/0.58      ! [A: rat] :
% 0.32/0.58        ~ ( ord_less_rat @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.irrefl
% 0.32/0.58  thf(fact_4154_dual__order_Oirrefl,axiom,
% 0.32/0.58      ! [A: num] :
% 0.32/0.58        ~ ( ord_less_num @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.irrefl
% 0.32/0.58  thf(fact_4155_dual__order_Oirrefl,axiom,
% 0.32/0.58      ! [A: nat] :
% 0.32/0.58        ~ ( ord_less_nat @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.irrefl
% 0.32/0.58  thf(fact_4156_dual__order_Oirrefl,axiom,
% 0.32/0.58      ! [A: int] :
% 0.32/0.58        ~ ( ord_less_int @ A @ A ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.irrefl
% 0.32/0.58  thf(fact_4157_dual__order_Oasym,axiom,
% 0.32/0.58      ! [B: real,A: real] :
% 0.32/0.58        ( ( ord_less_real @ B @ A )
% 0.32/0.58       => ~ ( ord_less_real @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.asym
% 0.32/0.58  thf(fact_4158_dual__order_Oasym,axiom,
% 0.32/0.58      ! [B: rat,A: rat] :
% 0.32/0.58        ( ( ord_less_rat @ B @ A )
% 0.32/0.58       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.asym
% 0.32/0.58  thf(fact_4159_dual__order_Oasym,axiom,
% 0.32/0.58      ! [B: num,A: num] :
% 0.32/0.58        ( ( ord_less_num @ B @ A )
% 0.32/0.58       => ~ ( ord_less_num @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.asym
% 0.32/0.58  thf(fact_4160_dual__order_Oasym,axiom,
% 0.32/0.58      ! [B: nat,A: nat] :
% 0.32/0.58        ( ( ord_less_nat @ B @ A )
% 0.32/0.58       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.asym
% 0.32/0.58  thf(fact_4161_dual__order_Oasym,axiom,
% 0.32/0.58      ! [B: int,A: int] :
% 0.32/0.58        ( ( ord_less_int @ B @ A )
% 0.32/0.58       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dual_order.asym
% 0.32/0.58  thf(fact_4162_linorder__cases,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ~ ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( ( X != Y )
% 0.32/0.58         => ( ord_less_real @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_cases
% 0.32/0.58  thf(fact_4163_linorder__cases,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ~ ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( ( X != Y )
% 0.32/0.58         => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_cases
% 0.32/0.58  thf(fact_4164_linorder__cases,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ~ ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( ( X != Y )
% 0.32/0.58         => ( ord_less_num @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_cases
% 0.32/0.58  thf(fact_4165_linorder__cases,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( ( X != Y )
% 0.32/0.58         => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_cases
% 0.32/0.58  thf(fact_4166_linorder__cases,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ~ ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( ( X != Y )
% 0.32/0.58         => ( ord_less_int @ Y @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_cases
% 0.32/0.58  thf(fact_4167_antisym__conv3,axiom,
% 0.32/0.58      ! [Y: real,X: real] :
% 0.32/0.58        ( ~ ( ord_less_real @ Y @ X )
% 0.32/0.58       => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym_conv3
% 0.32/0.58  thf(fact_4168_antisym__conv3,axiom,
% 0.32/0.58      ! [Y: rat,X: rat] :
% 0.32/0.58        ( ~ ( ord_less_rat @ Y @ X )
% 0.32/0.58       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym_conv3
% 0.32/0.58  thf(fact_4169_antisym__conv3,axiom,
% 0.32/0.58      ! [Y: num,X: num] :
% 0.32/0.58        ( ~ ( ord_less_num @ Y @ X )
% 0.32/0.58       => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym_conv3
% 0.32/0.58  thf(fact_4170_antisym__conv3,axiom,
% 0.32/0.58      ! [Y: nat,X: nat] :
% 0.32/0.58        ( ~ ( ord_less_nat @ Y @ X )
% 0.32/0.58       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym_conv3
% 0.32/0.58  thf(fact_4171_antisym__conv3,axiom,
% 0.32/0.58      ! [Y: int,X: int] :
% 0.32/0.58        ( ~ ( ord_less_int @ Y @ X )
% 0.32/0.58       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.32/0.58          = ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % antisym_conv3
% 0.32/0.58  thf(fact_4172_less__induct,axiom,
% 0.32/0.58      ! [P: nat > $o,A: nat] :
% 0.32/0.58        ( ! [X6: nat] :
% 0.32/0.58            ( ! [Y2: nat] :
% 0.32/0.58                ( ( ord_less_nat @ Y2 @ X6 )
% 0.32/0.58               => ( P @ Y2 ) )
% 0.32/0.58           => ( P @ X6 ) )
% 0.32/0.58       => ( P @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_induct
% 0.32/0.58  thf(fact_4173_ord__less__eq__trans,axiom,
% 0.32/0.58      ! [A: real,B: real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_real @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_trans
% 0.32/0.58  thf(fact_4174_ord__less__eq__trans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_trans
% 0.32/0.58  thf(fact_4175_ord__less__eq__trans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_trans
% 0.32/0.58  thf(fact_4176_ord__less__eq__trans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_trans
% 0.32/0.58  thf(fact_4177_ord__less__eq__trans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ( ( B = C )
% 0.32/0.58         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_less_eq_trans
% 0.32/0.58  thf(fact_4178_ord__eq__less__trans,axiom,
% 0.32/0.58      ! [A: real,B: real,C: real] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_real @ B @ C )
% 0.32/0.58         => ( ord_less_real @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_trans
% 0.32/0.58  thf(fact_4179_ord__eq__less__trans,axiom,
% 0.32/0.58      ! [A: rat,B: rat,C: rat] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_rat @ B @ C )
% 0.32/0.58         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_trans
% 0.32/0.58  thf(fact_4180_ord__eq__less__trans,axiom,
% 0.32/0.58      ! [A: num,B: num,C: num] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_num @ B @ C )
% 0.32/0.58         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_trans
% 0.32/0.58  thf(fact_4181_ord__eq__less__trans,axiom,
% 0.32/0.58      ! [A: nat,B: nat,C: nat] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_nat @ B @ C )
% 0.32/0.58         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_trans
% 0.32/0.58  thf(fact_4182_ord__eq__less__trans,axiom,
% 0.32/0.58      ! [A: int,B: int,C: int] :
% 0.32/0.58        ( ( A = B )
% 0.32/0.58       => ( ( ord_less_int @ B @ C )
% 0.32/0.58         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ord_eq_less_trans
% 0.32/0.58  thf(fact_4183_order_Oasym,axiom,
% 0.32/0.58      ! [A: real,B: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.asym
% 0.32/0.58  thf(fact_4184_order_Oasym,axiom,
% 0.32/0.58      ! [A: rat,B: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.asym
% 0.32/0.58  thf(fact_4185_order_Oasym,axiom,
% 0.32/0.58      ! [A: num,B: num] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ~ ( ord_less_num @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.asym
% 0.32/0.58  thf(fact_4186_order_Oasym,axiom,
% 0.32/0.58      ! [A: nat,B: nat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.asym
% 0.32/0.58  thf(fact_4187_order_Oasym,axiom,
% 0.32/0.58      ! [A: int,B: int] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order.asym
% 0.32/0.58  thf(fact_4188_less__imp__neq,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_imp_neq
% 0.32/0.58  thf(fact_4189_less__imp__neq,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_imp_neq
% 0.32/0.58  thf(fact_4190_less__imp__neq,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_num @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_imp_neq
% 0.32/0.58  thf(fact_4191_less__imp__neq,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_nat @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_imp_neq
% 0.32/0.58  thf(fact_4192_less__imp__neq,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_int @ X @ Y )
% 0.32/0.58       => ( X != Y ) ) ).
% 0.32/0.58  
% 0.32/0.58  % less_imp_neq
% 0.32/0.58  thf(fact_4193_dense,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ X @ Y )
% 0.32/0.58       => ? [Z5: real] :
% 0.32/0.58            ( ( ord_less_real @ X @ Z5 )
% 0.32/0.58            & ( ord_less_real @ Z5 @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dense
% 0.32/0.58  thf(fact_4194_dense,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_rat @ X @ Y )
% 0.32/0.58       => ? [Z5: rat] :
% 0.32/0.58            ( ( ord_less_rat @ X @ Z5 )
% 0.32/0.58            & ( ord_less_rat @ Z5 @ Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % dense
% 0.32/0.58  thf(fact_4195_gt__ex,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58      ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 0.32/0.58  
% 0.32/0.58  % gt_ex
% 0.32/0.58  thf(fact_4196_gt__ex,axiom,
% 0.32/0.58      ! [X: rat] :
% 0.32/0.58      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 0.32/0.58  
% 0.32/0.58  % gt_ex
% 0.32/0.58  thf(fact_4197_gt__ex,axiom,
% 0.32/0.58      ! [X: nat] :
% 0.32/0.58      ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.32/0.58  
% 0.32/0.58  % gt_ex
% 0.32/0.58  thf(fact_4198_gt__ex,axiom,
% 0.32/0.58      ! [X: int] :
% 0.32/0.58      ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 0.32/0.58  
% 0.32/0.58  % gt_ex
% 0.32/0.58  thf(fact_4199_lt__ex,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58      ? [Y5: real] : ( ord_less_real @ Y5 @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % lt_ex
% 0.32/0.58  thf(fact_4200_lt__ex,axiom,
% 0.32/0.58      ! [X: rat] :
% 0.32/0.58      ? [Y5: rat] : ( ord_less_rat @ Y5 @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % lt_ex
% 0.32/0.58  thf(fact_4201_lt__ex,axiom,
% 0.32/0.58      ! [X: int] :
% 0.32/0.58      ? [Y5: int] : ( ord_less_int @ Y5 @ X ) ).
% 0.32/0.58  
% 0.32/0.58  % lt_ex
% 0.32/0.58  thf(fact_4202_small__lazy_H_Ocases,axiom,
% 0.32/0.58      ! [X: product_prod_int_int] :
% 0.32/0.58        ~ ! [D3: int,I4: int] :
% 0.32/0.58            ( X
% 0.32/0.58           != ( product_Pair_int_int @ D3 @ I4 ) ) ).
% 0.32/0.58  
% 0.32/0.58  % small_lazy'.cases
% 0.32/0.58  thf(fact_4203_exhaustive__int_H_Ocases,axiom,
% 0.32/0.58      ! [X: produc7773217078559923341nt_int] :
% 0.32/0.58        ~ ! [F2: int > option6357759511663192854e_term,D3: int,I4: int] :
% 0.32/0.58            ( X
% 0.32/0.58           != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % exhaustive_int'.cases
% 0.32/0.58  thf(fact_4204_full__exhaustive__int_H_Ocases,axiom,
% 0.32/0.58      ! [X: produc2285326912895808259nt_int] :
% 0.32/0.58        ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I4: int] :
% 0.32/0.58            ( X
% 0.32/0.58           != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % full_exhaustive_int'.cases
% 0.32/0.58  thf(fact_4205_ln__ge__zero__imp__ge__one,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58         => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_ge_zero_imp_ge_one
% 0.32/0.58  thf(fact_4206_ln__add__one__self__le__self,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_add_one_self_le_self
% 0.32/0.58  thf(fact_4207_ln__mult,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 0.32/0.58            = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_mult
% 0.32/0.58  thf(fact_4208_ln__eq__minus__one,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ( ln_ln_real @ X )
% 0.32/0.58            = ( minus_minus_real @ X @ one_one_real ) )
% 0.32/0.58         => ( X = one_one_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_eq_minus_one
% 0.32/0.58  thf(fact_4209_ln__div,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 0.32/0.58            = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_div
% 0.32/0.58  thf(fact_4210_ln__le__minus__one,axiom,
% 0.32/0.58      ! [X: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_le_minus_one
% 0.32/0.58  thf(fact_4211_ln__diff__le,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.58       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.58         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % ln_diff_le
% 0.32/0.58  thf(fact_4212_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.58       => ( ( ord_less_real @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4213_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: set_int,Y: set_int] :
% 0.32/0.58        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_set_int @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4214_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_rat @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4215_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58       => ( ( ord_less_num @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4216_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58       => ( ( ord_less_nat @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4217_order__le__imp__less__or__eq,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58       => ( ( ord_less_int @ X @ Y )
% 0.32/0.58          | ( X = Y ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_le_imp_less_or_eq
% 0.32/0.58  thf(fact_4218_linorder__le__less__linear,axiom,
% 0.32/0.58      ! [X: real,Y: real] :
% 0.32/0.58        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.58        | ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_less_linear
% 0.32/0.58  thf(fact_4219_linorder__le__less__linear,axiom,
% 0.32/0.58      ! [X: rat,Y: rat] :
% 0.32/0.58        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.58        | ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_less_linear
% 0.32/0.58  thf(fact_4220_linorder__le__less__linear,axiom,
% 0.32/0.58      ! [X: num,Y: num] :
% 0.32/0.58        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.58        | ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_less_linear
% 0.32/0.58  thf(fact_4221_linorder__le__less__linear,axiom,
% 0.32/0.58      ! [X: nat,Y: nat] :
% 0.32/0.58        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.58        | ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_less_linear
% 0.32/0.58  thf(fact_4222_linorder__le__less__linear,axiom,
% 0.32/0.58      ! [X: int,Y: int] :
% 0.32/0.58        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.58        | ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.58  
% 0.32/0.58  % linorder_le_less_linear
% 0.32/0.58  thf(fact_4223_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > real,C: real] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4224_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4225_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > real,C: real] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4226_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > real,C: real] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4227_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: int,B: int,F: int > real,C: real] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4228_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: real,B: real,F: real > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_real @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: real,Y5: real] :
% 0.32/0.58                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4229_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4230_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_num @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: num,Y5: num] :
% 0.32/0.58                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4231_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_nat @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.58                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4232_order__less__le__subst2,axiom,
% 0.32/0.58      ! [A: int,B: int,F: int > rat,C: rat] :
% 0.32/0.58        ( ( ord_less_int @ A @ B )
% 0.32/0.58       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 0.32/0.58         => ( ! [X6: int,Y5: int] :
% 0.32/0.58                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst2
% 0.32/0.58  thf(fact_4233_order__less__le__subst1,axiom,
% 0.32/0.58      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.58       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.58         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.58                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.58               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.58           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.58  
% 0.32/0.58  % order_less_le_subst1
% 0.32/0.58  thf(fact_4234_order__less__le__subst1,axiom,
% 0.32/0.58      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.58        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4235_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: num,F: rat > num,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4236_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4237_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: int,F: rat > int,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4238_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: real,F: num > real,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4239_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4240_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: num,F: num > num,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_num @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4241_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: nat,F: num > nat,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4242_order__less__le__subst1,axiom,
% 0.32/0.59      ! [A: int,F: num > int,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_subst1
% 0.32/0.59  thf(fact_4243_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,F: rat > real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4244_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4245_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,F: rat > num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4246_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4247_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,F: rat > int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4248_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: num,B: num,F: num > real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_real @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4249_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: num,B: num,F: num > rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4250_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: num,B: num,F: num > num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_num @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4251_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: num,B: num,F: num > nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4252_order__le__less__subst2,axiom,
% 0.32/0.59      ! [A: num,B: num,F: num > int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_eq_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst2
% 0.32/0.59  thf(fact_4253_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: real,F: real > real,B: real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_real @ B @ C )
% 0.32/0.59         => ( ! [X6: real,Y5: real] :
% 0.32/0.59                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4254_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: real,F: rat > real,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4255_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: real,F: num > real,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4256_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: real,F: nat > real,B: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_nat @ B @ C )
% 0.32/0.59         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.59                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4257_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: real,F: int > real,B: int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_int @ B @ C )
% 0.32/0.59         => ( ! [X6: int,Y5: int] :
% 0.32/0.59                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4258_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: real > rat,B: real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_real @ B @ C )
% 0.32/0.59         => ( ! [X6: real,Y5: real] :
% 0.32/0.59                ( ( ord_less_real @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4259_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_rat @ B @ C )
% 0.32/0.59         => ( ! [X6: rat,Y5: rat] :
% 0.32/0.59                ( ( ord_less_rat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4260_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: num > rat,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_num @ B @ C )
% 0.32/0.59         => ( ! [X6: num,Y5: num] :
% 0.32/0.59                ( ( ord_less_num @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4261_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_nat @ B @ C )
% 0.32/0.59         => ( ! [X6: nat,Y5: nat] :
% 0.32/0.59                ( ( ord_less_nat @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4262_order__le__less__subst1,axiom,
% 0.32/0.59      ! [A: rat,F: int > rat,B: int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.32/0.59       => ( ( ord_less_int @ B @ C )
% 0.32/0.59         => ( ! [X6: int,Y5: int] :
% 0.32/0.59                ( ( ord_less_int @ X6 @ Y5 )
% 0.32/0.59               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 0.32/0.59           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_subst1
% 0.32/0.59  thf(fact_4263_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: real,Y: real,Z: real] :
% 0.32/0.59        ( ( ord_less_real @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_real @ Y @ Z )
% 0.32/0.59         => ( ord_less_real @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4264_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int,Z: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.32/0.59         => ( ord_less_set_int @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4265_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.59        ( ( ord_less_rat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.32/0.59         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4266_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: num,Y: num,Z: num] :
% 0.32/0.59        ( ( ord_less_num @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_num @ Y @ Z )
% 0.32/0.59         => ( ord_less_num @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4267_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.59        ( ( ord_less_nat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.32/0.59         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4268_order__less__le__trans,axiom,
% 0.32/0.59      ! [X: int,Y: int,Z: int] :
% 0.32/0.59        ( ( ord_less_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_int @ Y @ Z )
% 0.32/0.59         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le_trans
% 0.32/0.59  thf(fact_4269_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: real,Y: real,Z: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.59       => ( ( ord_less_real @ Y @ Z )
% 0.32/0.59         => ( ord_less_real @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4270_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int,Z: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_set_int @ Y @ Z )
% 0.32/0.59         => ( ord_less_set_int @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4271_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_rat @ Y @ Z )
% 0.32/0.59         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4272_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: num,Y: num,Z: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.59       => ( ( ord_less_num @ Y @ Z )
% 0.32/0.59         => ( ord_less_num @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4273_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_nat @ Y @ Z )
% 0.32/0.59         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4274_order__le__less__trans,axiom,
% 0.32/0.59      ! [X: int,Y: int,Z: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_int @ Y @ Z )
% 0.32/0.59         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less_trans
% 0.32/0.59  thf(fact_4275_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_real @ A @ B )
% 0.32/0.59         => ( ord_less_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4276_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.59         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4277_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4278_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: num,B: num] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59         => ( ord_less_num @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4279_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.59         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4280_order__neq__le__trans,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( A != B )
% 0.32/0.59       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.59         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_neq_le_trans
% 0.32/0.59  thf(fact_4281_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4282_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4283_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4284_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: num,B: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_num @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4285_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4286_order__le__neq__trans,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.59       => ( ( A != B )
% 0.32/0.59         => ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_neq_trans
% 0.32/0.59  thf(fact_4287_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( ord_less_real @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4288_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4289_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( ord_less_rat @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4290_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ( ord_less_num @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4291_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ( ord_less_nat @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4292_order__less__imp__le,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( ord_less_int @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_imp_le
% 0.32/0.59  thf(fact_4293_linorder__not__less,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.32/0.59        = ( ord_less_eq_real @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_less
% 0.32/0.59  thf(fact_4294_linorder__not__less,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.32/0.59        = ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_less
% 0.32/0.59  thf(fact_4295_linorder__not__less,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.32/0.59        = ( ord_less_eq_num @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_less
% 0.32/0.59  thf(fact_4296_linorder__not__less,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.32/0.59        = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_less
% 0.32/0.59  thf(fact_4297_linorder__not__less,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.32/0.59        = ( ord_less_eq_int @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_less
% 0.32/0.59  thf(fact_4298_linorder__not__le,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 0.32/0.59        = ( ord_less_real @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_le
% 0.32/0.59  thf(fact_4299_linorder__not__le,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 0.32/0.59        = ( ord_less_rat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_le
% 0.32/0.59  thf(fact_4300_linorder__not__le,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 0.32/0.59        = ( ord_less_num @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_le
% 0.32/0.59  thf(fact_4301_linorder__not__le,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.32/0.59        = ( ord_less_nat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_le
% 0.32/0.59  thf(fact_4302_linorder__not__le,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 0.32/0.59        = ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % linorder_not_le
% 0.32/0.59  thf(fact_4303_order__less__le,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [X3: real,Y3: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4304_order__less__le,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [X3: set_int,Y3: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4305_order__less__le,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [X3: rat,Y3: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4306_order__less__le,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [X3: num,Y3: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4307_order__less__le,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4308_order__less__le,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [X3: int,Y3: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.32/0.59            & ( X3 != Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_less_le
% 0.32/0.59  thf(fact_4309_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_real
% 0.32/0.59      = ( ^ [X3: real,Y3: real] :
% 0.32/0.59            ( ( ord_less_real @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4310_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_set_int
% 0.32/0.59      = ( ^ [X3: set_int,Y3: set_int] :
% 0.32/0.59            ( ( ord_less_set_int @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4311_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_rat
% 0.32/0.59      = ( ^ [X3: rat,Y3: rat] :
% 0.32/0.59            ( ( ord_less_rat @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4312_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_num
% 0.32/0.59      = ( ^ [X3: num,Y3: num] :
% 0.32/0.59            ( ( ord_less_num @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4313_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_nat
% 0.32/0.59      = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.59            ( ( ord_less_nat @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4314_order__le__less,axiom,
% 0.32/0.59      ( ord_less_eq_int
% 0.32/0.59      = ( ^ [X3: int,Y3: int] :
% 0.32/0.59            ( ( ord_less_int @ X3 @ Y3 )
% 0.32/0.59            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order_le_less
% 0.32/0.59  thf(fact_4315_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: real,A: real] :
% 0.32/0.59        ( ( ord_less_real @ B @ A )
% 0.32/0.59       => ( ord_less_eq_real @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4316_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: set_int,A: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ B @ A )
% 0.32/0.59       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4317_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: rat,A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ B @ A )
% 0.32/0.59       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4318_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: num,A: num] :
% 0.32/0.59        ( ( ord_less_num @ B @ A )
% 0.32/0.59       => ( ord_less_eq_num @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4319_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: nat,A: nat] :
% 0.32/0.59        ( ( ord_less_nat @ B @ A )
% 0.32/0.59       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4320_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [B: int,A: int] :
% 0.32/0.59        ( ( ord_less_int @ B @ A )
% 0.32/0.59       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_implies_order
% 0.32/0.59  thf(fact_4321_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ord_less_real @ A @ B )
% 0.32/0.59       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4322_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ A @ B )
% 0.32/0.59       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4323_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ord_less_rat @ A @ B )
% 0.32/0.59       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4324_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: num,B: num] :
% 0.32/0.59        ( ( ord_less_num @ A @ B )
% 0.32/0.59       => ( ord_less_eq_num @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4325_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( ord_less_nat @ A @ B )
% 0.32/0.59       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4326_order_Ostrict__implies__order,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( ord_less_int @ A @ B )
% 0.32/0.59       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_implies_order
% 0.32/0.59  thf(fact_4327_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [B2: real,A3: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4328_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [B2: set_int,A3: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4329_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4330_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [B2: num,A3: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4331_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4332_dual__order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [B2: int,A3: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.32/0.59            & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_not
% 0.32/0.59  thf(fact_4333_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: real,A: real,C: real] :
% 0.32/0.59        ( ( ord_less_real @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_real @ C @ B )
% 0.32/0.59         => ( ord_less_real @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4334_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: set_int,A: set_int,C: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_set_int @ C @ B )
% 0.32/0.59         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4335_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: rat,A: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_rat @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_rat @ C @ B )
% 0.32/0.59         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4336_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: num,A: num,C: num] :
% 0.32/0.59        ( ( ord_less_num @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_num @ C @ B )
% 0.32/0.59         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4337_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: nat,A: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_nat @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_nat @ C @ B )
% 0.32/0.59         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4338_dual__order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [B: int,A: int,C: int] :
% 0.32/0.59        ( ( ord_less_int @ B @ A )
% 0.32/0.59       => ( ( ord_less_eq_int @ C @ B )
% 0.32/0.59         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans2
% 0.32/0.59  thf(fact_4339_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: real,A: real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ B @ A )
% 0.32/0.59       => ( ( ord_less_real @ C @ B )
% 0.32/0.59         => ( ord_less_real @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4340_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: set_int,A: set_int,C: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ B @ A )
% 0.32/0.59       => ( ( ord_less_set_int @ C @ B )
% 0.32/0.59         => ( ord_less_set_int @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4341_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: rat,A: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ B @ A )
% 0.32/0.59       => ( ( ord_less_rat @ C @ B )
% 0.32/0.59         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4342_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: num,A: num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ B @ A )
% 0.32/0.59       => ( ( ord_less_num @ C @ B )
% 0.32/0.59         => ( ord_less_num @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4343_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: nat,A: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ B @ A )
% 0.32/0.59       => ( ( ord_less_nat @ C @ B )
% 0.32/0.59         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4344_dual__order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [B: int,A: int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ B @ A )
% 0.32/0.59       => ( ( ord_less_int @ C @ B )
% 0.32/0.59         => ( ord_less_int @ C @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_trans1
% 0.32/0.59  thf(fact_4345_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [B2: real,A3: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4346_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [B2: set_int,A3: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4347_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4348_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [B2: num,A3: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4349_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4350_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [B2: int,A3: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ B2 @ A3 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.strict_iff_order
% 0.32/0.59  thf(fact_4351_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_real
% 0.32/0.59      = ( ^ [B2: real,A3: real] :
% 0.32/0.59            ( ( ord_less_real @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4352_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_set_int
% 0.32/0.59      = ( ^ [B2: set_int,A3: set_int] :
% 0.32/0.59            ( ( ord_less_set_int @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4353_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_rat
% 0.32/0.59      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.59            ( ( ord_less_rat @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4354_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_num
% 0.32/0.59      = ( ^ [B2: num,A3: num] :
% 0.32/0.59            ( ( ord_less_num @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4355_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_nat
% 0.32/0.59      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.59            ( ( ord_less_nat @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4356_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_int
% 0.32/0.59      = ( ^ [B2: int,A3: int] :
% 0.32/0.59            ( ( ord_less_int @ B2 @ A3 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dual_order.order_iff_strict
% 0.32/0.59  thf(fact_4357_dense__le__bounded,axiom,
% 0.32/0.59      ! [X: real,Y: real,Z: real] :
% 0.32/0.59        ( ( ord_less_real @ X @ Y )
% 0.32/0.59       => ( ! [W2: real] :
% 0.32/0.59              ( ( ord_less_real @ X @ W2 )
% 0.32/0.59             => ( ( ord_less_real @ W2 @ Y )
% 0.32/0.59               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 0.32/0.59         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_le_bounded
% 0.32/0.59  thf(fact_4358_dense__le__bounded,axiom,
% 0.32/0.59      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.59        ( ( ord_less_rat @ X @ Y )
% 0.32/0.59       => ( ! [W2: rat] :
% 0.32/0.59              ( ( ord_less_rat @ X @ W2 )
% 0.32/0.59             => ( ( ord_less_rat @ W2 @ Y )
% 0.32/0.59               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 0.32/0.59         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_le_bounded
% 0.32/0.59  thf(fact_4359_dense__ge__bounded,axiom,
% 0.32/0.59      ! [Z: real,X: real,Y: real] :
% 0.32/0.59        ( ( ord_less_real @ Z @ X )
% 0.32/0.59       => ( ! [W2: real] :
% 0.32/0.59              ( ( ord_less_real @ Z @ W2 )
% 0.32/0.59             => ( ( ord_less_real @ W2 @ X )
% 0.32/0.59               => ( ord_less_eq_real @ Y @ W2 ) ) )
% 0.32/0.59         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_ge_bounded
% 0.32/0.59  thf(fact_4360_dense__ge__bounded,axiom,
% 0.32/0.59      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.59        ( ( ord_less_rat @ Z @ X )
% 0.32/0.59       => ( ! [W2: rat] :
% 0.32/0.59              ( ( ord_less_rat @ Z @ W2 )
% 0.32/0.59             => ( ( ord_less_rat @ W2 @ X )
% 0.32/0.59               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 0.32/0.59         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_ge_bounded
% 0.32/0.59  thf(fact_4361_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [A3: real,B2: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4362_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [A3: set_int,B2: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4363_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4364_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [A3: num,B2: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4365_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4366_order_Ostrict__iff__not,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [A3: int,B2: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.32/0.59            & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_not
% 0.32/0.59  thf(fact_4367_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: real,B: real,C: real] :
% 0.32/0.59        ( ( ord_less_real @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_real @ B @ C )
% 0.32/0.59         => ( ord_less_real @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4368_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int,C: set_int] :
% 0.32/0.59        ( ( ord_less_set_int @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_set_int @ B @ C )
% 0.32/0.59         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4369_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: rat,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_rat @ B @ C )
% 0.32/0.59         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4370_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: num,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_num @ B @ C )
% 0.32/0.59         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4371_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_nat @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_nat @ B @ C )
% 0.32/0.59         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4372_order_Ostrict__trans2,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( ord_less_int @ A @ B )
% 0.32/0.59       => ( ( ord_less_eq_int @ B @ C )
% 0.32/0.59         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans2
% 0.32/0.59  thf(fact_4373_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: real,B: real,C: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.59       => ( ( ord_less_real @ B @ C )
% 0.32/0.59         => ( ord_less_real @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4374_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int,C: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ A @ B )
% 0.32/0.59       => ( ( ord_less_set_int @ B @ C )
% 0.32/0.59         => ( ord_less_set_int @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4375_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: rat,B: rat,C: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.59       => ( ( ord_less_rat @ B @ C )
% 0.32/0.59         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4376_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: num,B: num,C: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ A @ B )
% 0.32/0.59       => ( ( ord_less_num @ B @ C )
% 0.32/0.59         => ( ord_less_num @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4377_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.59       => ( ( ord_less_nat @ B @ C )
% 0.32/0.59         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4378_order_Ostrict__trans1,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.59       => ( ( ord_less_int @ B @ C )
% 0.32/0.59         => ( ord_less_int @ A @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_trans1
% 0.32/0.59  thf(fact_4379_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [A3: real,B2: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4380_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [A3: set_int,B2: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4381_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4382_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [A3: num,B2: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4383_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4384_order_Ostrict__iff__order,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [A3: int,B2: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ A3 @ B2 )
% 0.32/0.59            & ( A3 != B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.strict_iff_order
% 0.32/0.59  thf(fact_4385_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_real
% 0.32/0.59      = ( ^ [A3: real,B2: real] :
% 0.32/0.59            ( ( ord_less_real @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4386_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_set_int
% 0.32/0.59      = ( ^ [A3: set_int,B2: set_int] :
% 0.32/0.59            ( ( ord_less_set_int @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4387_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_rat
% 0.32/0.59      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.59            ( ( ord_less_rat @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4388_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_num
% 0.32/0.59      = ( ^ [A3: num,B2: num] :
% 0.32/0.59            ( ( ord_less_num @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4389_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_nat
% 0.32/0.59      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.59            ( ( ord_less_nat @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4390_order_Oorder__iff__strict,axiom,
% 0.32/0.59      ( ord_less_eq_int
% 0.32/0.59      = ( ^ [A3: int,B2: int] :
% 0.32/0.59            ( ( ord_less_int @ A3 @ B2 )
% 0.32/0.59            | ( A3 = B2 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % order.order_iff_strict
% 0.32/0.59  thf(fact_4391_not__le__imp__less,axiom,
% 0.32/0.59      ! [Y: real,X: real] :
% 0.32/0.59        ( ~ ( ord_less_eq_real @ Y @ X )
% 0.32/0.59       => ( ord_less_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_le_imp_less
% 0.32/0.59  thf(fact_4392_not__le__imp__less,axiom,
% 0.32/0.59      ! [Y: rat,X: rat] :
% 0.32/0.59        ( ~ ( ord_less_eq_rat @ Y @ X )
% 0.32/0.59       => ( ord_less_rat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_le_imp_less
% 0.32/0.59  thf(fact_4393_not__le__imp__less,axiom,
% 0.32/0.59      ! [Y: num,X: num] :
% 0.32/0.59        ( ~ ( ord_less_eq_num @ Y @ X )
% 0.32/0.59       => ( ord_less_num @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_le_imp_less
% 0.32/0.59  thf(fact_4394_not__le__imp__less,axiom,
% 0.32/0.59      ! [Y: nat,X: nat] :
% 0.32/0.59        ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.32/0.59       => ( ord_less_nat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_le_imp_less
% 0.32/0.59  thf(fact_4395_not__le__imp__less,axiom,
% 0.32/0.59      ! [Y: int,X: int] :
% 0.32/0.59        ( ~ ( ord_less_eq_int @ Y @ X )
% 0.32/0.59       => ( ord_less_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_le_imp_less
% 0.32/0.59  thf(fact_4396_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_real
% 0.32/0.59      = ( ^ [X3: real,Y3: real] :
% 0.32/0.59            ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4397_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_set_int
% 0.32/0.59      = ( ^ [X3: set_int,Y3: set_int] :
% 0.32/0.59            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4398_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_rat
% 0.32/0.59      = ( ^ [X3: rat,Y3: rat] :
% 0.32/0.59            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4399_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_num
% 0.32/0.59      = ( ^ [X3: num,Y3: num] :
% 0.32/0.59            ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4400_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_nat
% 0.32/0.59      = ( ^ [X3: nat,Y3: nat] :
% 0.32/0.59            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4401_less__le__not__le,axiom,
% 0.32/0.59      ( ord_less_int
% 0.32/0.59      = ( ^ [X3: int,Y3: int] :
% 0.32/0.59            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.32/0.59            & ~ ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_le_not_le
% 0.32/0.59  thf(fact_4402_dense__le,axiom,
% 0.32/0.59      ! [Y: real,Z: real] :
% 0.32/0.59        ( ! [X6: real] :
% 0.32/0.59            ( ( ord_less_real @ X6 @ Y )
% 0.32/0.59           => ( ord_less_eq_real @ X6 @ Z ) )
% 0.32/0.59       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_le
% 0.32/0.59  thf(fact_4403_dense__le,axiom,
% 0.32/0.59      ! [Y: rat,Z: rat] :
% 0.32/0.59        ( ! [X6: rat] :
% 0.32/0.59            ( ( ord_less_rat @ X6 @ Y )
% 0.32/0.59           => ( ord_less_eq_rat @ X6 @ Z ) )
% 0.32/0.59       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_le
% 0.32/0.59  thf(fact_4404_dense__ge,axiom,
% 0.32/0.59      ! [Z: real,Y: real] :
% 0.32/0.59        ( ! [X6: real] :
% 0.32/0.59            ( ( ord_less_real @ Z @ X6 )
% 0.32/0.59           => ( ord_less_eq_real @ Y @ X6 ) )
% 0.32/0.59       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_ge
% 0.32/0.59  thf(fact_4405_dense__ge,axiom,
% 0.32/0.59      ! [Z: rat,Y: rat] :
% 0.32/0.59        ( ! [X6: rat] :
% 0.32/0.59            ( ( ord_less_rat @ Z @ X6 )
% 0.32/0.59           => ( ord_less_eq_rat @ Y @ X6 ) )
% 0.32/0.59       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dense_ge
% 0.32/0.59  thf(fact_4406_antisym__conv2,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4407_antisym__conv2,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4408_antisym__conv2,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4409_antisym__conv2,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4410_antisym__conv2,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4411_antisym__conv2,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.59       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv2
% 0.32/0.59  thf(fact_4412_antisym__conv1,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ~ ( ord_less_real @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4413_antisym__conv1,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int] :
% 0.32/0.59        ( ~ ( ord_less_set_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4414_antisym__conv1,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ~ ( ord_less_rat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4415_antisym__conv1,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ~ ( ord_less_num @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4416_antisym__conv1,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4417_antisym__conv1,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ~ ( ord_less_int @ X @ Y )
% 0.32/0.59       => ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.59          = ( X = Y ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % antisym_conv1
% 0.32/0.59  thf(fact_4418_nless__le,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ~ ( ord_less_real @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_real @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4419_nless__le,axiom,
% 0.32/0.59      ! [A: set_int,B: set_int] :
% 0.32/0.59        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4420_nless__le,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4421_nless__le,axiom,
% 0.32/0.59      ! [A: num,B: num] :
% 0.32/0.59        ( ( ~ ( ord_less_num @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_num @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4422_nless__le,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4423_nless__le,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.32/0.59        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.32/0.59          | ( A = B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nless_le
% 0.32/0.59  thf(fact_4424_leI,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ~ ( ord_less_real @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_real @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leI
% 0.32/0.59  thf(fact_4425_leI,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ~ ( ord_less_rat @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leI
% 0.32/0.59  thf(fact_4426_leI,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ~ ( ord_less_num @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leI
% 0.32/0.59  thf(fact_4427_leI,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leI
% 0.32/0.59  thf(fact_4428_leI,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ~ ( ord_less_int @ X @ Y )
% 0.32/0.59       => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leI
% 0.32/0.59  thf(fact_4429_leD,axiom,
% 0.32/0.59      ! [Y: real,X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4430_leD,axiom,
% 0.32/0.59      ! [Y: set_int,X: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4431_leD,axiom,
% 0.32/0.59      ! [Y: rat,X: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_rat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4432_leD,axiom,
% 0.32/0.59      ! [Y: num,X: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_num @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4433_leD,axiom,
% 0.32/0.59      ! [Y: nat,X: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4434_leD,axiom,
% 0.32/0.59      ! [Y: int,X: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ Y @ X )
% 0.32/0.59       => ~ ( ord_less_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % leD
% 0.32/0.59  thf(fact_4435_bot_Oextremum__uniqueI,axiom,
% 0.32/0.59      ! [A: set_nat] :
% 0.32/0.59        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.32/0.59       => ( A = bot_bot_set_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_uniqueI
% 0.32/0.59  thf(fact_4436_bot_Oextremum__uniqueI,axiom,
% 0.32/0.59      ! [A: extended_enat] :
% 0.32/0.59        ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 0.32/0.59       => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_uniqueI
% 0.32/0.59  thf(fact_4437_bot_Oextremum__uniqueI,axiom,
% 0.32/0.59      ! [A: set_real] :
% 0.32/0.59        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.32/0.59       => ( A = bot_bot_set_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_uniqueI
% 0.32/0.59  thf(fact_4438_bot_Oextremum__uniqueI,axiom,
% 0.32/0.59      ! [A: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.32/0.59       => ( A = bot_bot_set_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_uniqueI
% 0.32/0.59  thf(fact_4439_bot_Oextremum__uniqueI,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.32/0.59       => ( A = bot_bot_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_uniqueI
% 0.32/0.59  thf(fact_4440_bot_Oextremum__unique,axiom,
% 0.32/0.59      ! [A: set_nat] :
% 0.32/0.59        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.32/0.59        = ( A = bot_bot_set_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_unique
% 0.32/0.59  thf(fact_4441_bot_Oextremum__unique,axiom,
% 0.32/0.59      ! [A: extended_enat] :
% 0.32/0.59        ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 0.32/0.59        = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_unique
% 0.32/0.59  thf(fact_4442_bot_Oextremum__unique,axiom,
% 0.32/0.59      ! [A: set_real] :
% 0.32/0.59        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.32/0.59        = ( A = bot_bot_set_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_unique
% 0.32/0.59  thf(fact_4443_bot_Oextremum__unique,axiom,
% 0.32/0.59      ! [A: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.32/0.59        = ( A = bot_bot_set_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_unique
% 0.32/0.59  thf(fact_4444_bot_Oextremum__unique,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.32/0.59        = ( A = bot_bot_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_unique
% 0.32/0.59  thf(fact_4445_bot_Oextremum,axiom,
% 0.32/0.59      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum
% 0.32/0.59  thf(fact_4446_bot_Oextremum,axiom,
% 0.32/0.59      ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum
% 0.32/0.59  thf(fact_4447_bot_Oextremum,axiom,
% 0.32/0.59      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum
% 0.32/0.59  thf(fact_4448_bot_Oextremum,axiom,
% 0.32/0.59      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum
% 0.32/0.59  thf(fact_4449_bot_Oextremum,axiom,
% 0.32/0.59      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum
% 0.32/0.59  thf(fact_4450_bot_Onot__eq__extremum,axiom,
% 0.32/0.59      ! [A: set_nat] :
% 0.32/0.59        ( ( A != bot_bot_set_nat )
% 0.32/0.59        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.not_eq_extremum
% 0.32/0.59  thf(fact_4451_bot_Onot__eq__extremum,axiom,
% 0.32/0.59      ! [A: extended_enat] :
% 0.32/0.59        ( ( A != bot_bo4199563552545308370d_enat )
% 0.32/0.59        = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.not_eq_extremum
% 0.32/0.59  thf(fact_4452_bot_Onot__eq__extremum,axiom,
% 0.32/0.59      ! [A: set_int] :
% 0.32/0.59        ( ( A != bot_bot_set_int )
% 0.32/0.59        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.not_eq_extremum
% 0.32/0.59  thf(fact_4453_bot_Onot__eq__extremum,axiom,
% 0.32/0.59      ! [A: set_real] :
% 0.32/0.59        ( ( A != bot_bot_set_real )
% 0.32/0.59        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.not_eq_extremum
% 0.32/0.59  thf(fact_4454_bot_Onot__eq__extremum,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( A != bot_bot_nat )
% 0.32/0.59        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.not_eq_extremum
% 0.32/0.59  thf(fact_4455_bot_Oextremum__strict,axiom,
% 0.32/0.59      ! [A: set_nat] :
% 0.32/0.59        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_strict
% 0.32/0.59  thf(fact_4456_bot_Oextremum__strict,axiom,
% 0.32/0.59      ! [A: extended_enat] :
% 0.32/0.59        ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_strict
% 0.32/0.59  thf(fact_4457_bot_Oextremum__strict,axiom,
% 0.32/0.59      ! [A: set_int] :
% 0.32/0.59        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_strict
% 0.32/0.59  thf(fact_4458_bot_Oextremum__strict,axiom,
% 0.32/0.59      ! [A: set_real] :
% 0.32/0.59        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_strict
% 0.32/0.59  thf(fact_4459_bot_Oextremum__strict,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.32/0.59  
% 0.32/0.59  % bot.extremum_strict
% 0.32/0.59  thf(fact_4460_Euclid__induct,axiom,
% 0.32/0.59      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.32/0.59        ( ! [A5: nat,B5: nat] :
% 0.32/0.59            ( ( P @ A5 @ B5 )
% 0.32/0.59            = ( P @ B5 @ A5 ) )
% 0.32/0.59       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 0.32/0.59         => ( ! [A5: nat,B5: nat] :
% 0.32/0.59                ( ( P @ A5 @ B5 )
% 0.32/0.59               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 0.32/0.59           => ( P @ A @ B ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % Euclid_induct
% 0.32/0.59  thf(fact_4461_max__def,axiom,
% 0.32/0.59      ( ord_ma741700101516333627d_enat
% 0.32/0.59      = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4462_max__def,axiom,
% 0.32/0.59      ( ord_max_Code_integer
% 0.32/0.59      = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4463_max__def,axiom,
% 0.32/0.59      ( ord_max_set_int
% 0.32/0.59      = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4464_max__def,axiom,
% 0.32/0.59      ( ord_max_rat
% 0.32/0.59      = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4465_max__def,axiom,
% 0.32/0.59      ( ord_max_num
% 0.32/0.59      = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4466_max__def,axiom,
% 0.32/0.59      ( ord_max_nat
% 0.32/0.59      = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4467_max__def,axiom,
% 0.32/0.59      ( ord_max_int
% 0.32/0.59      = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_def
% 0.32/0.59  thf(fact_4468_max__absorb1,axiom,
% 0.32/0.59      ! [Y: extended_enat,X: extended_enat] :
% 0.32/0.59        ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 0.32/0.59       => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4469_max__absorb1,axiom,
% 0.32/0.59      ! [Y: code_integer,X: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ Y @ X )
% 0.32/0.59       => ( ( ord_max_Code_integer @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4470_max__absorb1,axiom,
% 0.32/0.59      ! [Y: set_int,X: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ Y @ X )
% 0.32/0.59       => ( ( ord_max_set_int @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4471_max__absorb1,axiom,
% 0.32/0.59      ! [Y: rat,X: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ Y @ X )
% 0.32/0.59       => ( ( ord_max_rat @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4472_max__absorb1,axiom,
% 0.32/0.59      ! [Y: num,X: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ Y @ X )
% 0.32/0.59       => ( ( ord_max_num @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4473_max__absorb1,axiom,
% 0.32/0.59      ! [Y: nat,X: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.59       => ( ( ord_max_nat @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4474_max__absorb1,axiom,
% 0.32/0.59      ! [Y: int,X: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ Y @ X )
% 0.32/0.59       => ( ( ord_max_int @ X @ Y )
% 0.32/0.59          = X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb1
% 0.32/0.59  thf(fact_4475_max__absorb2,axiom,
% 0.32/0.59      ! [X: extended_enat,Y: extended_enat] :
% 0.32/0.59        ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 0.32/0.59       => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4476_max__absorb2,axiom,
% 0.32/0.59      ! [X: code_integer,Y: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ X @ Y )
% 0.32/0.59       => ( ( ord_max_Code_integer @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4477_max__absorb2,axiom,
% 0.32/0.59      ! [X: set_int,Y: set_int] :
% 0.32/0.59        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.59       => ( ( ord_max_set_int @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4478_max__absorb2,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.59       => ( ( ord_max_rat @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4479_max__absorb2,axiom,
% 0.32/0.59      ! [X: num,Y: num] :
% 0.32/0.59        ( ( ord_less_eq_num @ X @ Y )
% 0.32/0.59       => ( ( ord_max_num @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4480_max__absorb2,axiom,
% 0.32/0.59      ! [X: nat,Y: nat] :
% 0.32/0.59        ( ( ord_less_eq_nat @ X @ Y )
% 0.32/0.59       => ( ( ord_max_nat @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4481_max__absorb2,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.59       => ( ( ord_max_int @ X @ Y )
% 0.32/0.59          = Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_absorb2
% 0.32/0.59  thf(fact_4482_ln__one__plus__pos__lower__bound,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.59       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.59         => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % ln_one_plus_pos_lower_bound
% 0.32/0.59  thf(fact_4483_ln__2__less__1,axiom,
% 0.32/0.59      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.32/0.59  
% 0.32/0.59  % ln_2_less_1
% 0.32/0.59  thf(fact_4484_tanh__ln__real,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.59       => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 0.32/0.59          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_ln_real
% 0.32/0.59  thf(fact_4485_ln__one__minus__pos__lower__bound,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.59       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.59         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % ln_one_minus_pos_lower_bound
% 0.32/0.59  thf(fact_4486_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.59       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_ln_one_plus_x_minus_x_bound
% 0.32/0.59  thf(fact_4487_even__succ__mod__exp,axiom,
% 0.32/0.59      ! [A: nat,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_mod_exp
% 0.32/0.59  thf(fact_4488_even__succ__mod__exp,axiom,
% 0.32/0.59      ! [A: int,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_mod_exp
% 0.32/0.59  thf(fact_4489_even__succ__mod__exp,axiom,
% 0.32/0.59      ! [A: code_integer,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_mod_exp
% 0.32/0.59  thf(fact_4490_even__succ__div__exp,axiom,
% 0.32/0.59      ! [A: code_integer,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_div_exp
% 0.32/0.59  thf(fact_4491_even__succ__div__exp,axiom,
% 0.32/0.59      ! [A: nat,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_div_exp
% 0.32/0.59  thf(fact_4492_even__succ__div__exp,axiom,
% 0.32/0.59      ! [A: int,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.59            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_succ_div_exp
% 0.32/0.59  thf(fact_4493_neg__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ A )
% 0.32/0.59          = ( uminus_uminus_real @ B ) )
% 0.32/0.59        = ( A = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_iff_equal
% 0.32/0.59  thf(fact_4494_neg__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ A )
% 0.32/0.59          = ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( A = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_iff_equal
% 0.32/0.59  thf(fact_4495_neg__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.59          = ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.59        = ( A = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_iff_equal
% 0.32/0.59  thf(fact_4496_neg__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.59          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( A = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_iff_equal
% 0.32/0.59  thf(fact_4497_neg__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.59          = ( uminus_uminus_rat @ B ) )
% 0.32/0.59        = ( A = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_iff_equal
% 0.32/0.59  thf(fact_4498_add_Oinverse__inverse,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_inverse
% 0.32/0.59  thf(fact_4499_add_Oinverse__inverse,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_inverse
% 0.32/0.59  thf(fact_4500_add_Oinverse__inverse,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_inverse
% 0.32/0.59  thf(fact_4501_add_Oinverse__inverse,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_inverse
% 0.32/0.59  thf(fact_4502_add_Oinverse__inverse,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_inverse
% 0.32/0.59  thf(fact_4503_abs__abs,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.32/0.59        = ( abs_abs_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_abs
% 0.32/0.59  thf(fact_4504_abs__abs,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.32/0.59        = ( abs_abs_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_abs
% 0.32/0.59  thf(fact_4505_abs__abs,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_abs
% 0.32/0.59  thf(fact_4506_abs__abs,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.32/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_abs
% 0.32/0.59  thf(fact_4507_abs__idempotent,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.32/0.59        = ( abs_abs_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_idempotent
% 0.32/0.59  thf(fact_4508_abs__idempotent,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.32/0.59        = ( abs_abs_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_idempotent
% 0.32/0.59  thf(fact_4509_abs__idempotent,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_idempotent
% 0.32/0.59  thf(fact_4510_abs__idempotent,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.32/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_idempotent
% 0.32/0.59  thf(fact_4511_nat__dvd__1__iff__1,axiom,
% 0.32/0.59      ! [M: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.32/0.59        = ( M = one_one_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nat_dvd_1_iff_1
% 0.32/0.59  thf(fact_4512_neg__le__iff__le,axiom,
% 0.32/0.59      ! [B: real,A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_eq_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_iff_le
% 0.32/0.59  thf(fact_4513_neg__le__iff__le,axiom,
% 0.32/0.59      ! [B: code_integer,A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_iff_le
% 0.32/0.59  thf(fact_4514_neg__le__iff__le,axiom,
% 0.32/0.59      ! [B: rat,A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_iff_le
% 0.32/0.59  thf(fact_4515_neg__le__iff__le,axiom,
% 0.32/0.59      ! [B: int,A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_iff_le
% 0.32/0.59  thf(fact_4516_neg__equal__zero,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ A )
% 0.32/0.59          = A )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_zero
% 0.32/0.59  thf(fact_4517_neg__equal__zero,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ A )
% 0.32/0.59          = A )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_zero
% 0.32/0.59  thf(fact_4518_neg__equal__zero,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.59          = A )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_zero
% 0.32/0.59  thf(fact_4519_neg__equal__zero,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.59          = A )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_zero
% 0.32/0.59  thf(fact_4520_equal__neg__zero,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % equal_neg_zero
% 0.32/0.59  thf(fact_4521_equal__neg__zero,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % equal_neg_zero
% 0.32/0.59  thf(fact_4522_equal__neg__zero,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % equal_neg_zero
% 0.32/0.59  thf(fact_4523_equal__neg__zero,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % equal_neg_zero
% 0.32/0.59  thf(fact_4524_neg__equal__0__iff__equal,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ A )
% 0.32/0.59          = zero_zero_real )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_0_iff_equal
% 0.32/0.59  thf(fact_4525_neg__equal__0__iff__equal,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ A )
% 0.32/0.59          = zero_zero_int )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_0_iff_equal
% 0.32/0.59  thf(fact_4526_neg__equal__0__iff__equal,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.59          = zero_zero_complex )
% 0.32/0.59        = ( A = zero_zero_complex ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_0_iff_equal
% 0.32/0.59  thf(fact_4527_neg__equal__0__iff__equal,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.59          = zero_z3403309356797280102nteger )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_0_iff_equal
% 0.32/0.59  thf(fact_4528_neg__equal__0__iff__equal,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.59          = zero_zero_rat )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_equal_0_iff_equal
% 0.32/0.59  thf(fact_4529_neg__0__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( zero_zero_real
% 0.32/0.59          = ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( zero_zero_real = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_equal_iff_equal
% 0.32/0.59  thf(fact_4530_neg__0__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( zero_zero_int
% 0.32/0.59          = ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( zero_zero_int = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_equal_iff_equal
% 0.32/0.59  thf(fact_4531_neg__0__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( zero_zero_complex
% 0.32/0.59          = ( uminus1482373934393186551omplex @ A ) )
% 0.32/0.59        = ( zero_zero_complex = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_equal_iff_equal
% 0.32/0.59  thf(fact_4532_neg__0__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( zero_z3403309356797280102nteger
% 0.32/0.59          = ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_equal_iff_equal
% 0.32/0.59  thf(fact_4533_neg__0__equal__iff__equal,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( zero_zero_rat
% 0.32/0.59          = ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( zero_zero_rat = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_equal_iff_equal
% 0.32/0.59  thf(fact_4534_add_Oinverse__neutral,axiom,
% 0.32/0.59      ( ( uminus_uminus_real @ zero_zero_real )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_neutral
% 0.32/0.59  thf(fact_4535_add_Oinverse__neutral,axiom,
% 0.32/0.59      ( ( uminus_uminus_int @ zero_zero_int )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_neutral
% 0.32/0.59  thf(fact_4536_add_Oinverse__neutral,axiom,
% 0.32/0.59      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_neutral
% 0.32/0.59  thf(fact_4537_add_Oinverse__neutral,axiom,
% 0.32/0.59      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_neutral
% 0.32/0.59  thf(fact_4538_add_Oinverse__neutral,axiom,
% 0.32/0.59      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % add.inverse_neutral
% 0.32/0.59  thf(fact_4539_neg__less__iff__less,axiom,
% 0.32/0.59      ! [B: real,A: real] :
% 0.32/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_iff_less
% 0.32/0.59  thf(fact_4540_neg__less__iff__less,axiom,
% 0.32/0.59      ! [B: int,A: int] :
% 0.32/0.59        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_iff_less
% 0.32/0.59  thf(fact_4541_neg__less__iff__less,axiom,
% 0.32/0.59      ! [B: code_integer,A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_iff_less
% 0.32/0.59  thf(fact_4542_neg__less__iff__less,axiom,
% 0.32/0.59      ! [B: rat,A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_iff_less
% 0.32/0.59  thf(fact_4543_neg__numeral__eq__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.32/0.59          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( M = N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_eq_iff
% 0.32/0.59  thf(fact_4544_neg__numeral__eq__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.32/0.59          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( M = N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_eq_iff
% 0.32/0.59  thf(fact_4545_neg__numeral__eq__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.32/0.59          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( M = N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_eq_iff
% 0.32/0.59  thf(fact_4546_neg__numeral__eq__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.32/0.59          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( M = N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_eq_iff
% 0.32/0.59  thf(fact_4547_neg__numeral__eq__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.32/0.59          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( M = N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_eq_iff
% 0.32/0.59  thf(fact_4548_mult__minus__left,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.59        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_left
% 0.32/0.59  thf(fact_4549_mult__minus__left,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.59        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_left
% 0.32/0.59  thf(fact_4550_mult__minus__left,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_left
% 0.32/0.59  thf(fact_4551_mult__minus__left,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_left
% 0.32/0.59  thf(fact_4552_mult__minus__left,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.59        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_left
% 0.32/0.59  thf(fact_4553_minus__mult__minus,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.32/0.59        = ( times_times_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mult_minus
% 0.32/0.59  thf(fact_4554_minus__mult__minus,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( times_times_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mult_minus
% 0.32/0.59  thf(fact_4555_minus__mult__minus,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.59        = ( times_times_complex @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mult_minus
% 0.32/0.59  thf(fact_4556_minus__mult__minus,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mult_minus
% 0.32/0.59  thf(fact_4557_minus__mult__minus,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.32/0.59        = ( times_times_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mult_minus
% 0.32/0.59  thf(fact_4558_mult__minus__right,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_right
% 0.32/0.59  thf(fact_4559_mult__minus__right,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_right
% 0.32/0.59  thf(fact_4560_mult__minus__right,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_right
% 0.32/0.59  thf(fact_4561_mult__minus__right,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_right
% 0.32/0.59  thf(fact_4562_mult__minus__right,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus_right
% 0.32/0.59  thf(fact_4563_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4564_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.32/0.59        = ( A = zero_zero_complex ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4565_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4566_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4567_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.32/0.59        = ( A = zero_zero_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4568_dvd__0__left__iff,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_left_iff
% 0.32/0.59  thf(fact_4569_dvd__0__right,axiom,
% 0.32/0.59      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4570_dvd__0__right,axiom,
% 0.32/0.59      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4571_dvd__0__right,axiom,
% 0.32/0.59      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4572_dvd__0__right,axiom,
% 0.32/0.59      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4573_dvd__0__right,axiom,
% 0.32/0.59      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4574_dvd__0__right,axiom,
% 0.32/0.59      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_0_right
% 0.32/0.59  thf(fact_4575_add__minus__cancel,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % add_minus_cancel
% 0.32/0.59  thf(fact_4576_add__minus__cancel,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % add_minus_cancel
% 0.32/0.59  thf(fact_4577_add__minus__cancel,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % add_minus_cancel
% 0.32/0.59  thf(fact_4578_add__minus__cancel,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % add_minus_cancel
% 0.32/0.59  thf(fact_4579_add__minus__cancel,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % add_minus_cancel
% 0.32/0.59  thf(fact_4580_minus__add__cancel,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_cancel
% 0.32/0.59  thf(fact_4581_minus__add__cancel,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_cancel
% 0.32/0.59  thf(fact_4582_minus__add__cancel,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_cancel
% 0.32/0.59  thf(fact_4583_minus__add__cancel,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_cancel
% 0.32/0.59  thf(fact_4584_minus__add__cancel,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.59        = B ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_cancel
% 0.32/0.59  thf(fact_4585_minus__add__distrib,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.32/0.59        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_distrib
% 0.32/0.59  thf(fact_4586_minus__add__distrib,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.59        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_distrib
% 0.32/0.59  thf(fact_4587_minus__add__distrib,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.32/0.59        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_distrib
% 0.32/0.59  thf(fact_4588_minus__add__distrib,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.59        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_distrib
% 0.32/0.59  thf(fact_4589_minus__add__distrib,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.59        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_add_distrib
% 0.32/0.59  thf(fact_4590_minus__diff__eq,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.32/0.59        = ( minus_minus_real @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_diff_eq
% 0.32/0.59  thf(fact_4591_minus__diff__eq,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.59        = ( minus_minus_int @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_diff_eq
% 0.32/0.59  thf(fact_4592_minus__diff__eq,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 0.32/0.59        = ( minus_minus_complex @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_diff_eq
% 0.32/0.59  thf(fact_4593_minus__diff__eq,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.59        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_diff_eq
% 0.32/0.59  thf(fact_4594_minus__diff__eq,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.59        = ( minus_minus_rat @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_diff_eq
% 0.32/0.59  thf(fact_4595_div__minus__minus,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( divide_divide_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_minus_minus
% 0.32/0.59  thf(fact_4596_div__minus__minus,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_minus_minus
% 0.32/0.59  thf(fact_4597_dvd__1__iff__1,axiom,
% 0.32/0.59      ! [M: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.32/0.59        = ( M
% 0.32/0.59          = ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_1_iff_1
% 0.32/0.59  thf(fact_4598_dvd__1__left,axiom,
% 0.32/0.59      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_1_left
% 0.32/0.59  thf(fact_4599_dvd__add__triv__left__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_left_iff
% 0.32/0.59  thf(fact_4600_dvd__add__triv__left__iff,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.32/0.59        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_left_iff
% 0.32/0.59  thf(fact_4601_dvd__add__triv__left__iff,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.59        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_left_iff
% 0.32/0.59  thf(fact_4602_dvd__add__triv__left__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.59        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_left_iff
% 0.32/0.59  thf(fact_4603_dvd__add__triv__left__iff,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.32/0.59        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_left_iff
% 0.32/0.59  thf(fact_4604_dvd__add__triv__right__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_right_iff
% 0.32/0.59  thf(fact_4605_dvd__add__triv__right__iff,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.32/0.59        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_right_iff
% 0.32/0.59  thf(fact_4606_dvd__add__triv__right__iff,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.32/0.59        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_right_iff
% 0.32/0.59  thf(fact_4607_dvd__add__triv__right__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.32/0.59        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_right_iff
% 0.32/0.59  thf(fact_4608_dvd__add__triv__right__iff,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.32/0.59        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_triv_right_iff
% 0.32/0.59  thf(fact_4609_abs__0,axiom,
% 0.32/0.59      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0
% 0.32/0.59  thf(fact_4610_abs__0,axiom,
% 0.32/0.59      ( ( abs_abs_complex @ zero_zero_complex )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0
% 0.32/0.59  thf(fact_4611_abs__0,axiom,
% 0.32/0.59      ( ( abs_abs_real @ zero_zero_real )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0
% 0.32/0.59  thf(fact_4612_abs__0,axiom,
% 0.32/0.59      ( ( abs_abs_rat @ zero_zero_rat )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0
% 0.32/0.59  thf(fact_4613_abs__0,axiom,
% 0.32/0.59      ( ( abs_abs_int @ zero_zero_int )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0
% 0.32/0.59  thf(fact_4614_abs__zero,axiom,
% 0.32/0.59      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_zero
% 0.32/0.59  thf(fact_4615_abs__zero,axiom,
% 0.32/0.59      ( ( abs_abs_real @ zero_zero_real )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_zero
% 0.32/0.59  thf(fact_4616_abs__zero,axiom,
% 0.32/0.59      ( ( abs_abs_rat @ zero_zero_rat )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_zero
% 0.32/0.59  thf(fact_4617_abs__zero,axiom,
% 0.32/0.59      ( ( abs_abs_int @ zero_zero_int )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_zero
% 0.32/0.59  thf(fact_4618_abs__eq__0,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.59          = zero_z3403309356797280102nteger )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_eq_0
% 0.32/0.59  thf(fact_4619_abs__eq__0,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ( abs_abs_real @ A )
% 0.32/0.59          = zero_zero_real )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_eq_0
% 0.32/0.59  thf(fact_4620_abs__eq__0,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ( abs_abs_rat @ A )
% 0.32/0.59          = zero_zero_rat )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_eq_0
% 0.32/0.59  thf(fact_4621_abs__eq__0,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ( abs_abs_int @ A )
% 0.32/0.59          = zero_zero_int )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_eq_0
% 0.32/0.59  thf(fact_4622_abs__0__eq,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( zero_z3403309356797280102nteger
% 0.32/0.59          = ( abs_abs_Code_integer @ A ) )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0_eq
% 0.32/0.59  thf(fact_4623_abs__0__eq,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( zero_zero_real
% 0.32/0.59          = ( abs_abs_real @ A ) )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0_eq
% 0.32/0.59  thf(fact_4624_abs__0__eq,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( zero_zero_rat
% 0.32/0.59          = ( abs_abs_rat @ A ) )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0_eq
% 0.32/0.59  thf(fact_4625_abs__0__eq,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( zero_zero_int
% 0.32/0.59          = ( abs_abs_int @ A ) )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_0_eq
% 0.32/0.59  thf(fact_4626_div__dvd__div,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.32/0.59         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 0.32/0.59            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_dvd_div
% 0.32/0.59  thf(fact_4627_div__dvd__div,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.59       => ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.59         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 0.32/0.59            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_dvd_div
% 0.32/0.59  thf(fact_4628_div__dvd__div,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.59       => ( ( dvd_dvd_int @ A @ C )
% 0.32/0.59         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 0.32/0.59            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_dvd_div
% 0.32/0.59  thf(fact_4629_minus__dvd__iff,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 0.32/0.59        = ( dvd_dvd_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_dvd_iff
% 0.32/0.59  thf(fact_4630_minus__dvd__iff,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 0.32/0.59        = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_dvd_iff
% 0.32/0.59  thf(fact_4631_minus__dvd__iff,axiom,
% 0.32/0.59      ! [X: complex,Y: complex] :
% 0.32/0.59        ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 0.32/0.59        = ( dvd_dvd_complex @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_dvd_iff
% 0.32/0.59  thf(fact_4632_minus__dvd__iff,axiom,
% 0.32/0.59      ! [X: code_integer,Y: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_dvd_iff
% 0.32/0.59  thf(fact_4633_minus__dvd__iff,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 0.32/0.59        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_dvd_iff
% 0.32/0.59  thf(fact_4634_dvd__minus__iff,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 0.32/0.59        = ( dvd_dvd_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_minus_iff
% 0.32/0.59  thf(fact_4635_dvd__minus__iff,axiom,
% 0.32/0.59      ! [X: int,Y: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 0.32/0.59        = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_minus_iff
% 0.32/0.59  thf(fact_4636_dvd__minus__iff,axiom,
% 0.32/0.59      ! [X: complex,Y: complex] :
% 0.32/0.59        ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 0.32/0.59        = ( dvd_dvd_complex @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_minus_iff
% 0.32/0.59  thf(fact_4637_dvd__minus__iff,axiom,
% 0.32/0.59      ! [X: code_integer,Y: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_minus_iff
% 0.32/0.59  thf(fact_4638_dvd__minus__iff,axiom,
% 0.32/0.59      ! [X: rat,Y: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 0.32/0.59        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_minus_iff
% 0.32/0.59  thf(fact_4639_abs__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.59        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_numeral
% 0.32/0.59  thf(fact_4640_abs__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 0.32/0.59        = ( numeral_numeral_real @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_numeral
% 0.32/0.59  thf(fact_4641_abs__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 0.32/0.59        = ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_numeral
% 0.32/0.59  thf(fact_4642_abs__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 0.32/0.59        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_numeral
% 0.32/0.59  thf(fact_4643_abs__mult__self__eq,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.59        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_mult_self_eq
% 0.32/0.59  thf(fact_4644_abs__mult__self__eq,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.32/0.59        = ( times_times_real @ A @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_mult_self_eq
% 0.32/0.59  thf(fact_4645_abs__mult__self__eq,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.32/0.59        = ( times_times_rat @ A @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_mult_self_eq
% 0.32/0.59  thf(fact_4646_abs__mult__self__eq,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.32/0.59        = ( times_times_int @ A @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_mult_self_eq
% 0.32/0.59  thf(fact_4647_abs__add__abs,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.32/0.59        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_add_abs
% 0.32/0.59  thf(fact_4648_abs__add__abs,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.32/0.59        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_add_abs
% 0.32/0.59  thf(fact_4649_abs__add__abs,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.32/0.59        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_add_abs
% 0.32/0.59  thf(fact_4650_abs__add__abs,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.32/0.59        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_add_abs
% 0.32/0.59  thf(fact_4651_abs__1,axiom,
% 0.32/0.59      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.32/0.59      = one_one_Code_integer ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_1
% 0.32/0.59  thf(fact_4652_abs__1,axiom,
% 0.32/0.59      ( ( abs_abs_complex @ one_one_complex )
% 0.32/0.59      = one_one_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_1
% 0.32/0.59  thf(fact_4653_abs__1,axiom,
% 0.32/0.59      ( ( abs_abs_real @ one_one_real )
% 0.32/0.59      = one_one_real ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_1
% 0.32/0.59  thf(fact_4654_abs__1,axiom,
% 0.32/0.59      ( ( abs_abs_rat @ one_one_rat )
% 0.32/0.59      = one_one_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_1
% 0.32/0.59  thf(fact_4655_abs__1,axiom,
% 0.32/0.59      ( ( abs_abs_int @ one_one_int )
% 0.32/0.59      = one_one_int ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_1
% 0.32/0.59  thf(fact_4656_abs__divide,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.59        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_divide
% 0.32/0.59  thf(fact_4657_abs__divide,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.59        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_divide
% 0.32/0.59  thf(fact_4658_abs__divide,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.59        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_divide
% 0.32/0.59  thf(fact_4659_abs__minus,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( abs_abs_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus
% 0.32/0.59  thf(fact_4660_abs__minus,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( abs_abs_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus
% 0.32/0.59  thf(fact_4661_abs__minus,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 0.32/0.59        = ( abs_abs_complex @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus
% 0.32/0.59  thf(fact_4662_abs__minus,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus
% 0.32/0.59  thf(fact_4663_abs__minus,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus
% 0.32/0.59  thf(fact_4664_abs__minus__cancel,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( abs_abs_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus_cancel
% 0.32/0.59  thf(fact_4665_abs__minus__cancel,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( abs_abs_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus_cancel
% 0.32/0.59  thf(fact_4666_abs__minus__cancel,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus_cancel
% 0.32/0.59  thf(fact_4667_abs__minus__cancel,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( abs_abs_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_minus_cancel
% 0.32/0.59  thf(fact_4668_mod__minus__minus,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mod_minus_minus
% 0.32/0.59  thf(fact_4669_mod__minus__minus,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mod_minus_minus
% 0.32/0.59  thf(fact_4670_nat__mult__dvd__cancel__disj,axiom,
% 0.32/0.59      ! [K: nat,M: nat,N: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.59        = ( ( K = zero_zero_nat )
% 0.32/0.59          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % nat_mult_dvd_cancel_disj
% 0.32/0.59  thf(fact_4671_dvd__abs__iff,axiom,
% 0.32/0.59      ! [M: real,K: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 0.32/0.59        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_abs_iff
% 0.32/0.59  thf(fact_4672_dvd__abs__iff,axiom,
% 0.32/0.59      ! [M: int,K: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 0.32/0.59        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_abs_iff
% 0.32/0.59  thf(fact_4673_dvd__abs__iff,axiom,
% 0.32/0.59      ! [M: code_integer,K: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_abs_iff
% 0.32/0.59  thf(fact_4674_dvd__abs__iff,axiom,
% 0.32/0.59      ! [M: rat,K: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 0.32/0.59        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_abs_iff
% 0.32/0.59  thf(fact_4675_abs__dvd__iff,axiom,
% 0.32/0.59      ! [M: real,K: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 0.32/0.59        = ( dvd_dvd_real @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_dvd_iff
% 0.32/0.59  thf(fact_4676_abs__dvd__iff,axiom,
% 0.32/0.59      ! [M: int,K: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 0.32/0.59        = ( dvd_dvd_int @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_dvd_iff
% 0.32/0.59  thf(fact_4677_abs__dvd__iff,axiom,
% 0.32/0.59      ! [M: code_integer,K: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_dvd_iff
% 0.32/0.59  thf(fact_4678_abs__dvd__iff,axiom,
% 0.32/0.59      ! [M: rat,K: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 0.32/0.59        = ( dvd_dvd_rat @ M @ K ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_dvd_iff
% 0.32/0.59  thf(fact_4679_tanh__0,axiom,
% 0.32/0.59      ( ( tanh_complex @ zero_zero_complex )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_0
% 0.32/0.59  thf(fact_4680_tanh__0,axiom,
% 0.32/0.59      ( ( tanh_real @ zero_zero_real )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_0
% 0.32/0.59  thf(fact_4681_tanh__real__zero__iff,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ( tanh_real @ X )
% 0.32/0.59          = zero_zero_real )
% 0.32/0.59        = ( X = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_zero_iff
% 0.32/0.59  thf(fact_4682_tanh__real__le__iff,axiom,
% 0.32/0.59      ! [X: real,Y: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 0.32/0.59        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_le_iff
% 0.32/0.59  thf(fact_4683_neg__less__eq__nonneg,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_eq_nonneg
% 0.32/0.59  thf(fact_4684_neg__less__eq__nonneg,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_eq_nonneg
% 0.32/0.59  thf(fact_4685_neg__less__eq__nonneg,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_eq_nonneg
% 0.32/0.59  thf(fact_4686_neg__less__eq__nonneg,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_eq_nonneg
% 0.32/0.59  thf(fact_4687_less__eq__neg__nonpos,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_eq_neg_nonpos
% 0.32/0.59  thf(fact_4688_less__eq__neg__nonpos,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_eq_neg_nonpos
% 0.32/0.59  thf(fact_4689_less__eq__neg__nonpos,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_eq_neg_nonpos
% 0.32/0.59  thf(fact_4690_less__eq__neg__nonpos,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_eq_neg_nonpos
% 0.32/0.59  thf(fact_4691_neg__le__0__iff__le,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.32/0.59        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_0_iff_le
% 0.32/0.59  thf(fact_4692_neg__le__0__iff__le,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_0_iff_le
% 0.32/0.59  thf(fact_4693_neg__le__0__iff__le,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.32/0.59        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_0_iff_le
% 0.32/0.59  thf(fact_4694_neg__le__0__iff__le,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.32/0.59        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_le_0_iff_le
% 0.32/0.59  thf(fact_4695_neg__0__le__iff__le,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_le_iff_le
% 0.32/0.59  thf(fact_4696_neg__0__le__iff__le,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_le_iff_le
% 0.32/0.59  thf(fact_4697_neg__0__le__iff__le,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_le_iff_le
% 0.32/0.59  thf(fact_4698_neg__0__le__iff__le,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_le_iff_le
% 0.32/0.59  thf(fact_4699_less__neg__neg,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_neg_neg
% 0.32/0.59  thf(fact_4700_less__neg__neg,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_neg_neg
% 0.32/0.59  thf(fact_4701_less__neg__neg,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_neg_neg
% 0.32/0.59  thf(fact_4702_less__neg__neg,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_neg_neg
% 0.32/0.59  thf(fact_4703_neg__less__pos,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.32/0.59        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_pos
% 0.32/0.59  thf(fact_4704_neg__less__pos,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.59        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_pos
% 0.32/0.59  thf(fact_4705_neg__less__pos,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.59        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_pos
% 0.32/0.59  thf(fact_4706_neg__less__pos,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.59        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_pos
% 0.32/0.59  thf(fact_4707_neg__0__less__iff__less,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_less_iff_less
% 0.32/0.59  thf(fact_4708_neg__0__less__iff__less,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_less_iff_less
% 0.32/0.59  thf(fact_4709_neg__0__less__iff__less,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_less_iff_less
% 0.32/0.59  thf(fact_4710_neg__0__less__iff__less,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_0_less_iff_less
% 0.32/0.59  thf(fact_4711_neg__less__0__iff__less,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.32/0.59        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_0_iff_less
% 0.32/0.59  thf(fact_4712_neg__less__0__iff__less,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.32/0.59        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_0_iff_less
% 0.32/0.59  thf(fact_4713_neg__less__0__iff__less,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.59        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_0_iff_less
% 0.32/0.59  thf(fact_4714_neg__less__0__iff__less,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.32/0.59        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_less_0_iff_less
% 0.32/0.59  thf(fact_4715_ab__left__minus,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.32/0.59        = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % ab_left_minus
% 0.32/0.59  thf(fact_4716_ab__left__minus,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.59        = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % ab_left_minus
% 0.32/0.59  thf(fact_4717_ab__left__minus,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.32/0.59        = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % ab_left_minus
% 0.32/0.59  thf(fact_4718_ab__left__minus,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.59        = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % ab_left_minus
% 0.32/0.59  thf(fact_4719_ab__left__minus,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.59        = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % ab_left_minus
% 0.32/0.59  thf(fact_4720_add_Oright__inverse,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.32/0.59        = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % add.right_inverse
% 0.32/0.59  thf(fact_4721_add_Oright__inverse,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.32/0.59        = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % add.right_inverse
% 0.32/0.59  thf(fact_4722_add_Oright__inverse,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.32/0.59        = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % add.right_inverse
% 0.32/0.59  thf(fact_4723_add_Oright__inverse,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.59        = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % add.right_inverse
% 0.32/0.59  thf(fact_4724_add_Oright__inverse,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.32/0.59        = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % add.right_inverse
% 0.32/0.59  thf(fact_4725_diff__0,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( minus_minus_real @ zero_zero_real @ A )
% 0.32/0.59        = ( uminus_uminus_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_0
% 0.32/0.59  thf(fact_4726_diff__0,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.32/0.59        = ( uminus_uminus_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_0
% 0.32/0.59  thf(fact_4727_diff__0,axiom,
% 0.32/0.59      ! [A: complex] :
% 0.32/0.59        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_0
% 0.32/0.59  thf(fact_4728_diff__0,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_0
% 0.32/0.59  thf(fact_4729_diff__0,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.32/0.59        = ( uminus_uminus_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_0
% 0.32/0.59  thf(fact_4730_verit__minus__simplify_I3_J,axiom,
% 0.32/0.59      ! [B: real] :
% 0.32/0.59        ( ( minus_minus_real @ zero_zero_real @ B )
% 0.32/0.59        = ( uminus_uminus_real @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % verit_minus_simplify(3)
% 0.32/0.59  thf(fact_4731_verit__minus__simplify_I3_J,axiom,
% 0.32/0.59      ! [B: int] :
% 0.32/0.59        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.32/0.59        = ( uminus_uminus_int @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % verit_minus_simplify(3)
% 0.32/0.59  thf(fact_4732_verit__minus__simplify_I3_J,axiom,
% 0.32/0.59      ! [B: complex] :
% 0.32/0.59        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % verit_minus_simplify(3)
% 0.32/0.59  thf(fact_4733_verit__minus__simplify_I3_J,axiom,
% 0.32/0.59      ! [B: code_integer] :
% 0.32/0.59        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % verit_minus_simplify(3)
% 0.32/0.59  thf(fact_4734_verit__minus__simplify_I3_J,axiom,
% 0.32/0.59      ! [B: rat] :
% 0.32/0.59        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.32/0.59        = ( uminus_uminus_rat @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % verit_minus_simplify(3)
% 0.32/0.59  thf(fact_4735_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4736_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4737_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4738_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4739_add__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4740_dvd__times__right__cancel__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 0.32/0.59          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_right_cancel_iff
% 0.32/0.59  thf(fact_4741_dvd__times__right__cancel__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( A != zero_zero_nat )
% 0.32/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.32/0.59          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_right_cancel_iff
% 0.32/0.59  thf(fact_4742_dvd__times__right__cancel__iff,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( A != zero_zero_int )
% 0.32/0.59       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.32/0.59          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_right_cancel_iff
% 0.32/0.59  thf(fact_4743_dvd__times__left__cancel__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.32/0.59          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_left_cancel_iff
% 0.32/0.59  thf(fact_4744_dvd__times__left__cancel__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( A != zero_zero_nat )
% 0.32/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.32/0.59          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_left_cancel_iff
% 0.32/0.59  thf(fact_4745_dvd__times__left__cancel__iff,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( A != zero_zero_int )
% 0.32/0.59       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.32/0.59          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_times_left_cancel_iff
% 0.32/0.59  thf(fact_4746_dvd__mult__cancel__right,axiom,
% 0.32/0.59      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.59        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.59          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_right
% 0.32/0.59  thf(fact_4747_dvd__mult__cancel__right,axiom,
% 0.32/0.59      ! [A: complex,C: complex,B: complex] :
% 0.32/0.59        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 0.32/0.59        = ( ( C = zero_zero_complex )
% 0.32/0.59          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_right
% 0.32/0.59  thf(fact_4748_dvd__mult__cancel__right,axiom,
% 0.32/0.59      ! [A: real,C: real,B: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 0.32/0.59        = ( ( C = zero_zero_real )
% 0.32/0.59          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_right
% 0.32/0.59  thf(fact_4749_dvd__mult__cancel__right,axiom,
% 0.32/0.59      ! [A: rat,C: rat,B: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.32/0.59        = ( ( C = zero_zero_rat )
% 0.32/0.59          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_right
% 0.32/0.59  thf(fact_4750_dvd__mult__cancel__right,axiom,
% 0.32/0.59      ! [A: int,C: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.32/0.59        = ( ( C = zero_zero_int )
% 0.32/0.59          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_right
% 0.32/0.59  thf(fact_4751_dvd__mult__cancel__left,axiom,
% 0.32/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.59        = ( ( C = zero_z3403309356797280102nteger )
% 0.32/0.59          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_left
% 0.32/0.59  thf(fact_4752_dvd__mult__cancel__left,axiom,
% 0.32/0.59      ! [C: complex,A: complex,B: complex] :
% 0.32/0.59        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 0.32/0.59        = ( ( C = zero_zero_complex )
% 0.32/0.59          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_left
% 0.32/0.59  thf(fact_4753_dvd__mult__cancel__left,axiom,
% 0.32/0.59      ! [C: real,A: real,B: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 0.32/0.59        = ( ( C = zero_zero_real )
% 0.32/0.59          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_left
% 0.32/0.59  thf(fact_4754_dvd__mult__cancel__left,axiom,
% 0.32/0.59      ! [C: rat,A: rat,B: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.32/0.59        = ( ( C = zero_zero_rat )
% 0.32/0.59          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_left
% 0.32/0.59  thf(fact_4755_dvd__mult__cancel__left,axiom,
% 0.32/0.59      ! [C: int,A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.59        = ( ( C = zero_zero_int )
% 0.32/0.59          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_cancel_left
% 0.32/0.59  thf(fact_4756_mult__minus1__right,axiom,
% 0.32/0.59      ! [Z: real] :
% 0.32/0.59        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59        = ( uminus_uminus_real @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1_right
% 0.32/0.59  thf(fact_4757_mult__minus1__right,axiom,
% 0.32/0.59      ! [Z: int] :
% 0.32/0.59        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59        = ( uminus_uminus_int @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1_right
% 0.32/0.59  thf(fact_4758_mult__minus1__right,axiom,
% 0.32/0.59      ! [Z: complex] :
% 0.32/0.59        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1_right
% 0.32/0.59  thf(fact_4759_mult__minus1__right,axiom,
% 0.32/0.59      ! [Z: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1_right
% 0.32/0.59  thf(fact_4760_mult__minus1__right,axiom,
% 0.32/0.59      ! [Z: rat] :
% 0.32/0.59        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59        = ( uminus_uminus_rat @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1_right
% 0.32/0.59  thf(fact_4761_mult__minus1,axiom,
% 0.32/0.59      ! [Z: real] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 0.32/0.59        = ( uminus_uminus_real @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1
% 0.32/0.59  thf(fact_4762_mult__minus1,axiom,
% 0.32/0.59      ! [Z: int] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.32/0.59        = ( uminus_uminus_int @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1
% 0.32/0.59  thf(fact_4763_mult__minus1,axiom,
% 0.32/0.59      ! [Z: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1
% 0.32/0.59  thf(fact_4764_mult__minus1,axiom,
% 0.32/0.59      ! [Z: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1
% 0.32/0.59  thf(fact_4765_mult__minus1,axiom,
% 0.32/0.59      ! [Z: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.32/0.59        = ( uminus_uminus_rat @ Z ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_minus1
% 0.32/0.59  thf(fact_4766_abs__le__zero__iff,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.32/0.59        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_zero_iff
% 0.32/0.59  thf(fact_4767_abs__le__zero__iff,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.32/0.59        = ( A = zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_zero_iff
% 0.32/0.59  thf(fact_4768_abs__le__zero__iff,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.32/0.59        = ( A = zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_zero_iff
% 0.32/0.59  thf(fact_4769_abs__le__zero__iff,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.32/0.59        = ( A = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_zero_iff
% 0.32/0.59  thf(fact_4770_abs__le__self__iff,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.32/0.59        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_self_iff
% 0.32/0.59  thf(fact_4771_abs__le__self__iff,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_self_iff
% 0.32/0.59  thf(fact_4772_abs__le__self__iff,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_self_iff
% 0.32/0.59  thf(fact_4773_abs__le__self__iff,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.32/0.59        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_le_self_iff
% 0.32/0.59  thf(fact_4774_abs__of__nonneg,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.59       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonneg
% 0.32/0.59  thf(fact_4775_abs__of__nonneg,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.59       => ( ( abs_abs_real @ A )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonneg
% 0.32/0.59  thf(fact_4776_abs__of__nonneg,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.59       => ( ( abs_abs_rat @ A )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonneg
% 0.32/0.59  thf(fact_4777_abs__of__nonneg,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.59       => ( ( abs_abs_int @ A )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonneg
% 0.32/0.59  thf(fact_4778_zero__less__abs__iff,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.32/0.59        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_less_abs_iff
% 0.32/0.59  thf(fact_4779_zero__less__abs__iff,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.32/0.59        = ( A != zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_less_abs_iff
% 0.32/0.59  thf(fact_4780_zero__less__abs__iff,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.32/0.59        = ( A != zero_zero_rat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_less_abs_iff
% 0.32/0.59  thf(fact_4781_zero__less__abs__iff,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.32/0.59        = ( A != zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_less_abs_iff
% 0.32/0.59  thf(fact_4782_uminus__add__conv__diff,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.59        = ( minus_minus_real @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % uminus_add_conv_diff
% 0.32/0.59  thf(fact_4783_uminus__add__conv__diff,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.59        = ( minus_minus_int @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % uminus_add_conv_diff
% 0.32/0.59  thf(fact_4784_uminus__add__conv__diff,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.32/0.59        = ( minus_minus_complex @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % uminus_add_conv_diff
% 0.32/0.59  thf(fact_4785_uminus__add__conv__diff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.59        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % uminus_add_conv_diff
% 0.32/0.59  thf(fact_4786_uminus__add__conv__diff,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.59        = ( minus_minus_rat @ B @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % uminus_add_conv_diff
% 0.32/0.59  thf(fact_4787_diff__minus__eq__add,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.32/0.59        = ( plus_plus_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_minus_eq_add
% 0.32/0.59  thf(fact_4788_diff__minus__eq__add,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.59        = ( plus_plus_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_minus_eq_add
% 0.32/0.59  thf(fact_4789_diff__minus__eq__add,axiom,
% 0.32/0.59      ! [A: complex,B: complex] :
% 0.32/0.59        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.59        = ( plus_plus_complex @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_minus_eq_add
% 0.32/0.59  thf(fact_4790_diff__minus__eq__add,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.59        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_minus_eq_add
% 0.32/0.59  thf(fact_4791_diff__minus__eq__add,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.59        = ( plus_plus_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_minus_eq_add
% 0.32/0.59  thf(fact_4792_divide__minus1,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59        = ( uminus_uminus_real @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_minus1
% 0.32/0.59  thf(fact_4793_divide__minus1,axiom,
% 0.32/0.59      ! [X: complex] :
% 0.32/0.59        ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_minus1
% 0.32/0.59  thf(fact_4794_divide__minus1,axiom,
% 0.32/0.59      ! [X: rat] :
% 0.32/0.59        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59        = ( uminus_uminus_rat @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_minus1
% 0.32/0.59  thf(fact_4795_div__minus1__right,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59        = ( uminus_uminus_int @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_minus1_right
% 0.32/0.59  thf(fact_4796_div__minus1__right,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_minus1_right
% 0.32/0.59  thf(fact_4797_dvd__add__times__triv__right__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_right_iff
% 0.32/0.59  thf(fact_4798_dvd__add__times__triv__right__iff,axiom,
% 0.32/0.59      ! [A: real,B: real,C: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 0.32/0.59        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_right_iff
% 0.32/0.59  thf(fact_4799_dvd__add__times__triv__right__iff,axiom,
% 0.32/0.59      ! [A: rat,B: rat,C: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.32/0.59        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_right_iff
% 0.32/0.59  thf(fact_4800_dvd__add__times__triv__right__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat,C: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.32/0.59        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_right_iff
% 0.32/0.59  thf(fact_4801_dvd__add__times__triv__right__iff,axiom,
% 0.32/0.59      ! [A: int,B: int,C: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.32/0.59        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_right_iff
% 0.32/0.59  thf(fact_4802_dvd__add__times__triv__left__iff,axiom,
% 0.32/0.59      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 0.32/0.59        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_left_iff
% 0.32/0.59  thf(fact_4803_dvd__add__times__triv__left__iff,axiom,
% 0.32/0.59      ! [A: real,C: real,B: real] :
% 0.32/0.59        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 0.32/0.59        = ( dvd_dvd_real @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_left_iff
% 0.32/0.59  thf(fact_4804_dvd__add__times__triv__left__iff,axiom,
% 0.32/0.59      ! [A: rat,C: rat,B: rat] :
% 0.32/0.59        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.32/0.59        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_left_iff
% 0.32/0.59  thf(fact_4805_dvd__add__times__triv__left__iff,axiom,
% 0.32/0.59      ! [A: nat,C: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.32/0.59        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_left_iff
% 0.32/0.59  thf(fact_4806_dvd__add__times__triv__left__iff,axiom,
% 0.32/0.59      ! [A: int,C: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.32/0.59        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_add_times_triv_left_iff
% 0.32/0.59  thf(fact_4807_unit__prod,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.59         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_prod
% 0.32/0.59  thf(fact_4808_unit__prod,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.59         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_prod
% 0.32/0.59  thf(fact_4809_unit__prod,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.59         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_prod
% 0.32/0.59  thf(fact_4810_dvd__div__mult__self,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.59       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_div_mult_self
% 0.32/0.59  thf(fact_4811_dvd__div__mult__self,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.59       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_div_mult_self
% 0.32/0.59  thf(fact_4812_dvd__div__mult__self,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.59       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_div_mult_self
% 0.32/0.59  thf(fact_4813_dvd__mult__div__cancel,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.59       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_div_cancel
% 0.32/0.59  thf(fact_4814_dvd__mult__div__cancel,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.59       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_div_cancel
% 0.32/0.59  thf(fact_4815_dvd__mult__div__cancel,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.59       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_mult_div_cancel
% 0.32/0.59  thf(fact_4816_div__add,axiom,
% 0.32/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.59         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.59            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_add
% 0.32/0.59  thf(fact_4817_div__add,axiom,
% 0.32/0.59      ! [C: nat,A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ C @ A )
% 0.32/0.59       => ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.59         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.59            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_add
% 0.32/0.59  thf(fact_4818_div__add,axiom,
% 0.32/0.59      ! [C: int,A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ C @ A )
% 0.32/0.59       => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.59         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.59            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_add
% 0.32/0.59  thf(fact_4819_unit__div,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.59         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div
% 0.32/0.59  thf(fact_4820_unit__div,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.59         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div
% 0.32/0.59  thf(fact_4821_unit__div,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.59         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div
% 0.32/0.59  thf(fact_4822_unit__div__1__unit,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_unit
% 0.32/0.59  thf(fact_4823_unit__div__1__unit,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_unit
% 0.32/0.59  thf(fact_4824_unit__div__1__unit,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_unit
% 0.32/0.59  thf(fact_4825_unit__div__1__div__1,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_div_1
% 0.32/0.59  thf(fact_4826_unit__div__1__div__1,axiom,
% 0.32/0.59      ! [A: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_div_1
% 0.32/0.59  thf(fact_4827_unit__div__1__div__1,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.32/0.59          = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_1_div_1
% 0.32/0.59  thf(fact_4828_div__diff,axiom,
% 0.32/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.32/0.59       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.59         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.32/0.59            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_diff
% 0.32/0.59  thf(fact_4829_div__diff,axiom,
% 0.32/0.59      ! [C: int,A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ C @ A )
% 0.32/0.59       => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.59         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.32/0.59            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % div_diff
% 0.32/0.59  thf(fact_4830_abs__neg__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_real @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_numeral
% 0.32/0.59  thf(fact_4831_abs__neg__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_numeral
% 0.32/0.59  thf(fact_4832_abs__neg__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_numeral
% 0.32/0.59  thf(fact_4833_abs__neg__numeral,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_numeral
% 0.32/0.59  thf(fact_4834_dvd__imp__mod__0,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.59       => ( ( modulo_modulo_nat @ B @ A )
% 0.32/0.59          = zero_zero_nat ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_imp_mod_0
% 0.32/0.59  thf(fact_4835_dvd__imp__mod__0,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.59       => ( ( modulo_modulo_int @ B @ A )
% 0.32/0.59          = zero_zero_int ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_imp_mod_0
% 0.32/0.59  thf(fact_4836_dvd__imp__mod__0,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.59       => ( ( modulo364778990260209775nteger @ B @ A )
% 0.32/0.59          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dvd_imp_mod_0
% 0.32/0.59  thf(fact_4837_abs__neg__one,axiom,
% 0.32/0.59      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59      = one_one_real ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_one
% 0.32/0.59  thf(fact_4838_abs__neg__one,axiom,
% 0.32/0.59      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59      = one_one_int ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_one
% 0.32/0.59  thf(fact_4839_abs__neg__one,axiom,
% 0.32/0.59      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59      = one_one_Code_integer ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_one
% 0.32/0.59  thf(fact_4840_abs__neg__one,axiom,
% 0.32/0.59      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59      = one_one_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_neg_one
% 0.32/0.59  thf(fact_4841_minus__mod__self1,axiom,
% 0.32/0.59      ! [B: int,A: int] :
% 0.32/0.59        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 0.32/0.59        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mod_self1
% 0.32/0.59  thf(fact_4842_minus__mod__self1,axiom,
% 0.32/0.59      ! [B: code_integer,A: code_integer] :
% 0.32/0.59        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 0.32/0.59        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_mod_self1
% 0.32/0.59  thf(fact_4843_abs__power__minus,axiom,
% 0.32/0.59      ! [A: real,N: nat] :
% 0.32/0.59        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.32/0.59        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_power_minus
% 0.32/0.59  thf(fact_4844_abs__power__minus,axiom,
% 0.32/0.59      ! [A: int,N: nat] :
% 0.32/0.59        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.32/0.59        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_power_minus
% 0.32/0.59  thf(fact_4845_abs__power__minus,axiom,
% 0.32/0.59      ! [A: code_integer,N: nat] :
% 0.32/0.59        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.32/0.59        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_power_minus
% 0.32/0.59  thf(fact_4846_abs__power__minus,axiom,
% 0.32/0.59      ! [A: rat,N: nat] :
% 0.32/0.59        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.32/0.59        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_power_minus
% 0.32/0.59  thf(fact_4847_real__add__minus__iff,axiom,
% 0.32/0.59      ! [X: real,A: real] :
% 0.32/0.59        ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 0.32/0.59          = zero_zero_real )
% 0.32/0.59        = ( X = A ) ) ).
% 0.32/0.59  
% 0.32/0.59  % real_add_minus_iff
% 0.32/0.59  thf(fact_4848_tanh__real__neg__iff,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.32/0.59        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_neg_iff
% 0.32/0.59  thf(fact_4849_tanh__real__pos__iff,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.32/0.59        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_pos_iff
% 0.32/0.59  thf(fact_4850_tanh__real__nonpos__iff,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.32/0.59        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_nonpos_iff
% 0.32/0.59  thf(fact_4851_tanh__real__nonneg__iff,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.32/0.59        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.59  
% 0.32/0.59  % tanh_real_nonneg_iff
% 0.32/0.59  thf(fact_4852_dbl__simps_I1_J,axiom,
% 0.32/0.59      ! [K: num] :
% 0.32/0.59        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dbl_simps(1)
% 0.32/0.59  thf(fact_4853_dbl__simps_I1_J,axiom,
% 0.32/0.59      ! [K: num] :
% 0.32/0.59        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dbl_simps(1)
% 0.32/0.59  thf(fact_4854_dbl__simps_I1_J,axiom,
% 0.32/0.59      ! [K: num] :
% 0.32/0.59        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dbl_simps(1)
% 0.32/0.59  thf(fact_4855_dbl__simps_I1_J,axiom,
% 0.32/0.59      ! [K: num] :
% 0.32/0.59        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dbl_simps(1)
% 0.32/0.59  thf(fact_4856_dbl__simps_I1_J,axiom,
% 0.32/0.59      ! [K: num] :
% 0.32/0.59        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % dbl_simps(1)
% 0.32/0.59  thf(fact_4857_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.59      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(7)
% 0.32/0.59  thf(fact_4858_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.59      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(7)
% 0.32/0.59  thf(fact_4859_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.59      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(7)
% 0.32/0.59  thf(fact_4860_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.59      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(7)
% 0.32/0.59  thf(fact_4861_add__neg__numeral__special_I7_J,axiom,
% 0.32/0.59      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(7)
% 0.32/0.59  thf(fact_4862_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.59      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(8)
% 0.32/0.59  thf(fact_4863_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.59      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(8)
% 0.32/0.59  thf(fact_4864_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.59      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(8)
% 0.32/0.59  thf(fact_4865_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.59      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(8)
% 0.32/0.59  thf(fact_4866_add__neg__numeral__special_I8_J,axiom,
% 0.32/0.59      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % add_neg_numeral_special(8)
% 0.32/0.59  thf(fact_4867_diff__numeral__special_I12_J,axiom,
% 0.32/0.59      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59      = zero_zero_real ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_special(12)
% 0.32/0.59  thf(fact_4868_diff__numeral__special_I12_J,axiom,
% 0.32/0.59      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59      = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_special(12)
% 0.32/0.59  thf(fact_4869_diff__numeral__special_I12_J,axiom,
% 0.32/0.59      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.59      = zero_zero_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_special(12)
% 0.32/0.59  thf(fact_4870_diff__numeral__special_I12_J,axiom,
% 0.32/0.59      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59      = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_special(12)
% 0.32/0.59  thf(fact_4871_diff__numeral__special_I12_J,axiom,
% 0.32/0.59      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59      = zero_zero_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_special(12)
% 0.32/0.59  thf(fact_4872_neg__one__eq__numeral__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ one_one_real )
% 0.32/0.59          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_one_eq_numeral_iff
% 0.32/0.59  thf(fact_4873_neg__one__eq__numeral__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ one_one_int )
% 0.32/0.59          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_one_eq_numeral_iff
% 0.32/0.59  thf(fact_4874_neg__one__eq__numeral__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.32/0.59          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_one_eq_numeral_iff
% 0.32/0.59  thf(fact_4875_neg__one__eq__numeral__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.32/0.59          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_one_eq_numeral_iff
% 0.32/0.59  thf(fact_4876_neg__one__eq__numeral__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.32/0.59          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_one_eq_numeral_iff
% 0.32/0.59  thf(fact_4877_numeral__eq__neg__one__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 0.32/0.59          = ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % numeral_eq_neg_one_iff
% 0.32/0.59  thf(fact_4878_numeral__eq__neg__one__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.32/0.59          = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % numeral_eq_neg_one_iff
% 0.32/0.59  thf(fact_4879_numeral__eq__neg__one__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 0.32/0.59          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % numeral_eq_neg_one_iff
% 0.32/0.59  thf(fact_4880_numeral__eq__neg__one__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.59          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % numeral_eq_neg_one_iff
% 0.32/0.59  thf(fact_4881_numeral__eq__neg__one__iff,axiom,
% 0.32/0.59      ! [N: num] :
% 0.32/0.59        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 0.32/0.59          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59        = ( N = one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % numeral_eq_neg_one_iff
% 0.32/0.59  thf(fact_4882_zero__le__divide__abs__iff,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.32/0.59        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.59          | ( B = zero_zero_real ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_le_divide_abs_iff
% 0.32/0.59  thf(fact_4883_zero__le__divide__abs__iff,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.32/0.59        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.59          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % zero_le_divide_abs_iff
% 0.32/0.59  thf(fact_4884_divide__le__0__abs__iff,axiom,
% 0.32/0.59      ! [A: real,B: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.32/0.59        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.32/0.59          | ( B = zero_zero_real ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_le_0_abs_iff
% 0.32/0.59  thf(fact_4885_divide__le__0__abs__iff,axiom,
% 0.32/0.59      ! [A: rat,B: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.32/0.59        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.59          | ( B = zero_zero_rat ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_le_0_abs_iff
% 0.32/0.59  thf(fact_4886_minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 0.32/0.59        = one_one_real ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_one_mult_self
% 0.32/0.59  thf(fact_4887_minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.32/0.59        = one_one_int ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_one_mult_self
% 0.32/0.59  thf(fact_4888_minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 0.32/0.59        = one_one_complex ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_one_mult_self
% 0.32/0.59  thf(fact_4889_minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.32/0.59        = one_one_Code_integer ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_one_mult_self
% 0.32/0.59  thf(fact_4890_minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.32/0.59        = one_one_rat ) ).
% 0.32/0.59  
% 0.32/0.59  % minus_one_mult_self
% 0.32/0.59  thf(fact_4891_left__minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat,A: real] :
% 0.32/0.59        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % left_minus_one_mult_self
% 0.32/0.59  thf(fact_4892_left__minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat,A: int] :
% 0.32/0.59        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % left_minus_one_mult_self
% 0.32/0.59  thf(fact_4893_left__minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat,A: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % left_minus_one_mult_self
% 0.32/0.59  thf(fact_4894_left__minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat,A: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % left_minus_one_mult_self
% 0.32/0.59  thf(fact_4895_left__minus__one__mult__self,axiom,
% 0.32/0.59      ! [N: nat,A: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 0.32/0.59        = A ) ).
% 0.32/0.59  
% 0.32/0.59  % left_minus_one_mult_self
% 0.32/0.59  thf(fact_4896_abs__of__nonpos,axiom,
% 0.32/0.59      ! [A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.32/0.59       => ( ( abs_abs_real @ A )
% 0.32/0.59          = ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonpos
% 0.32/0.59  thf(fact_4897_abs__of__nonpos,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.59       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.59          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonpos
% 0.32/0.59  thf(fact_4898_abs__of__nonpos,axiom,
% 0.32/0.59      ! [A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.32/0.59       => ( ( abs_abs_rat @ A )
% 0.32/0.59          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonpos
% 0.32/0.59  thf(fact_4899_abs__of__nonpos,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.32/0.59       => ( ( abs_abs_int @ A )
% 0.32/0.59          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % abs_of_nonpos
% 0.32/0.59  thf(fact_4900_even__Suc,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 0.32/0.59        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_Suc
% 0.32/0.59  thf(fact_4901_even__Suc__Suc__iff,axiom,
% 0.32/0.59      ! [N: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 0.32/0.59        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_Suc_Suc_iff
% 0.32/0.59  thf(fact_4902_unit__mult__div__div,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.32/0.59          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_mult_div_div
% 0.32/0.59  thf(fact_4903_unit__mult__div__div,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.32/0.59          = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_mult_div_div
% 0.32/0.59  thf(fact_4904_unit__mult__div__div,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.32/0.59          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_mult_div_div
% 0.32/0.59  thf(fact_4905_unit__div__mult__self,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.59       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_mult_self
% 0.32/0.59  thf(fact_4906_unit__div__mult__self,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.59       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_mult_self
% 0.32/0.59  thf(fact_4907_unit__div__mult__self,axiom,
% 0.32/0.59      ! [A: int,B: int] :
% 0.32/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.59       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.32/0.59          = B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % unit_div_mult_self
% 0.32/0.59  thf(fact_4908_mod__minus1__right,axiom,
% 0.32/0.59      ! [A: int] :
% 0.32/0.59        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59        = zero_zero_int ) ).
% 0.32/0.59  
% 0.32/0.59  % mod_minus1_right
% 0.32/0.59  thf(fact_4909_mod__minus1__right,axiom,
% 0.32/0.59      ! [A: code_integer] :
% 0.32/0.59        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59        = zero_z3403309356797280102nteger ) ).
% 0.32/0.59  
% 0.32/0.59  % mod_minus1_right
% 0.32/0.59  thf(fact_4910_max__number__of_I2_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59            = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(2)
% 0.32/0.59  thf(fact_4911_max__number__of_I2_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(2)
% 0.32/0.59  thf(fact_4912_max__number__of_I2_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(2)
% 0.32/0.59  thf(fact_4913_max__number__of_I2_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59            = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(2)
% 0.32/0.59  thf(fact_4914_max__number__of_I3_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.32/0.59         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.32/0.59            = ( numeral_numeral_real @ V ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.32/0.59         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 0.32/0.59            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(3)
% 0.32/0.59  thf(fact_4915_max__number__of_I3_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.32/0.59            = ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 0.32/0.59            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(3)
% 0.32/0.59  thf(fact_4916_max__number__of_I3_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.32/0.59            = ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 0.32/0.59            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(3)
% 0.32/0.59  thf(fact_4917_max__number__of_I3_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.32/0.59         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.32/0.59            = ( numeral_numeral_int @ V ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.32/0.59         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 0.32/0.59            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(3)
% 0.32/0.59  thf(fact_4918_max__number__of_I4_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(4)
% 0.32/0.59  thf(fact_4919_max__number__of_I4_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 0.32/0.59            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(4)
% 0.32/0.59  thf(fact_4920_max__number__of_I4_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(4)
% 0.32/0.59  thf(fact_4921_max__number__of_I4_J,axiom,
% 0.32/0.59      ! [U: num,V: num] :
% 0.32/0.59        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 0.32/0.59        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.32/0.59            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % max_number_of(4)
% 0.32/0.59  thf(fact_4922_pow__divides__pow__iff,axiom,
% 0.32/0.59      ! [N: nat,A: nat,B: nat] :
% 0.32/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.59          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % pow_divides_pow_iff
% 0.32/0.59  thf(fact_4923_pow__divides__pow__iff,axiom,
% 0.32/0.59      ! [N: nat,A: int,B: int] :
% 0.32/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.59       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.32/0.59          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % pow_divides_pow_iff
% 0.32/0.59  thf(fact_4924_semiring__norm_I168_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: real] :
% 0.32/0.59        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.32/0.59        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(168)
% 0.32/0.59  thf(fact_4925_semiring__norm_I168_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: int] :
% 0.32/0.59        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.32/0.59        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(168)
% 0.32/0.59  thf(fact_4926_semiring__norm_I168_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: complex] :
% 0.32/0.59        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.32/0.59        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(168)
% 0.32/0.59  thf(fact_4927_semiring__norm_I168_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: code_integer] :
% 0.32/0.59        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.32/0.59        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(168)
% 0.32/0.59  thf(fact_4928_semiring__norm_I168_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: rat] :
% 0.32/0.59        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.32/0.59        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(168)
% 0.32/0.59  thf(fact_4929_diff__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(3)
% 0.32/0.59  thf(fact_4930_diff__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(3)
% 0.32/0.59  thf(fact_4931_diff__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(3)
% 0.32/0.59  thf(fact_4932_diff__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(3)
% 0.32/0.59  thf(fact_4933_diff__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(3)
% 0.32/0.59  thf(fact_4934_diff__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(2)
% 0.32/0.59  thf(fact_4935_diff__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(2)
% 0.32/0.59  thf(fact_4936_diff__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(2)
% 0.32/0.59  thf(fact_4937_diff__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(2)
% 0.32/0.59  thf(fact_4938_diff__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % diff_numeral_simps(2)
% 0.32/0.59  thf(fact_4939_semiring__norm_I172_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: real] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(172)
% 0.32/0.59  thf(fact_4940_semiring__norm_I172_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: int] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(172)
% 0.32/0.59  thf(fact_4941_semiring__norm_I172_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(172)
% 0.32/0.59  thf(fact_4942_semiring__norm_I172_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(172)
% 0.32/0.59  thf(fact_4943_semiring__norm_I172_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(172)
% 0.32/0.59  thf(fact_4944_semiring__norm_I171_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: real] :
% 0.32/0.59        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(171)
% 0.32/0.59  thf(fact_4945_semiring__norm_I171_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: int] :
% 0.32/0.59        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(171)
% 0.32/0.59  thf(fact_4946_semiring__norm_I171_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(171)
% 0.32/0.59  thf(fact_4947_semiring__norm_I171_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(171)
% 0.32/0.59  thf(fact_4948_semiring__norm_I171_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.32/0.59        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(171)
% 0.32/0.59  thf(fact_4949_semiring__norm_I170_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: real] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 0.32/0.59        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(170)
% 0.32/0.59  thf(fact_4950_semiring__norm_I170_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: int] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 0.32/0.59        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(170)
% 0.32/0.59  thf(fact_4951_semiring__norm_I170_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: complex] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 0.32/0.59        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(170)
% 0.32/0.59  thf(fact_4952_semiring__norm_I170_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: code_integer] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 0.32/0.59        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(170)
% 0.32/0.59  thf(fact_4953_semiring__norm_I170_J,axiom,
% 0.32/0.59      ! [V: num,W: num,Y: rat] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 0.32/0.59        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.32/0.59  
% 0.32/0.59  % semiring_norm(170)
% 0.32/0.59  thf(fact_4954_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4955_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4956_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4957_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4958_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(3)
% 0.32/0.59  thf(fact_4959_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.59        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(2)
% 0.32/0.59  thf(fact_4960_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(2)
% 0.32/0.59  thf(fact_4961_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.32/0.59        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(2)
% 0.32/0.59  thf(fact_4962_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(2)
% 0.32/0.59  thf(fact_4963_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.32/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(2)
% 0.32/0.59  thf(fact_4964_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(1)
% 0.32/0.59  thf(fact_4965_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(1)
% 0.32/0.59  thf(fact_4966_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.59        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(1)
% 0.32/0.59  thf(fact_4967_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(1)
% 0.32/0.59  thf(fact_4968_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % mult_neg_numeral_simps(1)
% 0.32/0.59  thf(fact_4969_artanh__minus__real,axiom,
% 0.32/0.59      ! [X: real] :
% 0.32/0.59        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.59       => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 0.32/0.59          = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % artanh_minus_real
% 0.32/0.59  thf(fact_4970_neg__numeral__le__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_le_iff
% 0.32/0.59  thf(fact_4971_neg__numeral__le__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_le_iff
% 0.32/0.59  thf(fact_4972_neg__numeral__le__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_le_iff
% 0.32/0.59  thf(fact_4973_neg__numeral__le__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_le_iff
% 0.32/0.59  thf(fact_4974_neg__numeral__less__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.59        = ( ord_less_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_iff
% 0.32/0.59  thf(fact_4975_neg__numeral__less__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.59        = ( ord_less_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_iff
% 0.32/0.59  thf(fact_4976_neg__numeral__less__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.59        = ( ord_less_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_iff
% 0.32/0.59  thf(fact_4977_neg__numeral__less__iff,axiom,
% 0.32/0.59      ! [M: num,N: num] :
% 0.32/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.59        = ( ord_less_num @ N @ M ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_iff
% 0.32/0.59  thf(fact_4978_not__neg__one__le__neg__numeral__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_neg_one_le_neg_numeral_iff
% 0.32/0.59  thf(fact_4979_not__neg__one__le__neg__numeral__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_neg_one_le_neg_numeral_iff
% 0.32/0.59  thf(fact_4980_not__neg__one__le__neg__numeral__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_neg_one_le_neg_numeral_iff
% 0.32/0.59  thf(fact_4981_not__neg__one__le__neg__numeral__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % not_neg_one_le_neg_numeral_iff
% 0.32/0.59  thf(fact_4982_le__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: real,B: real,W: num] :
% 0.32/0.59        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.32/0.59        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % le_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4983_le__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: rat,B: rat,W: num] :
% 0.32/0.59        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.32/0.59        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % le_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4984_divide__le__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: real,W: num,A: real] :
% 0.32/0.59        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.32/0.59        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_le_eq_numeral1(2)
% 0.32/0.59  thf(fact_4985_divide__le__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: rat,W: num,A: rat] :
% 0.32/0.59        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.32/0.59        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_le_eq_numeral1(2)
% 0.32/0.59  thf(fact_4986_divide__eq__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: real,W: num,A: real] :
% 0.32/0.59        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.59          = A )
% 0.32/0.59        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.59             != zero_zero_real )
% 0.32/0.59           => ( B
% 0.32/0.59              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 0.32/0.59          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.59              = zero_zero_real )
% 0.32/0.59           => ( A = zero_zero_real ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_eq_eq_numeral1(2)
% 0.32/0.59  thf(fact_4987_divide__eq__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: complex,W: num,A: complex] :
% 0.32/0.59        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.59          = A )
% 0.32/0.59        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.59             != zero_zero_complex )
% 0.32/0.59           => ( B
% 0.32/0.59              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 0.32/0.59          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.59              = zero_zero_complex )
% 0.32/0.59           => ( A = zero_zero_complex ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_eq_eq_numeral1(2)
% 0.32/0.59  thf(fact_4988_divide__eq__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: rat,W: num,A: rat] :
% 0.32/0.59        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.32/0.59          = A )
% 0.32/0.59        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.59             != zero_zero_rat )
% 0.32/0.59           => ( B
% 0.32/0.59              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 0.32/0.59          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.59              = zero_zero_rat )
% 0.32/0.59           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_eq_eq_numeral1(2)
% 0.32/0.59  thf(fact_4989_eq__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: real,B: real,W: num] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.32/0.59        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.59             != zero_zero_real )
% 0.32/0.59           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.59              = B ) )
% 0.32/0.59          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.59              = zero_zero_real )
% 0.32/0.59           => ( A = zero_zero_real ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % eq_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4990_eq__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: complex,B: complex,W: num] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 0.32/0.59        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.59             != zero_zero_complex )
% 0.32/0.59           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.59              = B ) )
% 0.32/0.59          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.59              = zero_zero_complex )
% 0.32/0.59           => ( A = zero_zero_complex ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % eq_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4991_eq__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: rat,B: rat,W: num] :
% 0.32/0.59        ( ( A
% 0.32/0.59          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.32/0.59        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.59             != zero_zero_rat )
% 0.32/0.59           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.32/0.59              = B ) )
% 0.32/0.59          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.59              = zero_zero_rat )
% 0.32/0.59           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % eq_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4992_neg__numeral__less__neg__one__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_neg_one_iff
% 0.32/0.59  thf(fact_4993_neg__numeral__less__neg__one__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_neg_one_iff
% 0.32/0.59  thf(fact_4994_neg__numeral__less__neg__one__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_neg_one_iff
% 0.32/0.59  thf(fact_4995_neg__numeral__less__neg__one__iff,axiom,
% 0.32/0.59      ! [M: num] :
% 0.32/0.59        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.59        = ( M != one ) ) ).
% 0.32/0.59  
% 0.32/0.59  % neg_numeral_less_neg_one_iff
% 0.32/0.59  thf(fact_4996_divide__less__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: real,W: num,A: real] :
% 0.32/0.59        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 0.32/0.59        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_less_eq_numeral1(2)
% 0.32/0.59  thf(fact_4997_divide__less__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [B: rat,W: num,A: rat] :
% 0.32/0.59        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.32/0.59        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.32/0.59  
% 0.32/0.59  % divide_less_eq_numeral1(2)
% 0.32/0.59  thf(fact_4998_less__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: real,B: real,W: num] :
% 0.32/0.59        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 0.32/0.59        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_4999_less__divide__eq__numeral1_I2_J,axiom,
% 0.32/0.59      ! [A: rat,B: rat,W: num] :
% 0.32/0.59        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.32/0.59        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % less_divide_eq_numeral1(2)
% 0.32/0.59  thf(fact_5000_even__mult__iff,axiom,
% 0.32/0.59      ! [A: code_integer,B: code_integer] :
% 0.32/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.59        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.59          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.59  
% 0.32/0.59  % even_mult_iff
% 0.32/0.59  thf(fact_5001_even__mult__iff,axiom,
% 0.32/0.59      ! [A: nat,B: nat] :
% 0.32/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_mult_iff
% 0.32/0.60  thf(fact_5002_even__mult__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.32/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_mult_iff
% 0.32/0.60  thf(fact_5003_odd__add,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 0.32/0.60        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.60         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_add
% 0.32/0.60  thf(fact_5004_odd__add,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 0.32/0.60        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.60         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_add
% 0.32/0.60  thf(fact_5005_odd__add,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 0.32/0.60        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.60         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_add
% 0.32/0.60  thf(fact_5006_even__add,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_add
% 0.32/0.60  thf(fact_5007_even__add,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_add
% 0.32/0.60  thf(fact_5008_even__add,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 0.32/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_add
% 0.32/0.60  thf(fact_5009_power__minus__odd,axiom,
% 0.32/0.60      ! [N: nat,A: real] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.32/0.60          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus_odd
% 0.32/0.60  thf(fact_5010_power__minus__odd,axiom,
% 0.32/0.60      ! [N: nat,A: int] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.32/0.60          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus_odd
% 0.32/0.60  thf(fact_5011_power__minus__odd,axiom,
% 0.32/0.60      ! [N: nat,A: complex] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.32/0.60          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus_odd
% 0.32/0.60  thf(fact_5012_power__minus__odd,axiom,
% 0.32/0.60      ! [N: nat,A: code_integer] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.32/0.60          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus_odd
% 0.32/0.60  thf(fact_5013_power__minus__odd,axiom,
% 0.32/0.60      ! [N: nat,A: rat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.32/0.60          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus_odd
% 0.32/0.60  thf(fact_5014_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [N: nat,A: real] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.32/0.60          = ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Parity.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5015_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [N: nat,A: int] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.32/0.60          = ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Parity.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5016_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [N: nat,A: complex] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.32/0.60          = ( power_power_complex @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Parity.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5017_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [N: nat,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.32/0.60          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Parity.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5018_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [N: nat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.32/0.60          = ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Parity.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5019_power2__minus,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_minus
% 0.32/0.60  thf(fact_5020_power2__minus,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_minus
% 0.32/0.60  thf(fact_5021_power2__minus,axiom,
% 0.32/0.60      ! [A: complex] :
% 0.32/0.60        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_minus
% 0.32/0.60  thf(fact_5022_power2__minus,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_minus
% 0.32/0.60  thf(fact_5023_power2__minus,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_minus
% 0.32/0.60  thf(fact_5024_zero__less__power__abs__iff,axiom,
% 0.32/0.60      ! [A: code_integer,N: nat] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 0.32/0.60        = ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_abs_iff
% 0.32/0.60  thf(fact_5025_zero__less__power__abs__iff,axiom,
% 0.32/0.60      ! [A: real,N: nat] :
% 0.32/0.60        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.32/0.60        = ( ( A != zero_zero_real )
% 0.32/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_abs_iff
% 0.32/0.60  thf(fact_5026_zero__less__power__abs__iff,axiom,
% 0.32/0.60      ! [A: rat,N: nat] :
% 0.32/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 0.32/0.60        = ( ( A != zero_zero_rat )
% 0.32/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_abs_iff
% 0.32/0.60  thf(fact_5027_zero__less__power__abs__iff,axiom,
% 0.32/0.60      ! [A: int,N: nat] :
% 0.32/0.60        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 0.32/0.60        = ( ( A != zero_zero_int )
% 0.32/0.60          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_abs_iff
% 0.32/0.60  thf(fact_5028_even__mod__2__iff,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_mod_2_iff
% 0.32/0.60  thf(fact_5029_even__mod__2__iff,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_mod_2_iff
% 0.32/0.60  thf(fact_5030_even__mod__2__iff,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_mod_2_iff
% 0.32/0.60  thf(fact_5031_power__even__abs__numeral,axiom,
% 0.32/0.60      ! [W: num,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs_numeral
% 0.32/0.60  thf(fact_5032_power__even__abs__numeral,axiom,
% 0.32/0.60      ! [W: num,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs_numeral
% 0.32/0.60  thf(fact_5033_power__even__abs__numeral,axiom,
% 0.32/0.60      ! [W: num,A: real] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs_numeral
% 0.32/0.60  thf(fact_5034_power__even__abs__numeral,axiom,
% 0.32/0.60      ! [W: num,A: int] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs_numeral
% 0.32/0.60  thf(fact_5035_abs__power2,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_power2
% 0.32/0.60  thf(fact_5036_abs__power2,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_power2
% 0.32/0.60  thf(fact_5037_abs__power2,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_power2
% 0.32/0.60  thf(fact_5038_abs__power2,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_power2
% 0.32/0.60  thf(fact_5039_power2__abs,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_abs
% 0.32/0.60  thf(fact_5040_power2__abs,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_abs
% 0.32/0.60  thf(fact_5041_power2__abs,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_abs
% 0.32/0.60  thf(fact_5042_power2__abs,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power2_abs
% 0.32/0.60  thf(fact_5043_odd__Suc__div__two,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_Suc_div_two
% 0.32/0.60  thf(fact_5044_even__Suc__div__two,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_Suc_div_two
% 0.32/0.60  thf(fact_5045_zero__le__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: real,W: num] :
% 0.32/0.60        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_le_power_eq_numeral
% 0.32/0.60  thf(fact_5046_zero__le__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: rat,W: num] :
% 0.32/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_le_power_eq_numeral
% 0.32/0.60  thf(fact_5047_zero__le__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: int,W: num] :
% 0.32/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_le_power_eq_numeral
% 0.32/0.60  thf(fact_5048_power__less__zero__eq,axiom,
% 0.32/0.60      ! [A: real,N: nat] :
% 0.32/0.60        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq
% 0.32/0.60  thf(fact_5049_power__less__zero__eq,axiom,
% 0.32/0.60      ! [A: rat,N: nat] :
% 0.32/0.60        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq
% 0.32/0.60  thf(fact_5050_power__less__zero__eq,axiom,
% 0.32/0.60      ! [A: int,N: nat] :
% 0.32/0.60        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq
% 0.32/0.60  thf(fact_5051_power__less__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: real,W: num] :
% 0.32/0.60        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq_numeral
% 0.32/0.60  thf(fact_5052_power__less__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: rat,W: num] :
% 0.32/0.60        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq_numeral
% 0.32/0.60  thf(fact_5053_power__less__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: int,W: num] :
% 0.32/0.60        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_less_zero_eq_numeral
% 0.32/0.60  thf(fact_5054_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.60      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.60      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_neg_numeral_special(9)
% 0.32/0.60  thf(fact_5055_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.60      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_neg_numeral_special(9)
% 0.32/0.60  thf(fact_5056_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.60      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.60      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_neg_numeral_special(9)
% 0.32/0.60  thf(fact_5057_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.60      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_neg_numeral_special(9)
% 0.32/0.60  thf(fact_5058_add__neg__numeral__special_I9_J,axiom,
% 0.32/0.60      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.60      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_neg_numeral_special(9)
% 0.32/0.60  thf(fact_5059_diff__numeral__special_I11_J,axiom,
% 0.32/0.60      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.60      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(11)
% 0.32/0.60  thf(fact_5060_diff__numeral__special_I11_J,axiom,
% 0.32/0.60      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.60      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(11)
% 0.32/0.60  thf(fact_5061_diff__numeral__special_I11_J,axiom,
% 0.32/0.60      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.60      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(11)
% 0.32/0.60  thf(fact_5062_diff__numeral__special_I11_J,axiom,
% 0.32/0.60      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.60      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(11)
% 0.32/0.60  thf(fact_5063_diff__numeral__special_I11_J,axiom,
% 0.32/0.60      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.60      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(11)
% 0.32/0.60  thf(fact_5064_diff__numeral__special_I10_J,axiom,
% 0.32/0.60      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.32/0.60      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(10)
% 0.32/0.60  thf(fact_5065_diff__numeral__special_I10_J,axiom,
% 0.32/0.60      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.32/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(10)
% 0.32/0.60  thf(fact_5066_diff__numeral__special_I10_J,axiom,
% 0.32/0.60      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.32/0.60      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(10)
% 0.32/0.60  thf(fact_5067_diff__numeral__special_I10_J,axiom,
% 0.32/0.60      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.32/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(10)
% 0.32/0.60  thf(fact_5068_diff__numeral__special_I10_J,axiom,
% 0.32/0.60      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.32/0.60      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(10)
% 0.32/0.60  thf(fact_5069_minus__1__div__2__eq,axiom,
% 0.32/0.60      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_1_div_2_eq
% 0.32/0.60  thf(fact_5070_minus__1__div__2__eq,axiom,
% 0.32/0.60      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_1_div_2_eq
% 0.32/0.60  thf(fact_5071_even__plus__one__iff,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.32/0.60        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_plus_one_iff
% 0.32/0.60  thf(fact_5072_even__plus__one__iff,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.32/0.60        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_plus_one_iff
% 0.32/0.60  thf(fact_5073_even__plus__one__iff,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.32/0.60        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_plus_one_iff
% 0.32/0.60  thf(fact_5074_even__diff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_diff
% 0.32/0.60  thf(fact_5075_even__diff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 0.32/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_diff
% 0.32/0.60  thf(fact_5076_neg__one__odd__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.32/0.60          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_odd_power
% 0.32/0.60  thf(fact_5077_neg__one__odd__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.32/0.60          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_odd_power
% 0.32/0.60  thf(fact_5078_neg__one__odd__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.32/0.60          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_odd_power
% 0.32/0.60  thf(fact_5079_neg__one__odd__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.32/0.60          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_odd_power
% 0.32/0.60  thf(fact_5080_neg__one__odd__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.32/0.60          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_odd_power
% 0.32/0.60  thf(fact_5081_neg__one__even__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.32/0.60          = one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_even_power
% 0.32/0.60  thf(fact_5082_neg__one__even__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.32/0.60          = one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_even_power
% 0.32/0.60  thf(fact_5083_neg__one__even__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.32/0.60          = one_one_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_even_power
% 0.32/0.60  thf(fact_5084_neg__one__even__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.32/0.60          = one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_even_power
% 0.32/0.60  thf(fact_5085_neg__one__even__power,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.32/0.60          = one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_one_even_power
% 0.32/0.60  thf(fact_5086_bits__minus__1__mod__2__eq,axiom,
% 0.32/0.60      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60      = one_one_int ) ).
% 0.32/0.60  
% 0.32/0.60  % bits_minus_1_mod_2_eq
% 0.32/0.60  thf(fact_5087_bits__minus__1__mod__2__eq,axiom,
% 0.32/0.60      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60      = one_one_Code_integer ) ).
% 0.32/0.60  
% 0.32/0.60  % bits_minus_1_mod_2_eq
% 0.32/0.60  thf(fact_5088_minus__1__mod__2__eq,axiom,
% 0.32/0.60      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60      = one_one_int ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_1_mod_2_eq
% 0.32/0.60  thf(fact_5089_minus__1__mod__2__eq,axiom,
% 0.32/0.60      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60      = one_one_Code_integer ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_1_mod_2_eq
% 0.32/0.60  thf(fact_5090_odd__Suc__minus__one,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.32/0.60          = N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_Suc_minus_one
% 0.32/0.60  thf(fact_5091_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [A: real,N: nat] :
% 0.32/0.60        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Power.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5092_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [A: int,N: nat] :
% 0.32/0.60        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Power.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5093_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [A: complex,N: nat] :
% 0.32/0.60        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Power.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5094_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [A: code_integer,N: nat] :
% 0.32/0.60        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Power.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5095_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.32/0.60      ! [A: rat,N: nat] :
% 0.32/0.60        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % Power.ring_1_class.power_minus_even
% 0.32/0.60  thf(fact_5096_even__diff__nat,axiom,
% 0.32/0.60      ! [M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.60        = ( ( ord_less_nat @ M @ N )
% 0.32/0.60          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_diff_nat
% 0.32/0.60  thf(fact_5097_diff__numeral__special_I3_J,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.60        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(3)
% 0.32/0.60  thf(fact_5098_diff__numeral__special_I3_J,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.60        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(3)
% 0.32/0.60  thf(fact_5099_diff__numeral__special_I3_J,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.60        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(3)
% 0.32/0.60  thf(fact_5100_diff__numeral__special_I3_J,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.60        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(3)
% 0.32/0.60  thf(fact_5101_diff__numeral__special_I3_J,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.60        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(3)
% 0.32/0.60  thf(fact_5102_diff__numeral__special_I4_J,axiom,
% 0.32/0.60      ! [M: num] :
% 0.32/0.60        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 0.32/0.60        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(4)
% 0.32/0.60  thf(fact_5103_diff__numeral__special_I4_J,axiom,
% 0.32/0.60      ! [M: num] :
% 0.32/0.60        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.32/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(4)
% 0.32/0.60  thf(fact_5104_diff__numeral__special_I4_J,axiom,
% 0.32/0.60      ! [M: num] :
% 0.32/0.60        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 0.32/0.60        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(4)
% 0.32/0.60  thf(fact_5105_diff__numeral__special_I4_J,axiom,
% 0.32/0.60      ! [M: num] :
% 0.32/0.60        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.32/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(4)
% 0.32/0.60  thf(fact_5106_diff__numeral__special_I4_J,axiom,
% 0.32/0.60      ! [M: num] :
% 0.32/0.60        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.32/0.60        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_numeral_special(4)
% 0.32/0.60  thf(fact_5107_dbl__simps_I4_J,axiom,
% 0.32/0.60      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.60      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dbl_simps(4)
% 0.32/0.60  thf(fact_5108_dbl__simps_I4_J,axiom,
% 0.32/0.60      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dbl_simps(4)
% 0.32/0.60  thf(fact_5109_dbl__simps_I4_J,axiom,
% 0.32/0.60      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.60      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dbl_simps(4)
% 0.32/0.60  thf(fact_5110_dbl__simps_I4_J,axiom,
% 0.32/0.60      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dbl_simps(4)
% 0.32/0.60  thf(fact_5111_dbl__simps_I4_J,axiom,
% 0.32/0.60      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.60      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dbl_simps(4)
% 0.32/0.60  thf(fact_5112_zero__less__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: real,W: num] :
% 0.32/0.60        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.32/0.60            = zero_zero_nat )
% 0.32/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( A != zero_zero_real ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_eq_numeral
% 0.32/0.60  thf(fact_5113_zero__less__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: rat,W: num] :
% 0.32/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.32/0.60            = zero_zero_nat )
% 0.32/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( A != zero_zero_rat ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_eq_numeral
% 0.32/0.60  thf(fact_5114_zero__less__power__eq__numeral,axiom,
% 0.32/0.60      ! [A: int,W: num] :
% 0.32/0.60        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 0.32/0.60        = ( ( ( numeral_numeral_nat @ W )
% 0.32/0.60            = zero_zero_nat )
% 0.32/0.60          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( A != zero_zero_int ) )
% 0.32/0.60          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_less_power_eq_numeral
% 0.32/0.60  thf(fact_5115_even__succ__div__2,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_2
% 0.32/0.60  thf(fact_5116_even__succ__div__2,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_2
% 0.32/0.60  thf(fact_5117_even__succ__div__2,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_2
% 0.32/0.60  thf(fact_5118_odd__succ__div__two,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_succ_div_two
% 0.32/0.60  thf(fact_5119_odd__succ__div__two,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_succ_div_two
% 0.32/0.60  thf(fact_5120_odd__succ__div__two,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_succ_div_two
% 0.32/0.60  thf(fact_5121_even__succ__div__two,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_two
% 0.32/0.60  thf(fact_5122_even__succ__div__two,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_two
% 0.32/0.60  thf(fact_5123_even__succ__div__two,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.60          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_succ_div_two
% 0.32/0.60  thf(fact_5124_even__power,axiom,
% 0.32/0.60      ! [A: code_integer,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.32/0.60        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_power
% 0.32/0.60  thf(fact_5125_even__power,axiom,
% 0.32/0.60      ! [A: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_power
% 0.32/0.60  thf(fact_5126_even__power,axiom,
% 0.32/0.60      ! [A: int,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 0.32/0.60        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_power
% 0.32/0.60  thf(fact_5127_power__minus1__even,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = one_one_real ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus1_even
% 0.32/0.60  thf(fact_5128_power__minus1__even,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = one_one_int ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus1_even
% 0.32/0.60  thf(fact_5129_power__minus1__even,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = one_one_complex ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus1_even
% 0.32/0.60  thf(fact_5130_power__minus1__even,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = one_one_Code_integer ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus1_even
% 0.32/0.60  thf(fact_5131_power__minus1__even,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.60        = one_one_rat ) ).
% 0.32/0.60  
% 0.32/0.60  % power_minus1_even
% 0.32/0.60  thf(fact_5132_odd__two__times__div__two__nat,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.60          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_two_times_div_two_nat
% 0.32/0.60  thf(fact_5133_odd__two__times__div__two__succ,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_two_times_div_two_succ
% 0.32/0.60  thf(fact_5134_odd__two__times__div__two__succ,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_two_times_div_two_succ
% 0.32/0.60  thf(fact_5135_odd__two__times__div__two__succ,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.60       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % odd_two_times_div_two_succ
% 0.32/0.60  thf(fact_5136_power__le__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: real,W: num] :
% 0.32/0.60        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 0.32/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.32/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_zero_eq_numeral
% 0.32/0.60  thf(fact_5137_power__le__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: rat,W: num] :
% 0.32/0.60        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 0.32/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.32/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_zero_eq_numeral
% 0.32/0.60  thf(fact_5138_power__le__zero__eq__numeral,axiom,
% 0.32/0.60      ! [A: int,W: num] :
% 0.32/0.60        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 0.32/0.60        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.32/0.60            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 0.32/0.60              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_zero_eq_numeral
% 0.32/0.60  thf(fact_5139_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 0.32/0.60        = ( N = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % semiring_parity_class.even_mask_iff
% 0.32/0.60  thf(fact_5140_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 0.32/0.60        = ( N = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % semiring_parity_class.even_mask_iff
% 0.32/0.60  thf(fact_5141_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.32/0.60      ! [N: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.32/0.60        = ( N = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % semiring_parity_class.even_mask_iff
% 0.32/0.60  thf(fact_5142_dvd__div__neg,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.32/0.60       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 0.32/0.60          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_neg
% 0.32/0.60  thf(fact_5143_dvd__div__neg,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.60          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_neg
% 0.32/0.60  thf(fact_5144_dvd__div__neg,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( dvd_dvd_complex @ B @ A )
% 0.32/0.60       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_neg
% 0.32/0.60  thf(fact_5145_dvd__div__neg,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_neg
% 0.32/0.60  thf(fact_5146_dvd__div__neg,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ B @ A )
% 0.32/0.60       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_neg
% 0.32/0.60  thf(fact_5147_dvd__neg__div,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.32/0.60       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.60          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_neg_div
% 0.32/0.60  thf(fact_5148_dvd__neg__div,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_neg_div
% 0.32/0.60  thf(fact_5149_dvd__neg__div,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( dvd_dvd_complex @ B @ A )
% 0.32/0.60       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.32/0.60          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_neg_div
% 0.32/0.60  thf(fact_5150_dvd__neg__div,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_neg_div
% 0.32/0.60  thf(fact_5151_dvd__neg__div,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ B @ A )
% 0.32/0.60       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.60          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_neg_div
% 0.32/0.60  thf(fact_5152_dvd__if__abs__eq,axiom,
% 0.32/0.60      ! [L2: real,K: real] :
% 0.32/0.60        ( ( ( abs_abs_real @ L2 )
% 0.32/0.60          = ( abs_abs_real @ K ) )
% 0.32/0.60       => ( dvd_dvd_real @ L2 @ K ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_if_abs_eq
% 0.32/0.60  thf(fact_5153_dvd__if__abs__eq,axiom,
% 0.32/0.60      ! [L2: int,K: int] :
% 0.32/0.60        ( ( ( abs_abs_int @ L2 )
% 0.32/0.60          = ( abs_abs_int @ K ) )
% 0.32/0.60       => ( dvd_dvd_int @ L2 @ K ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_if_abs_eq
% 0.32/0.60  thf(fact_5154_dvd__if__abs__eq,axiom,
% 0.32/0.60      ! [L2: code_integer,K: code_integer] :
% 0.32/0.60        ( ( ( abs_abs_Code_integer @ L2 )
% 0.32/0.60          = ( abs_abs_Code_integer @ K ) )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_if_abs_eq
% 0.32/0.60  thf(fact_5155_dvd__if__abs__eq,axiom,
% 0.32/0.60      ! [L2: rat,K: rat] :
% 0.32/0.60        ( ( ( abs_abs_rat @ L2 )
% 0.32/0.60          = ( abs_abs_rat @ K ) )
% 0.32/0.60       => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_if_abs_eq
% 0.32/0.60  thf(fact_5156_abs__eq__iff,axiom,
% 0.32/0.60      ! [X: real,Y: real] :
% 0.32/0.60        ( ( ( abs_abs_real @ X )
% 0.32/0.60          = ( abs_abs_real @ Y ) )
% 0.32/0.60        = ( ( X = Y )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff
% 0.32/0.60  thf(fact_5157_abs__eq__iff,axiom,
% 0.32/0.60      ! [X: int,Y: int] :
% 0.32/0.60        ( ( ( abs_abs_int @ X )
% 0.32/0.60          = ( abs_abs_int @ Y ) )
% 0.32/0.60        = ( ( X = Y )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff
% 0.32/0.60  thf(fact_5158_abs__eq__iff,axiom,
% 0.32/0.60      ! [X: code_integer,Y: code_integer] :
% 0.32/0.60        ( ( ( abs_abs_Code_integer @ X )
% 0.32/0.60          = ( abs_abs_Code_integer @ Y ) )
% 0.32/0.60        = ( ( X = Y )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff
% 0.32/0.60  thf(fact_5159_abs__eq__iff,axiom,
% 0.32/0.60      ! [X: rat,Y: rat] :
% 0.32/0.60        ( ( ( abs_abs_rat @ X )
% 0.32/0.60          = ( abs_abs_rat @ Y ) )
% 0.32/0.60        = ( ( X = Y )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff
% 0.32/0.60  thf(fact_5160_dvd__trans,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ B @ C )
% 0.32/0.60         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_trans
% 0.32/0.60  thf(fact_5161_dvd__trans,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ B @ C )
% 0.32/0.60         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_trans
% 0.32/0.60  thf(fact_5162_dvd__trans,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ B @ C )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_trans
% 0.32/0.60  thf(fact_5163_dvd__refl,axiom,
% 0.32/0.60      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_refl
% 0.32/0.60  thf(fact_5164_dvd__refl,axiom,
% 0.32/0.60      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_refl
% 0.32/0.60  thf(fact_5165_dvd__refl,axiom,
% 0.32/0.60      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_refl
% 0.32/0.60  thf(fact_5166_minus__equation__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( uminus_uminus_real @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( uminus_uminus_real @ B )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_equation_iff
% 0.32/0.60  thf(fact_5167_minus__equation__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( uminus_uminus_int @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( uminus_uminus_int @ B )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_equation_iff
% 0.32/0.60  thf(fact_5168_minus__equation__iff,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( uminus1482373934393186551omplex @ B )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_equation_iff
% 0.32/0.60  thf(fact_5169_minus__equation__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( uminus1351360451143612070nteger @ B )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_equation_iff
% 0.32/0.60  thf(fact_5170_minus__equation__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( uminus_uminus_rat @ B )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_equation_iff
% 0.32/0.60  thf(fact_5171_equation__minus__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % equation_minus_iff
% 0.32/0.60  thf(fact_5172_equation__minus__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % equation_minus_iff
% 0.32/0.60  thf(fact_5173_equation__minus__iff,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % equation_minus_iff
% 0.32/0.60  thf(fact_5174_equation__minus__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % equation_minus_iff
% 0.32/0.60  thf(fact_5175_equation__minus__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % equation_minus_iff
% 0.32/0.60  thf(fact_5176_abs__less__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_real @ A @ B )
% 0.32/0.60          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_less_iff
% 0.32/0.60  thf(fact_5177_abs__less__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_int @ A @ B )
% 0.32/0.60          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_less_iff
% 0.32/0.60  thf(fact_5178_abs__less__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.60        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.60          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_less_iff
% 0.32/0.60  thf(fact_5179_abs__less__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_rat @ A @ B )
% 0.32/0.60          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_less_iff
% 0.32/0.60  thf(fact_5180_abs__leI,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.60       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.60         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_leI
% 0.32/0.60  thf(fact_5181_abs__leI,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.60       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_leI
% 0.32/0.60  thf(fact_5182_abs__leI,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.60       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.60         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_leI
% 0.32/0.60  thf(fact_5183_abs__leI,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.60       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_leI
% 0.32/0.60  thf(fact_5184_abs__le__D2,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D2
% 0.32/0.60  thf(fact_5185_abs__le__D2,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.60       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D2
% 0.32/0.60  thf(fact_5186_abs__le__D2,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D2
% 0.32/0.60  thf(fact_5187_abs__le__D2,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D2
% 0.32/0.60  thf(fact_5188_abs__le__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_eq_real @ A @ B )
% 0.32/0.60          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_iff
% 0.32/0.60  thf(fact_5189_abs__le__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.60        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.60          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_iff
% 0.32/0.60  thf(fact_5190_abs__le__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.60          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_iff
% 0.32/0.60  thf(fact_5191_abs__le__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.60        = ( ( ord_less_eq_int @ A @ B )
% 0.32/0.60          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_iff
% 0.32/0.60  thf(fact_5192_abs__ge__minus__self,axiom,
% 0.32/0.60      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_minus_self
% 0.32/0.60  thf(fact_5193_abs__ge__minus__self,axiom,
% 0.32/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_minus_self
% 0.32/0.60  thf(fact_5194_abs__ge__minus__self,axiom,
% 0.32/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_minus_self
% 0.32/0.60  thf(fact_5195_abs__ge__minus__self,axiom,
% 0.32/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_minus_self
% 0.32/0.60  thf(fact_5196_abs__minus__le__zero,axiom,
% 0.32/0.60      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_le_zero
% 0.32/0.60  thf(fact_5197_abs__minus__le__zero,axiom,
% 0.32/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_le_zero
% 0.32/0.60  thf(fact_5198_abs__minus__le__zero,axiom,
% 0.32/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_le_zero
% 0.32/0.60  thf(fact_5199_abs__minus__le__zero,axiom,
% 0.32/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_le_zero
% 0.32/0.60  thf(fact_5200_eq__abs__iff_H,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( abs_abs_real @ B ) )
% 0.32/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.60          & ( ( B = A )
% 0.32/0.60            | ( B
% 0.32/0.60              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_abs_iff'
% 0.32/0.60  thf(fact_5201_eq__abs__iff_H,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( abs_abs_Code_integer @ B ) )
% 0.32/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.60          & ( ( B = A )
% 0.32/0.60            | ( B
% 0.32/0.60              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_abs_iff'
% 0.32/0.60  thf(fact_5202_eq__abs__iff_H,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( abs_abs_rat @ B ) )
% 0.32/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.60          & ( ( B = A )
% 0.32/0.60            | ( B
% 0.32/0.60              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_abs_iff'
% 0.32/0.60  thf(fact_5203_eq__abs__iff_H,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( abs_abs_int @ B ) )
% 0.32/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.60          & ( ( B = A )
% 0.32/0.60            | ( B
% 0.32/0.60              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_abs_iff'
% 0.32/0.60  thf(fact_5204_abs__eq__iff_H,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( abs_abs_real @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.32/0.60          & ( ( A = B )
% 0.32/0.60            | ( A
% 0.32/0.60              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff'
% 0.32/0.60  thf(fact_5205_abs__eq__iff_H,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.60          & ( ( A = B )
% 0.32/0.60            | ( A
% 0.32/0.60              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff'
% 0.32/0.60  thf(fact_5206_abs__eq__iff_H,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( abs_abs_rat @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.60          & ( ( A = B )
% 0.32/0.60            | ( A
% 0.32/0.60              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff'
% 0.32/0.60  thf(fact_5207_abs__eq__iff_H,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( abs_abs_int @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.60          & ( ( A = B )
% 0.32/0.60            | ( A
% 0.32/0.60              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_iff'
% 0.32/0.60  thf(fact_5208_abs__if,axiom,
% 0.32/0.60      ( abs_abs_real
% 0.32/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if
% 0.32/0.60  thf(fact_5209_abs__if,axiom,
% 0.32/0.60      ( abs_abs_int
% 0.32/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if
% 0.32/0.60  thf(fact_5210_abs__if,axiom,
% 0.32/0.60      ( abs_abs_Code_integer
% 0.32/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if
% 0.32/0.60  thf(fact_5211_abs__if,axiom,
% 0.32/0.60      ( abs_abs_rat
% 0.32/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if
% 0.32/0.60  thf(fact_5212_abs__of__neg,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( ord_less_real @ A @ zero_zero_real )
% 0.32/0.60       => ( ( abs_abs_real @ A )
% 0.32/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_neg
% 0.32/0.60  thf(fact_5213_abs__of__neg,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( ord_less_int @ A @ zero_zero_int )
% 0.32/0.60       => ( ( abs_abs_int @ A )
% 0.32/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_neg
% 0.32/0.60  thf(fact_5214_abs__of__neg,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.32/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_neg
% 0.32/0.60  thf(fact_5215_abs__of__neg,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.32/0.60       => ( ( abs_abs_rat @ A )
% 0.32/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_neg
% 0.32/0.60  thf(fact_5216_abs__if__raw,axiom,
% 0.32/0.60      ( abs_abs_real
% 0.32/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if_raw
% 0.32/0.60  thf(fact_5217_abs__if__raw,axiom,
% 0.32/0.60      ( abs_abs_int
% 0.32/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if_raw
% 0.32/0.60  thf(fact_5218_abs__if__raw,axiom,
% 0.32/0.60      ( abs_abs_Code_integer
% 0.32/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if_raw
% 0.32/0.60  thf(fact_5219_abs__if__raw,axiom,
% 0.32/0.60      ( abs_abs_rat
% 0.32/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_if_raw
% 0.32/0.60  thf(fact_5220_abs__real__def,axiom,
% 0.32/0.60      ( abs_abs_real
% 0.32/0.60      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_real_def
% 0.32/0.60  thf(fact_5221_abs__le__D1,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D1
% 0.32/0.60  thf(fact_5222_abs__le__D1,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.32/0.60       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D1
% 0.32/0.60  thf(fact_5223_abs__le__D1,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D1
% 0.32/0.60  thf(fact_5224_abs__le__D1,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.32/0.60       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_le_D1
% 0.32/0.60  thf(fact_5225_abs__ge__self,axiom,
% 0.32/0.60      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_self
% 0.32/0.60  thf(fact_5226_abs__ge__self,axiom,
% 0.32/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_self
% 0.32/0.60  thf(fact_5227_abs__ge__self,axiom,
% 0.32/0.60      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_self
% 0.32/0.60  thf(fact_5228_abs__ge__self,axiom,
% 0.32/0.60      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_self
% 0.32/0.60  thf(fact_5229_abs__eq__0__iff,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.32/0.60          = zero_z3403309356797280102nteger )
% 0.32/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_0_iff
% 0.32/0.60  thf(fact_5230_abs__eq__0__iff,axiom,
% 0.32/0.60      ! [A: complex] :
% 0.32/0.60        ( ( ( abs_abs_complex @ A )
% 0.32/0.60          = zero_zero_complex )
% 0.32/0.60        = ( A = zero_zero_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_0_iff
% 0.32/0.60  thf(fact_5231_abs__eq__0__iff,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( ( abs_abs_real @ A )
% 0.32/0.60          = zero_zero_real )
% 0.32/0.60        = ( A = zero_zero_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_0_iff
% 0.32/0.60  thf(fact_5232_abs__eq__0__iff,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( ( abs_abs_rat @ A )
% 0.32/0.60          = zero_zero_rat )
% 0.32/0.60        = ( A = zero_zero_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_0_iff
% 0.32/0.60  thf(fact_5233_abs__eq__0__iff,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( ( abs_abs_int @ A )
% 0.32/0.60          = zero_zero_int )
% 0.32/0.60        = ( A = zero_zero_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_eq_0_iff
% 0.32/0.60  thf(fact_5234_abs__mult,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.60        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult
% 0.32/0.60  thf(fact_5235_abs__mult,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.32/0.60        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult
% 0.32/0.60  thf(fact_5236_abs__mult,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.60        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult
% 0.32/0.60  thf(fact_5237_abs__mult,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.32/0.60        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult
% 0.32/0.60  thf(fact_5238_abs__one,axiom,
% 0.32/0.60      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.32/0.60      = one_one_Code_integer ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_one
% 0.32/0.60  thf(fact_5239_abs__one,axiom,
% 0.32/0.60      ( ( abs_abs_real @ one_one_real )
% 0.32/0.60      = one_one_real ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_one
% 0.32/0.60  thf(fact_5240_abs__one,axiom,
% 0.32/0.60      ( ( abs_abs_rat @ one_one_rat )
% 0.32/0.60      = one_one_rat ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_one
% 0.32/0.60  thf(fact_5241_abs__one,axiom,
% 0.32/0.60      ( ( abs_abs_int @ one_one_int )
% 0.32/0.60      = one_one_int ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_one
% 0.32/0.60  thf(fact_5242_abs__minus__commute,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.32/0.60        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_commute
% 0.32/0.60  thf(fact_5243_abs__minus__commute,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.32/0.60        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_commute
% 0.32/0.60  thf(fact_5244_abs__minus__commute,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.32/0.60        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_commute
% 0.32/0.60  thf(fact_5245_abs__minus__commute,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.32/0.60        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_minus_commute
% 0.32/0.60  thf(fact_5246_tanh__real__gt__neg1,axiom,
% 0.32/0.60      ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 0.32/0.60  
% 0.32/0.60  % tanh_real_gt_neg1
% 0.32/0.60  thf(fact_5247_power__abs,axiom,
% 0.32/0.60      ! [A: code_integer,N: nat] :
% 0.32/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.32/0.60        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_abs
% 0.32/0.60  thf(fact_5248_power__abs,axiom,
% 0.32/0.60      ! [A: rat,N: nat] :
% 0.32/0.60        ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 0.32/0.60        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_abs
% 0.32/0.60  thf(fact_5249_power__abs,axiom,
% 0.32/0.60      ! [A: real,N: nat] :
% 0.32/0.60        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 0.32/0.60        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_abs
% 0.32/0.60  thf(fact_5250_power__abs,axiom,
% 0.32/0.60      ! [A: int,N: nat] :
% 0.32/0.60        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 0.32/0.60        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_abs
% 0.32/0.60  thf(fact_5251_bot__nat__def,axiom,
% 0.32/0.60      bot_bot_nat = zero_zero_nat ).
% 0.32/0.60  
% 0.32/0.60  % bot_nat_def
% 0.32/0.60  thf(fact_5252_dvd__0__left,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 0.32/0.60       => ( A = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5253_dvd__0__left,axiom,
% 0.32/0.60      ! [A: complex] :
% 0.32/0.60        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.32/0.60       => ( A = zero_zero_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5254_dvd__0__left,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.32/0.60       => ( A = zero_zero_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5255_dvd__0__left,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.32/0.60       => ( A = zero_zero_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5256_dvd__0__left,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.32/0.60       => ( A = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5257_dvd__0__left,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.32/0.60       => ( A = zero_zero_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_0_left
% 0.32/0.60  thf(fact_5258_dvd__field__iff,axiom,
% 0.32/0.60      ( dvd_dvd_complex
% 0.32/0.60      = ( ^ [A3: complex,B2: complex] :
% 0.32/0.60            ( ( A3 = zero_zero_complex )
% 0.32/0.60           => ( B2 = zero_zero_complex ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_field_iff
% 0.32/0.60  thf(fact_5259_dvd__field__iff,axiom,
% 0.32/0.60      ( dvd_dvd_real
% 0.32/0.60      = ( ^ [A3: real,B2: real] :
% 0.32/0.60            ( ( A3 = zero_zero_real )
% 0.32/0.60           => ( B2 = zero_zero_real ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_field_iff
% 0.32/0.60  thf(fact_5260_dvd__field__iff,axiom,
% 0.32/0.60      ( dvd_dvd_rat
% 0.32/0.60      = ( ^ [A3: rat,B2: rat] :
% 0.32/0.60            ( ( A3 = zero_zero_rat )
% 0.32/0.60           => ( B2 = zero_zero_rat ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_field_iff
% 0.32/0.60  thf(fact_5261_dvdE,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ~ ! [K3: code_integer] :
% 0.32/0.60              ( A
% 0.32/0.60             != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdE
% 0.32/0.60  thf(fact_5262_dvdE,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.32/0.60       => ~ ! [K3: real] :
% 0.32/0.60              ( A
% 0.32/0.60             != ( times_times_real @ B @ K3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdE
% 0.32/0.60  thf(fact_5263_dvdE,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ B @ A )
% 0.32/0.60       => ~ ! [K3: rat] :
% 0.32/0.60              ( A
% 0.32/0.60             != ( times_times_rat @ B @ K3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdE
% 0.32/0.60  thf(fact_5264_dvdE,axiom,
% 0.32/0.60      ! [B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60       => ~ ! [K3: nat] :
% 0.32/0.60              ( A
% 0.32/0.60             != ( times_times_nat @ B @ K3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdE
% 0.32/0.60  thf(fact_5265_dvdE,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ~ ! [K3: int] :
% 0.32/0.60              ( A
% 0.32/0.60             != ( times_times_int @ B @ K3 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdE
% 0.32/0.60  thf(fact_5266_dvdI,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,K: code_integer] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( times_3573771949741848930nteger @ B @ K ) )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdI
% 0.32/0.60  thf(fact_5267_dvdI,axiom,
% 0.32/0.60      ! [A: real,B: real,K: real] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( times_times_real @ B @ K ) )
% 0.32/0.60       => ( dvd_dvd_real @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdI
% 0.32/0.60  thf(fact_5268_dvdI,axiom,
% 0.32/0.60      ! [A: rat,B: rat,K: rat] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( times_times_rat @ B @ K ) )
% 0.32/0.60       => ( dvd_dvd_rat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdI
% 0.32/0.60  thf(fact_5269_dvdI,axiom,
% 0.32/0.60      ! [A: nat,B: nat,K: nat] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( times_times_nat @ B @ K ) )
% 0.32/0.60       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdI
% 0.32/0.60  thf(fact_5270_dvdI,axiom,
% 0.32/0.60      ! [A: int,B: int,K: int] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( times_times_int @ B @ K ) )
% 0.32/0.60       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvdI
% 0.32/0.60  thf(fact_5271_dvd__def,axiom,
% 0.32/0.60      ( dvd_dvd_Code_integer
% 0.32/0.60      = ( ^ [B2: code_integer,A3: code_integer] :
% 0.32/0.60          ? [K2: code_integer] :
% 0.32/0.60            ( A3
% 0.32/0.60            = ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_def
% 0.32/0.60  thf(fact_5272_dvd__def,axiom,
% 0.32/0.60      ( dvd_dvd_real
% 0.32/0.60      = ( ^ [B2: real,A3: real] :
% 0.32/0.60          ? [K2: real] :
% 0.32/0.60            ( A3
% 0.32/0.60            = ( times_times_real @ B2 @ K2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_def
% 0.32/0.60  thf(fact_5273_dvd__def,axiom,
% 0.32/0.60      ( dvd_dvd_rat
% 0.32/0.60      = ( ^ [B2: rat,A3: rat] :
% 0.32/0.60          ? [K2: rat] :
% 0.32/0.60            ( A3
% 0.32/0.60            = ( times_times_rat @ B2 @ K2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_def
% 0.32/0.60  thf(fact_5274_dvd__def,axiom,
% 0.32/0.60      ( dvd_dvd_nat
% 0.32/0.60      = ( ^ [B2: nat,A3: nat] :
% 0.32/0.60          ? [K2: nat] :
% 0.32/0.60            ( A3
% 0.32/0.60            = ( times_times_nat @ B2 @ K2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_def
% 0.32/0.60  thf(fact_5275_dvd__def,axiom,
% 0.32/0.60      ( dvd_dvd_int
% 0.32/0.60      = ( ^ [B2: int,A3: int] :
% 0.32/0.60          ? [K2: int] :
% 0.32/0.60            ( A3
% 0.32/0.60            = ( times_times_int @ B2 @ K2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_def
% 0.32/0.60  thf(fact_5276_dvd__mult,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult
% 0.32/0.60  thf(fact_5277_dvd__mult,axiom,
% 0.32/0.60      ! [A: real,C: real,B: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ C )
% 0.32/0.60       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult
% 0.32/0.60  thf(fact_5278_dvd__mult,axiom,
% 0.32/0.60      ! [A: rat,C: rat,B: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ C )
% 0.32/0.60       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult
% 0.32/0.60  thf(fact_5279_dvd__mult,axiom,
% 0.32/0.60      ! [A: nat,C: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.60       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult
% 0.32/0.60  thf(fact_5280_dvd__mult,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ C )
% 0.32/0.60       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult
% 0.32/0.60  thf(fact_5281_dvd__mult2,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult2
% 0.32/0.60  thf(fact_5282_dvd__mult2,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.32/0.60       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult2
% 0.32/0.60  thf(fact_5283_dvd__mult2,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.32/0.60       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult2
% 0.32/0.60  thf(fact_5284_dvd__mult2,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult2
% 0.32/0.60  thf(fact_5285_dvd__mult2,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult2
% 0.32/0.60  thf(fact_5286_dvd__mult__left,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_left
% 0.32/0.60  thf(fact_5287_dvd__mult__left,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_real @ A @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_left
% 0.32/0.60  thf(fact_5288_dvd__mult__left,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_rat @ A @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_left
% 0.32/0.60  thf(fact_5289_dvd__mult__left,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_nat @ A @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_left
% 0.32/0.60  thf(fact_5290_dvd__mult__left,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_int @ A @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_left
% 0.32/0.60  thf(fact_5291_dvd__triv__left,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_left
% 0.32/0.60  thf(fact_5292_dvd__triv__left,axiom,
% 0.32/0.60      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_left
% 0.32/0.60  thf(fact_5293_dvd__triv__left,axiom,
% 0.32/0.60      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_left
% 0.32/0.60  thf(fact_5294_dvd__triv__left,axiom,
% 0.32/0.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_left
% 0.32/0.60  thf(fact_5295_dvd__triv__left,axiom,
% 0.32/0.60      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_left
% 0.32/0.60  thf(fact_5296_mult__dvd__mono,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ C @ D )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_dvd_mono
% 0.32/0.60  thf(fact_5297_mult__dvd__mono,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_real @ C @ D )
% 0.32/0.60         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_dvd_mono
% 0.32/0.60  thf(fact_5298_mult__dvd__mono,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_rat @ C @ D )
% 0.32/0.60         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_dvd_mono
% 0.32/0.60  thf(fact_5299_mult__dvd__mono,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ C @ D )
% 0.32/0.60         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_dvd_mono
% 0.32/0.60  thf(fact_5300_mult__dvd__mono,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ C @ D )
% 0.32/0.60         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_dvd_mono
% 0.32/0.60  thf(fact_5301_dvd__mult__right,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_right
% 0.32/0.60  thf(fact_5302_dvd__mult__right,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_real @ B @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_right
% 0.32/0.60  thf(fact_5303_dvd__mult__right,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_rat @ B @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_right
% 0.32/0.60  thf(fact_5304_dvd__mult__right,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_nat @ B @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_right
% 0.32/0.60  thf(fact_5305_dvd__mult__right,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.32/0.60       => ( dvd_dvd_int @ B @ C ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_right
% 0.32/0.60  thf(fact_5306_dvd__triv__right,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_right
% 0.32/0.60  thf(fact_5307_dvd__triv__right,axiom,
% 0.32/0.60      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_right
% 0.32/0.60  thf(fact_5308_dvd__triv__right,axiom,
% 0.32/0.60      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_right
% 0.32/0.60  thf(fact_5309_dvd__triv__right,axiom,
% 0.32/0.60      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_right
% 0.32/0.60  thf(fact_5310_dvd__triv__right,axiom,
% 0.32/0.60      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_triv_right
% 0.32/0.60  thf(fact_5311_division__decomp,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.60       => ? [B7: nat,C5: nat] :
% 0.32/0.60            ( ( A
% 0.32/0.60              = ( times_times_nat @ B7 @ C5 ) )
% 0.32/0.60            & ( dvd_dvd_nat @ B7 @ B )
% 0.32/0.60            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % division_decomp
% 0.32/0.60  thf(fact_5312_division__decomp,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.60       => ? [B7: int,C5: int] :
% 0.32/0.60            ( ( A
% 0.32/0.60              = ( times_times_int @ B7 @ C5 ) )
% 0.32/0.60            & ( dvd_dvd_int @ B7 @ B )
% 0.32/0.60            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % division_decomp
% 0.32/0.60  thf(fact_5313_dvd__productE,axiom,
% 0.32/0.60      ! [P5: nat,A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 0.32/0.60       => ~ ! [X6: nat,Y5: nat] :
% 0.32/0.60              ( ( P5
% 0.32/0.60                = ( times_times_nat @ X6 @ Y5 ) )
% 0.32/0.60             => ( ( dvd_dvd_nat @ X6 @ A )
% 0.32/0.60               => ~ ( dvd_dvd_nat @ Y5 @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_productE
% 0.32/0.60  thf(fact_5314_dvd__productE,axiom,
% 0.32/0.60      ! [P5: int,A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 0.32/0.60       => ~ ! [X6: int,Y5: int] :
% 0.32/0.60              ( ( P5
% 0.32/0.60                = ( times_times_int @ X6 @ Y5 ) )
% 0.32/0.60             => ( ( dvd_dvd_int @ X6 @ A )
% 0.32/0.60               => ~ ( dvd_dvd_int @ Y5 @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_productE
% 0.32/0.60  thf(fact_5315_dvd__add,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ C )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add
% 0.32/0.60  thf(fact_5316_dvd__add,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_real @ A @ C )
% 0.32/0.60         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add
% 0.32/0.60  thf(fact_5317_dvd__add,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_rat @ A @ C )
% 0.32/0.60         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add
% 0.32/0.60  thf(fact_5318_dvd__add,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.60         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add
% 0.32/0.60  thf(fact_5319_dvd__add,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ C )
% 0.32/0.60         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add
% 0.32/0.60  thf(fact_5320_dvd__add__left__iff,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_left_iff
% 0.32/0.60  thf(fact_5321_dvd__add__left__iff,axiom,
% 0.32/0.60      ! [A: real,C: real,B: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ C )
% 0.32/0.60       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_left_iff
% 0.32/0.60  thf(fact_5322_dvd__add__left__iff,axiom,
% 0.32/0.60      ! [A: rat,C: rat,B: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ C )
% 0.32/0.60       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_left_iff
% 0.32/0.60  thf(fact_5323_dvd__add__left__iff,axiom,
% 0.32/0.60      ! [A: nat,C: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_left_iff
% 0.32/0.60  thf(fact_5324_dvd__add__left__iff,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ C )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_left_iff
% 0.32/0.60  thf(fact_5325_dvd__add__right__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_right_iff
% 0.32/0.60  thf(fact_5326_dvd__add__right__iff,axiom,
% 0.32/0.60      ! [A: real,B: real,C: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_right_iff
% 0.32/0.60  thf(fact_5327_dvd__add__right__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat,C: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_right_iff
% 0.32/0.60  thf(fact_5328_dvd__add__right__iff,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_right_iff
% 0.32/0.60  thf(fact_5329_dvd__add__right__iff,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_add_right_iff
% 0.32/0.60  thf(fact_5330_one__dvd,axiom,
% 0.32/0.60      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5331_one__dvd,axiom,
% 0.32/0.60      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5332_one__dvd,axiom,
% 0.32/0.60      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5333_one__dvd,axiom,
% 0.32/0.60      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5334_one__dvd,axiom,
% 0.32/0.60      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5335_one__dvd,axiom,
% 0.32/0.60      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.32/0.60  
% 0.32/0.60  % one_dvd
% 0.32/0.60  thf(fact_5336_unit__imp__dvd,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_imp_dvd
% 0.32/0.60  thf(fact_5337_unit__imp__dvd,axiom,
% 0.32/0.60      ! [B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_imp_dvd
% 0.32/0.60  thf(fact_5338_unit__imp__dvd,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_imp_dvd
% 0.32/0.60  thf(fact_5339_dvd__unit__imp__unit,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_unit_imp_unit
% 0.32/0.60  thf(fact_5340_dvd__unit__imp__unit,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_unit_imp_unit
% 0.32/0.60  thf(fact_5341_dvd__unit__imp__unit,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_unit_imp_unit
% 0.32/0.60  thf(fact_5342_le__minus__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_iff
% 0.32/0.60  thf(fact_5343_le__minus__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_iff
% 0.32/0.60  thf(fact_5344_le__minus__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_iff
% 0.32/0.60  thf(fact_5345_le__minus__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_iff
% 0.32/0.60  thf(fact_5346_minus__le__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.60        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_le_iff
% 0.32/0.60  thf(fact_5347_minus__le__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_le_iff
% 0.32/0.60  thf(fact_5348_minus__le__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.60        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_le_iff
% 0.32/0.60  thf(fact_5349_minus__le__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_le_iff
% 0.32/0.60  thf(fact_5350_le__imp__neg__le,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.60       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_neg_le
% 0.32/0.60  thf(fact_5351_le__imp__neg__le,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.32/0.60       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_neg_le
% 0.32/0.60  thf(fact_5352_le__imp__neg__le,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.60       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_neg_le
% 0.32/0.60  thf(fact_5353_le__imp__neg__le,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ A @ B )
% 0.32/0.60       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_neg_le
% 0.32/0.60  thf(fact_5354_dvd__diff__commute,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff_commute
% 0.32/0.60  thf(fact_5355_dvd__diff__commute,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.32/0.60        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff_commute
% 0.32/0.60  thf(fact_5356_dvd__diff,axiom,
% 0.32/0.60      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ X @ Y )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ X @ Z )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff
% 0.32/0.60  thf(fact_5357_dvd__diff,axiom,
% 0.32/0.60      ! [X: real,Y: real,Z: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ X @ Y )
% 0.32/0.60       => ( ( dvd_dvd_real @ X @ Z )
% 0.32/0.60         => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff
% 0.32/0.60  thf(fact_5358_dvd__diff,axiom,
% 0.32/0.60      ! [X: rat,Y: rat,Z: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ X @ Y )
% 0.32/0.60       => ( ( dvd_dvd_rat @ X @ Z )
% 0.32/0.60         => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff
% 0.32/0.60  thf(fact_5359_dvd__diff,axiom,
% 0.32/0.60      ! [X: int,Y: int,Z: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ X @ Y )
% 0.32/0.60       => ( ( dvd_dvd_int @ X @ Z )
% 0.32/0.60         => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff
% 0.32/0.60  thf(fact_5360_less__minus__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_iff
% 0.32/0.60  thf(fact_5361_less__minus__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_iff
% 0.32/0.60  thf(fact_5362_less__minus__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_iff
% 0.32/0.60  thf(fact_5363_less__minus__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_iff
% 0.32/0.60  thf(fact_5364_minus__less__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.60        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_less_iff
% 0.32/0.60  thf(fact_5365_minus__less__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_less_iff
% 0.32/0.60  thf(fact_5366_minus__less__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_less_iff
% 0.32/0.60  thf(fact_5367_minus__less__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.60        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_less_iff
% 0.32/0.60  thf(fact_5368_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ord_less_real @ A @ B )
% 0.32/0.60       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % verit_negate_coefficient(2)
% 0.32/0.60  thf(fact_5369_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_int @ A @ B )
% 0.32/0.60       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % verit_negate_coefficient(2)
% 0.32/0.60  thf(fact_5370_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.32/0.60       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % verit_negate_coefficient(2)
% 0.32/0.60  thf(fact_5371_verit__negate__coefficient_I2_J,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ord_less_rat @ A @ B )
% 0.32/0.60       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % verit_negate_coefficient(2)
% 0.32/0.60  thf(fact_5372_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.32/0.60              = ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5373_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: complex,A: complex,B: complex] :
% 0.32/0.60        ( ( dvd_dvd_complex @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_complex @ C @ B )
% 0.32/0.60         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.32/0.60              = ( divide1717551699836669952omplex @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5374_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: real,A: real,B: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_real @ C @ B )
% 0.32/0.60         => ( ( ( divide_divide_real @ A @ C )
% 0.32/0.60              = ( divide_divide_real @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5375_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: rat,A: rat,B: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_rat @ C @ B )
% 0.32/0.60         => ( ( ( divide_divide_rat @ A @ C )
% 0.32/0.60              = ( divide_divide_rat @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5376_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: nat,A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60         => ( ( ( divide_divide_nat @ A @ C )
% 0.32/0.60              = ( divide_divide_nat @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5377_dvd__div__eq__iff,axiom,
% 0.32/0.60      ! [C: int,A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.32/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60         => ( ( ( divide_divide_int @ A @ C )
% 0.32/0.60              = ( divide_divide_int @ B @ C ) )
% 0.32/0.60            = ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_iff
% 0.32/0.60  thf(fact_5378_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( divide6298287555418463151nteger @ A @ C )
% 0.32/0.60          = ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5379_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: complex,C: complex,B: complex] :
% 0.32/0.60        ( ( ( divide1717551699836669952omplex @ A @ C )
% 0.32/0.60          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_complex @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_complex @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5380_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: real,C: real,B: real] :
% 0.32/0.60        ( ( ( divide_divide_real @ A @ C )
% 0.32/0.60          = ( divide_divide_real @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_real @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_real @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5381_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: rat,C: rat,B: rat] :
% 0.32/0.60        ( ( ( divide_divide_rat @ A @ C )
% 0.32/0.60          = ( divide_divide_rat @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_rat @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_rat @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5382_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: nat,C: nat,B: nat] :
% 0.32/0.60        ( ( ( divide_divide_nat @ A @ C )
% 0.32/0.60          = ( divide_divide_nat @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_nat @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5383_dvd__div__eq__cancel,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( ( divide_divide_int @ A @ C )
% 0.32/0.60          = ( divide_divide_int @ B @ C ) )
% 0.32/0.60       => ( ( dvd_dvd_int @ C @ A )
% 0.32/0.60         => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60           => ( A = B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_cancel
% 0.32/0.60  thf(fact_5384_div__div__div__same,axiom,
% 0.32/0.60      ! [D: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ D @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 0.32/0.60            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_div_same
% 0.32/0.60  thf(fact_5385_div__div__div__same,axiom,
% 0.32/0.60      ! [D: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ D @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 0.32/0.60            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_div_same
% 0.32/0.60  thf(fact_5386_div__div__div__same,axiom,
% 0.32/0.60      ! [D: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ D @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 0.32/0.60            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_div_same
% 0.32/0.60  thf(fact_5387_neg__numeral__neq__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 0.32/0.60       != ( numeral_numeral_real @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_neq_numeral
% 0.32/0.60  thf(fact_5388_neg__numeral__neq__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.32/0.60       != ( numeral_numeral_int @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_neq_numeral
% 0.32/0.60  thf(fact_5389_neg__numeral__neq__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 0.32/0.60       != ( numera6690914467698888265omplex @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_neq_numeral
% 0.32/0.60  thf(fact_5390_neg__numeral__neq__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.32/0.60       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_neq_numeral
% 0.32/0.60  thf(fact_5391_neg__numeral__neq__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.32/0.60       != ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_neq_numeral
% 0.32/0.60  thf(fact_5392_numeral__neq__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( numeral_numeral_real @ M )
% 0.32/0.60       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_numeral
% 0.32/0.60  thf(fact_5393_numeral__neq__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( numeral_numeral_int @ M )
% 0.32/0.60       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_numeral
% 0.32/0.60  thf(fact_5394_numeral__neq__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( numera6690914467698888265omplex @ M )
% 0.32/0.60       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_numeral
% 0.32/0.60  thf(fact_5395_numeral__neq__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( numera6620942414471956472nteger @ M )
% 0.32/0.60       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_numeral
% 0.32/0.60  thf(fact_5396_numeral__neq__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ( ( numeral_numeral_rat @ M )
% 0.32/0.60       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_numeral
% 0.32/0.60  thf(fact_5397_dvd__power__same,axiom,
% 0.32/0.60      ! [X: code_integer,Y: code_integer,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ X @ Y )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_same
% 0.32/0.60  thf(fact_5398_dvd__power__same,axiom,
% 0.32/0.60      ! [X: nat,Y: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.60       => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_same
% 0.32/0.60  thf(fact_5399_dvd__power__same,axiom,
% 0.32/0.60      ! [X: real,Y: real,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_real @ X @ Y )
% 0.32/0.60       => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_same
% 0.32/0.60  thf(fact_5400_dvd__power__same,axiom,
% 0.32/0.60      ! [X: int,Y: int,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ X @ Y )
% 0.32/0.60       => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_same
% 0.32/0.60  thf(fact_5401_dvd__power__same,axiom,
% 0.32/0.60      ! [X: complex,Y: complex,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_complex @ X @ Y )
% 0.32/0.60       => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_same
% 0.32/0.60  thf(fact_5402_square__eq__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( times_times_real @ A @ A )
% 0.32/0.60          = ( times_times_real @ B @ B ) )
% 0.32/0.60        = ( ( A = B )
% 0.32/0.60          | ( A
% 0.32/0.60            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_iff
% 0.32/0.60  thf(fact_5403_square__eq__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( times_times_int @ A @ A )
% 0.32/0.60          = ( times_times_int @ B @ B ) )
% 0.32/0.60        = ( ( A = B )
% 0.32/0.60          | ( A
% 0.32/0.60            = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_iff
% 0.32/0.60  thf(fact_5404_square__eq__iff,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ( times_times_complex @ A @ A )
% 0.32/0.60          = ( times_times_complex @ B @ B ) )
% 0.32/0.60        = ( ( A = B )
% 0.32/0.60          | ( A
% 0.32/0.60            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_iff
% 0.32/0.60  thf(fact_5405_square__eq__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.32/0.60          = ( times_3573771949741848930nteger @ B @ B ) )
% 0.32/0.60        = ( ( A = B )
% 0.32/0.60          | ( A
% 0.32/0.60            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_iff
% 0.32/0.60  thf(fact_5406_square__eq__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( times_times_rat @ A @ A )
% 0.32/0.60          = ( times_times_rat @ B @ B ) )
% 0.32/0.60        = ( ( A = B )
% 0.32/0.60          | ( A
% 0.32/0.60            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_iff
% 0.32/0.60  thf(fact_5407_minus__mult__commute,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.32/0.60        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_mult_commute
% 0.32/0.60  thf(fact_5408_minus__mult__commute,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_mult_commute
% 0.32/0.60  thf(fact_5409_minus__mult__commute,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.32/0.60        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_mult_commute
% 0.32/0.60  thf(fact_5410_minus__mult__commute,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_mult_commute
% 0.32/0.60  thf(fact_5411_minus__mult__commute,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.32/0.60        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_mult_commute
% 0.32/0.60  thf(fact_5412_group__cancel_Oneg1,axiom,
% 0.32/0.60      ! [A2: real,K: real,A: real] :
% 0.32/0.60        ( ( A2
% 0.32/0.60          = ( plus_plus_real @ K @ A ) )
% 0.32/0.60       => ( ( uminus_uminus_real @ A2 )
% 0.32/0.60          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.neg1
% 0.32/0.60  thf(fact_5413_group__cancel_Oneg1,axiom,
% 0.32/0.60      ! [A2: int,K: int,A: int] :
% 0.32/0.60        ( ( A2
% 0.32/0.60          = ( plus_plus_int @ K @ A ) )
% 0.32/0.60       => ( ( uminus_uminus_int @ A2 )
% 0.32/0.60          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.neg1
% 0.32/0.60  thf(fact_5414_group__cancel_Oneg1,axiom,
% 0.32/0.60      ! [A2: complex,K: complex,A: complex] :
% 0.32/0.60        ( ( A2
% 0.32/0.60          = ( plus_plus_complex @ K @ A ) )
% 0.32/0.60       => ( ( uminus1482373934393186551omplex @ A2 )
% 0.32/0.60          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.neg1
% 0.32/0.60  thf(fact_5415_group__cancel_Oneg1,axiom,
% 0.32/0.60      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.32/0.60        ( ( A2
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.32/0.60       => ( ( uminus1351360451143612070nteger @ A2 )
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.neg1
% 0.32/0.60  thf(fact_5416_group__cancel_Oneg1,axiom,
% 0.32/0.60      ! [A2: rat,K: rat,A: rat] :
% 0.32/0.60        ( ( A2
% 0.32/0.60          = ( plus_plus_rat @ K @ A ) )
% 0.32/0.60       => ( ( uminus_uminus_rat @ A2 )
% 0.32/0.60          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.neg1
% 0.32/0.60  thf(fact_5417_add_Oinverse__distrib__swap,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.32/0.60        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_distrib_swap
% 0.32/0.60  thf(fact_5418_add_Oinverse__distrib__swap,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.60        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_distrib_swap
% 0.32/0.60  thf(fact_5419_add_Oinverse__distrib__swap,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.32/0.60        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_distrib_swap
% 0.32/0.60  thf(fact_5420_add_Oinverse__distrib__swap,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.60        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_distrib_swap
% 0.32/0.60  thf(fact_5421_add_Oinverse__distrib__swap,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.60        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_distrib_swap
% 0.32/0.60  thf(fact_5422_is__num__normalize_I8_J,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.32/0.60        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_num_normalize(8)
% 0.32/0.60  thf(fact_5423_is__num__normalize_I8_J,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.32/0.60        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_num_normalize(8)
% 0.32/0.60  thf(fact_5424_is__num__normalize_I8_J,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.32/0.60        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_num_normalize(8)
% 0.32/0.60  thf(fact_5425_is__num__normalize_I8_J,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.32/0.60        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_num_normalize(8)
% 0.32/0.60  thf(fact_5426_is__num__normalize_I8_J,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.32/0.60        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_num_normalize(8)
% 0.32/0.60  thf(fact_5427_one__neq__neg__one,axiom,
% 0.32/0.60      ( one_one_real
% 0.32/0.60     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_one
% 0.32/0.60  thf(fact_5428_one__neq__neg__one,axiom,
% 0.32/0.60      ( one_one_int
% 0.32/0.60     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_one
% 0.32/0.60  thf(fact_5429_one__neq__neg__one,axiom,
% 0.32/0.60      ( one_one_complex
% 0.32/0.60     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_one
% 0.32/0.60  thf(fact_5430_one__neq__neg__one,axiom,
% 0.32/0.60      ( one_one_Code_integer
% 0.32/0.60     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_one
% 0.32/0.60  thf(fact_5431_one__neq__neg__one,axiom,
% 0.32/0.60      ( one_one_rat
% 0.32/0.60     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_one
% 0.32/0.60  thf(fact_5432_minus__diff__minus,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_minus
% 0.32/0.60  thf(fact_5433_minus__diff__minus,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_minus
% 0.32/0.60  thf(fact_5434_minus__diff__minus,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_minus
% 0.32/0.60  thf(fact_5435_minus__diff__minus,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_minus
% 0.32/0.60  thf(fact_5436_minus__diff__minus,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_minus
% 0.32/0.60  thf(fact_5437_minus__diff__commute,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.32/0.60        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_commute
% 0.32/0.60  thf(fact_5438_minus__diff__commute,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.32/0.60        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_commute
% 0.32/0.60  thf(fact_5439_minus__diff__commute,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 0.32/0.60        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_commute
% 0.32/0.60  thf(fact_5440_minus__diff__commute,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.32/0.60        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_commute
% 0.32/0.60  thf(fact_5441_minus__diff__commute,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.32/0.60        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_diff_commute
% 0.32/0.60  thf(fact_5442_minus__divide__right,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.60        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_right
% 0.32/0.60  thf(fact_5443_minus__divide__right,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.60        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_right
% 0.32/0.60  thf(fact_5444_minus__divide__right,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.60        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_right
% 0.32/0.60  thf(fact_5445_minus__divide__divide,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( divide_divide_real @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_divide
% 0.32/0.60  thf(fact_5446_minus__divide__divide,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_divide
% 0.32/0.60  thf(fact_5447_minus__divide__divide,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( divide_divide_rat @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_divide
% 0.32/0.60  thf(fact_5448_minus__divide__left,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.60        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_left
% 0.32/0.60  thf(fact_5449_minus__divide__left,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.60        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_left
% 0.32/0.60  thf(fact_5450_minus__divide__left,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.60        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minus_divide_left
% 0.32/0.60  thf(fact_5451_div__minus__right,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_minus_right
% 0.32/0.60  thf(fact_5452_div__minus__right,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_minus_right
% 0.32/0.60  thf(fact_5453_gcd__nat_Oextremum,axiom,
% 0.32/0.60      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.32/0.60  
% 0.32/0.60  % gcd_nat.extremum
% 0.32/0.60  thf(fact_5454_gcd__nat_Oextremum__strict,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.32/0.60          & ( zero_zero_nat != A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % gcd_nat.extremum_strict
% 0.32/0.60  thf(fact_5455_gcd__nat_Oextremum__unique,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.32/0.60        = ( A = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % gcd_nat.extremum_unique
% 0.32/0.60  thf(fact_5456_gcd__nat_Onot__eq__extremum,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( A != zero_zero_nat )
% 0.32/0.60        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.32/0.60          & ( A != zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % gcd_nat.not_eq_extremum
% 0.32/0.60  thf(fact_5457_gcd__nat_Oextremum__uniqueI,axiom,
% 0.32/0.60      ! [A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.32/0.60       => ( A = zero_zero_nat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % gcd_nat.extremum_uniqueI
% 0.32/0.60  thf(fact_5458_mod__mod__cancel,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 0.32/0.60          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_mod_cancel
% 0.32/0.60  thf(fact_5459_mod__mod__cancel,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 0.32/0.60          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_mod_cancel
% 0.32/0.60  thf(fact_5460_mod__mod__cancel,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 0.32/0.60          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_mod_cancel
% 0.32/0.60  thf(fact_5461_dvd__mod,axiom,
% 0.32/0.60      ! [K: nat,M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ K @ M )
% 0.32/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.60         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod
% 0.32/0.60  thf(fact_5462_dvd__mod,axiom,
% 0.32/0.60      ! [K: int,M: int,N: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ K @ M )
% 0.32/0.60       => ( ( dvd_dvd_int @ K @ N )
% 0.32/0.60         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod
% 0.32/0.60  thf(fact_5463_dvd__mod,axiom,
% 0.32/0.60      ! [K: code_integer,M: code_integer,N: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ K @ M )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ K @ N )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod
% 0.32/0.60  thf(fact_5464_dvd__mod__imp__dvd,axiom,
% 0.32/0.60      ! [C: nat,A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.32/0.60       => ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_imp_dvd
% 0.32/0.60  thf(fact_5465_dvd__mod__imp__dvd,axiom,
% 0.32/0.60      ! [C: int,A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.32/0.60       => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_imp_dvd
% 0.32/0.60  thf(fact_5466_dvd__mod__imp__dvd,axiom,
% 0.32/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_imp_dvd
% 0.32/0.60  thf(fact_5467_dvd__mod__iff,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.32/0.60          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_iff
% 0.32/0.60  thf(fact_5468_dvd__mod__iff,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.32/0.60          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_iff
% 0.32/0.60  thf(fact_5469_dvd__mod__iff,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mod_iff
% 0.32/0.60  thf(fact_5470_mod__minus__right,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_right
% 0.32/0.60  thf(fact_5471_mod__minus__right,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_right
% 0.32/0.60  thf(fact_5472_mod__minus__cong,axiom,
% 0.32/0.60      ! [A: int,B: int,A4: int] :
% 0.32/0.60        ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.60          = ( modulo_modulo_int @ A4 @ B ) )
% 0.32/0.60       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.60          = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_cong
% 0.32/0.60  thf(fact_5473_mod__minus__cong,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,A4: code_integer] :
% 0.32/0.60        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.32/0.60          = ( modulo364778990260209775nteger @ A4 @ B ) )
% 0.32/0.60       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.32/0.60          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_cong
% 0.32/0.60  thf(fact_5474_mod__minus__eq,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 0.32/0.60        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_eq
% 0.32/0.60  thf(fact_5475_mod__minus__eq,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 0.32/0.60        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_minus_eq
% 0.32/0.60  thf(fact_5476_dvd__diff__nat,axiom,
% 0.32/0.60      ! [K: nat,M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ K @ M )
% 0.32/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.60         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diff_nat
% 0.32/0.60  thf(fact_5477_zdvd__zdiffD,axiom,
% 0.32/0.60      ! [K: int,M: int,N: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.32/0.60       => ( ( dvd_dvd_int @ K @ N )
% 0.32/0.60         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zdvd_zdiffD
% 0.32/0.60  thf(fact_5478_bot__enat__def,axiom,
% 0.32/0.60      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 0.32/0.60  
% 0.32/0.60  % bot_enat_def
% 0.32/0.60  thf(fact_5479_even__minus,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 0.32/0.60        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_minus
% 0.32/0.60  thf(fact_5480_even__minus,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % even_minus
% 0.32/0.60  thf(fact_5481_subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ord_le211207098394363844omplex
% 0.32/0.60          @ ( collect_complex
% 0.32/0.60            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 0.32/0.60          @ ( collect_complex
% 0.32/0.60            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 0.32/0.60        = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % subset_divisors_dvd
% 0.32/0.60  thf(fact_5482_subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( ord_less_eq_set_nat
% 0.32/0.60          @ ( collect_nat
% 0.32/0.60            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 0.32/0.60          @ ( collect_nat
% 0.32/0.60            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 0.32/0.60        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % subset_divisors_dvd
% 0.32/0.60  thf(fact_5483_subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le7084787975880047091nteger
% 0.32/0.60          @ ( collect_Code_integer
% 0.32/0.60            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 0.32/0.60          @ ( collect_Code_integer
% 0.32/0.60            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % subset_divisors_dvd
% 0.32/0.60  thf(fact_5484_subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_eq_set_int
% 0.32/0.60          @ ( collect_int
% 0.32/0.60            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 0.32/0.60          @ ( collect_int
% 0.32/0.60            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 0.32/0.60        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % subset_divisors_dvd
% 0.32/0.60  thf(fact_5485_strict__subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ord_less_set_complex
% 0.32/0.60          @ ( collect_complex
% 0.32/0.60            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 0.32/0.60          @ ( collect_complex
% 0.32/0.60            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 0.32/0.60        = ( ( dvd_dvd_complex @ A @ B )
% 0.32/0.60          & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % strict_subset_divisors_dvd
% 0.32/0.60  thf(fact_5486_strict__subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( ord_less_set_nat
% 0.32/0.60          @ ( collect_nat
% 0.32/0.60            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 0.32/0.60          @ ( collect_nat
% 0.32/0.60            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 0.32/0.60        = ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.60          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % strict_subset_divisors_dvd
% 0.32/0.60  thf(fact_5487_strict__subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ord_less_set_int
% 0.32/0.60          @ ( collect_int
% 0.32/0.60            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 0.32/0.60          @ ( collect_int
% 0.32/0.60            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 0.32/0.60        = ( ( dvd_dvd_int @ A @ B )
% 0.32/0.60          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % strict_subset_divisors_dvd
% 0.32/0.60  thf(fact_5488_strict__subset__divisors__dvd,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ord_le1307284697595431911nteger
% 0.32/0.60          @ ( collect_Code_integer
% 0.32/0.60            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 0.32/0.60          @ ( collect_Code_integer
% 0.32/0.60            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 0.32/0.60        = ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.60          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % strict_subset_divisors_dvd
% 0.32/0.60  thf(fact_5489_power__even__abs,axiom,
% 0.32/0.60      ! [N: nat,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 0.32/0.60          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs
% 0.32/0.60  thf(fact_5490_power__even__abs,axiom,
% 0.32/0.60      ! [N: nat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 0.32/0.60          = ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs
% 0.32/0.60  thf(fact_5491_power__even__abs,axiom,
% 0.32/0.60      ! [N: nat,A: real] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 0.32/0.60          = ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs
% 0.32/0.60  thf(fact_5492_power__even__abs,axiom,
% 0.32/0.60      ! [N: nat,A: int] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 0.32/0.60          = ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_even_abs
% 0.32/0.60  thf(fact_5493_abs__ge__zero,axiom,
% 0.32/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_zero
% 0.32/0.60  thf(fact_5494_abs__ge__zero,axiom,
% 0.32/0.60      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_zero
% 0.32/0.60  thf(fact_5495_abs__ge__zero,axiom,
% 0.32/0.60      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_zero
% 0.32/0.60  thf(fact_5496_abs__ge__zero,axiom,
% 0.32/0.60      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_ge_zero
% 0.32/0.60  thf(fact_5497_abs__of__pos,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_pos
% 0.32/0.60  thf(fact_5498_abs__of__pos,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.60       => ( ( abs_abs_real @ A )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_pos
% 0.32/0.60  thf(fact_5499_abs__of__pos,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.32/0.60       => ( ( abs_abs_rat @ A )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_pos
% 0.32/0.60  thf(fact_5500_abs__of__pos,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.60       => ( ( abs_abs_int @ A )
% 0.32/0.60          = A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_of_pos
% 0.32/0.60  thf(fact_5501_abs__not__less__zero,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_not_less_zero
% 0.32/0.60  thf(fact_5502_abs__not__less__zero,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_not_less_zero
% 0.32/0.60  thf(fact_5503_abs__not__less__zero,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_not_less_zero
% 0.32/0.60  thf(fact_5504_abs__not__less__zero,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_not_less_zero
% 0.32/0.60  thf(fact_5505_uminus__power__if,axiom,
% 0.32/0.60      ! [N: nat,A: real] :
% 0.32/0.60        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.32/0.60            = ( power_power_real @ A @ N ) ) )
% 0.32/0.60        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.32/0.60            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % uminus_power_if
% 0.32/0.60  thf(fact_5506_uminus__power__if,axiom,
% 0.32/0.60      ! [N: nat,A: int] :
% 0.32/0.60        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.32/0.60            = ( power_power_int @ A @ N ) ) )
% 0.32/0.60        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.32/0.60            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % uminus_power_if
% 0.32/0.60  thf(fact_5507_uminus__power__if,axiom,
% 0.32/0.60      ! [N: nat,A: complex] :
% 0.32/0.60        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.32/0.60            = ( power_power_complex @ A @ N ) ) )
% 0.32/0.60        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.32/0.60            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % uminus_power_if
% 0.32/0.60  thf(fact_5508_uminus__power__if,axiom,
% 0.32/0.60      ! [N: nat,A: code_integer] :
% 0.32/0.60        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.32/0.60            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 0.32/0.60        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.32/0.60            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % uminus_power_if
% 0.32/0.60  thf(fact_5509_uminus__power__if,axiom,
% 0.32/0.60      ! [N: nat,A: rat] :
% 0.32/0.60        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.32/0.60            = ( power_power_rat @ A @ N ) ) )
% 0.32/0.60        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.60         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.32/0.60            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % uminus_power_if
% 0.32/0.60  thf(fact_5510_abs__triangle__ineq,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq
% 0.32/0.60  thf(fact_5511_abs__triangle__ineq,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq
% 0.32/0.60  thf(fact_5512_abs__triangle__ineq,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq
% 0.32/0.60  thf(fact_5513_abs__triangle__ineq,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq
% 0.32/0.60  thf(fact_5514_abs__mult__less,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.32/0.60       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 0.32/0.60         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult_less
% 0.32/0.60  thf(fact_5515_abs__mult__less,axiom,
% 0.32/0.60      ! [A: real,C: real,B: real,D: real] :
% 0.32/0.60        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 0.32/0.60       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 0.32/0.60         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult_less
% 0.32/0.60  thf(fact_5516_abs__mult__less,axiom,
% 0.32/0.60      ! [A: rat,C: rat,B: rat,D: rat] :
% 0.32/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.32/0.60       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 0.32/0.60         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult_less
% 0.32/0.60  thf(fact_5517_abs__mult__less,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int,D: int] :
% 0.32/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.32/0.60       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 0.32/0.60         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_mult_less
% 0.32/0.60  thf(fact_5518_abs__triangle__ineq2__sym,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2_sym
% 0.32/0.60  thf(fact_5519_abs__triangle__ineq2__sym,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2_sym
% 0.32/0.60  thf(fact_5520_abs__triangle__ineq2__sym,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2_sym
% 0.32/0.60  thf(fact_5521_abs__triangle__ineq2__sym,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2_sym
% 0.32/0.60  thf(fact_5522_abs__triangle__ineq3,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq3
% 0.32/0.60  thf(fact_5523_abs__triangle__ineq3,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq3
% 0.32/0.60  thf(fact_5524_abs__triangle__ineq3,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq3
% 0.32/0.60  thf(fact_5525_abs__triangle__ineq3,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq3
% 0.32/0.60  thf(fact_5526_abs__triangle__ineq2,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2
% 0.32/0.60  thf(fact_5527_abs__triangle__ineq2,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2
% 0.32/0.60  thf(fact_5528_abs__triangle__ineq2,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2
% 0.32/0.60  thf(fact_5529_abs__triangle__ineq2,axiom,
% 0.32/0.60      ! [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 ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % abs_triangle_ineq2
% 0.32/0.60  thf(fact_5530_nonzero__abs__divide,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( B != zero_zero_real )
% 0.32/0.60       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.60          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_abs_divide
% 0.32/0.60  thf(fact_5531_nonzero__abs__divide,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( B != zero_zero_rat )
% 0.32/0.60       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.60          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_abs_divide
% 0.32/0.60  thf(fact_5532_not__is__unit__0,axiom,
% 0.32/0.60      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.32/0.60  
% 0.32/0.60  % not_is_unit_0
% 0.32/0.60  thf(fact_5533_not__is__unit__0,axiom,
% 0.32/0.60      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.32/0.60  
% 0.32/0.60  % not_is_unit_0
% 0.32/0.60  thf(fact_5534_not__is__unit__0,axiom,
% 0.32/0.60      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.32/0.60  
% 0.32/0.60  % not_is_unit_0
% 0.32/0.60  thf(fact_5535_pinf_I9_J,axiom,
% 0.32/0.60      ! [D: code_integer,S: code_integer] :
% 0.32/0.60      ? [Z5: code_integer] :
% 0.32/0.60      ! [X4: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(9)
% 0.32/0.60  thf(fact_5536_pinf_I9_J,axiom,
% 0.32/0.60      ! [D: real,S: real] :
% 0.32/0.60      ? [Z5: real] :
% 0.32/0.60      ! [X4: real] :
% 0.32/0.60        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.60       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(9)
% 0.32/0.60  thf(fact_5537_pinf_I9_J,axiom,
% 0.32/0.60      ! [D: rat,S: rat] :
% 0.32/0.60      ? [Z5: rat] :
% 0.32/0.60      ! [X4: rat] :
% 0.32/0.60        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.60       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(9)
% 0.32/0.60  thf(fact_5538_pinf_I9_J,axiom,
% 0.32/0.60      ! [D: nat,S: nat] :
% 0.32/0.60      ? [Z5: nat] :
% 0.32/0.60      ! [X4: nat] :
% 0.32/0.60        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.60       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(9)
% 0.32/0.60  thf(fact_5539_pinf_I9_J,axiom,
% 0.32/0.60      ! [D: int,S: int] :
% 0.32/0.60      ? [Z5: int] :
% 0.32/0.60      ! [X4: int] :
% 0.32/0.60        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.60       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(9)
% 0.32/0.60  thf(fact_5540_pinf_I10_J,axiom,
% 0.32/0.60      ! [D: code_integer,S: code_integer] :
% 0.32/0.60      ? [Z5: code_integer] :
% 0.32/0.60      ! [X4: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(10)
% 0.32/0.60  thf(fact_5541_pinf_I10_J,axiom,
% 0.32/0.60      ! [D: real,S: real] :
% 0.32/0.60      ? [Z5: real] :
% 0.32/0.60      ! [X4: real] :
% 0.32/0.60        ( ( ord_less_real @ Z5 @ X4 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(10)
% 0.32/0.60  thf(fact_5542_pinf_I10_J,axiom,
% 0.32/0.60      ! [D: rat,S: rat] :
% 0.32/0.60      ? [Z5: rat] :
% 0.32/0.60      ! [X4: rat] :
% 0.32/0.60        ( ( ord_less_rat @ Z5 @ X4 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(10)
% 0.32/0.60  thf(fact_5543_pinf_I10_J,axiom,
% 0.32/0.60      ! [D: nat,S: nat] :
% 0.32/0.60      ? [Z5: nat] :
% 0.32/0.60      ! [X4: nat] :
% 0.32/0.60        ( ( ord_less_nat @ Z5 @ X4 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(10)
% 0.32/0.60  thf(fact_5544_pinf_I10_J,axiom,
% 0.32/0.60      ! [D: int,S: int] :
% 0.32/0.60      ? [Z5: int] :
% 0.32/0.60      ! [X4: int] :
% 0.32/0.60        ( ( ord_less_int @ Z5 @ X4 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % pinf(10)
% 0.32/0.60  thf(fact_5545_minf_I9_J,axiom,
% 0.32/0.60      ! [D: code_integer,S: code_integer] :
% 0.32/0.60      ? [Z5: code_integer] :
% 0.32/0.60      ! [X4: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(9)
% 0.32/0.60  thf(fact_5546_minf_I9_J,axiom,
% 0.32/0.60      ! [D: real,S: real] :
% 0.32/0.60      ? [Z5: real] :
% 0.32/0.60      ! [X4: real] :
% 0.32/0.60        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.60       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(9)
% 0.32/0.60  thf(fact_5547_minf_I9_J,axiom,
% 0.32/0.60      ! [D: rat,S: rat] :
% 0.32/0.60      ? [Z5: rat] :
% 0.32/0.60      ! [X4: rat] :
% 0.32/0.60        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.60       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(9)
% 0.32/0.60  thf(fact_5548_minf_I9_J,axiom,
% 0.32/0.60      ! [D: nat,S: nat] :
% 0.32/0.60      ? [Z5: nat] :
% 0.32/0.60      ! [X4: nat] :
% 0.32/0.60        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.60       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(9)
% 0.32/0.60  thf(fact_5549_minf_I9_J,axiom,
% 0.32/0.60      ! [D: int,S: int] :
% 0.32/0.60      ? [Z5: int] :
% 0.32/0.60      ! [X4: int] :
% 0.32/0.60        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.60       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 0.32/0.60          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(9)
% 0.32/0.60  thf(fact_5550_minf_I10_J,axiom,
% 0.32/0.60      ! [D: code_integer,S: code_integer] :
% 0.32/0.60      ? [Z5: code_integer] :
% 0.32/0.60      ! [X4: code_integer] :
% 0.32/0.60        ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(10)
% 0.32/0.60  thf(fact_5551_minf_I10_J,axiom,
% 0.32/0.60      ! [D: real,S: real] :
% 0.32/0.60      ? [Z5: real] :
% 0.32/0.60      ! [X4: real] :
% 0.32/0.60        ( ( ord_less_real @ X4 @ Z5 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(10)
% 0.32/0.60  thf(fact_5552_minf_I10_J,axiom,
% 0.32/0.60      ! [D: rat,S: rat] :
% 0.32/0.60      ? [Z5: rat] :
% 0.32/0.60      ! [X4: rat] :
% 0.32/0.60        ( ( ord_less_rat @ X4 @ Z5 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(10)
% 0.32/0.60  thf(fact_5553_minf_I10_J,axiom,
% 0.32/0.60      ! [D: nat,S: nat] :
% 0.32/0.60      ? [Z5: nat] :
% 0.32/0.60      ! [X4: nat] :
% 0.32/0.60        ( ( ord_less_nat @ X4 @ Z5 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(10)
% 0.32/0.60  thf(fact_5554_minf_I10_J,axiom,
% 0.32/0.60      ! [D: int,S: int] :
% 0.32/0.60      ? [Z5: int] :
% 0.32/0.60      ! [X4: int] :
% 0.32/0.60        ( ( ord_less_int @ X4 @ Z5 )
% 0.32/0.60       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 0.32/0.60          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % minf(10)
% 0.32/0.60  thf(fact_5555_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.32/0.60            = zero_z3403309356797280102nteger )
% 0.32/0.60          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5556_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( dvd_dvd_complex @ B @ A )
% 0.32/0.60       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.32/0.60            = zero_zero_complex )
% 0.32/0.60          = ( A = zero_zero_complex ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5557_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( dvd_dvd_real @ B @ A )
% 0.32/0.60       => ( ( ( divide_divide_real @ A @ B )
% 0.32/0.60            = zero_zero_real )
% 0.32/0.60          = ( A = zero_zero_real ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5558_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( dvd_dvd_rat @ B @ A )
% 0.32/0.60       => ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.60            = zero_zero_rat )
% 0.32/0.60          = ( A = zero_zero_rat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5559_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60       => ( ( ( divide_divide_nat @ A @ B )
% 0.32/0.60            = zero_zero_nat )
% 0.32/0.60          = ( A = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5560_dvd__div__eq__0__iff,axiom,
% 0.32/0.60      ! [B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ( ( ( divide_divide_int @ A @ B )
% 0.32/0.60            = zero_zero_int )
% 0.32/0.60          = ( A = zero_zero_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_eq_0_iff
% 0.32/0.60  thf(fact_5561_is__unit__mult__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.32/0.60        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.60          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_unit_mult_iff
% 0.32/0.60  thf(fact_5562_is__unit__mult__iff,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.32/0.60        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.60          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_unit_mult_iff
% 0.32/0.60  thf(fact_5563_is__unit__mult__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.32/0.60        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.60          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % is_unit_mult_iff
% 0.32/0.60  thf(fact_5564_dvd__mult__unit__iff,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff
% 0.32/0.60  thf(fact_5565_dvd__mult__unit__iff,axiom,
% 0.32/0.60      ! [B: nat,A: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff
% 0.32/0.60  thf(fact_5566_dvd__mult__unit__iff,axiom,
% 0.32/0.60      ! [B: int,A: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff
% 0.32/0.60  thf(fact_5567_mult__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff
% 0.32/0.60  thf(fact_5568_mult__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: nat,A: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff
% 0.32/0.60  thf(fact_5569_mult__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: int,A: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff
% 0.32/0.60  thf(fact_5570_dvd__mult__unit__iff_H,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff'
% 0.32/0.60  thf(fact_5571_dvd__mult__unit__iff_H,axiom,
% 0.32/0.60      ! [B: nat,A: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff'
% 0.32/0.60  thf(fact_5572_dvd__mult__unit__iff_H,axiom,
% 0.32/0.60      ! [B: int,A: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_unit_iff'
% 0.32/0.60  thf(fact_5573_mult__unit__dvd__iff_H,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff'
% 0.32/0.60  thf(fact_5574_mult__unit__dvd__iff_H,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff'
% 0.32/0.60  thf(fact_5575_mult__unit__dvd__iff_H,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mult_unit_dvd_iff'
% 0.32/0.60  thf(fact_5576_unit__mult__left__cancel,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.60       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.60            = ( times_3573771949741848930nteger @ A @ C ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_left_cancel
% 0.32/0.60  thf(fact_5577_unit__mult__left__cancel,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.60       => ( ( ( times_times_nat @ A @ B )
% 0.32/0.60            = ( times_times_nat @ A @ C ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_left_cancel
% 0.32/0.60  thf(fact_5578_unit__mult__left__cancel,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.60       => ( ( ( times_times_int @ A @ B )
% 0.32/0.60            = ( times_times_int @ A @ C ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_left_cancel
% 0.32/0.60  thf(fact_5579_unit__mult__right__cancel,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.60       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.32/0.60            = ( times_3573771949741848930nteger @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_right_cancel
% 0.32/0.60  thf(fact_5580_unit__mult__right__cancel,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.60       => ( ( ( times_times_nat @ B @ A )
% 0.32/0.60            = ( times_times_nat @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_right_cancel
% 0.32/0.60  thf(fact_5581_unit__mult__right__cancel,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.60       => ( ( ( times_times_int @ B @ A )
% 0.32/0.60            = ( times_times_int @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_mult_right_cancel
% 0.32/0.60  thf(fact_5582_dvd__div__mult,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 0.32/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult
% 0.32/0.60  thf(fact_5583_dvd__div__mult,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 0.32/0.60          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult
% 0.32/0.60  thf(fact_5584_dvd__div__mult,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 0.32/0.60          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult
% 0.32/0.60  thf(fact_5585_div__mult__swap,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.60          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_swap
% 0.32/0.60  thf(fact_5586_div__mult__swap,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.32/0.60          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_swap
% 0.32/0.60  thf(fact_5587_div__mult__swap,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.32/0.60          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_swap
% 0.32/0.60  thf(fact_5588_div__div__eq__right,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.60            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_eq_right
% 0.32/0.60  thf(fact_5589_div__div__eq__right,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.32/0.60            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_eq_right
% 0.32/0.60  thf(fact_5590_div__div__eq__right,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.32/0.60            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_div_eq_right
% 0.32/0.60  thf(fact_5591_dvd__div__mult2__eq,axiom,
% 0.32/0.60      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.60          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult2_eq
% 0.32/0.60  thf(fact_5592_dvd__div__mult2__eq,axiom,
% 0.32/0.60      ! [B: nat,C: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 0.32/0.60       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.60          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult2_eq
% 0.32/0.60  thf(fact_5593_dvd__div__mult2__eq,axiom,
% 0.32/0.60      ! [B: int,C: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 0.32/0.60       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.60          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_mult2_eq
% 0.32/0.60  thf(fact_5594_dvd__mult__imp__div,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_imp_div
% 0.32/0.60  thf(fact_5595_dvd__mult__imp__div,axiom,
% 0.32/0.60      ! [A: nat,C: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 0.32/0.60       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_imp_div
% 0.32/0.60  thf(fact_5596_dvd__mult__imp__div,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 0.32/0.60       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_mult_imp_div
% 0.32/0.60  thf(fact_5597_div__mult__div__if__dvd,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ D @ C )
% 0.32/0.60         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 0.32/0.60            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_div_if_dvd
% 0.32/0.60  thf(fact_5598_div__mult__div__if__dvd,axiom,
% 0.32/0.60      ! [B: nat,A: nat,D: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60       => ( ( dvd_dvd_nat @ D @ C )
% 0.32/0.60         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 0.32/0.60            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_div_if_dvd
% 0.32/0.60  thf(fact_5599_div__mult__div__if__dvd,axiom,
% 0.32/0.60      ! [B: int,A: int,D: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ( ( dvd_dvd_int @ D @ C )
% 0.32/0.60         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 0.32/0.60            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_mult_div_if_dvd
% 0.32/0.60  thf(fact_5600_not__numeral__le__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_le_neg_numeral
% 0.32/0.60  thf(fact_5601_not__numeral__le__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_le_neg_numeral
% 0.32/0.60  thf(fact_5602_not__numeral__le__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_le_neg_numeral
% 0.32/0.60  thf(fact_5603_not__numeral__le__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_le_neg_numeral
% 0.32/0.60  thf(fact_5604_neg__numeral__le__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_le_numeral
% 0.32/0.60  thf(fact_5605_neg__numeral__le__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_le_numeral
% 0.32/0.60  thf(fact_5606_neg__numeral__le__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_le_numeral
% 0.32/0.60  thf(fact_5607_neg__numeral__le__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_le_numeral
% 0.32/0.60  thf(fact_5608_zero__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( zero_zero_real
% 0.32/0.60       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_numeral
% 0.32/0.60  thf(fact_5609_zero__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( zero_zero_int
% 0.32/0.60       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_numeral
% 0.32/0.60  thf(fact_5610_zero__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( zero_zero_complex
% 0.32/0.60       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_numeral
% 0.32/0.60  thf(fact_5611_zero__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( zero_z3403309356797280102nteger
% 0.32/0.60       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_numeral
% 0.32/0.60  thf(fact_5612_zero__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( zero_zero_rat
% 0.32/0.60       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_numeral
% 0.32/0.60  thf(fact_5613_div__plus__div__distrib__dvd__right,axiom,
% 0.32/0.60      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_right
% 0.32/0.60  thf(fact_5614_div__plus__div__distrib__dvd__right,axiom,
% 0.32/0.60      ! [C: nat,B: nat,A: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_right
% 0.32/0.60  thf(fact_5615_div__plus__div__distrib__dvd__right,axiom,
% 0.32/0.60      ! [C: int,B: int,A: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ B )
% 0.32/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_right
% 0.32/0.60  thf(fact_5616_div__plus__div__distrib__dvd__left,axiom,
% 0.32/0.60      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ C @ A )
% 0.32/0.60       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_left
% 0.32/0.60  thf(fact_5617_div__plus__div__distrib__dvd__left,axiom,
% 0.32/0.60      ! [C: nat,A: nat,B: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ C @ A )
% 0.32/0.60       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.32/0.60          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_left
% 0.32/0.60  thf(fact_5618_div__plus__div__distrib__dvd__left,axiom,
% 0.32/0.60      ! [C: int,A: int,B: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ C @ A )
% 0.32/0.60       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.32/0.60          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_plus_div_distrib_dvd_left
% 0.32/0.60  thf(fact_5619_unit__div__cancel,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.60       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.32/0.60            = ( divide6298287555418463151nteger @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_div_cancel
% 0.32/0.60  thf(fact_5620_unit__div__cancel,axiom,
% 0.32/0.60      ! [A: nat,B: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.60       => ( ( ( divide_divide_nat @ B @ A )
% 0.32/0.60            = ( divide_divide_nat @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_div_cancel
% 0.32/0.60  thf(fact_5621_unit__div__cancel,axiom,
% 0.32/0.60      ! [A: int,B: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.60       => ( ( ( divide_divide_int @ B @ A )
% 0.32/0.60            = ( divide_divide_int @ C @ A ) )
% 0.32/0.60          = ( B = C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % unit_div_cancel
% 0.32/0.60  thf(fact_5622_div__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_unit_dvd_iff
% 0.32/0.60  thf(fact_5623_div__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: nat,A: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_unit_dvd_iff
% 0.32/0.60  thf(fact_5624_div__unit__dvd__iff,axiom,
% 0.32/0.60      ! [B: int,A: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_unit_dvd_iff
% 0.32/0.60  thf(fact_5625_dvd__div__unit__iff,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.60       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_unit_iff
% 0.32/0.60  thf(fact_5626_dvd__div__unit__iff,axiom,
% 0.32/0.60      ! [B: nat,A: nat,C: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.60       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_unit_iff
% 0.32/0.60  thf(fact_5627_dvd__div__unit__iff,axiom,
% 0.32/0.60      ! [B: int,A: int,C: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.32/0.60          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_div_unit_iff
% 0.32/0.60  thf(fact_5628_neg__numeral__less__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_less_numeral
% 0.32/0.60  thf(fact_5629_neg__numeral__less__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_less_numeral
% 0.32/0.60  thf(fact_5630_neg__numeral__less__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_less_numeral
% 0.32/0.60  thf(fact_5631_neg__numeral__less__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_numeral_less_numeral
% 0.32/0.60  thf(fact_5632_not__numeral__less__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_less_neg_numeral
% 0.32/0.60  thf(fact_5633_not__numeral__less__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_less_neg_numeral
% 0.32/0.60  thf(fact_5634_not__numeral__less__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_less_neg_numeral
% 0.32/0.60  thf(fact_5635_not__numeral__less__neg__numeral,axiom,
% 0.32/0.60      ! [M: num,N: num] :
% 0.32/0.60        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % not_numeral_less_neg_numeral
% 0.32/0.60  thf(fact_5636_le__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(4)
% 0.32/0.60  thf(fact_5637_le__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(4)
% 0.32/0.60  thf(fact_5638_le__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(4)
% 0.32/0.60  thf(fact_5639_le__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(4)
% 0.32/0.60  thf(fact_5640_le__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(2)
% 0.32/0.60  thf(fact_5641_le__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(2)
% 0.32/0.60  thf(fact_5642_le__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(2)
% 0.32/0.60  thf(fact_5643_le__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.32/0.60  
% 0.32/0.60  % le_minus_one_simps(2)
% 0.32/0.60  thf(fact_5644_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( uminus_uminus_real @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( plus_plus_real @ A @ B )
% 0.32/0.60          = zero_zero_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_eq_iff_add_eq_0
% 0.32/0.60  thf(fact_5645_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( uminus_uminus_int @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( plus_plus_int @ A @ B )
% 0.32/0.60          = zero_zero_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_eq_iff_add_eq_0
% 0.32/0.60  thf(fact_5646_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( plus_plus_complex @ A @ B )
% 0.32/0.60          = zero_zero_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_eq_iff_add_eq_0
% 0.32/0.60  thf(fact_5647_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_eq_iff_add_eq_0
% 0.32/0.60  thf(fact_5648_neg__eq__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( uminus_uminus_rat @ A )
% 0.32/0.60          = B )
% 0.32/0.60        = ( ( plus_plus_rat @ A @ B )
% 0.32/0.60          = zero_zero_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % neg_eq_iff_add_eq_0
% 0.32/0.60  thf(fact_5649_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_real @ B ) )
% 0.32/0.60        = ( ( plus_plus_real @ A @ B )
% 0.32/0.60          = zero_zero_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_neg_iff_add_eq_0
% 0.32/0.60  thf(fact_5650_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_int @ B ) )
% 0.32/0.60        = ( ( plus_plus_int @ A @ B )
% 0.32/0.60          = zero_zero_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_neg_iff_add_eq_0
% 0.32/0.60  thf(fact_5651_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60        = ( ( plus_plus_complex @ A @ B )
% 0.32/0.60          = zero_zero_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_neg_iff_add_eq_0
% 0.32/0.60  thf(fact_5652_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus1351360451143612070nteger @ B ) )
% 0.32/0.60        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_neg_iff_add_eq_0
% 0.32/0.60  thf(fact_5653_eq__neg__iff__add__eq__0,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( A
% 0.32/0.60          = ( uminus_uminus_rat @ B ) )
% 0.32/0.60        = ( ( plus_plus_rat @ A @ B )
% 0.32/0.60          = zero_zero_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % eq_neg_iff_add_eq_0
% 0.32/0.60  thf(fact_5654_add_Oinverse__unique,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( plus_plus_real @ A @ B )
% 0.32/0.60          = zero_zero_real )
% 0.32/0.60       => ( ( uminus_uminus_real @ A )
% 0.32/0.60          = B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_unique
% 0.32/0.60  thf(fact_5655_add_Oinverse__unique,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.60          = zero_zero_int )
% 0.32/0.60       => ( ( uminus_uminus_int @ A )
% 0.32/0.60          = B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_unique
% 0.32/0.60  thf(fact_5656_add_Oinverse__unique,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ( plus_plus_complex @ A @ B )
% 0.32/0.60          = zero_zero_complex )
% 0.32/0.60       => ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.60          = B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_unique
% 0.32/0.60  thf(fact_5657_add_Oinverse__unique,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger )
% 0.32/0.60       => ( ( uminus1351360451143612070nteger @ A )
% 0.32/0.60          = B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_unique
% 0.32/0.60  thf(fact_5658_add_Oinverse__unique,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.60          = zero_zero_rat )
% 0.32/0.60       => ( ( uminus_uminus_rat @ A )
% 0.32/0.60          = B ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add.inverse_unique
% 0.32/0.60  thf(fact_5659_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.60      ! [A: real] :
% 0.32/0.60        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.32/0.60        = zero_zero_real ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_left_minus
% 0.32/0.60  thf(fact_5660_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.60      ! [A: int] :
% 0.32/0.60        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.32/0.60        = zero_zero_int ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_left_minus
% 0.32/0.60  thf(fact_5661_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.60      ! [A: complex] :
% 0.32/0.60        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.32/0.60        = zero_zero_complex ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_left_minus
% 0.32/0.60  thf(fact_5662_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.60      ! [A: code_integer] :
% 0.32/0.60        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.32/0.60        = zero_z3403309356797280102nteger ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_left_minus
% 0.32/0.60  thf(fact_5663_ab__group__add__class_Oab__left__minus,axiom,
% 0.32/0.60      ! [A: rat] :
% 0.32/0.60        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.32/0.60        = zero_zero_rat ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_left_minus
% 0.32/0.60  thf(fact_5664_add__eq__0__iff,axiom,
% 0.32/0.60      ! [A: real,B: real] :
% 0.32/0.60        ( ( ( plus_plus_real @ A @ B )
% 0.32/0.60          = zero_zero_real )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_real @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_eq_0_iff
% 0.32/0.60  thf(fact_5665_add__eq__0__iff,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( plus_plus_int @ A @ B )
% 0.32/0.60          = zero_zero_int )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_eq_0_iff
% 0.32/0.60  thf(fact_5666_add__eq__0__iff,axiom,
% 0.32/0.60      ! [A: complex,B: complex] :
% 0.32/0.60        ( ( ( plus_plus_complex @ A @ B )
% 0.32/0.60          = zero_zero_complex )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_eq_0_iff
% 0.32/0.60  thf(fact_5667_add__eq__0__iff,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_eq_0_iff
% 0.32/0.60  thf(fact_5668_add__eq__0__iff,axiom,
% 0.32/0.60      ! [A: rat,B: rat] :
% 0.32/0.60        ( ( ( plus_plus_rat @ A @ B )
% 0.32/0.60          = zero_zero_rat )
% 0.32/0.60        = ( B
% 0.32/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % add_eq_0_iff
% 0.32/0.60  thf(fact_5669_zero__neq__neg__one,axiom,
% 0.32/0.60      ( zero_zero_real
% 0.32/0.60     != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_one
% 0.32/0.60  thf(fact_5670_zero__neq__neg__one,axiom,
% 0.32/0.60      ( zero_zero_int
% 0.32/0.60     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_one
% 0.32/0.60  thf(fact_5671_zero__neq__neg__one,axiom,
% 0.32/0.60      ( zero_zero_complex
% 0.32/0.60     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_one
% 0.32/0.60  thf(fact_5672_zero__neq__neg__one,axiom,
% 0.32/0.60      ( zero_z3403309356797280102nteger
% 0.32/0.60     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_one
% 0.32/0.60  thf(fact_5673_zero__neq__neg__one,axiom,
% 0.32/0.60      ( zero_zero_rat
% 0.32/0.60     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zero_neq_neg_one
% 0.32/0.60  thf(fact_5674_less__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(2)
% 0.32/0.60  thf(fact_5675_less__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(2)
% 0.32/0.60  thf(fact_5676_less__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(2)
% 0.32/0.60  thf(fact_5677_less__minus__one__simps_I2_J,axiom,
% 0.32/0.60      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(2)
% 0.32/0.60  thf(fact_5678_less__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(4)
% 0.32/0.60  thf(fact_5679_less__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(4)
% 0.32/0.60  thf(fact_5680_less__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(4)
% 0.32/0.60  thf(fact_5681_less__minus__one__simps_I4_J,axiom,
% 0.32/0.60      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_minus_one_simps(4)
% 0.32/0.60  thf(fact_5682_numeral__times__minus__swap,axiom,
% 0.32/0.60      ! [W: num,X: real] :
% 0.32/0.60        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 0.32/0.60        = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_times_minus_swap
% 0.32/0.60  thf(fact_5683_numeral__times__minus__swap,axiom,
% 0.32/0.60      ! [W: num,X: int] :
% 0.32/0.60        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 0.32/0.60        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_times_minus_swap
% 0.32/0.60  thf(fact_5684_numeral__times__minus__swap,axiom,
% 0.32/0.60      ! [W: num,X: complex] :
% 0.32/0.60        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 0.32/0.60        = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_times_minus_swap
% 0.32/0.60  thf(fact_5685_numeral__times__minus__swap,axiom,
% 0.32/0.60      ! [W: num,X: code_integer] :
% 0.32/0.60        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 0.32/0.60        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_times_minus_swap
% 0.32/0.60  thf(fact_5686_numeral__times__minus__swap,axiom,
% 0.32/0.60      ! [W: num,X: rat] :
% 0.32/0.60        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 0.32/0.60        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_times_minus_swap
% 0.32/0.60  thf(fact_5687_div__power,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.60       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 0.32/0.60          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_power
% 0.32/0.60  thf(fact_5688_div__power,axiom,
% 0.32/0.60      ! [B: nat,A: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.60       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 0.32/0.60          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_power
% 0.32/0.60  thf(fact_5689_div__power,axiom,
% 0.32/0.60      ! [B: int,A: int,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ B @ A )
% 0.32/0.60       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 0.32/0.60          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % div_power
% 0.32/0.60  thf(fact_5690_nonzero__minus__divide__divide,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( B != zero_zero_real )
% 0.32/0.60       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.32/0.60          = ( divide_divide_real @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_divide
% 0.32/0.60  thf(fact_5691_nonzero__minus__divide__divide,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( B != zero_zero_complex )
% 0.32/0.60       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.32/0.60          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_divide
% 0.32/0.60  thf(fact_5692_nonzero__minus__divide__divide,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( B != zero_zero_rat )
% 0.32/0.60       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.32/0.60          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_divide
% 0.32/0.60  thf(fact_5693_nonzero__minus__divide__right,axiom,
% 0.32/0.60      ! [B: real,A: real] :
% 0.32/0.60        ( ( B != zero_zero_real )
% 0.32/0.60       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.60          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_right
% 0.32/0.60  thf(fact_5694_nonzero__minus__divide__right,axiom,
% 0.32/0.60      ! [B: complex,A: complex] :
% 0.32/0.60        ( ( B != zero_zero_complex )
% 0.32/0.60       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.60          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_right
% 0.32/0.60  thf(fact_5695_nonzero__minus__divide__right,axiom,
% 0.32/0.60      ! [B: rat,A: rat] :
% 0.32/0.60        ( ( B != zero_zero_rat )
% 0.32/0.60       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.60          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nonzero_minus_divide_right
% 0.32/0.60  thf(fact_5696_one__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( one_one_real
% 0.32/0.60       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_numeral
% 0.32/0.60  thf(fact_5697_one__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( one_one_int
% 0.32/0.60       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_numeral
% 0.32/0.60  thf(fact_5698_one__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( one_one_complex
% 0.32/0.60       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_numeral
% 0.32/0.60  thf(fact_5699_one__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( one_one_Code_integer
% 0.32/0.60       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_numeral
% 0.32/0.60  thf(fact_5700_one__neq__neg__numeral,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( one_one_rat
% 0.32/0.60       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % one_neq_neg_numeral
% 0.32/0.60  thf(fact_5701_numeral__neq__neg__one,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( numeral_numeral_real @ N )
% 0.32/0.60       != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_one
% 0.32/0.60  thf(fact_5702_numeral__neq__neg__one,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( numeral_numeral_int @ N )
% 0.32/0.60       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_one
% 0.32/0.60  thf(fact_5703_numeral__neq__neg__one,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( numera6690914467698888265omplex @ N )
% 0.32/0.60       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_one
% 0.32/0.60  thf(fact_5704_numeral__neq__neg__one,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( numera6620942414471956472nteger @ N )
% 0.32/0.60       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_one
% 0.32/0.60  thf(fact_5705_numeral__neq__neg__one,axiom,
% 0.32/0.60      ! [N: num] :
% 0.32/0.60        ( ( numeral_numeral_rat @ N )
% 0.32/0.60       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.60  
% 0.32/0.60  % numeral_neq_neg_one
% 0.32/0.60  thf(fact_5706_square__eq__1__iff,axiom,
% 0.32/0.60      ! [X: real] :
% 0.32/0.60        ( ( ( times_times_real @ X @ X )
% 0.32/0.60          = one_one_real )
% 0.32/0.60        = ( ( X = one_one_real )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_1_iff
% 0.32/0.60  thf(fact_5707_square__eq__1__iff,axiom,
% 0.32/0.60      ! [X: int] :
% 0.32/0.60        ( ( ( times_times_int @ X @ X )
% 0.32/0.60          = one_one_int )
% 0.32/0.60        = ( ( X = one_one_int )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_1_iff
% 0.32/0.60  thf(fact_5708_square__eq__1__iff,axiom,
% 0.32/0.60      ! [X: complex] :
% 0.32/0.60        ( ( ( times_times_complex @ X @ X )
% 0.32/0.60          = one_one_complex )
% 0.32/0.60        = ( ( X = one_one_complex )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_1_iff
% 0.32/0.60  thf(fact_5709_square__eq__1__iff,axiom,
% 0.32/0.60      ! [X: code_integer] :
% 0.32/0.60        ( ( ( times_3573771949741848930nteger @ X @ X )
% 0.32/0.60          = one_one_Code_integer )
% 0.32/0.60        = ( ( X = one_one_Code_integer )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_1_iff
% 0.32/0.60  thf(fact_5710_square__eq__1__iff,axiom,
% 0.32/0.60      ! [X: rat] :
% 0.32/0.60        ( ( ( times_times_rat @ X @ X )
% 0.32/0.60          = one_one_rat )
% 0.32/0.60        = ( ( X = one_one_rat )
% 0.32/0.60          | ( X
% 0.32/0.60            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % square_eq_1_iff
% 0.32/0.60  thf(fact_5711_mod__eq__0__iff__dvd,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( ( modulo_modulo_nat @ A @ B )
% 0.32/0.60          = zero_zero_nat )
% 0.32/0.60        = ( dvd_dvd_nat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_eq_0_iff_dvd
% 0.32/0.60  thf(fact_5712_mod__eq__0__iff__dvd,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.60          = zero_zero_int )
% 0.32/0.60        = ( dvd_dvd_int @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_eq_0_iff_dvd
% 0.32/0.60  thf(fact_5713_mod__eq__0__iff__dvd,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_eq_0_iff_dvd
% 0.32/0.60  thf(fact_5714_dvd__eq__mod__eq__0,axiom,
% 0.32/0.60      ( dvd_dvd_nat
% 0.32/0.60      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.60            ( ( modulo_modulo_nat @ B2 @ A3 )
% 0.32/0.60            = zero_zero_nat ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_eq_mod_eq_0
% 0.32/0.60  thf(fact_5715_dvd__eq__mod__eq__0,axiom,
% 0.32/0.60      ( dvd_dvd_int
% 0.32/0.60      = ( ^ [A3: int,B2: int] :
% 0.32/0.60            ( ( modulo_modulo_int @ B2 @ A3 )
% 0.32/0.60            = zero_zero_int ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_eq_mod_eq_0
% 0.32/0.60  thf(fact_5716_dvd__eq__mod__eq__0,axiom,
% 0.32/0.60      ( dvd_dvd_Code_integer
% 0.32/0.60      = ( ^ [A3: code_integer,B2: code_integer] :
% 0.32/0.60            ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 0.32/0.60            = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_eq_mod_eq_0
% 0.32/0.60  thf(fact_5717_mod__0__imp__dvd,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60        ( ( ( modulo_modulo_nat @ A @ B )
% 0.32/0.60          = zero_zero_nat )
% 0.32/0.60       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_0_imp_dvd
% 0.32/0.60  thf(fact_5718_mod__0__imp__dvd,axiom,
% 0.32/0.60      ! [A: int,B: int] :
% 0.32/0.60        ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.60          = zero_zero_int )
% 0.32/0.60       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_0_imp_dvd
% 0.32/0.60  thf(fact_5719_mod__0__imp__dvd,axiom,
% 0.32/0.60      ! [A: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.32/0.60          = zero_z3403309356797280102nteger )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_0_imp_dvd
% 0.32/0.60  thf(fact_5720_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_real
% 0.32/0.60      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.60  thf(fact_5721_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_int
% 0.32/0.60      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.60  thf(fact_5722_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_complex
% 0.32/0.60      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.60  thf(fact_5723_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_8373710615458151222nteger
% 0.32/0.60      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.60  thf(fact_5724_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_rat
% 0.32/0.60      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.32/0.60  thf(fact_5725_diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_real
% 0.32/0.60      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_conv_add_uminus
% 0.32/0.60  thf(fact_5726_diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_int
% 0.32/0.60      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_conv_add_uminus
% 0.32/0.60  thf(fact_5727_diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_complex
% 0.32/0.60      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_conv_add_uminus
% 0.32/0.60  thf(fact_5728_diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_8373710615458151222nteger
% 0.32/0.60      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_conv_add_uminus
% 0.32/0.60  thf(fact_5729_diff__conv__add__uminus,axiom,
% 0.32/0.60      ( minus_minus_rat
% 0.32/0.60      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % diff_conv_add_uminus
% 0.32/0.60  thf(fact_5730_group__cancel_Osub2,axiom,
% 0.32/0.60      ! [B3: real,K: real,B: real,A: real] :
% 0.32/0.60        ( ( B3
% 0.32/0.60          = ( plus_plus_real @ K @ B ) )
% 0.32/0.60       => ( ( minus_minus_real @ A @ B3 )
% 0.32/0.60          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.sub2
% 0.32/0.60  thf(fact_5731_group__cancel_Osub2,axiom,
% 0.32/0.60      ! [B3: int,K: int,B: int,A: int] :
% 0.32/0.60        ( ( B3
% 0.32/0.60          = ( plus_plus_int @ K @ B ) )
% 0.32/0.60       => ( ( minus_minus_int @ A @ B3 )
% 0.32/0.60          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.sub2
% 0.32/0.60  thf(fact_5732_group__cancel_Osub2,axiom,
% 0.32/0.60      ! [B3: complex,K: complex,B: complex,A: complex] :
% 0.32/0.60        ( ( B3
% 0.32/0.60          = ( plus_plus_complex @ K @ B ) )
% 0.32/0.60       => ( ( minus_minus_complex @ A @ B3 )
% 0.32/0.60          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.sub2
% 0.32/0.60  thf(fact_5733_group__cancel_Osub2,axiom,
% 0.32/0.60      ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.60        ( ( B3
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.32/0.60       => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 0.32/0.60          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.sub2
% 0.32/0.60  thf(fact_5734_group__cancel_Osub2,axiom,
% 0.32/0.60      ! [B3: rat,K: rat,B: rat,A: rat] :
% 0.32/0.60        ( ( B3
% 0.32/0.60          = ( plus_plus_rat @ K @ B ) )
% 0.32/0.60       => ( ( minus_minus_rat @ A @ B3 )
% 0.32/0.60          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % group_cancel.sub2
% 0.32/0.60  thf(fact_5735_le__imp__power__dvd,axiom,
% 0.32/0.60      ! [M: nat,N: nat,A: code_integer] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_power_dvd
% 0.32/0.60  thf(fact_5736_le__imp__power__dvd,axiom,
% 0.32/0.60      ! [M: nat,N: nat,A: nat] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_power_dvd
% 0.32/0.60  thf(fact_5737_le__imp__power__dvd,axiom,
% 0.32/0.60      ! [M: nat,N: nat,A: real] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_power_dvd
% 0.32/0.60  thf(fact_5738_le__imp__power__dvd,axiom,
% 0.32/0.60      ! [M: nat,N: nat,A: int] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_power_dvd
% 0.32/0.60  thf(fact_5739_le__imp__power__dvd,axiom,
% 0.32/0.60      ! [M: nat,N: nat,A: complex] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % le_imp_power_dvd
% 0.32/0.60  thf(fact_5740_power__le__dvd,axiom,
% 0.32/0.60      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 0.32/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_dvd
% 0.32/0.60  thf(fact_5741_power__le__dvd,axiom,
% 0.32/0.60      ! [A: nat,N: nat,B: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 0.32/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_dvd
% 0.32/0.60  thf(fact_5742_power__le__dvd,axiom,
% 0.32/0.60      ! [A: real,N: nat,B: real,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 0.32/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_dvd
% 0.32/0.60  thf(fact_5743_power__le__dvd,axiom,
% 0.32/0.60      ! [A: int,N: nat,B: int,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 0.32/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_dvd
% 0.32/0.60  thf(fact_5744_power__le__dvd,axiom,
% 0.32/0.60      ! [A: complex,N: nat,B: complex,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 0.32/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % power_le_dvd
% 0.32/0.60  thf(fact_5745_dvd__power__le,axiom,
% 0.32/0.60      ! [X: code_integer,Y: code_integer,N: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_Code_integer @ X @ Y )
% 0.32/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_le
% 0.32/0.60  thf(fact_5746_dvd__power__le,axiom,
% 0.32/0.60      ! [X: nat,Y: nat,N: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_le
% 0.32/0.60  thf(fact_5747_dvd__power__le,axiom,
% 0.32/0.60      ! [X: real,Y: real,N: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_real @ X @ Y )
% 0.32/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60         => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_le
% 0.32/0.60  thf(fact_5748_dvd__power__le,axiom,
% 0.32/0.60      ! [X: int,Y: int,N: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_int @ X @ Y )
% 0.32/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60         => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_le
% 0.32/0.60  thf(fact_5749_dvd__power__le,axiom,
% 0.32/0.60      ! [X: complex,Y: complex,N: nat,M: nat] :
% 0.32/0.60        ( ( dvd_dvd_complex @ X @ Y )
% 0.32/0.60       => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60         => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_power_le
% 0.32/0.60  thf(fact_5750_mod__eq__dvd__iff,axiom,
% 0.32/0.60      ! [A: int,C: int,B: int] :
% 0.32/0.60        ( ( ( modulo_modulo_int @ A @ C )
% 0.32/0.60          = ( modulo_modulo_int @ B @ C ) )
% 0.32/0.60        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_eq_dvd_iff
% 0.32/0.60  thf(fact_5751_mod__eq__dvd__iff,axiom,
% 0.32/0.60      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.32/0.60        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.32/0.60          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.32/0.60        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % mod_eq_dvd_iff
% 0.32/0.60  thf(fact_5752_dvd__minus__mod,axiom,
% 0.32/0.60      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_minus_mod
% 0.32/0.60  thf(fact_5753_dvd__minus__mod,axiom,
% 0.32/0.60      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_minus_mod
% 0.32/0.60  thf(fact_5754_dvd__minus__mod,axiom,
% 0.32/0.60      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_minus_mod
% 0.32/0.60  thf(fact_5755_nat__dvd__not__less,axiom,
% 0.32/0.60      ! [M: nat,N: nat] :
% 0.32/0.60        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.60       => ( ( ord_less_nat @ M @ N )
% 0.32/0.60         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % nat_dvd_not_less
% 0.32/0.60  thf(fact_5756_dvd__pos__nat,axiom,
% 0.32/0.60      ! [N: nat,M: nat] :
% 0.32/0.60        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.60       => ( ( dvd_dvd_nat @ M @ N )
% 0.32/0.60         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_pos_nat
% 0.32/0.60  thf(fact_5757_sin__bound__lemma,axiom,
% 0.32/0.60      ! [X: real,Y: real,U: real,V: real] :
% 0.32/0.60        ( ( X = Y )
% 0.32/0.60       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 0.32/0.60         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % sin_bound_lemma
% 0.32/0.60  thf(fact_5758_dvd__minus__self,axiom,
% 0.32/0.60      ! [M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.60        = ( ( ord_less_nat @ N @ M )
% 0.32/0.60          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_minus_self
% 0.32/0.60  thf(fact_5759_zdvd__antisym__nonneg,axiom,
% 0.32/0.60      ! [M: int,N: int] :
% 0.32/0.60        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.32/0.60       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.60         => ( ( dvd_dvd_int @ M @ N )
% 0.32/0.60           => ( ( dvd_dvd_int @ N @ M )
% 0.32/0.60             => ( M = N ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zdvd_antisym_nonneg
% 0.32/0.60  thf(fact_5760_less__eq__dvd__minus,axiom,
% 0.32/0.60      ! [M: nat,N: nat] :
% 0.32/0.60        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.60       => ( ( dvd_dvd_nat @ M @ N )
% 0.32/0.60          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % less_eq_dvd_minus
% 0.32/0.60  thf(fact_5761_dvd__diffD1,axiom,
% 0.32/0.60      ! [K: nat,M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.60       => ( ( dvd_dvd_nat @ K @ M )
% 0.32/0.60         => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diffD1
% 0.32/0.60  thf(fact_5762_dvd__diffD,axiom,
% 0.32/0.60      ! [K: nat,M: nat,N: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.60       => ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.60         => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.60           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % dvd_diffD
% 0.32/0.60  thf(fact_5763_zdvd__not__zless,axiom,
% 0.32/0.60      ! [M: int,N: int] :
% 0.32/0.60        ( ( ord_less_int @ zero_zero_int @ M )
% 0.32/0.60       => ( ( ord_less_int @ M @ N )
% 0.32/0.60         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zdvd_not_zless
% 0.32/0.60  thf(fact_5764_bezout__lemma__nat,axiom,
% 0.32/0.60      ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ D @ A )
% 0.32/0.60       => ( ( dvd_dvd_nat @ D @ B )
% 0.32/0.60         => ( ( ( ( times_times_nat @ A @ X )
% 0.32/0.60                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 0.32/0.60              | ( ( times_times_nat @ B @ X )
% 0.32/0.60                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 0.32/0.60           => ? [X6: nat,Y5: nat] :
% 0.32/0.60                ( ( dvd_dvd_nat @ D @ A )
% 0.32/0.60                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.60                & ( ( ( times_times_nat @ A @ X6 )
% 0.32/0.60                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D ) )
% 0.32/0.60                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X6 )
% 0.32/0.60                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % bezout_lemma_nat
% 0.32/0.60  thf(fact_5765_bezout__add__nat,axiom,
% 0.32/0.60      ! [A: nat,B: nat] :
% 0.32/0.60      ? [D3: nat,X6: nat,Y5: nat] :
% 0.32/0.60        ( ( dvd_dvd_nat @ D3 @ A )
% 0.32/0.60        & ( dvd_dvd_nat @ D3 @ B )
% 0.32/0.60        & ( ( ( times_times_nat @ A @ X6 )
% 0.32/0.60            = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) )
% 0.32/0.60          | ( ( times_times_nat @ B @ X6 )
% 0.32/0.60            = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D3 ) ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % bezout_add_nat
% 0.32/0.60  thf(fact_5766_zdvd__mult__cancel,axiom,
% 0.32/0.60      ! [K: int,M: int,N: int] :
% 0.32/0.60        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 0.32/0.60       => ( ( K != zero_zero_int )
% 0.32/0.60         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 0.32/0.60  
% 0.32/0.60  % zdvd_mult_cancel
% 0.32/0.60  thf(fact_5767_zdvd__mono,axiom,
% 0.32/0.60      ! [K: int,M: int,T: int] :
% 0.32/0.60        ( ( K != zero_zero_int )
% 0.32/0.60       => ( ( dvd_dvd_int @ M @ T )
% 0.32/0.61          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd_mono
% 0.32/0.61  thf(fact_5768_bezout1__nat,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61      ? [D3: nat,X6: nat,Y5: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ D3 @ A )
% 0.32/0.61        & ( dvd_dvd_nat @ D3 @ B )
% 0.32/0.61        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 0.32/0.61            = D3 )
% 0.32/0.61          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 0.32/0.61            = D3 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bezout1_nat
% 0.32/0.61  thf(fact_5769_real__minus__mult__self__le,axiom,
% 0.32/0.61      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % real_minus_mult_self_le
% 0.32/0.61  thf(fact_5770_zdvd__period,axiom,
% 0.32/0.61      ! [A: int,D: int,X: int,T: int,C: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ A @ D )
% 0.32/0.61       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 0.32/0.61          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd_period
% 0.32/0.61  thf(fact_5771_zdvd__reduce,axiom,
% 0.32/0.61      ! [K: int,N: int,M: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 0.32/0.61        = ( dvd_dvd_int @ K @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd_reduce
% 0.32/0.61  thf(fact_5772_power__mono__even,axiom,
% 0.32/0.61      ! [N: nat,A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.32/0.61         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_even
% 0.32/0.61  thf(fact_5773_power__mono__even,axiom,
% 0.32/0.61      ! [N: nat,A: real,B: real] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.32/0.61         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_even
% 0.32/0.61  thf(fact_5774_power__mono__even,axiom,
% 0.32/0.61      ! [N: nat,A: rat,B: rat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 0.32/0.61         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_even
% 0.32/0.61  thf(fact_5775_power__mono__even,axiom,
% 0.32/0.61      ! [N: nat,A: int,B: int] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.32/0.61         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_even
% 0.32/0.61  thf(fact_5776_minus__real__def,axiom,
% 0.32/0.61      ( minus_minus_real
% 0.32/0.61      = ( ^ [X3: real,Y3: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_real_def
% 0.32/0.61  thf(fact_5777_minus__one__power__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.32/0.61            = one_one_real ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 0.32/0.61            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_one_power_iff
% 0.32/0.61  thf(fact_5778_minus__one__power__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.32/0.61            = one_one_int ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.32/0.61            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_one_power_iff
% 0.32/0.61  thf(fact_5779_minus__one__power__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.32/0.61            = one_one_complex ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 0.32/0.61            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_one_power_iff
% 0.32/0.61  thf(fact_5780_minus__one__power__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.32/0.61            = one_one_Code_integer ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.32/0.61            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_one_power_iff
% 0.32/0.61  thf(fact_5781_minus__one__power__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.32/0.61            = one_one_rat ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.32/0.61            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_one_power_iff
% 0.32/0.61  thf(fact_5782_tanh__real__lt__1,axiom,
% 0.32/0.61      ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 0.32/0.61  
% 0.32/0.61  % tanh_real_lt_1
% 0.32/0.61  thf(fact_5783_dense__eq0__I,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ! [E2: real] :
% 0.32/0.61            ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.32/0.61           => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 0.32/0.61       => ( X = zero_zero_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dense_eq0_I
% 0.32/0.61  thf(fact_5784_dense__eq0__I,axiom,
% 0.32/0.61      ! [X: rat] :
% 0.32/0.61        ( ! [E2: rat] :
% 0.32/0.61            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.32/0.61           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 0.32/0.61       => ( X = zero_zero_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dense_eq0_I
% 0.32/0.61  thf(fact_5785_abs__eq__mult,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.32/0.61            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.32/0.61          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.32/0.61            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.32/0.61       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.61          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_eq_mult
% 0.32/0.61  thf(fact_5786_abs__eq__mult,axiom,
% 0.32/0.61      ! [A: real,B: real] :
% 0.32/0.61        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.61            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.32/0.61          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.32/0.61            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.32/0.61       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.32/0.61          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_eq_mult
% 0.32/0.61  thf(fact_5787_abs__eq__mult,axiom,
% 0.32/0.61      ! [A: rat,B: rat] :
% 0.32/0.61        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.32/0.61            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.32/0.61          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.32/0.61            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.32/0.61       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.32/0.61          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_eq_mult
% 0.32/0.61  thf(fact_5788_abs__eq__mult,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.61            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.32/0.61          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.61            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.32/0.61       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.32/0.61          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_eq_mult
% 0.32/0.61  thf(fact_5789_abs__mult__pos,axiom,
% 0.32/0.61      ! [X: code_integer,Y: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.32/0.61       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 0.32/0.61          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_mult_pos
% 0.32/0.61  thf(fact_5790_abs__mult__pos,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.61       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 0.32/0.61          = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_mult_pos
% 0.32/0.61  thf(fact_5791_abs__mult__pos,axiom,
% 0.32/0.61      ! [X: rat,Y: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.32/0.61       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 0.32/0.61          = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_mult_pos
% 0.32/0.61  thf(fact_5792_abs__mult__pos,axiom,
% 0.32/0.61      ! [X: int,Y: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.61       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 0.32/0.61          = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_mult_pos
% 0.32/0.61  thf(fact_5793_abs__div__pos,axiom,
% 0.32/0.61      ! [Y: real,X: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.61       => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 0.32/0.61          = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_div_pos
% 0.32/0.61  thf(fact_5794_abs__div__pos,axiom,
% 0.32/0.61      ! [Y: rat,X: rat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.32/0.61       => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 0.32/0.61          = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_div_pos
% 0.32/0.61  thf(fact_5795_zero__le__power__abs,axiom,
% 0.32/0.61      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_abs
% 0.32/0.61  thf(fact_5796_zero__le__power__abs,axiom,
% 0.32/0.61      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_abs
% 0.32/0.61  thf(fact_5797_zero__le__power__abs,axiom,
% 0.32/0.61      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_abs
% 0.32/0.61  thf(fact_5798_zero__le__power__abs,axiom,
% 0.32/0.61      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_abs
% 0.32/0.61  thf(fact_5799_abs__triangle__ineq4,axiom,
% 0.32/0.61      ! [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 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_triangle_ineq4
% 0.32/0.61  thf(fact_5800_abs__triangle__ineq4,axiom,
% 0.32/0.61      ! [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 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_triangle_ineq4
% 0.32/0.61  thf(fact_5801_abs__triangle__ineq4,axiom,
% 0.32/0.61      ! [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 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_triangle_ineq4
% 0.32/0.61  thf(fact_5802_abs__triangle__ineq4,axiom,
% 0.32/0.61      ! [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 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_triangle_ineq4
% 0.32/0.61  thf(fact_5803_abs__diff__triangle__ineq,axiom,
% 0.32/0.61      ! [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 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_triangle_ineq
% 0.32/0.61  thf(fact_5804_abs__diff__triangle__ineq,axiom,
% 0.32/0.61      ! [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 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_triangle_ineq
% 0.32/0.61  thf(fact_5805_abs__diff__triangle__ineq,axiom,
% 0.32/0.61      ! [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 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_triangle_ineq
% 0.32/0.61  thf(fact_5806_abs__diff__triangle__ineq,axiom,
% 0.32/0.61      ! [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 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_triangle_ineq
% 0.32/0.61  thf(fact_5807_abs__diff__le__iff,axiom,
% 0.32/0.61      ! [X: code_integer,A: code_integer,R: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 0.32/0.61          & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_le_iff
% 0.32/0.61  thf(fact_5808_abs__diff__le__iff,axiom,
% 0.32/0.61      ! [X: real,A: real,R: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_le_iff
% 0.32/0.61  thf(fact_5809_abs__diff__le__iff,axiom,
% 0.32/0.61      ! [X: rat,A: rat,R: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_le_iff
% 0.32/0.61  thf(fact_5810_abs__diff__le__iff,axiom,
% 0.32/0.61      ! [X: int,A: int,R: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_le_iff
% 0.32/0.61  thf(fact_5811_abs__diff__less__iff,axiom,
% 0.32/0.61      ! [X: code_integer,A: code_integer,R: code_integer] :
% 0.32/0.61        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 0.32/0.61          & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_less_iff
% 0.32/0.61  thf(fact_5812_abs__diff__less__iff,axiom,
% 0.32/0.61      ! [X: real,A: real,R: real] :
% 0.32/0.61        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_less_iff
% 0.32/0.61  thf(fact_5813_abs__diff__less__iff,axiom,
% 0.32/0.61      ! [X: rat,A: rat,R: rat] :
% 0.32/0.61        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_less_iff
% 0.32/0.61  thf(fact_5814_abs__diff__less__iff,axiom,
% 0.32/0.61      ! [X: int,A: int,R: int] :
% 0.32/0.61        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 0.32/0.61        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 0.32/0.61          & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_diff_less_iff
% 0.32/0.61  thf(fact_5815_finite__divisors__int,axiom,
% 0.32/0.61      ! [I: int] :
% 0.32/0.61        ( ( I != zero_zero_int )
% 0.32/0.61       => ( finite_finite_int
% 0.32/0.61          @ ( collect_int
% 0.32/0.61            @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % finite_divisors_int
% 0.32/0.61  thf(fact_5816_div2__even__ext__nat,axiom,
% 0.32/0.61      ! [X: nat,Y: nat] :
% 0.32/0.61        ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 0.32/0.61            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 0.32/0.61         => ( X = Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div2_even_ext_nat
% 0.32/0.61  thf(fact_5817_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: code_integer > $o,L2: code_integer] :
% 0.32/0.61        ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: code_integer] :
% 0.32/0.61              ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5818_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: complex > $o,L2: complex] :
% 0.32/0.61        ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: complex] :
% 0.32/0.61              ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5819_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: real > $o,L2: real] :
% 0.32/0.61        ( ( ? [X3: real] : ( P @ ( times_times_real @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: real] :
% 0.32/0.61              ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5820_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: rat > $o,L2: rat] :
% 0.32/0.61        ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: rat] :
% 0.32/0.61              ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5821_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: nat > $o,L2: nat] :
% 0.32/0.61        ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: nat] :
% 0.32/0.61              ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5822_unity__coeff__ex,axiom,
% 0.32/0.61      ! [P: int > $o,L2: int] :
% 0.32/0.61        ( ( ? [X3: int] : ( P @ ( times_times_int @ L2 @ X3 ) ) )
% 0.32/0.61        = ( ? [X3: int] :
% 0.32/0.61              ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 0.32/0.61              & ( P @ X3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unity_coeff_ex
% 0.32/0.61  thf(fact_5823_unit__dvdE,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.61       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61           => ! [C2: code_integer] :
% 0.32/0.61                ( B
% 0.32/0.61               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_dvdE
% 0.32/0.61  thf(fact_5824_unit__dvdE,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.61       => ~ ( ( A != zero_zero_nat )
% 0.32/0.61           => ! [C2: nat] :
% 0.32/0.61                ( B
% 0.32/0.61               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_dvdE
% 0.32/0.61  thf(fact_5825_unit__dvdE,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.61       => ~ ( ( A != zero_zero_int )
% 0.32/0.61           => ! [C2: int] :
% 0.32/0.61                ( B
% 0.32/0.61               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_dvdE
% 0.32/0.61  thf(fact_5826_dvd__div__eq__mult,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.32/0.61        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.61         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.32/0.61              = C )
% 0.32/0.61            = ( B
% 0.32/0.61              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_eq_mult
% 0.32/0.61  thf(fact_5827_dvd__div__eq__mult,axiom,
% 0.32/0.61      ! [A: nat,B: nat,C: nat] :
% 0.32/0.61        ( ( A != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.61         => ( ( ( divide_divide_nat @ B @ A )
% 0.32/0.61              = C )
% 0.32/0.61            = ( B
% 0.32/0.61              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_eq_mult
% 0.32/0.61  thf(fact_5828_dvd__div__eq__mult,axiom,
% 0.32/0.61      ! [A: int,B: int,C: int] :
% 0.32/0.61        ( ( A != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ A @ B )
% 0.32/0.61         => ( ( ( divide_divide_int @ B @ A )
% 0.32/0.61              = C )
% 0.32/0.61            = ( B
% 0.32/0.61              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_eq_mult
% 0.32/0.61  thf(fact_5829_div__dvd__iff__mult,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.61        ( ( B != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.61         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.32/0.61            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_dvd_iff_mult
% 0.32/0.61  thf(fact_5830_div__dvd__iff__mult,axiom,
% 0.32/0.61      ! [B: nat,A: nat,C: nat] :
% 0.32/0.61        ( ( B != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.61         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.32/0.61            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_dvd_iff_mult
% 0.32/0.61  thf(fact_5831_div__dvd__iff__mult,axiom,
% 0.32/0.61      ! [B: int,A: int,C: int] :
% 0.32/0.61        ( ( B != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ B @ A )
% 0.32/0.61         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.32/0.61            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_dvd_iff_mult
% 0.32/0.61  thf(fact_5832_dvd__div__iff__mult,axiom,
% 0.32/0.61      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.61        ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.32/0.61         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.61            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_iff_mult
% 0.32/0.61  thf(fact_5833_dvd__div__iff__mult,axiom,
% 0.32/0.61      ! [C: nat,B: nat,A: nat] :
% 0.32/0.61        ( ( C != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ C @ B )
% 0.32/0.61         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.32/0.61            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_iff_mult
% 0.32/0.61  thf(fact_5834_dvd__div__iff__mult,axiom,
% 0.32/0.61      ! [C: int,B: int,A: int] :
% 0.32/0.61        ( ( C != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ C @ B )
% 0.32/0.61         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.32/0.61            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_iff_mult
% 0.32/0.61  thf(fact_5835_dvd__div__div__eq__mult,axiom,
% 0.32/0.61      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 0.32/0.61        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( C != zero_z3403309356797280102nteger )
% 0.32/0.61         => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.32/0.61           => ( ( dvd_dvd_Code_integer @ C @ D )
% 0.32/0.61             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.32/0.61                  = ( divide6298287555418463151nteger @ D @ C ) )
% 0.32/0.61                = ( ( times_3573771949741848930nteger @ B @ C )
% 0.32/0.61                  = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_div_eq_mult
% 0.32/0.61  thf(fact_5836_dvd__div__div__eq__mult,axiom,
% 0.32/0.61      ! [A: nat,C: nat,B: nat,D: nat] :
% 0.32/0.61        ( ( A != zero_zero_nat )
% 0.32/0.61       => ( ( C != zero_zero_nat )
% 0.32/0.61         => ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.61           => ( ( dvd_dvd_nat @ C @ D )
% 0.32/0.61             => ( ( ( divide_divide_nat @ B @ A )
% 0.32/0.61                  = ( divide_divide_nat @ D @ C ) )
% 0.32/0.61                = ( ( times_times_nat @ B @ C )
% 0.32/0.61                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_div_eq_mult
% 0.32/0.61  thf(fact_5837_dvd__div__div__eq__mult,axiom,
% 0.32/0.61      ! [A: int,C: int,B: int,D: int] :
% 0.32/0.61        ( ( A != zero_zero_int )
% 0.32/0.61       => ( ( C != zero_zero_int )
% 0.32/0.61         => ( ( dvd_dvd_int @ A @ B )
% 0.32/0.61           => ( ( dvd_dvd_int @ C @ D )
% 0.32/0.61             => ( ( ( divide_divide_int @ B @ A )
% 0.32/0.61                  = ( divide_divide_int @ D @ C ) )
% 0.32/0.61                = ( ( times_times_int @ B @ C )
% 0.32/0.61                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_div_div_eq_mult
% 0.32/0.61  thf(fact_5838_unit__div__eq__0__iff,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.32/0.61            = zero_z3403309356797280102nteger )
% 0.32/0.61          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_eq_0_iff
% 0.32/0.61  thf(fact_5839_unit__div__eq__0__iff,axiom,
% 0.32/0.61      ! [B: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( ( divide_divide_nat @ A @ B )
% 0.32/0.61            = zero_zero_nat )
% 0.32/0.61          = ( A = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_eq_0_iff
% 0.32/0.61  thf(fact_5840_unit__div__eq__0__iff,axiom,
% 0.32/0.61      ! [B: int,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( ( divide_divide_int @ A @ B )
% 0.32/0.61            = zero_zero_int )
% 0.32/0.61          = ( A = zero_zero_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_eq_0_iff
% 0.32/0.61  thf(fact_5841_even__numeral,axiom,
% 0.32/0.61      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_numeral
% 0.32/0.61  thf(fact_5842_even__numeral,axiom,
% 0.32/0.61      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_numeral
% 0.32/0.61  thf(fact_5843_even__numeral,axiom,
% 0.32/0.61      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_numeral
% 0.32/0.61  thf(fact_5844_inf__period_I3_J,axiom,
% 0.32/0.61      ! [D: code_integer,D4: code_integer,T: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 0.32/0.61       => ! [X4: code_integer,K4: code_integer] :
% 0.32/0.61            ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) )
% 0.32/0.61            = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(3)
% 0.32/0.61  thf(fact_5845_inf__period_I3_J,axiom,
% 0.32/0.61      ! [D: real,D4: real,T: real] :
% 0.32/0.61        ( ( dvd_dvd_real @ D @ D4 )
% 0.32/0.61       => ! [X4: real,K4: real] :
% 0.32/0.61            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) )
% 0.32/0.61            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(3)
% 0.32/0.61  thf(fact_5846_inf__period_I3_J,axiom,
% 0.32/0.61      ! [D: rat,D4: rat,T: rat] :
% 0.32/0.61        ( ( dvd_dvd_rat @ D @ D4 )
% 0.32/0.61       => ! [X4: rat,K4: rat] :
% 0.32/0.61            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) )
% 0.32/0.61            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(3)
% 0.32/0.61  thf(fact_5847_inf__period_I3_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int,K4: int] :
% 0.32/0.61            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.32/0.61            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(3)
% 0.32/0.61  thf(fact_5848_inf__period_I4_J,axiom,
% 0.32/0.61      ! [D: code_integer,D4: code_integer,T: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 0.32/0.61       => ! [X4: code_integer,K4: code_integer] :
% 0.32/0.61            ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) ) )
% 0.32/0.61            = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(4)
% 0.32/0.61  thf(fact_5849_inf__period_I4_J,axiom,
% 0.32/0.61      ! [D: real,D4: real,T: real] :
% 0.32/0.61        ( ( dvd_dvd_real @ D @ D4 )
% 0.32/0.61       => ! [X4: real,K4: real] :
% 0.32/0.61            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) ) )
% 0.32/0.61            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(4)
% 0.32/0.61  thf(fact_5850_inf__period_I4_J,axiom,
% 0.32/0.61      ! [D: rat,D4: rat,T: rat] :
% 0.32/0.61        ( ( dvd_dvd_rat @ D @ D4 )
% 0.32/0.61       => ! [X4: rat,K4: rat] :
% 0.32/0.61            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) ) )
% 0.32/0.61            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(4)
% 0.32/0.61  thf(fact_5851_inf__period_I4_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int,K4: int] :
% 0.32/0.61            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) ) )
% 0.32/0.61            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % inf_period(4)
% 0.32/0.61  thf(fact_5852_not__zero__le__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_le_neg_numeral
% 0.32/0.61  thf(fact_5853_not__zero__le__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_le_neg_numeral
% 0.32/0.61  thf(fact_5854_not__zero__le__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_le_neg_numeral
% 0.32/0.61  thf(fact_5855_not__zero__le__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_le_neg_numeral
% 0.32/0.61  thf(fact_5856_neg__numeral__le__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_zero
% 0.32/0.61  thf(fact_5857_neg__numeral__le__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_zero
% 0.32/0.61  thf(fact_5858_neg__numeral__le__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_zero
% 0.32/0.61  thf(fact_5859_neg__numeral__le__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_zero
% 0.32/0.61  thf(fact_5860_unit__eq__div1,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.32/0.61            = C )
% 0.32/0.61          = ( A
% 0.32/0.61            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div1
% 0.32/0.61  thf(fact_5861_unit__eq__div1,axiom,
% 0.32/0.61      ! [B: nat,A: nat,C: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( ( divide_divide_nat @ A @ B )
% 0.32/0.61            = C )
% 0.32/0.61          = ( A
% 0.32/0.61            = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div1
% 0.32/0.61  thf(fact_5862_unit__eq__div1,axiom,
% 0.32/0.61      ! [B: int,A: int,C: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( ( divide_divide_int @ A @ B )
% 0.32/0.61            = C )
% 0.32/0.61          = ( A
% 0.32/0.61            = ( times_times_int @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div1
% 0.32/0.61  thf(fact_5863_unit__eq__div2,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( A
% 0.32/0.61            = ( divide6298287555418463151nteger @ C @ B ) )
% 0.32/0.61          = ( ( times_3573771949741848930nteger @ A @ B )
% 0.32/0.61            = C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div2
% 0.32/0.61  thf(fact_5864_unit__eq__div2,axiom,
% 0.32/0.61      ! [B: nat,A: nat,C: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( A
% 0.32/0.61            = ( divide_divide_nat @ C @ B ) )
% 0.32/0.61          = ( ( times_times_nat @ A @ B )
% 0.32/0.61            = C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div2
% 0.32/0.61  thf(fact_5865_unit__eq__div2,axiom,
% 0.32/0.61      ! [B: int,A: int,C: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( A
% 0.32/0.61            = ( divide_divide_int @ C @ B ) )
% 0.32/0.61          = ( ( times_times_int @ A @ B )
% 0.32/0.61            = C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_eq_div2
% 0.32/0.61  thf(fact_5866_div__mult__unit2,axiom,
% 0.32/0.61      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.32/0.61         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.61            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_mult_unit2
% 0.32/0.61  thf(fact_5867_div__mult__unit2,axiom,
% 0.32/0.61      ! [C: nat,B: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.61         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.61            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_mult_unit2
% 0.32/0.61  thf(fact_5868_div__mult__unit2,axiom,
% 0.32/0.61      ! [C: int,B: int,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ B @ A )
% 0.32/0.61         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.61            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_mult_unit2
% 0.32/0.61  thf(fact_5869_unit__div__commute,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.32/0.61          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_commute
% 0.32/0.61  thf(fact_5870_unit__div__commute,axiom,
% 0.32/0.61      ! [B: nat,A: nat,C: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.32/0.61          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_commute
% 0.32/0.61  thf(fact_5871_unit__div__commute,axiom,
% 0.32/0.61      ! [B: int,A: int,C: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.32/0.61          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_commute
% 0.32/0.61  thf(fact_5872_unit__div__mult__swap,axiom,
% 0.32/0.61      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.32/0.61       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.32/0.61          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_mult_swap
% 0.32/0.61  thf(fact_5873_unit__div__mult__swap,axiom,
% 0.32/0.61      ! [C: nat,A: nat,B: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.32/0.61       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.32/0.61          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_mult_swap
% 0.32/0.61  thf(fact_5874_unit__div__mult__swap,axiom,
% 0.32/0.61      ! [C: int,A: int,B: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.32/0.61       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.32/0.61          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_div_mult_swap
% 0.32/0.61  thf(fact_5875_is__unit__div__mult2__eq,axiom,
% 0.32/0.61      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.32/0.61         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.32/0.61            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult2_eq
% 0.32/0.61  thf(fact_5876_is__unit__div__mult2__eq,axiom,
% 0.32/0.61      ! [B: nat,C: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.32/0.61         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.32/0.61            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult2_eq
% 0.32/0.61  thf(fact_5877_is__unit__div__mult2__eq,axiom,
% 0.32/0.61      ! [B: int,C: int,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.32/0.61         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.32/0.61            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult2_eq
% 0.32/0.61  thf(fact_5878_neg__numeral__less__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_zero
% 0.32/0.61  thf(fact_5879_neg__numeral__less__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_zero
% 0.32/0.61  thf(fact_5880_neg__numeral__less__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_zero
% 0.32/0.61  thf(fact_5881_neg__numeral__less__zero,axiom,
% 0.32/0.61      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_zero
% 0.32/0.61  thf(fact_5882_not__zero__less__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_less_neg_numeral
% 0.32/0.61  thf(fact_5883_not__zero__less__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_less_neg_numeral
% 0.32/0.61  thf(fact_5884_not__zero__less__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_less_neg_numeral
% 0.32/0.61  thf(fact_5885_not__zero__less__neg__numeral,axiom,
% 0.32/0.61      ! [N: num] :
% 0.32/0.61        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_zero_less_neg_numeral
% 0.32/0.61  thf(fact_5886_le__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(1)
% 0.32/0.61  thf(fact_5887_le__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(1)
% 0.32/0.61  thf(fact_5888_le__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(1)
% 0.32/0.61  thf(fact_5889_le__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(1)
% 0.32/0.61  thf(fact_5890_le__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(3)
% 0.32/0.61  thf(fact_5891_le__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(3)
% 0.32/0.61  thf(fact_5892_le__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(3)
% 0.32/0.61  thf(fact_5893_le__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_one_simps(3)
% 0.32/0.61  thf(fact_5894_less__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(3)
% 0.32/0.61  thf(fact_5895_less__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(3)
% 0.32/0.61  thf(fact_5896_less__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(3)
% 0.32/0.61  thf(fact_5897_less__minus__one__simps_I3_J,axiom,
% 0.32/0.61      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(3)
% 0.32/0.61  thf(fact_5898_less__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(1)
% 0.32/0.61  thf(fact_5899_less__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(1)
% 0.32/0.61  thf(fact_5900_less__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(1)
% 0.32/0.61  thf(fact_5901_less__minus__one__simps_I1_J,axiom,
% 0.32/0.61      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_one_simps(1)
% 0.32/0.61  thf(fact_5902_not__one__le__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_le_neg_numeral
% 0.32/0.61  thf(fact_5903_not__one__le__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_le_neg_numeral
% 0.32/0.61  thf(fact_5904_not__one__le__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_le_neg_numeral
% 0.32/0.61  thf(fact_5905_not__one__le__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_le_neg_numeral
% 0.32/0.61  thf(fact_5906_not__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_le_neg_one
% 0.32/0.61  thf(fact_5907_not__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_le_neg_one
% 0.32/0.61  thf(fact_5908_not__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_le_neg_one
% 0.32/0.61  thf(fact_5909_not__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_le_neg_one
% 0.32/0.61  thf(fact_5910_neg__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_neg_one
% 0.32/0.61  thf(fact_5911_neg__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_neg_one
% 0.32/0.61  thf(fact_5912_neg__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_neg_one
% 0.32/0.61  thf(fact_5913_neg__numeral__le__neg__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_neg_one
% 0.32/0.61  thf(fact_5914_neg__one__le__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_le_numeral
% 0.32/0.61  thf(fact_5915_neg__one__le__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_le_numeral
% 0.32/0.61  thf(fact_5916_neg__one__le__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_le_numeral
% 0.32/0.61  thf(fact_5917_neg__one__le__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_le_numeral
% 0.32/0.61  thf(fact_5918_neg__numeral__le__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_one
% 0.32/0.61  thf(fact_5919_neg__numeral__le__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_one
% 0.32/0.61  thf(fact_5920_neg__numeral__le__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_one
% 0.32/0.61  thf(fact_5921_neg__numeral__le__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_le_one
% 0.32/0.61  thf(fact_5922_neg__numeral__less__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_one
% 0.32/0.61  thf(fact_5923_neg__numeral__less__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_one
% 0.32/0.61  thf(fact_5924_neg__numeral__less__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_one
% 0.32/0.61  thf(fact_5925_neg__numeral__less__one,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_numeral_less_one
% 0.32/0.61  thf(fact_5926_neg__one__less__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_less_numeral
% 0.32/0.61  thf(fact_5927_neg__one__less__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_less_numeral
% 0.32/0.61  thf(fact_5928_neg__one__less__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_less_numeral
% 0.32/0.61  thf(fact_5929_neg__one__less__numeral,axiom,
% 0.32/0.61      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_less_numeral
% 0.32/0.61  thf(fact_5930_not__numeral__less__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_less_neg_one
% 0.32/0.61  thf(fact_5931_not__numeral__less__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_less_neg_one
% 0.32/0.61  thf(fact_5932_not__numeral__less__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_less_neg_one
% 0.32/0.61  thf(fact_5933_not__numeral__less__neg__one,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_numeral_less_neg_one
% 0.32/0.61  thf(fact_5934_not__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_less_neg_numeral
% 0.32/0.61  thf(fact_5935_not__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_less_neg_numeral
% 0.32/0.61  thf(fact_5936_not__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_less_neg_numeral
% 0.32/0.61  thf(fact_5937_not__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_one_less_neg_numeral
% 0.32/0.61  thf(fact_5938_not__neg__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_neg_one_less_neg_numeral
% 0.32/0.61  thf(fact_5939_not__neg__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_neg_one_less_neg_numeral
% 0.32/0.61  thf(fact_5940_not__neg__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_neg_one_less_neg_numeral
% 0.32/0.61  thf(fact_5941_not__neg__one__less__neg__numeral,axiom,
% 0.32/0.61      ! [M: num] :
% 0.32/0.61        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % not_neg_one_less_neg_numeral
% 0.32/0.61  thf(fact_5942_is__unit__power__iff,axiom,
% 0.32/0.61      ! [A: code_integer,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 0.32/0.61        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_power_iff
% 0.32/0.61  thf(fact_5943_is__unit__power__iff,axiom,
% 0.32/0.61      ! [A: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 0.32/0.61        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_power_iff
% 0.32/0.61  thf(fact_5944_is__unit__power__iff,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 0.32/0.61        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_power_iff
% 0.32/0.61  thf(fact_5945_unit__imp__mod__eq__0,axiom,
% 0.32/0.61      ! [B: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61       => ( ( modulo_modulo_nat @ A @ B )
% 0.32/0.61          = zero_zero_nat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_imp_mod_eq_0
% 0.32/0.61  thf(fact_5946_unit__imp__mod__eq__0,axiom,
% 0.32/0.61      ! [B: int,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61       => ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61          = zero_zero_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_imp_mod_eq_0
% 0.32/0.61  thf(fact_5947_unit__imp__mod__eq__0,axiom,
% 0.32/0.61      ! [B: code_integer,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61       => ( ( modulo364778990260209775nteger @ A @ B )
% 0.32/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.61  
% 0.32/0.61  % unit_imp_mod_eq_0
% 0.32/0.61  thf(fact_5948_eq__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: real,B: real,C: real] :
% 0.32/0.61        ( ( A
% 0.32/0.61          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_real )
% 0.32/0.61           => ( ( times_times_real @ A @ C )
% 0.32/0.61              = ( uminus_uminus_real @ B ) ) )
% 0.32/0.61          & ( ( C = zero_zero_real )
% 0.32/0.61           => ( A = zero_zero_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_minus_divide_eq
% 0.32/0.61  thf(fact_5949_eq__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: complex,B: complex,C: complex] :
% 0.32/0.61        ( ( A
% 0.32/0.61          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_complex )
% 0.32/0.61           => ( ( times_times_complex @ A @ C )
% 0.32/0.61              = ( uminus1482373934393186551omplex @ B ) ) )
% 0.32/0.61          & ( ( C = zero_zero_complex )
% 0.32/0.61           => ( A = zero_zero_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_minus_divide_eq
% 0.32/0.61  thf(fact_5950_eq__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: rat,B: rat,C: rat] :
% 0.32/0.61        ( ( A
% 0.32/0.61          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_rat )
% 0.32/0.61           => ( ( times_times_rat @ A @ C )
% 0.32/0.61              = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61          & ( ( C = zero_zero_rat )
% 0.32/0.61           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_minus_divide_eq
% 0.32/0.61  thf(fact_5951_minus__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: real,C: real,A: real] :
% 0.32/0.61        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 0.32/0.61          = A )
% 0.32/0.61        = ( ( ( C != zero_zero_real )
% 0.32/0.61           => ( ( uminus_uminus_real @ B )
% 0.32/0.61              = ( times_times_real @ A @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_real )
% 0.32/0.61           => ( A = zero_zero_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_eq_eq
% 0.32/0.61  thf(fact_5952_minus__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: complex,C: complex,A: complex] :
% 0.32/0.61        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 0.32/0.61          = A )
% 0.32/0.61        = ( ( ( C != zero_zero_complex )
% 0.32/0.61           => ( ( uminus1482373934393186551omplex @ B )
% 0.32/0.61              = ( times_times_complex @ A @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_complex )
% 0.32/0.61           => ( A = zero_zero_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_eq_eq
% 0.32/0.61  thf(fact_5953_minus__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: rat,C: rat,A: rat] :
% 0.32/0.61        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.61          = A )
% 0.32/0.61        = ( ( ( C != zero_zero_rat )
% 0.32/0.61           => ( ( uminus_uminus_rat @ B )
% 0.32/0.61              = ( times_times_rat @ A @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_rat )
% 0.32/0.61           => ( A = zero_zero_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_eq_eq
% 0.32/0.61  thf(fact_5954_nonzero__neg__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: real,A: real,C: real] :
% 0.32/0.61        ( ( B != zero_zero_real )
% 0.32/0.61       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.61            = C )
% 0.32/0.61          = ( ( uminus_uminus_real @ A )
% 0.32/0.61            = ( times_times_real @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq
% 0.32/0.61  thf(fact_5955_nonzero__neg__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: complex,A: complex,C: complex] :
% 0.32/0.61        ( ( B != zero_zero_complex )
% 0.32/0.61       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.61            = C )
% 0.32/0.61          = ( ( uminus1482373934393186551omplex @ A )
% 0.32/0.61            = ( times_times_complex @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq
% 0.32/0.61  thf(fact_5956_nonzero__neg__divide__eq__eq,axiom,
% 0.32/0.61      ! [B: rat,A: rat,C: rat] :
% 0.32/0.61        ( ( B != zero_zero_rat )
% 0.32/0.61       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.32/0.61            = C )
% 0.32/0.61          = ( ( uminus_uminus_rat @ A )
% 0.32/0.61            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq
% 0.32/0.61  thf(fact_5957_nonzero__neg__divide__eq__eq2,axiom,
% 0.32/0.61      ! [B: real,C: real,A: real] :
% 0.32/0.61        ( ( B != zero_zero_real )
% 0.32/0.61       => ( ( C
% 0.32/0.61            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.32/0.61          = ( ( times_times_real @ C @ B )
% 0.32/0.61            = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq2
% 0.32/0.61  thf(fact_5958_nonzero__neg__divide__eq__eq2,axiom,
% 0.32/0.61      ! [B: complex,C: complex,A: complex] :
% 0.32/0.61        ( ( B != zero_zero_complex )
% 0.32/0.61       => ( ( C
% 0.32/0.61            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.61          = ( ( times_times_complex @ C @ B )
% 0.32/0.61            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq2
% 0.32/0.61  thf(fact_5959_nonzero__neg__divide__eq__eq2,axiom,
% 0.32/0.61      ! [B: rat,C: rat,A: rat] :
% 0.32/0.61        ( ( B != zero_zero_rat )
% 0.32/0.61       => ( ( C
% 0.32/0.61            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.32/0.61          = ( ( times_times_rat @ C @ B )
% 0.32/0.61            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nonzero_neg_divide_eq_eq2
% 0.32/0.61  thf(fact_5960_mult__1s__ring__1_I2_J,axiom,
% 0.32/0.61      ! [B: real] :
% 0.32/0.61        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.32/0.61        = ( uminus_uminus_real @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(2)
% 0.32/0.61  thf(fact_5961_mult__1s__ring__1_I2_J,axiom,
% 0.32/0.61      ! [B: int] :
% 0.32/0.61        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.32/0.61        = ( uminus_uminus_int @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(2)
% 0.32/0.61  thf(fact_5962_mult__1s__ring__1_I2_J,axiom,
% 0.32/0.61      ! [B: complex] :
% 0.32/0.61        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 0.32/0.61        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(2)
% 0.32/0.61  thf(fact_5963_mult__1s__ring__1_I2_J,axiom,
% 0.32/0.61      ! [B: code_integer] :
% 0.32/0.61        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.32/0.61        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(2)
% 0.32/0.61  thf(fact_5964_mult__1s__ring__1_I2_J,axiom,
% 0.32/0.61      ! [B: rat] :
% 0.32/0.61        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.32/0.61        = ( uminus_uminus_rat @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(2)
% 0.32/0.61  thf(fact_5965_mult__1s__ring__1_I1_J,axiom,
% 0.32/0.61      ! [B: real] :
% 0.32/0.61        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.32/0.61        = ( uminus_uminus_real @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(1)
% 0.32/0.61  thf(fact_5966_mult__1s__ring__1_I1_J,axiom,
% 0.32/0.61      ! [B: int] :
% 0.32/0.61        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.32/0.61        = ( uminus_uminus_int @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(1)
% 0.32/0.61  thf(fact_5967_mult__1s__ring__1_I1_J,axiom,
% 0.32/0.61      ! [B: complex] :
% 0.32/0.61        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 0.32/0.61        = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(1)
% 0.32/0.61  thf(fact_5968_mult__1s__ring__1_I1_J,axiom,
% 0.32/0.61      ! [B: code_integer] :
% 0.32/0.61        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.32/0.61        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(1)
% 0.32/0.61  thf(fact_5969_mult__1s__ring__1_I1_J,axiom,
% 0.32/0.61      ! [B: rat] :
% 0.32/0.61        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.32/0.61        = ( uminus_uminus_rat @ B ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mult_1s_ring_1(1)
% 0.32/0.61  thf(fact_5970_divide__eq__minus__1__iff,axiom,
% 0.32/0.61      ! [A: real,B: real] :
% 0.32/0.61        ( ( ( divide_divide_real @ A @ B )
% 0.32/0.61          = ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.61        = ( ( B != zero_zero_real )
% 0.32/0.61          & ( A
% 0.32/0.61            = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_minus_1_iff
% 0.32/0.61  thf(fact_5971_divide__eq__minus__1__iff,axiom,
% 0.32/0.61      ! [A: complex,B: complex] :
% 0.32/0.61        ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.32/0.61          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.61        = ( ( B != zero_zero_complex )
% 0.32/0.61          & ( A
% 0.32/0.61            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_minus_1_iff
% 0.32/0.61  thf(fact_5972_divide__eq__minus__1__iff,axiom,
% 0.32/0.61      ! [A: rat,B: rat] :
% 0.32/0.61        ( ( ( divide_divide_rat @ A @ B )
% 0.32/0.61          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.61        = ( ( B != zero_zero_rat )
% 0.32/0.61          & ( A
% 0.32/0.61            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_minus_1_iff
% 0.32/0.61  thf(fact_5973_uminus__numeral__One,axiom,
% 0.32/0.61      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.32/0.61      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_numeral_One
% 0.32/0.61  thf(fact_5974_uminus__numeral__One,axiom,
% 0.32/0.61      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.32/0.61      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_numeral_One
% 0.32/0.61  thf(fact_5975_uminus__numeral__One,axiom,
% 0.32/0.61      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.32/0.61      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_numeral_One
% 0.32/0.61  thf(fact_5976_uminus__numeral__One,axiom,
% 0.32/0.61      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.32/0.61      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_numeral_One
% 0.32/0.61  thf(fact_5977_uminus__numeral__One,axiom,
% 0.32/0.61      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.32/0.61      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_numeral_One
% 0.32/0.61  thf(fact_5978_power__minus,axiom,
% 0.32/0.61      ! [A: real,N: nat] :
% 0.32/0.61        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.32/0.61        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus
% 0.32/0.61  thf(fact_5979_power__minus,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.32/0.61        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus
% 0.32/0.61  thf(fact_5980_power__minus,axiom,
% 0.32/0.61      ! [A: complex,N: nat] :
% 0.32/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.32/0.61        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus
% 0.32/0.61  thf(fact_5981_power__minus,axiom,
% 0.32/0.61      ! [A: code_integer,N: nat] :
% 0.32/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.32/0.61        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus
% 0.32/0.61  thf(fact_5982_power__minus,axiom,
% 0.32/0.61      ! [A: rat,N: nat] :
% 0.32/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.32/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus
% 0.32/0.61  thf(fact_5983_power__minus__Bit0,axiom,
% 0.32/0.61      ! [X: real,K: num] :
% 0.32/0.61        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus_Bit0
% 0.32/0.61  thf(fact_5984_power__minus__Bit0,axiom,
% 0.32/0.61      ! [X: int,K: num] :
% 0.32/0.61        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus_Bit0
% 0.32/0.61  thf(fact_5985_power__minus__Bit0,axiom,
% 0.32/0.61      ! [X: complex,K: num] :
% 0.32/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus_Bit0
% 0.32/0.61  thf(fact_5986_power__minus__Bit0,axiom,
% 0.32/0.61      ! [X: code_integer,K: num] :
% 0.32/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus_Bit0
% 0.32/0.61  thf(fact_5987_power__minus__Bit0,axiom,
% 0.32/0.61      ! [X: rat,K: num] :
% 0.32/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus_Bit0
% 0.32/0.61  thf(fact_5988_lemma__interval__lt,axiom,
% 0.32/0.61      ! [A: real,X: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ A @ X )
% 0.32/0.61       => ( ( ord_less_real @ X @ B )
% 0.32/0.61         => ? [D3: real] :
% 0.32/0.61              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.61              & ! [Y2: real] :
% 0.32/0.61                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 0.32/0.61                 => ( ( ord_less_real @ A @ Y2 )
% 0.32/0.61                    & ( ord_less_real @ Y2 @ B ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % lemma_interval_lt
% 0.32/0.61  thf(fact_5989_dvd__imp__le,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.61       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_imp_le
% 0.32/0.61  thf(fact_5990_dvd__mult__cancel,axiom,
% 0.32/0.61      ! [K: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.61       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.61         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_mult_cancel
% 0.32/0.61  thf(fact_5991_nat__mult__dvd__cancel1,axiom,
% 0.32/0.61      ! [K: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.61       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.61          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nat_mult_dvd_cancel1
% 0.32/0.61  thf(fact_5992_bezout__add__strong__nat,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61        ( ( A != zero_zero_nat )
% 0.32/0.61       => ? [D3: nat,X6: nat,Y5: nat] :
% 0.32/0.61            ( ( dvd_dvd_nat @ D3 @ A )
% 0.32/0.61            & ( dvd_dvd_nat @ D3 @ B )
% 0.32/0.61            & ( ( times_times_nat @ A @ X6 )
% 0.32/0.61              = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bezout_add_strong_nat
% 0.32/0.61  thf(fact_5993_zdvd__imp__le,axiom,
% 0.32/0.61      ! [Z: int,N: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ Z @ N )
% 0.32/0.61       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.61         => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd_imp_le
% 0.32/0.61  thf(fact_5994_mod__greater__zero__iff__not__dvd,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.61        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod_greater_zero_iff_not_dvd
% 0.32/0.61  thf(fact_5995_real__0__less__add__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 0.32/0.61        = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 0.32/0.61  
% 0.32/0.61  % real_0_less_add_iff
% 0.32/0.61  thf(fact_5996_real__add__less__0__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.32/0.61        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % real_add_less_0_iff
% 0.32/0.61  thf(fact_5997_real__add__le__0__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.32/0.61        = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % real_add_le_0_iff
% 0.32/0.61  thf(fact_5998_real__0__le__add__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 0.32/0.61        = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 0.32/0.61  
% 0.32/0.61  % real_0_le_add_iff
% 0.32/0.61  thf(fact_5999_mod__eq__dvd__iff__nat,axiom,
% 0.32/0.61      ! [N: nat,M: nat,Q2: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.61       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 0.32/0.61            = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.32/0.61          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod_eq_dvd_iff_nat
% 0.32/0.61  thf(fact_6000_prod__decode__aux_Ocases,axiom,
% 0.32/0.61      ! [X: product_prod_nat_nat] :
% 0.32/0.61        ~ ! [K3: nat,M4: nat] :
% 0.32/0.61            ( X
% 0.32/0.61           != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % prod_decode_aux.cases
% 0.32/0.61  thf(fact_6001_finite__divisors__nat,axiom,
% 0.32/0.61      ! [M: nat] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.61       => ( finite_finite_nat
% 0.32/0.61          @ ( collect_nat
% 0.32/0.61            @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % finite_divisors_nat
% 0.32/0.61  thf(fact_6002_abs__add__one__gt__zero,axiom,
% 0.32/0.61      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_add_one_gt_zero
% 0.32/0.61  thf(fact_6003_abs__add__one__gt__zero,axiom,
% 0.32/0.61      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_add_one_gt_zero
% 0.32/0.61  thf(fact_6004_abs__add__one__gt__zero,axiom,
% 0.32/0.61      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_add_one_gt_zero
% 0.32/0.61  thf(fact_6005_abs__add__one__gt__zero,axiom,
% 0.32/0.61      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_add_one_gt_zero
% 0.32/0.61  thf(fact_6006_even__zero,axiom,
% 0.32/0.61      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 0.32/0.61  
% 0.32/0.61  % even_zero
% 0.32/0.61  thf(fact_6007_even__zero,axiom,
% 0.32/0.61      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.32/0.61  
% 0.32/0.61  % even_zero
% 0.32/0.61  thf(fact_6008_even__zero,axiom,
% 0.32/0.61      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.32/0.61  
% 0.32/0.61  % even_zero
% 0.32/0.61  thf(fact_6009_is__unitE,axiom,
% 0.32/0.61      ! [A: code_integer,C: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.32/0.61       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61           => ! [B5: code_integer] :
% 0.32/0.61                ( ( B5 != zero_z3403309356797280102nteger )
% 0.32/0.61               => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 0.32/0.61                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.32/0.61                      = B5 )
% 0.32/0.61                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 0.32/0.61                        = A )
% 0.32/0.61                     => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 0.32/0.61                          = one_one_Code_integer )
% 0.32/0.61                       => ( ( divide6298287555418463151nteger @ C @ A )
% 0.32/0.61                         != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unitE
% 0.32/0.61  thf(fact_6010_is__unitE,axiom,
% 0.32/0.61      ! [A: nat,C: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.32/0.61       => ~ ( ( A != zero_zero_nat )
% 0.32/0.61           => ! [B5: nat] :
% 0.32/0.61                ( ( B5 != zero_zero_nat )
% 0.32/0.61               => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 0.32/0.61                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.32/0.61                      = B5 )
% 0.32/0.61                   => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 0.32/0.61                        = A )
% 0.32/0.61                     => ( ( ( times_times_nat @ A @ B5 )
% 0.32/0.61                          = one_one_nat )
% 0.32/0.61                       => ( ( divide_divide_nat @ C @ A )
% 0.32/0.61                         != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unitE
% 0.32/0.61  thf(fact_6011_is__unitE,axiom,
% 0.32/0.61      ! [A: int,C: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.32/0.61       => ~ ( ( A != zero_zero_int )
% 0.32/0.61           => ! [B5: int] :
% 0.32/0.61                ( ( B5 != zero_zero_int )
% 0.32/0.61               => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 0.32/0.61                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.32/0.61                      = B5 )
% 0.32/0.61                   => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 0.32/0.61                        = A )
% 0.32/0.61                     => ( ( ( times_times_int @ A @ B5 )
% 0.32/0.61                          = one_one_int )
% 0.32/0.61                       => ( ( divide_divide_int @ C @ A )
% 0.32/0.61                         != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unitE
% 0.32/0.61  thf(fact_6012_is__unit__div__mult__cancel__left,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.32/0.61            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_left
% 0.32/0.61  thf(fact_6013_is__unit__div__mult__cancel__left,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61        ( ( A != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.32/0.61            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_left
% 0.32/0.61  thf(fact_6014_is__unit__div__mult__cancel__left,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( A != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.32/0.61            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_left
% 0.32/0.61  thf(fact_6015_is__unit__div__mult__cancel__right,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer] :
% 0.32/0.61        ( ( A != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.32/0.61         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.32/0.61            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_right
% 0.32/0.61  thf(fact_6016_is__unit__div__mult__cancel__right,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61        ( ( A != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.32/0.61         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.32/0.61            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_right
% 0.32/0.61  thf(fact_6017_is__unit__div__mult__cancel__right,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( A != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.32/0.61         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.32/0.61            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % is_unit_div_mult_cancel_right
% 0.32/0.61  thf(fact_6018_evenE,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: code_integer] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % evenE
% 0.32/0.61  thf(fact_6019_evenE,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: nat] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % evenE
% 0.32/0.61  thf(fact_6020_evenE,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: int] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % evenE
% 0.32/0.61  thf(fact_6021_odd__even__add,axiom,
% 0.32/0.61      ! [A: code_integer,B: code_integer] :
% 0.32/0.61        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 0.32/0.61         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_even_add
% 0.32/0.61  thf(fact_6022_odd__even__add,axiom,
% 0.32/0.61      ! [A: nat,B: nat] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.32/0.61         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_even_add
% 0.32/0.61  thf(fact_6023_odd__even__add,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 0.32/0.61         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_even_add
% 0.32/0.61  thf(fact_6024_odd__one,axiom,
% 0.32/0.61      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_one
% 0.32/0.61  thf(fact_6025_odd__one,axiom,
% 0.32/0.61      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_one
% 0.32/0.61  thf(fact_6026_odd__one,axiom,
% 0.32/0.61      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_one
% 0.32/0.61  thf(fact_6027_bit__eq__rec,axiom,
% 0.32/0.61      ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 0.32/0.61      = ( ^ [A3: code_integer,B2: code_integer] :
% 0.32/0.61            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 0.32/0.61              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 0.32/0.61            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61              = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bit_eq_rec
% 0.32/0.61  thf(fact_6028_bit__eq__rec,axiom,
% 0.32/0.61      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.32/0.61      = ( ^ [A3: nat,B2: nat] :
% 0.32/0.61            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 0.32/0.61              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 0.32/0.61            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61              = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bit_eq_rec
% 0.32/0.61  thf(fact_6029_bit__eq__rec,axiom,
% 0.32/0.61      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 0.32/0.61      = ( ^ [A3: int,B2: int] :
% 0.32/0.61            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 0.32/0.61              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 0.32/0.61            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61              = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bit_eq_rec
% 0.32/0.61  thf(fact_6030_dvd__power__iff,axiom,
% 0.32/0.61      ! [X: code_integer,M: nat,N: nat] :
% 0.32/0.61        ( ( X != zero_z3403309356797280102nteger )
% 0.32/0.61       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.32/0.61          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 0.32/0.61            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power_iff
% 0.32/0.61  thf(fact_6031_dvd__power__iff,axiom,
% 0.32/0.61      ! [X: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( X != zero_zero_nat )
% 0.32/0.61       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 0.32/0.61          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 0.32/0.61            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power_iff
% 0.32/0.61  thf(fact_6032_dvd__power__iff,axiom,
% 0.32/0.61      ! [X: int,M: nat,N: nat] :
% 0.32/0.61        ( ( X != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 0.32/0.61          = ( ( dvd_dvd_int @ X @ one_one_int )
% 0.32/0.61            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power_iff
% 0.32/0.61  thf(fact_6033_less__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: real,B: real,C: real] :
% 0.32/0.61        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_divide_eq
% 0.32/0.61  thf(fact_6034_less__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: rat,B: rat,C: rat] :
% 0.32/0.61        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_minus_divide_eq
% 0.32/0.61  thf(fact_6035_minus__divide__less__eq,axiom,
% 0.32/0.61      ! [B: real,C: real,A: real] :
% 0.32/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_less_eq
% 0.32/0.61  thf(fact_6036_minus__divide__less__eq,axiom,
% 0.32/0.61      ! [B: rat,C: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_less_eq
% 0.32/0.61  thf(fact_6037_neg__less__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: real,A: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_less_minus_divide_eq
% 0.32/0.61  thf(fact_6038_neg__less__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_less_minus_divide_eq
% 0.32/0.61  thf(fact_6039_neg__minus__divide__less__eq,axiom,
% 0.32/0.61      ! [C: real,B: real,A: real] :
% 0.32/0.61        ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_minus_divide_less_eq
% 0.32/0.61  thf(fact_6040_neg__minus__divide__less__eq,axiom,
% 0.32/0.61      ! [C: rat,B: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_minus_divide_less_eq
% 0.32/0.61  thf(fact_6041_pos__less__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: real,A: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_less_minus_divide_eq
% 0.32/0.61  thf(fact_6042_pos__less__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_less_minus_divide_eq
% 0.32/0.61  thf(fact_6043_pos__minus__divide__less__eq,axiom,
% 0.32/0.61      ! [C: real,B: real,A: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_minus_divide_less_eq
% 0.32/0.61  thf(fact_6044_pos__minus__divide__less__eq,axiom,
% 0.32/0.61      ! [C: rat,B: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_minus_divide_less_eq
% 0.32/0.61  thf(fact_6045_divide__eq__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: real,C: real,W: num] :
% 0.32/0.61        ( ( ( divide_divide_real @ B @ C )
% 0.32/0.61          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_real )
% 0.32/0.61           => ( B
% 0.32/0.61              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_real )
% 0.32/0.61           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.61              = zero_zero_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_eq_numeral(2)
% 0.32/0.61  thf(fact_6046_divide__eq__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: complex,C: complex,W: num] :
% 0.32/0.61        ( ( ( divide1717551699836669952omplex @ B @ C )
% 0.32/0.61          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_complex )
% 0.32/0.61           => ( B
% 0.32/0.61              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_complex )
% 0.32/0.61           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.61              = zero_zero_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_eq_numeral(2)
% 0.32/0.61  thf(fact_6047_divide__eq__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: rat,C: rat,W: num] :
% 0.32/0.61        ( ( ( divide_divide_rat @ B @ C )
% 0.32/0.61          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.32/0.61        = ( ( ( C != zero_zero_rat )
% 0.32/0.61           => ( B
% 0.32/0.61              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ( C = zero_zero_rat )
% 0.32/0.61           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.61              = zero_zero_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_eq_eq_numeral(2)
% 0.32/0.61  thf(fact_6048_eq__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: real,C: real] :
% 0.32/0.61        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.61          = ( divide_divide_real @ B @ C ) )
% 0.32/0.61        = ( ( ( C != zero_zero_real )
% 0.32/0.61           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 0.32/0.61              = B ) )
% 0.32/0.61          & ( ( C = zero_zero_real )
% 0.32/0.61           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.61              = zero_zero_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6049_eq__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: complex,C: complex] :
% 0.32/0.61        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.61          = ( divide1717551699836669952omplex @ B @ C ) )
% 0.32/0.61        = ( ( ( C != zero_zero_complex )
% 0.32/0.61           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 0.32/0.61              = B ) )
% 0.32/0.61          & ( ( C = zero_zero_complex )
% 0.32/0.61           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.61              = zero_zero_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6050_eq__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: rat,C: rat] :
% 0.32/0.61        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.61          = ( divide_divide_rat @ B @ C ) )
% 0.32/0.61        = ( ( ( C != zero_zero_rat )
% 0.32/0.61           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 0.32/0.61              = B ) )
% 0.32/0.61          & ( ( C = zero_zero_rat )
% 0.32/0.61           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.32/0.61              = zero_zero_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6051_minus__divide__add__eq__iff,axiom,
% 0.32/0.61      ! [Z: real,X: real,Y: real] :
% 0.32/0.61        ( ( Z != zero_zero_real )
% 0.32/0.61       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_add_eq_iff
% 0.32/0.61  thf(fact_6052_minus__divide__add__eq__iff,axiom,
% 0.32/0.61      ! [Z: complex,X: complex,Y: complex] :
% 0.32/0.61        ( ( Z != zero_zero_complex )
% 0.32/0.61       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_add_eq_iff
% 0.32/0.61  thf(fact_6053_minus__divide__add__eq__iff,axiom,
% 0.32/0.61      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.61        ( ( Z != zero_zero_rat )
% 0.32/0.61       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_add_eq_iff
% 0.32/0.61  thf(fact_6054_add__divide__eq__if__simps_I3_J,axiom,
% 0.32/0.61      ! [Z: real,A: real,B: real] :
% 0.32/0.61        ( ( ( Z = zero_zero_real )
% 0.32/0.61         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.32/0.61            = B ) )
% 0.32/0.61        & ( ( Z != zero_zero_real )
% 0.32/0.61         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(3)
% 0.32/0.61  thf(fact_6055_add__divide__eq__if__simps_I3_J,axiom,
% 0.32/0.61      ! [Z: complex,A: complex,B: complex] :
% 0.32/0.61        ( ( ( Z = zero_zero_complex )
% 0.32/0.61         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.32/0.61            = B ) )
% 0.32/0.61        & ( ( Z != zero_zero_complex )
% 0.32/0.61         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(3)
% 0.32/0.61  thf(fact_6056_add__divide__eq__if__simps_I3_J,axiom,
% 0.32/0.61      ! [Z: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ( Z = zero_zero_rat )
% 0.32/0.61         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.32/0.61            = B ) )
% 0.32/0.61        & ( ( Z != zero_zero_rat )
% 0.32/0.61         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(3)
% 0.32/0.61  thf(fact_6057_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: code_integer] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_Code_integer ) )
% 0.32/0.61       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6058_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: rat] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_rat ) )
% 0.32/0.61       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6059_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: nat] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_nat ) )
% 0.32/0.61       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6060_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: real] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_real ) )
% 0.32/0.61       => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6061_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: int] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_int ) )
% 0.32/0.61       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6062_dvd__power,axiom,
% 0.32/0.61      ! [N: nat,X: complex] :
% 0.32/0.61        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          | ( X = one_one_complex ) )
% 0.32/0.61       => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power
% 0.32/0.61  thf(fact_6063_add__divide__eq__if__simps_I6_J,axiom,
% 0.32/0.61      ! [Z: real,A: real,B: real] :
% 0.32/0.61        ( ( ( Z = zero_zero_real )
% 0.32/0.61         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.32/0.61            = ( uminus_uminus_real @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_real )
% 0.32/0.61         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(6)
% 0.32/0.61  thf(fact_6064_add__divide__eq__if__simps_I6_J,axiom,
% 0.32/0.61      ! [Z: complex,A: complex,B: complex] :
% 0.32/0.61        ( ( ( Z = zero_zero_complex )
% 0.32/0.61         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.32/0.61            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_complex )
% 0.32/0.61         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(6)
% 0.32/0.61  thf(fact_6065_add__divide__eq__if__simps_I6_J,axiom,
% 0.32/0.61      ! [Z: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ( Z = zero_zero_rat )
% 0.32/0.61         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.32/0.61            = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_rat )
% 0.32/0.61         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.32/0.61            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(6)
% 0.32/0.61  thf(fact_6066_add__divide__eq__if__simps_I5_J,axiom,
% 0.32/0.61      ! [Z: real,A: real,B: real] :
% 0.32/0.61        ( ( ( Z = zero_zero_real )
% 0.32/0.61         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.32/0.61            = ( uminus_uminus_real @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_real )
% 0.32/0.61         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 0.32/0.61            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(5)
% 0.32/0.61  thf(fact_6067_add__divide__eq__if__simps_I5_J,axiom,
% 0.32/0.61      ! [Z: complex,A: complex,B: complex] :
% 0.32/0.61        ( ( ( Z = zero_zero_complex )
% 0.32/0.61         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.32/0.61            = ( uminus1482373934393186551omplex @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_complex )
% 0.32/0.61         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 0.32/0.61            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(5)
% 0.32/0.61  thf(fact_6068_add__divide__eq__if__simps_I5_J,axiom,
% 0.32/0.61      ! [Z: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ( Z = zero_zero_rat )
% 0.32/0.61         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.32/0.61            = ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61        & ( ( Z != zero_zero_rat )
% 0.32/0.61         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.32/0.61            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % add_divide_eq_if_simps(5)
% 0.32/0.61  thf(fact_6069_minus__divide__diff__eq__iff,axiom,
% 0.32/0.61      ! [Z: real,X: real,Y: real] :
% 0.32/0.61        ( ( Z != zero_zero_real )
% 0.32/0.61       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_diff_eq_iff
% 0.32/0.61  thf(fact_6070_minus__divide__diff__eq__iff,axiom,
% 0.32/0.61      ! [Z: complex,X: complex,Y: complex] :
% 0.32/0.61        ( ( Z != zero_zero_complex )
% 0.32/0.61       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_diff_eq_iff
% 0.32/0.61  thf(fact_6071_minus__divide__diff__eq__iff,axiom,
% 0.32/0.61      ! [Z: rat,X: rat,Y: rat] :
% 0.32/0.61        ( ( Z != zero_zero_rat )
% 0.32/0.61       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 0.32/0.61          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_diff_eq_iff
% 0.32/0.61  thf(fact_6072_power2__eq__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          | ( X
% 0.32/0.61            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_iff
% 0.32/0.61  thf(fact_6073_power2__eq__iff,axiom,
% 0.32/0.61      ! [X: int,Y: int] :
% 0.32/0.61        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          | ( X
% 0.32/0.61            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_iff
% 0.32/0.61  thf(fact_6074_power2__eq__iff,axiom,
% 0.32/0.61      ! [X: complex,Y: complex] :
% 0.32/0.61        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          | ( X
% 0.32/0.61            = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_iff
% 0.32/0.61  thf(fact_6075_power2__eq__iff,axiom,
% 0.32/0.61      ! [X: code_integer,Y: code_integer] :
% 0.32/0.61        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          | ( X
% 0.32/0.61            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_iff
% 0.32/0.61  thf(fact_6076_power2__eq__iff,axiom,
% 0.32/0.61      ! [X: rat,Y: rat] :
% 0.32/0.61        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          | ( X
% 0.32/0.61            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_iff
% 0.32/0.61  thf(fact_6077_lemma__interval,axiom,
% 0.32/0.61      ! [A: real,X: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ A @ X )
% 0.32/0.61       => ( ( ord_less_real @ X @ B )
% 0.32/0.61         => ? [D3: real] :
% 0.32/0.61              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.61              & ! [Y2: real] :
% 0.32/0.61                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 0.32/0.61                 => ( ( ord_less_eq_real @ A @ Y2 )
% 0.32/0.61                    & ( ord_less_eq_real @ Y2 @ B ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % lemma_interval
% 0.32/0.61  thf(fact_6078_even__even__mod__4__iff,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_even_mod_4_iff
% 0.32/0.61  thf(fact_6079_dvd__mult__cancel1,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.61       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.32/0.61          = ( N = one_one_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_mult_cancel1
% 0.32/0.61  thf(fact_6080_dvd__mult__cancel2,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.61       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.32/0.61          = ( N = one_one_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_mult_cancel2
% 0.32/0.61  thf(fact_6081_dvd__minus__add,axiom,
% 0.32/0.61      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ Q2 @ N )
% 0.32/0.61       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 0.32/0.61         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 0.32/0.61            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_minus_add
% 0.32/0.61  thf(fact_6082_power__dvd__imp__le,axiom,
% 0.32/0.61      ! [I: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.32/0.61       => ( ( ord_less_nat @ one_one_nat @ I )
% 0.32/0.61         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_dvd_imp_le
% 0.32/0.61  thf(fact_6083_mod__nat__eqI,axiom,
% 0.32/0.61      ! [R: nat,N: nat,M: nat] :
% 0.32/0.61        ( ( ord_less_nat @ R @ N )
% 0.32/0.61       => ( ( ord_less_eq_nat @ R @ M )
% 0.32/0.61         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 0.32/0.61           => ( ( modulo_modulo_nat @ M @ N )
% 0.32/0.61              = R ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod_nat_eqI
% 0.32/0.61  thf(fact_6084_ln__add__one__self__le__self2,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.61       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % ln_add_one_self_le_self2
% 0.32/0.61  thf(fact_6085_mod__int__pos__iff,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 0.32/0.61        = ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.61          | ( ( L2 = zero_zero_int )
% 0.32/0.61            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.32/0.61          | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod_int_pos_iff
% 0.32/0.61  thf(fact_6086_aset_I10_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,A2: set_int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int] :
% 0.32/0.61            ( ! [Xa3: int] :
% 0.32/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.61               => ! [Xb2: int] :
% 0.32/0.61                    ( ( member_int @ Xb2 @ A2 )
% 0.32/0.61                   => ( X4
% 0.32/0.61                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.61           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.32/0.61             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % aset(10)
% 0.32/0.61  thf(fact_6087_aset_I9_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,A2: set_int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int] :
% 0.32/0.61            ( ! [Xa3: int] :
% 0.32/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.61               => ! [Xb2: int] :
% 0.32/0.61                    ( ( member_int @ Xb2 @ A2 )
% 0.32/0.61                   => ( X4
% 0.32/0.61                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.61           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.32/0.61             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % aset(9)
% 0.32/0.61  thf(fact_6088_bset_I10_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,B3: set_int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int] :
% 0.32/0.61            ( ! [Xa3: int] :
% 0.32/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.61               => ! [Xb2: int] :
% 0.32/0.61                    ( ( member_int @ Xb2 @ B3 )
% 0.32/0.61                   => ( X4
% 0.32/0.61                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.61           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.32/0.61             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bset(10)
% 0.32/0.61  thf(fact_6089_bset_I9_J,axiom,
% 0.32/0.61      ! [D: int,D4: int,B3: set_int,T: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ D @ D4 )
% 0.32/0.61       => ! [X4: int] :
% 0.32/0.61            ( ! [Xa3: int] :
% 0.32/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.32/0.61               => ! [Xb2: int] :
% 0.32/0.61                    ( ( member_int @ Xb2 @ B3 )
% 0.32/0.61                   => ( X4
% 0.32/0.61                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.32/0.61           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 0.32/0.61             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bset(9)
% 0.32/0.61  thf(fact_6090_abs__le__square__iff,axiom,
% 0.32/0.61      ! [X: code_integer,Y: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 0.32/0.61        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_le_square_iff
% 0.32/0.61  thf(fact_6091_abs__le__square__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 0.32/0.61        = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_le_square_iff
% 0.32/0.61  thf(fact_6092_abs__le__square__iff,axiom,
% 0.32/0.61      ! [X: rat,Y: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 0.32/0.61        = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_le_square_iff
% 0.32/0.61  thf(fact_6093_abs__le__square__iff,axiom,
% 0.32/0.61      ! [X: int,Y: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 0.32/0.61        = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_le_square_iff
% 0.32/0.61  thf(fact_6094_abs__square__eq__1,axiom,
% 0.32/0.61      ! [X: code_integer] :
% 0.32/0.61        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_Code_integer )
% 0.32/0.61        = ( ( abs_abs_Code_integer @ X )
% 0.32/0.61          = one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_eq_1
% 0.32/0.61  thf(fact_6095_abs__square__eq__1,axiom,
% 0.32/0.61      ! [X: rat] :
% 0.32/0.61        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_rat )
% 0.32/0.61        = ( ( abs_abs_rat @ X )
% 0.32/0.61          = one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_eq_1
% 0.32/0.61  thf(fact_6096_abs__square__eq__1,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_real )
% 0.32/0.61        = ( ( abs_abs_real @ X )
% 0.32/0.61          = one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_eq_1
% 0.32/0.61  thf(fact_6097_abs__square__eq__1,axiom,
% 0.32/0.61      ! [X: int] :
% 0.32/0.61        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_int )
% 0.32/0.61        = ( ( abs_abs_int @ X )
% 0.32/0.61          = one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_eq_1
% 0.32/0.61  thf(fact_6098_even__two__times__div__two,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = A ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_two_times_div_two
% 0.32/0.61  thf(fact_6099_even__two__times__div__two,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = A ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_two_times_div_two
% 0.32/0.61  thf(fact_6100_even__two__times__div__two,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = A ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_two_times_div_two
% 0.32/0.61  thf(fact_6101_even__iff__mod__2__eq__zero,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = zero_zero_nat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_iff_mod_2_eq_zero
% 0.32/0.61  thf(fact_6102_even__iff__mod__2__eq__zero,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61          = zero_zero_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_iff_mod_2_eq_zero
% 0.32/0.61  thf(fact_6103_even__iff__mod__2__eq__zero,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_iff_mod_2_eq_zero
% 0.32/0.61  thf(fact_6104_le__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: real,B: real,C: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_divide_eq
% 0.32/0.61  thf(fact_6105_le__minus__divide__eq,axiom,
% 0.32/0.61      ! [A: rat,B: rat,C: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_minus_divide_eq
% 0.32/0.61  thf(fact_6106_minus__divide__le__eq,axiom,
% 0.32/0.61      ! [B: real,C: real,A: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_le_eq
% 0.32/0.61  thf(fact_6107_minus__divide__le__eq,axiom,
% 0.32/0.61      ! [B: rat,C: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_divide_le_eq
% 0.32/0.61  thf(fact_6108_neg__le__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: real,A: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_le_minus_divide_eq
% 0.32/0.61  thf(fact_6109_neg__le__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_le_minus_divide_eq
% 0.32/0.61  thf(fact_6110_neg__minus__divide__le__eq,axiom,
% 0.32/0.61      ! [C: real,B: real,A: real] :
% 0.32/0.61        ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_minus_divide_le_eq
% 0.32/0.61  thf(fact_6111_neg__minus__divide__le__eq,axiom,
% 0.32/0.61      ! [C: rat,B: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_minus_divide_le_eq
% 0.32/0.61  thf(fact_6112_pos__le__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: real,A: real,B: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_le_minus_divide_eq
% 0.32/0.61  thf(fact_6113_pos__le__minus__divide__eq,axiom,
% 0.32/0.61      ! [C: rat,A: rat,B: rat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.32/0.61          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_le_minus_divide_eq
% 0.32/0.61  thf(fact_6114_pos__minus__divide__le__eq,axiom,
% 0.32/0.61      ! [C: real,B: real,A: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_minus_divide_le_eq
% 0.32/0.61  thf(fact_6115_pos__minus__divide__le__eq,axiom,
% 0.32/0.61      ! [C: rat,B: rat,A: rat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.32/0.61          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_minus_divide_le_eq
% 0.32/0.61  thf(fact_6116_odd__iff__mod__2__eq__one,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_nat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_iff_mod_2_eq_one
% 0.32/0.61  thf(fact_6117_odd__iff__mod__2__eq__one,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_iff_mod_2_eq_one
% 0.32/0.61  thf(fact_6118_odd__iff__mod__2__eq__one,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_iff_mod_2_eq_one
% 0.32/0.61  thf(fact_6119_less__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: real,C: real] :
% 0.32/0.61        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6120_less__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: rat,C: rat] :
% 0.32/0.61        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % less_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6121_divide__less__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: real,C: real,W: num] :
% 0.32/0.61        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_less_eq_numeral(2)
% 0.32/0.61  thf(fact_6122_divide__less__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: rat,C: rat,W: num] :
% 0.32/0.61        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_less_eq_numeral(2)
% 0.32/0.61  thf(fact_6123_power__mono__odd,axiom,
% 0.32/0.61      ! [N: nat,A: real,B: real] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_real @ A @ B )
% 0.32/0.61         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_odd
% 0.32/0.61  thf(fact_6124_power__mono__odd,axiom,
% 0.32/0.61      ! [N: nat,A: rat,B: rat] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_rat @ A @ B )
% 0.32/0.61         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_odd
% 0.32/0.61  thf(fact_6125_power__mono__odd,axiom,
% 0.32/0.61      ! [N: nat,A: int,B: int] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.61         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_mono_odd
% 0.32/0.61  thf(fact_6126_power2__eq__1__iff,axiom,
% 0.32/0.61      ! [A: real] :
% 0.32/0.61        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_real )
% 0.32/0.61        = ( ( A = one_one_real )
% 0.32/0.61          | ( A
% 0.32/0.61            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_1_iff
% 0.32/0.61  thf(fact_6127_power2__eq__1__iff,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_int )
% 0.32/0.61        = ( ( A = one_one_int )
% 0.32/0.61          | ( A
% 0.32/0.61            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_1_iff
% 0.32/0.61  thf(fact_6128_power2__eq__1__iff,axiom,
% 0.32/0.61      ! [A: complex] :
% 0.32/0.61        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_complex )
% 0.32/0.61        = ( ( A = one_one_complex )
% 0.32/0.61          | ( A
% 0.32/0.61            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_1_iff
% 0.32/0.61  thf(fact_6129_power2__eq__1__iff,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_Code_integer )
% 0.32/0.61        = ( ( A = one_one_Code_integer )
% 0.32/0.61          | ( A
% 0.32/0.61            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_1_iff
% 0.32/0.61  thf(fact_6130_power2__eq__1__iff,axiom,
% 0.32/0.61      ! [A: rat] :
% 0.32/0.61        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61          = one_one_rat )
% 0.32/0.61        = ( ( A = one_one_rat )
% 0.32/0.61          | ( A
% 0.32/0.61            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_eq_1_iff
% 0.32/0.61  thf(fact_6131_odd__pos,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_pos
% 0.32/0.61  thf(fact_6132_dvd__power__iff__le,axiom,
% 0.32/0.61      ! [K: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.32/0.61       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 0.32/0.61          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_power_iff_le
% 0.32/0.61  thf(fact_6133_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.61       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.61          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_power_add_eq_neg_one_power_diff
% 0.32/0.61  thf(fact_6134_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.61       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.61          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_power_add_eq_neg_one_power_diff
% 0.32/0.61  thf(fact_6135_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.61       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.61          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_power_add_eq_neg_one_power_diff
% 0.32/0.61  thf(fact_6136_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.61       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.61          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_power_add_eq_neg_one_power_diff
% 0.32/0.61  thf(fact_6137_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.32/0.61      ! [K: nat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.61       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.61          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % neg_one_power_add_eq_neg_one_power_diff
% 0.32/0.61  thf(fact_6138_even__unset__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_unset_bit_iff
% 0.32/0.61  thf(fact_6139_even__unset__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_unset_bit_iff
% 0.32/0.61  thf(fact_6140_even__unset__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          | ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_unset_bit_iff
% 0.32/0.61  thf(fact_6141_even__set__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_set_bit_iff
% 0.32/0.61  thf(fact_6142_even__set__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_set_bit_iff
% 0.32/0.61  thf(fact_6143_even__set__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61          & ( M != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_set_bit_iff
% 0.32/0.61  thf(fact_6144_realpow__square__minus__le,axiom,
% 0.32/0.61      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % realpow_square_minus_le
% 0.32/0.61  thf(fact_6145_even__flip__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_flip_bit_iff
% 0.32/0.61  thf(fact_6146_even__flip__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_flip_bit_iff
% 0.32/0.61  thf(fact_6147_even__flip__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         != ( M = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_flip_bit_iff
% 0.32/0.61  thf(fact_6148_even__diff__iff,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 0.32/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_diff_iff
% 0.32/0.61  thf(fact_6149_ln__one__minus__pos__upper__bound,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.61       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.61         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % ln_one_minus_pos_upper_bound
% 0.32/0.61  thf(fact_6150_abs__sqrt__wlog,axiom,
% 0.32/0.61      ! [P: code_integer > code_integer > $o,X: code_integer] :
% 0.32/0.61        ( ! [X6: code_integer] :
% 0.32/0.61            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X6 )
% 0.32/0.61           => ( P @ X6 @ ( power_8256067586552552935nteger @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.61       => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_sqrt_wlog
% 0.32/0.61  thf(fact_6151_abs__sqrt__wlog,axiom,
% 0.32/0.61      ! [P: real > real > $o,X: real] :
% 0.32/0.61        ( ! [X6: real] :
% 0.32/0.61            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 0.32/0.61           => ( P @ X6 @ ( power_power_real @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.61       => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_sqrt_wlog
% 0.32/0.61  thf(fact_6152_abs__sqrt__wlog,axiom,
% 0.32/0.61      ! [P: rat > rat > $o,X: rat] :
% 0.32/0.61        ( ! [X6: rat] :
% 0.32/0.61            ( ( ord_less_eq_rat @ zero_zero_rat @ X6 )
% 0.32/0.61           => ( P @ X6 @ ( power_power_rat @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.61       => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_sqrt_wlog
% 0.32/0.61  thf(fact_6153_abs__sqrt__wlog,axiom,
% 0.32/0.61      ! [P: int > int > $o,X: int] :
% 0.32/0.61        ( ! [X6: int] :
% 0.32/0.61            ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 0.32/0.61           => ( P @ X6 @ ( power_power_int @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.61       => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_sqrt_wlog
% 0.32/0.61  thf(fact_6154_power2__le__iff__abs__le,axiom,
% 0.32/0.61      ! [Y: code_integer,X: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.32/0.61       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_le_iff_abs_le
% 0.32/0.61  thf(fact_6155_power2__le__iff__abs__le,axiom,
% 0.32/0.61      ! [Y: real,X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.61       => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_le_iff_abs_le
% 0.32/0.61  thf(fact_6156_power2__le__iff__abs__le,axiom,
% 0.32/0.61      ! [Y: rat,X: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.32/0.61       => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_le_iff_abs_le
% 0.32/0.61  thf(fact_6157_power2__le__iff__abs__le,axiom,
% 0.32/0.61      ! [Y: int,X: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.61       => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power2_le_iff_abs_le
% 0.32/0.61  thf(fact_6158_abs__square__le__1,axiom,
% 0.32/0.61      ! [X: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.32/0.61        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_le_1
% 0.32/0.61  thf(fact_6159_abs__square__le__1,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.32/0.61        = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_le_1
% 0.32/0.61  thf(fact_6160_abs__square__le__1,axiom,
% 0.32/0.61      ! [X: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.32/0.61        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_le_1
% 0.32/0.61  thf(fact_6161_abs__square__le__1,axiom,
% 0.32/0.61      ! [X: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.32/0.61        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_le_1
% 0.32/0.61  thf(fact_6162_abs__square__less__1,axiom,
% 0.32/0.61      ! [X: code_integer] :
% 0.32/0.61        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.32/0.61        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_less_1
% 0.32/0.61  thf(fact_6163_abs__square__less__1,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.32/0.61        = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_less_1
% 0.32/0.61  thf(fact_6164_abs__square__less__1,axiom,
% 0.32/0.61      ! [X: rat] :
% 0.32/0.61        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.32/0.61        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_less_1
% 0.32/0.61  thf(fact_6165_abs__square__less__1,axiom,
% 0.32/0.61      ! [X: int] :
% 0.32/0.61        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.32/0.61        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_square_less_1
% 0.32/0.61  thf(fact_6166_oddE,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: code_integer] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % oddE
% 0.32/0.61  thf(fact_6167_oddE,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: nat] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % oddE
% 0.32/0.61  thf(fact_6168_oddE,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61       => ~ ! [B5: int] :
% 0.32/0.61              ( A
% 0.32/0.61             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % oddE
% 0.32/0.61  thf(fact_6169_mod2__eq__if,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61            = zero_zero_nat ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61            = one_one_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod2_eq_if
% 0.32/0.61  thf(fact_6170_mod2__eq__if,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61            = zero_zero_int ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61            = one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod2_eq_if
% 0.32/0.61  thf(fact_6171_mod2__eq__if,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61            = zero_z3403309356797280102nteger ) )
% 0.32/0.61        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61            = one_one_Code_integer ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % mod2_eq_if
% 0.32/0.61  thf(fact_6172_parity__cases,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61           != zero_zero_nat ) )
% 0.32/0.61       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.61           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61             != one_one_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % parity_cases
% 0.32/0.61  thf(fact_6173_parity__cases,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61           != zero_zero_int ) )
% 0.32/0.61       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.61           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61             != one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % parity_cases
% 0.32/0.61  thf(fact_6174_parity__cases,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61           != zero_z3403309356797280102nteger ) )
% 0.32/0.61       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.61           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61             != one_one_Code_integer ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % parity_cases
% 0.32/0.61  thf(fact_6175_le__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: real,C: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6176_le__divide__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [W: num,B: rat,C: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % le_divide_eq_numeral(2)
% 0.32/0.61  thf(fact_6177_divide__le__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: real,C: real,W: num] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.61        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.61           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 0.32/0.61              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 0.32/0.61               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_le_eq_numeral(2)
% 0.32/0.61  thf(fact_6178_divide__le__eq__numeral_I2_J,axiom,
% 0.32/0.61      ! [B: rat,C: rat,W: num] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.32/0.61        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.32/0.61          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.32/0.61           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.32/0.61              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.32/0.61               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % divide_le_eq_numeral(2)
% 0.32/0.61  thf(fact_6179_zero__le__power__eq,axiom,
% 0.32/0.61      ! [A: real,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_eq
% 0.32/0.61  thf(fact_6180_zero__le__power__eq,axiom,
% 0.32/0.61      ! [A: rat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_eq
% 0.32/0.61  thf(fact_6181_zero__le__power__eq,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.32/0.61        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_power_eq
% 0.32/0.61  thf(fact_6182_zero__le__odd__power,axiom,
% 0.32/0.61      ! [N: nat,A: real] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.32/0.61          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_odd_power
% 0.32/0.61  thf(fact_6183_zero__le__odd__power,axiom,
% 0.32/0.61      ! [N: nat,A: rat] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.32/0.61          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_odd_power
% 0.32/0.61  thf(fact_6184_zero__le__odd__power,axiom,
% 0.32/0.61      ! [N: nat,A: int] :
% 0.32/0.61        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.32/0.61          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_odd_power
% 0.32/0.61  thf(fact_6185_zero__le__even__power,axiom,
% 0.32/0.61      ! [N: nat,A: real] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_even_power
% 0.32/0.61  thf(fact_6186_zero__le__even__power,axiom,
% 0.32/0.61      ! [N: nat,A: rat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_even_power
% 0.32/0.61  thf(fact_6187_zero__le__even__power,axiom,
% 0.32/0.61      ! [N: nat,A: int] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_even_power
% 0.32/0.61  thf(fact_6188_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.61       => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.61         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.32/0.61  thf(fact_6189_square__le__1,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.61       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.61         => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % square_le_1
% 0.32/0.61  thf(fact_6190_square__le__1,axiom,
% 0.32/0.61      ! [X: code_integer] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.32/0.61       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 0.32/0.61         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % square_le_1
% 0.32/0.61  thf(fact_6191_square__le__1,axiom,
% 0.32/0.61      ! [X: rat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 0.32/0.61       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 0.32/0.61         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % square_le_1
% 0.32/0.61  thf(fact_6192_square__le__1,axiom,
% 0.32/0.61      ! [X: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.32/0.61       => ( ( ord_less_eq_int @ X @ one_one_int )
% 0.32/0.61         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % square_le_1
% 0.32/0.61  thf(fact_6193_minus__power__mult__self,axiom,
% 0.32/0.61      ! [A: real,N: nat] :
% 0.32/0.61        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.32/0.61        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_power_mult_self
% 0.32/0.61  thf(fact_6194_minus__power__mult__self,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.32/0.61        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_power_mult_self
% 0.32/0.61  thf(fact_6195_minus__power__mult__self,axiom,
% 0.32/0.61      ! [A: complex,N: nat] :
% 0.32/0.61        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 0.32/0.61        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_power_mult_self
% 0.32/0.61  thf(fact_6196_minus__power__mult__self,axiom,
% 0.32/0.61      ! [A: code_integer,N: nat] :
% 0.32/0.61        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.32/0.61        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_power_mult_self
% 0.32/0.61  thf(fact_6197_minus__power__mult__self,axiom,
% 0.32/0.61      ! [A: rat,N: nat] :
% 0.32/0.61        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.32/0.61        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_power_mult_self
% 0.32/0.61  thf(fact_6198_list__decode_Ocases,axiom,
% 0.32/0.61      ! [X: nat] :
% 0.32/0.61        ( ( X != zero_zero_nat )
% 0.32/0.61       => ~ ! [N3: nat] :
% 0.32/0.61              ( X
% 0.32/0.61             != ( suc @ N3 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % list_decode.cases
% 0.32/0.61  thf(fact_6199_zero__less__power__eq,axiom,
% 0.32/0.61      ! [A: real,N: nat] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.32/0.61        = ( ( N = zero_zero_nat )
% 0.32/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( A != zero_zero_real ) )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_power_eq
% 0.32/0.61  thf(fact_6200_zero__less__power__eq,axiom,
% 0.32/0.61      ! [A: rat,N: nat] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.32/0.61        = ( ( N = zero_zero_nat )
% 0.32/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( A != zero_zero_rat ) )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_power_eq
% 0.32/0.61  thf(fact_6201_zero__less__power__eq,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.32/0.61        = ( ( N = zero_zero_nat )
% 0.32/0.61          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( A != zero_zero_int ) )
% 0.32/0.61          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_power_eq
% 0.32/0.61  thf(fact_6202_power__minus1__odd,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus1_odd
% 0.32/0.61  thf(fact_6203_power__minus1__odd,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus1_odd
% 0.32/0.61  thf(fact_6204_power__minus1__odd,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus1_odd
% 0.32/0.61  thf(fact_6205_power__minus1__odd,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus1_odd
% 0.32/0.61  thf(fact_6206_power__minus1__odd,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_minus1_odd
% 0.32/0.61  thf(fact_6207_eq__diff__eq_H,axiom,
% 0.32/0.61      ! [X: real,Y: real,Z: real] :
% 0.32/0.61        ( ( X
% 0.32/0.61          = ( minus_minus_real @ Y @ Z ) )
% 0.32/0.61        = ( Y
% 0.32/0.61          = ( plus_plus_real @ X @ Z ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % eq_diff_eq'
% 0.32/0.61  thf(fact_6208_even__mask__div__iff_H,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff'
% 0.32/0.61  thf(fact_6209_even__mask__div__iff_H,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff'
% 0.32/0.61  thf(fact_6210_even__mask__div__iff_H,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff'
% 0.32/0.61  thf(fact_6211_power__le__zero__eq,axiom,
% 0.32/0.61      ! [A: real,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.32/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.32/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( A = zero_zero_real ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_le_zero_eq
% 0.32/0.61  thf(fact_6212_power__le__zero__eq,axiom,
% 0.32/0.61      ! [A: rat,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.32/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.32/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_le_zero_eq
% 0.32/0.61  thf(fact_6213_power__le__zero__eq,axiom,
% 0.32/0.61      ! [A: int,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.32/0.61        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.61          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.32/0.61            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61              & ( A = zero_zero_int ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % power_le_zero_eq
% 0.32/0.61  thf(fact_6214_even__mod__4__div__2,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.61          = ( suc @ zero_zero_nat ) )
% 0.32/0.61       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mod_4_div_2
% 0.32/0.61  thf(fact_6215_even__mask__div__iff,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_z3403309356797280102nteger )
% 0.32/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff
% 0.32/0.61  thf(fact_6216_even__mask__div__iff,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_zero_nat )
% 0.32/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff
% 0.32/0.61  thf(fact_6217_even__mask__div__iff,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_zero_int )
% 0.32/0.61          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mask_div_iff
% 0.32/0.61  thf(fact_6218_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.61       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.61         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_ln_one_plus_x_minus_x_bound_nonneg
% 0.32/0.61  thf(fact_6219_even__mult__exp__div__exp__iff,axiom,
% 0.32/0.61      ! [A: code_integer,M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ord_less_nat @ N @ M )
% 0.32/0.61          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_z3403309356797280102nteger )
% 0.32/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.61            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mult_exp_div_exp_iff
% 0.32/0.61  thf(fact_6220_even__mult__exp__div__exp__iff,axiom,
% 0.32/0.61      ! [A: nat,M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ord_less_nat @ N @ M )
% 0.32/0.61          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_zero_nat )
% 0.32/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.61            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mult_exp_div_exp_iff
% 0.32/0.61  thf(fact_6221_even__mult__exp__div__exp__iff,axiom,
% 0.32/0.61      ! [A: int,M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61        = ( ( ord_less_nat @ N @ M )
% 0.32/0.61          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.32/0.61            = zero_zero_int )
% 0.32/0.61          | ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.61            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_mult_exp_div_exp_iff
% 0.32/0.61  thf(fact_6222_compl__le__compl__iff,axiom,
% 0.32/0.61      ! [X: set_int,Y: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 0.32/0.61        = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % compl_le_compl_iff
% 0.32/0.61  thf(fact_6223_signed__take__bit__rec,axiom,
% 0.32/0.61      ( bit_ri6519982836138164636nteger
% 0.32/0.61      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_rec
% 0.32/0.61  thf(fact_6224_signed__take__bit__rec,axiom,
% 0.32/0.61      ( bit_ri631733984087533419it_int
% 0.32/0.61      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_rec
% 0.32/0.61  thf(fact_6225_triangle__def,axiom,
% 0.32/0.61      ( nat_triangle
% 0.32/0.61      = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % triangle_def
% 0.32/0.61  thf(fact_6226_arctan__double,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.61       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 0.32/0.61          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_double
% 0.32/0.61  thf(fact_6227_vebt__buildup_Oelims,axiom,
% 0.32/0.61      ! [X: nat,Y: vEBT_VEBT] :
% 0.32/0.61        ( ( ( vEBT_vebt_buildup @ X )
% 0.32/0.61          = Y )
% 0.32/0.61       => ( ( ( X = zero_zero_nat )
% 0.32/0.61           => ( Y
% 0.32/0.61             != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.32/0.61         => ( ( ( X
% 0.32/0.61                = ( suc @ zero_zero_nat ) )
% 0.32/0.61             => ( Y
% 0.32/0.61               != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.32/0.61           => ~ ! [Va2: nat] :
% 0.32/0.61                  ( ( X
% 0.32/0.61                    = ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.61                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.61                       => ( Y
% 0.32/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.32/0.61                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.61                       => ( Y
% 0.32/0.61                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % vebt_buildup.elims
% 0.32/0.61  thf(fact_6228_flip__bit__0,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.32/0.61        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % flip_bit_0
% 0.32/0.61  thf(fact_6229_flip__bit__0,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.32/0.61        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % flip_bit_0
% 0.32/0.61  thf(fact_6230_flip__bit__0,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.32/0.61        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % flip_bit_0
% 0.32/0.61  thf(fact_6231_intind,axiom,
% 0.32/0.61      ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( P @ X )
% 0.32/0.61         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % intind
% 0.32/0.61  thf(fact_6232_intind,axiom,
% 0.32/0.61      ! [I: nat,N: nat,P: int > $o,X: int] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( P @ X )
% 0.32/0.61         => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % intind
% 0.32/0.61  thf(fact_6233_intind,axiom,
% 0.32/0.61      ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( P @ X )
% 0.32/0.61         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % intind
% 0.32/0.61  thf(fact_6234_Compl__anti__mono,axiom,
% 0.32/0.61      ! [A2: set_int,B3: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.61       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Compl_anti_mono
% 0.32/0.61  thf(fact_6235_Compl__subset__Compl__iff,axiom,
% 0.32/0.61      ! [A2: set_int,B3: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 0.32/0.61        = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Compl_subset_Compl_iff
% 0.32/0.61  thf(fact_6236_of__bool__less__eq__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.32/0.61        = ( P
% 0.32/0.61         => Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_iff
% 0.32/0.61  thf(fact_6237_of__bool__less__eq__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.32/0.61        = ( P
% 0.32/0.61         => Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_iff
% 0.32/0.61  thf(fact_6238_of__bool__less__eq__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.32/0.61        = ( P
% 0.32/0.61         => Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_iff
% 0.32/0.61  thf(fact_6239_of__bool__less__eq__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.32/0.61        = ( P
% 0.32/0.61         => Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_iff
% 0.32/0.61  thf(fact_6240_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n1201886186963655149omplex @ $false )
% 0.32/0.61      = zero_zero_complex ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6241_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n3304061248610475627l_real @ $false )
% 0.32/0.61      = zero_zero_real ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6242_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n2052037380579107095ol_rat @ $false )
% 0.32/0.61      = zero_zero_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6243_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n2687167440665602831ol_nat @ $false )
% 0.32/0.61      = zero_zero_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6244_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n2684676970156552555ol_int @ $false )
% 0.32/0.61      = zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6245_of__bool__eq_I1_J,axiom,
% 0.32/0.61      ( ( zero_n356916108424825756nteger @ $false )
% 0.32/0.61      = zero_z3403309356797280102nteger ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(1)
% 0.32/0.61  thf(fact_6246_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.32/0.61          = zero_zero_complex )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6247_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.32/0.61          = zero_zero_real )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6248_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.32/0.61          = zero_zero_rat )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6249_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.32/0.61          = zero_zero_nat )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6250_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.32/0.61          = zero_zero_int )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6251_of__bool__eq__0__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n356916108424825756nteger @ P )
% 0.32/0.61          = zero_z3403309356797280102nteger )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_0_iff
% 0.32/0.61  thf(fact_6252_of__bool__less__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 0.32/0.61        = ( ~ P
% 0.32/0.61          & Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_iff
% 0.32/0.61  thf(fact_6253_of__bool__less__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.32/0.61        = ( ~ P
% 0.32/0.61          & Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_iff
% 0.32/0.61  thf(fact_6254_of__bool__less__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.32/0.61        = ( ~ P
% 0.32/0.61          & Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_iff
% 0.32/0.61  thf(fact_6255_of__bool__less__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.32/0.61        = ( ~ P
% 0.32/0.61          & Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_iff
% 0.32/0.61  thf(fact_6256_of__bool__less__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.32/0.61        = ( ~ P
% 0.32/0.61          & Q ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_iff
% 0.32/0.61  thf(fact_6257_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n1201886186963655149omplex @ P )
% 0.32/0.61          = one_one_complex )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6258_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n3304061248610475627l_real @ P )
% 0.32/0.61          = one_one_real )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6259_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.32/0.61          = one_one_rat )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6260_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.32/0.61          = one_one_nat )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6261_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.32/0.61          = one_one_int )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6262_of__bool__eq__1__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ( zero_n356916108424825756nteger @ P )
% 0.32/0.61          = one_one_Code_integer )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_1_iff
% 0.32/0.61  thf(fact_6263_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n1201886186963655149omplex @ $true )
% 0.32/0.61      = one_one_complex ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6264_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n3304061248610475627l_real @ $true )
% 0.32/0.61      = one_one_real ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6265_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.32/0.61      = one_one_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6266_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.32/0.61      = one_one_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6267_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n2684676970156552555ol_int @ $true )
% 0.32/0.61      = one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6268_of__bool__eq_I2_J,axiom,
% 0.32/0.61      ( ( zero_n356916108424825756nteger @ $true )
% 0.32/0.61      = one_one_Code_integer ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq(2)
% 0.32/0.61  thf(fact_6269_signed__take__bit__of__0,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 0.32/0.61        = zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_of_0
% 0.32/0.61  thf(fact_6270_replicate__eq__replicate,axiom,
% 0.32/0.61      ! [M: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 0.32/0.61        ( ( ( replicate_VEBT_VEBT @ M @ X )
% 0.32/0.61          = ( replicate_VEBT_VEBT @ N @ Y ) )
% 0.32/0.61        = ( ( M = N )
% 0.32/0.61          & ( ( M != zero_zero_nat )
% 0.32/0.61           => ( X = Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eq_replicate
% 0.32/0.61  thf(fact_6271_abs__bool__eq,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.32/0.61        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_bool_eq
% 0.32/0.61  thf(fact_6272_abs__bool__eq,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.32/0.61        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_bool_eq
% 0.32/0.61  thf(fact_6273_abs__bool__eq,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.32/0.61        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_bool_eq
% 0.32/0.61  thf(fact_6274_abs__bool__eq,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 0.32/0.61        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_bool_eq
% 0.32/0.61  thf(fact_6275_zdvd1__eq,axiom,
% 0.32/0.61      ! [X: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ X @ one_one_int )
% 0.32/0.61        = ( ( abs_abs_int @ X )
% 0.32/0.61          = one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd1_eq
% 0.32/0.61  thf(fact_6276_length__replicate,axiom,
% 0.32/0.61      ! [N: nat,X: vEBT_VEBT] :
% 0.32/0.61        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.32/0.61        = N ) ).
% 0.32/0.61  
% 0.32/0.61  % length_replicate
% 0.32/0.61  thf(fact_6277_length__replicate,axiom,
% 0.32/0.61      ! [N: nat,X: $o] :
% 0.32/0.61        ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 0.32/0.61        = N ) ).
% 0.32/0.61  
% 0.32/0.61  % length_replicate
% 0.32/0.61  thf(fact_6278_length__replicate,axiom,
% 0.32/0.61      ! [N: nat,X: nat] :
% 0.32/0.61        ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 0.32/0.61        = N ) ).
% 0.32/0.61  
% 0.32/0.61  % length_replicate
% 0.32/0.61  thf(fact_6279_length__replicate,axiom,
% 0.32/0.61      ! [N: nat,X: int] :
% 0.32/0.61        ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 0.32/0.61        = N ) ).
% 0.32/0.61  
% 0.32/0.61  % length_replicate
% 0.32/0.61  thf(fact_6280_arctan__eq__zero__iff,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ( arctan @ X )
% 0.32/0.61          = zero_zero_real )
% 0.32/0.61        = ( X = zero_zero_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_eq_zero_iff
% 0.32/0.61  thf(fact_6281_arctan__zero__zero,axiom,
% 0.32/0.61      ( ( arctan @ zero_zero_real )
% 0.32/0.61      = zero_zero_real ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_zero_zero
% 0.32/0.61  thf(fact_6282_of__bool__or__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n2687167440665602831ol_nat
% 0.32/0.61          @ ( P
% 0.32/0.61            | Q ) )
% 0.32/0.61        = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_or_iff
% 0.32/0.61  thf(fact_6283_of__bool__or__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n2684676970156552555ol_int
% 0.32/0.61          @ ( P
% 0.32/0.61            | Q ) )
% 0.32/0.61        = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_or_iff
% 0.32/0.61  thf(fact_6284_of__bool__or__iff,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n356916108424825756nteger
% 0.32/0.61          @ ( P
% 0.32/0.61            | Q ) )
% 0.32/0.61        = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_or_iff
% 0.32/0.61  thf(fact_6285_triangle__0,axiom,
% 0.32/0.61      ( ( nat_triangle @ zero_zero_nat )
% 0.32/0.61      = zero_zero_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % triangle_0
% 0.32/0.61  thf(fact_6286_zero__less__of__bool__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_of_bool_iff
% 0.32/0.61  thf(fact_6287_zero__less__of__bool__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_of_bool_iff
% 0.32/0.61  thf(fact_6288_zero__less__of__bool__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_of_bool_iff
% 0.32/0.61  thf(fact_6289_zero__less__of__bool__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_of_bool_iff
% 0.32/0.61  thf(fact_6290_zero__less__of__bool__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 0.32/0.61        = P ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_of_bool_iff
% 0.32/0.61  thf(fact_6291_of__bool__less__one__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_one_iff
% 0.32/0.61  thf(fact_6292_of__bool__less__one__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_one_iff
% 0.32/0.61  thf(fact_6293_of__bool__less__one__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_one_iff
% 0.32/0.61  thf(fact_6294_of__bool__less__one__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_one_iff
% 0.32/0.61  thf(fact_6295_of__bool__less__one__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 0.32/0.61        = ( ~ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_one_iff
% 0.32/0.61  thf(fact_6296_of__bool__not__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( zero_n1201886186963655149omplex @ ~ P )
% 0.32/0.61        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_not_iff
% 0.32/0.61  thf(fact_6297_of__bool__not__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( zero_n3304061248610475627l_real @ ~ P )
% 0.32/0.61        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_not_iff
% 0.32/0.61  thf(fact_6298_of__bool__not__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.32/0.61        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_not_iff
% 0.32/0.61  thf(fact_6299_of__bool__not__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.32/0.61        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_not_iff
% 0.32/0.61  thf(fact_6300_of__bool__not__iff,axiom,
% 0.32/0.61      ! [P: $o] :
% 0.32/0.61        ( ( zero_n356916108424825756nteger @ ~ P )
% 0.32/0.61        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_not_iff
% 0.32/0.61  thf(fact_6301_Suc__0__mod__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.61        = ( zero_n2687167440665602831ol_nat
% 0.32/0.61          @ ( N
% 0.32/0.61           != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Suc_0_mod_eq
% 0.32/0.61  thf(fact_6302_zabs__less__one__iff,axiom,
% 0.32/0.61      ! [Z: int] :
% 0.32/0.61        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.32/0.61        = ( Z = zero_zero_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zabs_less_one_iff
% 0.32/0.61  thf(fact_6303_signed__take__bit__Suc__1,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 0.32/0.61        = one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_Suc_1
% 0.32/0.61  thf(fact_6304_signed__take__bit__of__minus__1,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.61        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_of_minus_1
% 0.32/0.61  thf(fact_6305_signed__take__bit__of__minus__1,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_of_minus_1
% 0.32/0.61  thf(fact_6306_signed__take__bit__numeral__of__1,axiom,
% 0.32/0.61      ! [K: num] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.32/0.61        = one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_numeral_of_1
% 0.32/0.61  thf(fact_6307_Ball__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.32/0.61        ( ( ! [X3: int] :
% 0.32/0.61              ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.32/0.61             => ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Ball_set_replicate
% 0.32/0.61  thf(fact_6308_Ball__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.32/0.61        ( ( ! [X3: nat] :
% 0.32/0.61              ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.32/0.61             => ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Ball_set_replicate
% 0.32/0.61  thf(fact_6309_Ball__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.32/0.61        ( ( ! [X3: vEBT_VEBT] :
% 0.32/0.61              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.32/0.61             => ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Ball_set_replicate
% 0.32/0.61  thf(fact_6310_Bex__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: int,P: int > $o] :
% 0.32/0.61        ( ( ? [X3: int] :
% 0.32/0.61              ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 0.32/0.61              & ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Bex_set_replicate
% 0.32/0.61  thf(fact_6311_Bex__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: nat,P: nat > $o] :
% 0.32/0.61        ( ( ? [X3: nat] :
% 0.32/0.61              ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.32/0.61              & ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Bex_set_replicate
% 0.32/0.61  thf(fact_6312_Bex__set__replicate,axiom,
% 0.32/0.61      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 0.32/0.61        ( ( ? [X3: vEBT_VEBT] :
% 0.32/0.61              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.32/0.61              & ( P @ X3 ) ) )
% 0.32/0.61        = ( ( P @ A )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % Bex_set_replicate
% 0.32/0.61  thf(fact_6313_in__set__replicate,axiom,
% 0.32/0.61      ! [X: complex,N: nat,Y: complex] :
% 0.32/0.61        ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6314_in__set__replicate,axiom,
% 0.32/0.61      ! [X: real,N: nat,Y: real] :
% 0.32/0.61        ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6315_in__set__replicate,axiom,
% 0.32/0.61      ! [X: set_nat,N: nat,Y: set_nat] :
% 0.32/0.61        ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6316_in__set__replicate,axiom,
% 0.32/0.61      ! [X: int,N: nat,Y: int] :
% 0.32/0.61        ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6317_in__set__replicate,axiom,
% 0.32/0.61      ! [X: nat,N: nat,Y: nat] :
% 0.32/0.61        ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6318_in__set__replicate,axiom,
% 0.32/0.61      ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 0.32/0.61        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 0.32/0.61        = ( ( X = Y )
% 0.32/0.61          & ( N != zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % in_set_replicate
% 0.32/0.61  thf(fact_6319_zero__less__arctan__iff,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 0.32/0.61        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_arctan_iff
% 0.32/0.61  thf(fact_6320_arctan__less__zero__iff,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 0.32/0.61        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_less_zero_iff
% 0.32/0.61  thf(fact_6321_nth__replicate,axiom,
% 0.32/0.61      ! [I: nat,N: nat,X: nat] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I )
% 0.32/0.61          = X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nth_replicate
% 0.32/0.61  thf(fact_6322_nth__replicate,axiom,
% 0.32/0.61      ! [I: nat,N: nat,X: int] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( nth_int @ ( replicate_int @ N @ X ) @ I )
% 0.32/0.61          = X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nth_replicate
% 0.32/0.61  thf(fact_6323_nth__replicate,axiom,
% 0.32/0.61      ! [I: nat,N: nat,X: vEBT_VEBT] :
% 0.32/0.61        ( ( ord_less_nat @ I @ N )
% 0.32/0.61       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I )
% 0.32/0.61          = X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nth_replicate
% 0.32/0.61  thf(fact_6324_arctan__le__zero__iff,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 0.32/0.61        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_le_zero_iff
% 0.32/0.61  thf(fact_6325_zero__le__arctan__iff,axiom,
% 0.32/0.61      ! [X: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 0.32/0.61        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_le_arctan_iff
% 0.32/0.61  thf(fact_6326_triangle__Suc,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( nat_triangle @ ( suc @ N ) )
% 0.32/0.61        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % triangle_Suc
% 0.32/0.61  thf(fact_6327_signed__take__bit__Suc__minus__bit0,axiom,
% 0.32/0.61      ! [N: nat,K: num] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_Suc_minus_bit0
% 0.32/0.61  thf(fact_6328_signed__take__bit__Suc__bit0,axiom,
% 0.32/0.61      ! [N: nat,K: num] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.32/0.61        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_Suc_bit0
% 0.32/0.61  thf(fact_6329_odd__of__bool__self,axiom,
% 0.32/0.61      ! [P5: $o] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P5 ) ) )
% 0.32/0.61        = P5 ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_of_bool_self
% 0.32/0.61  thf(fact_6330_odd__of__bool__self,axiom,
% 0.32/0.61      ! [P5: $o] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P5 ) ) )
% 0.32/0.61        = P5 ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_of_bool_self
% 0.32/0.61  thf(fact_6331_odd__of__bool__self,axiom,
% 0.32/0.61      ! [P5: $o] :
% 0.32/0.61        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P5 ) ) )
% 0.32/0.61        = P5 ) ).
% 0.32/0.61  
% 0.32/0.61  % odd_of_bool_self
% 0.32/0.61  thf(fact_6332_of__bool__half__eq__0,axiom,
% 0.32/0.61      ! [B: $o] :
% 0.32/0.61        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61        = zero_zero_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_half_eq_0
% 0.32/0.61  thf(fact_6333_of__bool__half__eq__0,axiom,
% 0.32/0.61      ! [B: $o] :
% 0.32/0.61        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61        = zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_half_eq_0
% 0.32/0.61  thf(fact_6334_of__bool__half__eq__0,axiom,
% 0.32/0.61      ! [B: $o] :
% 0.32/0.61        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61        = zero_z3403309356797280102nteger ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_half_eq_0
% 0.32/0.61  thf(fact_6335_signed__take__bit__0,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.32/0.61        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_0
% 0.32/0.61  thf(fact_6336_signed__take__bit__0,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.32/0.61        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_0
% 0.32/0.61  thf(fact_6337_one__div__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_div_2_pow_eq
% 0.32/0.61  thf(fact_6338_one__div__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_div_2_pow_eq
% 0.32/0.61  thf(fact_6339_one__div__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_div_2_pow_eq
% 0.32/0.61  thf(fact_6340_bits__1__div__exp,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_1_div_exp
% 0.32/0.61  thf(fact_6341_bits__1__div__exp,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_1_div_exp
% 0.32/0.61  thf(fact_6342_bits__1__div__exp,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_1_div_exp
% 0.32/0.61  thf(fact_6343_one__mod__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_mod_2_pow_eq
% 0.32/0.61  thf(fact_6344_one__mod__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_mod_2_pow_eq
% 0.32/0.61  thf(fact_6345_one__mod__2__pow__eq,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % one_mod_2_pow_eq
% 0.32/0.61  thf(fact_6346_dvd__antisym,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( dvd_dvd_nat @ M @ N )
% 0.32/0.61       => ( ( dvd_dvd_nat @ N @ M )
% 0.32/0.61         => ( M = N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_antisym
% 0.32/0.61  thf(fact_6347_of__bool__eq__iff,axiom,
% 0.32/0.61      ! [P5: $o,Q2: $o] :
% 0.32/0.61        ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 0.32/0.61          = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 0.32/0.61        = ( P5 = Q2 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_iff
% 0.32/0.61  thf(fact_6348_of__bool__eq__iff,axiom,
% 0.32/0.61      ! [P5: $o,Q2: $o] :
% 0.32/0.61        ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 0.32/0.61          = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 0.32/0.61        = ( P5 = Q2 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_iff
% 0.32/0.61  thf(fact_6349_of__bool__eq__iff,axiom,
% 0.32/0.61      ! [P5: $o,Q2: $o] :
% 0.32/0.61        ( ( ( zero_n356916108424825756nteger @ P5 )
% 0.32/0.61          = ( zero_n356916108424825756nteger @ Q2 ) )
% 0.32/0.61        = ( P5 = Q2 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_eq_iff
% 0.32/0.61  thf(fact_6350_zabs__def,axiom,
% 0.32/0.61      ( abs_abs_int
% 0.32/0.61      = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zabs_def
% 0.32/0.61  thf(fact_6351_of__bool__conj,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n3304061248610475627l_real
% 0.32/0.61          @ ( P
% 0.32/0.61            & Q ) )
% 0.32/0.61        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_conj
% 0.32/0.61  thf(fact_6352_of__bool__conj,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n2052037380579107095ol_rat
% 0.32/0.61          @ ( P
% 0.32/0.61            & Q ) )
% 0.32/0.61        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_conj
% 0.32/0.61  thf(fact_6353_of__bool__conj,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n2687167440665602831ol_nat
% 0.32/0.61          @ ( P
% 0.32/0.61            & Q ) )
% 0.32/0.61        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_conj
% 0.32/0.61  thf(fact_6354_of__bool__conj,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n2684676970156552555ol_int
% 0.32/0.61          @ ( P
% 0.32/0.61            & Q ) )
% 0.32/0.61        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_conj
% 0.32/0.61  thf(fact_6355_of__bool__conj,axiom,
% 0.32/0.61      ! [P: $o,Q: $o] :
% 0.32/0.61        ( ( zero_n356916108424825756nteger
% 0.32/0.61          @ ( P
% 0.32/0.61            & Q ) )
% 0.32/0.61        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_conj
% 0.32/0.61  thf(fact_6356_signed__take__bit__mult,axiom,
% 0.32/0.61      ! [N: nat,K: int,L2: int] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.32/0.61        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_mult
% 0.32/0.61  thf(fact_6357_signed__take__bit__add,axiom,
% 0.32/0.61      ! [N: nat,K: int,L2: int] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.32/0.61        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_add
% 0.32/0.61  thf(fact_6358_uminus__int__code_I1_J,axiom,
% 0.32/0.61      ( ( uminus_uminus_int @ zero_zero_int )
% 0.32/0.61      = zero_zero_int ) ).
% 0.32/0.61  
% 0.32/0.61  % uminus_int_code(1)
% 0.32/0.61  thf(fact_6359_abs__div,axiom,
% 0.32/0.61      ! [Y: int,X: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ Y @ X )
% 0.32/0.61       => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 0.32/0.61          = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_div
% 0.32/0.61  thf(fact_6360_signed__take__bit__diff,axiom,
% 0.32/0.61      ! [N: nat,K: int,L2: int] :
% 0.32/0.61        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 0.32/0.61        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_diff
% 0.32/0.61  thf(fact_6361_arctan__monotone_H,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.61       => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_monotone'
% 0.32/0.61  thf(fact_6362_arctan__le__iff,axiom,
% 0.32/0.61      ! [X: real,Y: real] :
% 0.32/0.61        ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.32/0.61        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.61  
% 0.32/0.61  % arctan_le_iff
% 0.32/0.61  thf(fact_6363_zero__less__eq__of__bool,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_eq_of_bool
% 0.32/0.61  thf(fact_6364_zero__less__eq__of__bool,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_eq_of_bool
% 0.32/0.61  thf(fact_6365_zero__less__eq__of__bool,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_eq_of_bool
% 0.32/0.61  thf(fact_6366_zero__less__eq__of__bool,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_eq_of_bool
% 0.32/0.61  thf(fact_6367_zero__less__eq__of__bool,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zero_less_eq_of_bool
% 0.32/0.61  thf(fact_6368_of__bool__less__eq__one,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_one
% 0.32/0.61  thf(fact_6369_of__bool__less__eq__one,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_one
% 0.32/0.61  thf(fact_6370_of__bool__less__eq__one,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_one
% 0.32/0.61  thf(fact_6371_of__bool__less__eq__one,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_one
% 0.32/0.61  thf(fact_6372_of__bool__less__eq__one,axiom,
% 0.32/0.61      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_less_eq_one
% 0.32/0.61  thf(fact_6373_of__bool__def,axiom,
% 0.32/0.61      ( zero_n1201886186963655149omplex
% 0.32/0.61      = ( ^ [P2: $o] : ( if_complex @ P2 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6374_of__bool__def,axiom,
% 0.32/0.61      ( zero_n3304061248610475627l_real
% 0.32/0.61      = ( ^ [P2: $o] : ( if_real @ P2 @ one_one_real @ zero_zero_real ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6375_of__bool__def,axiom,
% 0.32/0.61      ( zero_n2052037380579107095ol_rat
% 0.32/0.61      = ( ^ [P2: $o] : ( if_rat @ P2 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6376_of__bool__def,axiom,
% 0.32/0.61      ( zero_n2687167440665602831ol_nat
% 0.32/0.61      = ( ^ [P2: $o] : ( if_nat @ P2 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6377_of__bool__def,axiom,
% 0.32/0.61      ( zero_n2684676970156552555ol_int
% 0.32/0.61      = ( ^ [P2: $o] : ( if_int @ P2 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6378_of__bool__def,axiom,
% 0.32/0.61      ( zero_n356916108424825756nteger
% 0.32/0.61      = ( ^ [P2: $o] : ( if_Code_integer @ P2 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_def
% 0.32/0.61  thf(fact_6379_split__of__bool,axiom,
% 0.32/0.61      ! [P: complex > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_complex ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_zero_complex ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6380_split__of__bool,axiom,
% 0.32/0.61      ! [P: real > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_real ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_zero_real ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6381_split__of__bool,axiom,
% 0.32/0.61      ! [P: rat > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_rat ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_zero_rat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6382_split__of__bool,axiom,
% 0.32/0.61      ! [P: nat > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_nat ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6383_split__of__bool,axiom,
% 0.32/0.61      ! [P: int > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_int ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_zero_int ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6384_split__of__bool,axiom,
% 0.32/0.61      ! [P: code_integer > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 0.32/0.61        = ( ( P5
% 0.32/0.61           => ( P @ one_one_Code_integer ) )
% 0.32/0.61          & ( ~ P5
% 0.32/0.61           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool
% 0.32/0.61  thf(fact_6385_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: complex > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_complex ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6386_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: real > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_real ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6387_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: rat > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_rat ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6388_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: nat > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_nat ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6389_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: int > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_int ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6390_split__of__bool__asm,axiom,
% 0.32/0.61      ! [P: code_integer > $o,P5: $o] :
% 0.32/0.61        ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 0.32/0.61        = ( ~ ( ( P5
% 0.32/0.61                & ~ ( P @ one_one_Code_integer ) )
% 0.32/0.61              | ( ~ P5
% 0.32/0.61                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % split_of_bool_asm
% 0.32/0.61  thf(fact_6391_dvd__imp__le__int,axiom,
% 0.32/0.61      ! [I: int,D: int] :
% 0.32/0.61        ( ( I != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ D @ I )
% 0.32/0.61         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % dvd_imp_le_int
% 0.32/0.61  thf(fact_6392_replicate__length__same,axiom,
% 0.32/0.61      ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.32/0.61        ( ! [X6: vEBT_VEBT] :
% 0.32/0.61            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.32/0.61           => ( X6 = X ) )
% 0.32/0.61       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X )
% 0.32/0.61          = Xs ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_length_same
% 0.32/0.61  thf(fact_6393_replicate__length__same,axiom,
% 0.32/0.61      ! [Xs: list_o,X: $o] :
% 0.32/0.61        ( ! [X6: $o] :
% 0.32/0.61            ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 0.32/0.61           => ( X6 = X ) )
% 0.32/0.61       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X )
% 0.32/0.61          = Xs ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_length_same
% 0.32/0.61  thf(fact_6394_replicate__length__same,axiom,
% 0.32/0.61      ! [Xs: list_nat,X: nat] :
% 0.32/0.61        ( ! [X6: nat] :
% 0.32/0.61            ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 0.32/0.61           => ( X6 = X ) )
% 0.32/0.61       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X )
% 0.32/0.61          = Xs ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_length_same
% 0.32/0.61  thf(fact_6395_replicate__length__same,axiom,
% 0.32/0.61      ! [Xs: list_int,X: int] :
% 0.32/0.61        ( ! [X6: int] :
% 0.32/0.61            ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 0.32/0.61           => ( X6 = X ) )
% 0.32/0.61       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X )
% 0.32/0.61          = Xs ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_length_same
% 0.32/0.61  thf(fact_6396_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_complex,N: nat,X: complex] :
% 0.32/0.61        ( ( ( size_s3451745648224563538omplex @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: complex] :
% 0.32/0.61              ( ( member_complex @ Y5 @ ( set_complex2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_complex @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6397_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_real,N: nat,X: real] :
% 0.32/0.61        ( ( ( size_size_list_real @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: real] :
% 0.32/0.61              ( ( member_real @ Y5 @ ( set_real2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_real @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6398_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_set_nat,N: nat,X: set_nat] :
% 0.32/0.61        ( ( ( size_s3254054031482475050et_nat @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: set_nat] :
% 0.32/0.61              ( ( member_set_nat @ Y5 @ ( set_set_nat2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6399_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 0.32/0.61        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: vEBT_VEBT] :
% 0.32/0.61              ( ( member_VEBT_VEBT @ Y5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6400_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_o,N: nat,X: $o] :
% 0.32/0.61        ( ( ( size_size_list_o @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: $o] :
% 0.32/0.61              ( ( member_o @ Y5 @ ( set_o2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_o @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6401_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_nat,N: nat,X: nat] :
% 0.32/0.61        ( ( ( size_size_list_nat @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: nat] :
% 0.32/0.61              ( ( member_nat @ Y5 @ ( set_nat2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_nat @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6402_replicate__eqI,axiom,
% 0.32/0.61      ! [Xs: list_int,N: nat,X: int] :
% 0.32/0.61        ( ( ( size_size_list_int @ Xs )
% 0.32/0.61          = N )
% 0.32/0.61       => ( ! [Y5: int] :
% 0.32/0.61              ( ( member_int @ Y5 @ ( set_int2 @ Xs ) )
% 0.32/0.61             => ( Y5 = X ) )
% 0.32/0.61         => ( Xs
% 0.32/0.61            = ( replicate_int @ N @ X ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % replicate_eqI
% 0.32/0.61  thf(fact_6403_abs__zmult__eq__1,axiom,
% 0.32/0.61      ! [M: int,N: int] :
% 0.32/0.61        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.32/0.61          = one_one_int )
% 0.32/0.61       => ( ( abs_abs_int @ M )
% 0.32/0.61          = one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_zmult_eq_1
% 0.32/0.61  thf(fact_6404_subset__Compl__self__eq,axiom,
% 0.32/0.61      ! [A2: set_nat] :
% 0.32/0.61        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.32/0.61        = ( A2 = bot_bot_set_nat ) ) ).
% 0.32/0.61  
% 0.32/0.61  % subset_Compl_self_eq
% 0.32/0.61  thf(fact_6405_subset__Compl__self__eq,axiom,
% 0.32/0.61      ! [A2: set_real] :
% 0.32/0.61        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 0.32/0.61        = ( A2 = bot_bot_set_real ) ) ).
% 0.32/0.61  
% 0.32/0.61  % subset_Compl_self_eq
% 0.32/0.61  thf(fact_6406_subset__Compl__self__eq,axiom,
% 0.32/0.61      ! [A2: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.32/0.61        = ( A2 = bot_bot_set_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % subset_Compl_self_eq
% 0.32/0.61  thf(fact_6407_zmult__eq__1__iff,axiom,
% 0.32/0.61      ! [M: int,N: int] :
% 0.32/0.61        ( ( ( times_times_int @ M @ N )
% 0.32/0.61          = one_one_int )
% 0.32/0.61        = ( ( ( M = one_one_int )
% 0.32/0.61            & ( N = one_one_int ) )
% 0.32/0.61          | ( ( M
% 0.32/0.61              = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.61            & ( N
% 0.32/0.61              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmult_eq_1_iff
% 0.32/0.61  thf(fact_6408_pos__zmult__eq__1__iff__lemma,axiom,
% 0.32/0.61      ! [M: int,N: int] :
% 0.32/0.61        ( ( ( times_times_int @ M @ N )
% 0.32/0.61          = one_one_int )
% 0.32/0.61       => ( ( M = one_one_int )
% 0.32/0.61          | ( M
% 0.32/0.61            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % pos_zmult_eq_1_iff_lemma
% 0.32/0.61  thf(fact_6409_minus__int__code_I2_J,axiom,
% 0.32/0.61      ! [L2: int] :
% 0.32/0.61        ( ( minus_minus_int @ zero_zero_int @ L2 )
% 0.32/0.61        = ( uminus_uminus_int @ L2 ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_int_code(2)
% 0.32/0.61  thf(fact_6410_zmod__zminus1__not__zero,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 0.32/0.61         != zero_zero_int )
% 0.32/0.61       => ( ( modulo_modulo_int @ K @ L2 )
% 0.32/0.61         != zero_zero_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmod_zminus1_not_zero
% 0.32/0.61  thf(fact_6411_zmod__zminus2__not__zero,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 0.32/0.61         != zero_zero_int )
% 0.32/0.61       => ( ( modulo_modulo_int @ K @ L2 )
% 0.32/0.61         != zero_zero_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmod_zminus2_not_zero
% 0.32/0.61  thf(fact_6412_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.32/0.61      ! [N: nat,K: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.32/0.61        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_less_eq_self_iff
% 0.32/0.61  thf(fact_6413_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.32/0.61      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_greater_eq_minus_exp
% 0.32/0.61  thf(fact_6414_signed__take__bit__int__greater__self__iff,axiom,
% 0.32/0.61      ! [K: int,N: nat] :
% 0.32/0.61        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.32/0.61        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_greater_self_iff
% 0.32/0.61  thf(fact_6415_signed__take__bit__int__eq__self,axiom,
% 0.32/0.61      ! [N: nat,K: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.32/0.61       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.32/0.61            = K ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_eq_self
% 0.32/0.61  thf(fact_6416_signed__take__bit__int__eq__self__iff,axiom,
% 0.32/0.61      ! [N: nat,K: int] :
% 0.32/0.61        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.32/0.61          = K )
% 0.32/0.61        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.32/0.61          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_eq_self_iff
% 0.32/0.61  thf(fact_6417_zdvd__mult__cancel1,axiom,
% 0.32/0.61      ! [M: int,N: int] :
% 0.32/0.61        ( ( M != zero_zero_int )
% 0.32/0.61       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 0.32/0.61          = ( ( abs_abs_int @ N )
% 0.32/0.61            = one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdvd_mult_cancel1
% 0.32/0.61  thf(fact_6418_abs__mod__less,axiom,
% 0.32/0.61      ! [L2: int,K: int] :
% 0.32/0.61        ( ( L2 != zero_zero_int )
% 0.32/0.61       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % abs_mod_less
% 0.32/0.61  thf(fact_6419_zmod__zminus1__eq__if,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61            = zero_zero_int )
% 0.32/0.61         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.61            = zero_zero_int ) )
% 0.32/0.61        & ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61           != zero_zero_int )
% 0.32/0.61         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.61            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmod_zminus1_eq_if
% 0.32/0.61  thf(fact_6420_zmod__zminus2__eq__if,axiom,
% 0.32/0.61      ! [A: int,B: int] :
% 0.32/0.61        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61            = zero_zero_int )
% 0.32/0.61         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.61            = zero_zero_int ) )
% 0.32/0.61        & ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61           != zero_zero_int )
% 0.32/0.61         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.61            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmod_zminus2_eq_if
% 0.32/0.61  thf(fact_6421_even__abs__add__iff,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 0.32/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_abs_add_iff
% 0.32/0.61  thf(fact_6422_even__add__abs__iff,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 0.32/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_add_abs_iff
% 0.32/0.61  thf(fact_6423_signed__take__bit__int__greater__eq,axiom,
% 0.32/0.61      ! [K: int,N: nat] :
% 0.32/0.61        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.61       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_greater_eq
% 0.32/0.61  thf(fact_6424_verit__less__mono__div__int2,axiom,
% 0.32/0.61      ! [A2: int,B3: int,N: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ A2 @ B3 )
% 0.32/0.61       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.32/0.61         => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % verit_less_mono_div_int2
% 0.32/0.61  thf(fact_6425_div__eq__minus1,axiom,
% 0.32/0.61      ! [B: int] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.61       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.32/0.61          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_eq_minus1
% 0.32/0.61  thf(fact_6426_of__bool__odd__eq__mod__2,axiom,
% 0.32/0.61      ! [A: nat] :
% 0.32/0.61        ( ( zero_n2687167440665602831ol_nat
% 0.32/0.61          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_odd_eq_mod_2
% 0.32/0.61  thf(fact_6427_of__bool__odd__eq__mod__2,axiom,
% 0.32/0.61      ! [A: int] :
% 0.32/0.61        ( ( zero_n2684676970156552555ol_int
% 0.32/0.61          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_odd_eq_mod_2
% 0.32/0.61  thf(fact_6428_of__bool__odd__eq__mod__2,axiom,
% 0.32/0.61      ! [A: code_integer] :
% 0.32/0.61        ( ( zero_n356916108424825756nteger
% 0.32/0.61          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.32/0.61        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % of_bool_odd_eq_mod_2
% 0.32/0.61  thf(fact_6429_signed__take__bit__int__less__exp,axiom,
% 0.32/0.61      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_less_exp
% 0.32/0.61  thf(fact_6430_even__signed__take__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: code_integer] :
% 0.32/0.61        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 0.32/0.61        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_signed_take_bit_iff
% 0.32/0.61  thf(fact_6431_even__signed__take__bit__iff,axiom,
% 0.32/0.61      ! [M: nat,A: int] :
% 0.32/0.61        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 0.32/0.61        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.32/0.61  
% 0.32/0.61  % even_signed_take_bit_iff
% 0.32/0.61  thf(fact_6432_minus__mod__int__eq,axiom,
% 0.32/0.61      ! [L2: int,K: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 0.32/0.61       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 0.32/0.61          = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_mod_int_eq
% 0.32/0.61  thf(fact_6433_zmod__minus1,axiom,
% 0.32/0.61      ! [B: int] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.61       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.32/0.61          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zmod_minus1
% 0.32/0.61  thf(fact_6434_zdiv__zminus1__eq__if,axiom,
% 0.32/0.61      ! [B: int,A: int] :
% 0.32/0.61        ( ( B != zero_zero_int )
% 0.32/0.61       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61              = zero_zero_int )
% 0.32/0.61           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.61              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.32/0.61          & ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61             != zero_zero_int )
% 0.32/0.61           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.32/0.61              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdiv_zminus1_eq_if
% 0.32/0.61  thf(fact_6435_zdiv__zminus2__eq__if,axiom,
% 0.32/0.61      ! [B: int,A: int] :
% 0.32/0.61        ( ( B != zero_zero_int )
% 0.32/0.61       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61              = zero_zero_int )
% 0.32/0.61           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.61              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.32/0.61          & ( ( ( modulo_modulo_int @ A @ B )
% 0.32/0.61             != zero_zero_int )
% 0.32/0.61           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.32/0.61              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zdiv_zminus2_eq_if
% 0.32/0.61  thf(fact_6436_zminus1__lemma,axiom,
% 0.32/0.61      ! [A: int,B: int,Q2: int,R: int] :
% 0.32/0.61        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.61       => ( ( B != zero_zero_int )
% 0.32/0.61         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % zminus1_lemma
% 0.32/0.61  thf(fact_6437_bits__induct,axiom,
% 0.32/0.61      ! [P: nat > $o,A: nat] :
% 0.32/0.61        ( ! [A5: nat] :
% 0.32/0.61            ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61              = A5 )
% 0.32/0.61           => ( P @ A5 ) )
% 0.32/0.61       => ( ! [A5: nat,B5: $o] :
% 0.32/0.61              ( ( P @ A5 )
% 0.32/0.61             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.61                  = A5 )
% 0.32/0.61               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.32/0.61         => ( P @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_induct
% 0.32/0.61  thf(fact_6438_bits__induct,axiom,
% 0.32/0.61      ! [P: int > $o,A: int] :
% 0.32/0.61        ( ! [A5: int] :
% 0.32/0.61            ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61              = A5 )
% 0.32/0.61           => ( P @ A5 ) )
% 0.32/0.61       => ( ! [A5: int,B5: $o] :
% 0.32/0.61              ( ( P @ A5 )
% 0.32/0.61             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.61                  = A5 )
% 0.32/0.61               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.32/0.61         => ( P @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_induct
% 0.32/0.61  thf(fact_6439_bits__induct,axiom,
% 0.32/0.61      ! [P: code_integer > $o,A: code_integer] :
% 0.32/0.61        ( ! [A5: code_integer] :
% 0.32/0.61            ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61              = A5 )
% 0.32/0.61           => ( P @ A5 ) )
% 0.32/0.61       => ( ! [A5: code_integer,B5: $o] :
% 0.32/0.61              ( ( P @ A5 )
% 0.32/0.61             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.61                  = A5 )
% 0.32/0.61               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 0.32/0.61         => ( P @ A ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % bits_induct
% 0.32/0.61  thf(fact_6440_nat__intermed__int__val,axiom,
% 0.32/0.61      ! [M: nat,N: nat,F: nat > int,K: int] :
% 0.32/0.61        ( ! [I4: nat] :
% 0.32/0.61            ( ( ( ord_less_eq_nat @ M @ I4 )
% 0.32/0.61              & ( ord_less_nat @ I4 @ N ) )
% 0.32/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.32/0.61       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.61         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.32/0.61           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.61             => ? [I4: nat] :
% 0.32/0.61                  ( ( ord_less_eq_nat @ M @ I4 )
% 0.32/0.61                  & ( ord_less_eq_nat @ I4 @ N )
% 0.32/0.61                  & ( ( F @ I4 )
% 0.32/0.61                    = K ) ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nat_intermed_int_val
% 0.32/0.61  thf(fact_6441_decr__lemma,axiom,
% 0.32/0.61      ! [D: int,X: int,Z: int] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.61       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 0.32/0.61  
% 0.32/0.61  % decr_lemma
% 0.32/0.61  thf(fact_6442_incr__lemma,axiom,
% 0.32/0.61      ! [D: int,Z: int,X: int] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.61       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % incr_lemma
% 0.32/0.61  thf(fact_6443_signed__take__bit__int__less__self__iff,axiom,
% 0.32/0.61      ! [N: nat,K: int] :
% 0.32/0.61        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.32/0.61        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_less_self_iff
% 0.32/0.61  thf(fact_6444_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.32/0.61      ! [K: int,N: nat] :
% 0.32/0.61        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.32/0.61        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_greater_eq_self_iff
% 0.32/0.61  thf(fact_6445_minus__1__div__exp__eq__int,axiom,
% 0.32/0.61      ! [N: nat] :
% 0.32/0.61        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.61  
% 0.32/0.61  % minus_1_div_exp_eq_int
% 0.32/0.61  thf(fact_6446_div__pos__neg__trivial,axiom,
% 0.32/0.61      ! [K: int,L2: int] :
% 0.32/0.61        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.61       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 0.32/0.61         => ( ( divide_divide_int @ K @ L2 )
% 0.32/0.61            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % div_pos_neg_trivial
% 0.32/0.61  thf(fact_6447_compl__mono,axiom,
% 0.32/0.61      ! [X: set_int,Y: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ X @ Y )
% 0.32/0.61       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % compl_mono
% 0.32/0.61  thf(fact_6448_compl__le__swap1,axiom,
% 0.32/0.61      ! [Y: set_int,X: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 0.32/0.61       => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % compl_le_swap1
% 0.32/0.61  thf(fact_6449_compl__le__swap2,axiom,
% 0.32/0.61      ! [Y: set_int,X: set_int] :
% 0.32/0.61        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 0.32/0.61       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 0.32/0.61  
% 0.32/0.61  % compl_le_swap2
% 0.32/0.61  thf(fact_6450_exp__mod__exp,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % exp_mod_exp
% 0.32/0.61  thf(fact_6451_exp__mod__exp,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % exp_mod_exp
% 0.32/0.61  thf(fact_6452_exp__mod__exp,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % exp_mod_exp
% 0.32/0.61  thf(fact_6453_nat__ivt__aux,axiom,
% 0.32/0.61      ! [N: nat,F: nat > int,K: int] :
% 0.32/0.61        ( ! [I4: nat] :
% 0.32/0.61            ( ( ord_less_nat @ I4 @ N )
% 0.32/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.32/0.61       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.32/0.61         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.61           => ? [I4: nat] :
% 0.32/0.61                ( ( ord_less_eq_nat @ I4 @ N )
% 0.32/0.61                & ( ( F @ I4 )
% 0.32/0.61                  = K ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nat_ivt_aux
% 0.32/0.61  thf(fact_6454_signed__take__bit__int__less__eq,axiom,
% 0.32/0.61      ! [N: nat,K: int] :
% 0.32/0.61        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.32/0.61       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % signed_take_bit_int_less_eq
% 0.32/0.61  thf(fact_6455_int__bit__induct,axiom,
% 0.32/0.61      ! [P: int > $o,K: int] :
% 0.32/0.61        ( ( P @ zero_zero_int )
% 0.32/0.61       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.61         => ( ! [K3: int] :
% 0.32/0.61                ( ( P @ K3 )
% 0.32/0.61               => ( ( K3 != zero_zero_int )
% 0.32/0.61                 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.61           => ( ! [K3: int] :
% 0.32/0.61                  ( ( P @ K3 )
% 0.32/0.61                 => ( ( K3
% 0.32/0.61                     != ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.61                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.32/0.61             => ( P @ K ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % int_bit_induct
% 0.32/0.61  thf(fact_6456_nat0__intermed__int__val,axiom,
% 0.32/0.61      ! [N: nat,F: nat > int,K: int] :
% 0.32/0.61        ( ! [I4: nat] :
% 0.32/0.61            ( ( ord_less_nat @ I4 @ N )
% 0.32/0.61           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 0.32/0.61       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.32/0.61         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.32/0.61           => ? [I4: nat] :
% 0.32/0.61                ( ( ord_less_eq_nat @ I4 @ N )
% 0.32/0.61                & ( ( F @ I4 )
% 0.32/0.61                  = K ) ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % nat0_intermed_int_val
% 0.32/0.61  thf(fact_6457_exp__div__exp__eq,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( times_times_nat
% 0.32/0.61          @ ( zero_n2687167440665602831ol_nat
% 0.32/0.61            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.32/0.61               != zero_zero_nat )
% 0.32/0.61              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.32/0.61          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.61  
% 0.32/0.61  % exp_div_exp_eq
% 0.32/0.61  thf(fact_6458_exp__div__exp__eq,axiom,
% 0.32/0.61      ! [M: nat,N: nat] :
% 0.32/0.61        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.61        = ( times_times_int
% 0.32/0.61          @ ( zero_n2684676970156552555ol_int
% 0.32/0.61            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.32/0.61               != zero_zero_int )
% 0.32/0.61              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.32/0.61          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % exp_div_exp_eq
% 0.32/0.62  thf(fact_6459_exp__div__exp__eq,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.62        = ( times_3573771949741848930nteger
% 0.32/0.62          @ ( zero_n356916108424825756nteger
% 0.32/0.62            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.32/0.62               != zero_z3403309356797280102nteger )
% 0.32/0.62              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.32/0.62          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % exp_div_exp_eq
% 0.32/0.62  thf(fact_6460_arctan__add,axiom,
% 0.32/0.62      ! [X: real,Y: real] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.62       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.62         => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.32/0.62            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % arctan_add
% 0.32/0.62  thf(fact_6461_vebt__buildup_Osimps_I3_J,axiom,
% 0.32/0.62      ! [Va: nat] :
% 0.32/0.62        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.62         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.62            = ( 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 ) ) ) ) ) ) )
% 0.32/0.62        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.62         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 0.32/0.62            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % vebt_buildup.simps(3)
% 0.32/0.62  thf(fact_6462_diff__shunt__var,axiom,
% 0.32/0.62      ! [X: set_real,Y: set_real] :
% 0.32/0.62        ( ( ( minus_minus_set_real @ X @ Y )
% 0.32/0.62          = bot_bot_set_real )
% 0.32/0.62        = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % diff_shunt_var
% 0.32/0.62  thf(fact_6463_diff__shunt__var,axiom,
% 0.32/0.62      ! [X: set_nat,Y: set_nat] :
% 0.32/0.62        ( ( ( minus_minus_set_nat @ X @ Y )
% 0.32/0.62          = bot_bot_set_nat )
% 0.32/0.62        = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % diff_shunt_var
% 0.32/0.62  thf(fact_6464_diff__shunt__var,axiom,
% 0.32/0.62      ! [X: set_int,Y: set_int] :
% 0.32/0.62        ( ( ( minus_minus_set_int @ X @ Y )
% 0.32/0.62          = bot_bot_set_int )
% 0.32/0.62        = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % diff_shunt_var
% 0.32/0.62  thf(fact_6465_signed__take__bit__Suc,axiom,
% 0.32/0.62      ! [N: nat,A: code_integer] :
% 0.32/0.62        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 0.32/0.62        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_Suc
% 0.32/0.62  thf(fact_6466_signed__take__bit__Suc,axiom,
% 0.32/0.62      ! [N: nat,A: int] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 0.32/0.62        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_Suc
% 0.32/0.62  thf(fact_6467_Divides_Oadjust__div__eq,axiom,
% 0.32/0.62      ! [Q2: int,R: int] :
% 0.32/0.62        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 0.32/0.62        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Divides.adjust_div_eq
% 0.32/0.62  thf(fact_6468_vebt__buildup_Opelims,axiom,
% 0.32/0.62      ! [X: nat,Y: vEBT_VEBT] :
% 0.32/0.62        ( ( ( vEBT_vebt_buildup @ X )
% 0.32/0.62          = Y )
% 0.32/0.62       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 0.32/0.62         => ( ( ( X = zero_zero_nat )
% 0.32/0.62             => ( ( Y
% 0.32/0.62                  = ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.62               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.32/0.62           => ( ( ( X
% 0.32/0.62                  = ( suc @ zero_zero_nat ) )
% 0.32/0.62               => ( ( Y
% 0.32/0.62                    = ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.62                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.32/0.62             => ~ ! [Va2: nat] :
% 0.32/0.62                    ( ( X
% 0.32/0.62                      = ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.62                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.62                         => ( Y
% 0.32/0.62                            = ( 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 ) ) ) ) ) ) )
% 0.32/0.62                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.32/0.62                         => ( Y
% 0.32/0.62                            = ( 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 ) ) ) ) ) ) ) ) )
% 0.32/0.62                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % vebt_buildup.pelims
% 0.32/0.62  thf(fact_6469_option_Osize__gen_I2_J,axiom,
% 0.32/0.62      ! [X: nat > nat,X22: nat] :
% 0.32/0.62        ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 0.32/0.62        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(2)
% 0.32/0.62  thf(fact_6470_option_Osize__gen_I2_J,axiom,
% 0.32/0.62      ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 0.32/0.62        ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 0.32/0.62        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(2)
% 0.32/0.62  thf(fact_6471_option_Osize__gen_I2_J,axiom,
% 0.32/0.62      ! [X: num > nat,X22: num] :
% 0.32/0.62        ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 0.32/0.62        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(2)
% 0.32/0.62  thf(fact_6472_set__decode__0,axiom,
% 0.32/0.62      ! [X: nat] :
% 0.32/0.62        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 0.32/0.62        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % set_decode_0
% 0.32/0.62  thf(fact_6473_set__decode__Suc,axiom,
% 0.32/0.62      ! [N: nat,X: nat] :
% 0.32/0.62        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 0.32/0.62        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % set_decode_Suc
% 0.32/0.62  thf(fact_6474_add__scale__eq__noteq,axiom,
% 0.32/0.62      ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
% 0.32/0.62        ( ( R != zero_zero_complex )
% 0.32/0.62       => ( ( ( A = B )
% 0.32/0.62            & ( C != D ) )
% 0.32/0.62         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 0.32/0.62           != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_scale_eq_noteq
% 0.32/0.62  thf(fact_6475_add__scale__eq__noteq,axiom,
% 0.32/0.62      ! [R: real,A: real,B: real,C: real,D: real] :
% 0.32/0.62        ( ( R != zero_zero_real )
% 0.32/0.62       => ( ( ( A = B )
% 0.32/0.62            & ( C != D ) )
% 0.32/0.62         => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 0.32/0.62           != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_scale_eq_noteq
% 0.32/0.62  thf(fact_6476_add__scale__eq__noteq,axiom,
% 0.32/0.62      ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.62        ( ( R != zero_zero_rat )
% 0.32/0.62       => ( ( ( A = B )
% 0.32/0.62            & ( C != D ) )
% 0.32/0.62         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 0.32/0.62           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_scale_eq_noteq
% 0.32/0.62  thf(fact_6477_add__scale__eq__noteq,axiom,
% 0.32/0.62      ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.62        ( ( R != zero_zero_nat )
% 0.32/0.62       => ( ( ( A = B )
% 0.32/0.62            & ( C != D ) )
% 0.32/0.62         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 0.32/0.62           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_scale_eq_noteq
% 0.32/0.62  thf(fact_6478_add__scale__eq__noteq,axiom,
% 0.32/0.62      ! [R: int,A: int,B: int,C: int,D: int] :
% 0.32/0.62        ( ( R != zero_zero_int )
% 0.32/0.62       => ( ( ( A = B )
% 0.32/0.62            & ( C != D ) )
% 0.32/0.62         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 0.32/0.62           != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_scale_eq_noteq
% 0.32/0.62  thf(fact_6479_set__decode__zero,axiom,
% 0.32/0.62      ( ( nat_set_decode @ zero_zero_nat )
% 0.32/0.62      = bot_bot_set_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % set_decode_zero
% 0.32/0.62  thf(fact_6480_signed__take__bit__minus,axiom,
% 0.32/0.62      ! [N: nat,K: int] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 0.32/0.62        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_minus
% 0.32/0.62  thf(fact_6481_subset__decode__imp__le,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 0.32/0.62       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % subset_decode_imp_le
% 0.32/0.62  thf(fact_6482_add__0__iff,axiom,
% 0.32/0.62      ! [B: complex,A: complex] :
% 0.32/0.62        ( ( B
% 0.32/0.62          = ( plus_plus_complex @ B @ A ) )
% 0.32/0.62        = ( A = zero_zero_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_0_iff
% 0.32/0.62  thf(fact_6483_add__0__iff,axiom,
% 0.32/0.62      ! [B: real,A: real] :
% 0.32/0.62        ( ( B
% 0.32/0.62          = ( plus_plus_real @ B @ A ) )
% 0.32/0.62        = ( A = zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_0_iff
% 0.32/0.62  thf(fact_6484_add__0__iff,axiom,
% 0.32/0.62      ! [B: rat,A: rat] :
% 0.32/0.62        ( ( B
% 0.32/0.62          = ( plus_plus_rat @ B @ A ) )
% 0.32/0.62        = ( A = zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_0_iff
% 0.32/0.62  thf(fact_6485_add__0__iff,axiom,
% 0.32/0.62      ! [B: nat,A: nat] :
% 0.32/0.62        ( ( B
% 0.32/0.62          = ( plus_plus_nat @ B @ A ) )
% 0.32/0.62        = ( A = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_0_iff
% 0.32/0.62  thf(fact_6486_add__0__iff,axiom,
% 0.32/0.62      ! [B: int,A: int] :
% 0.32/0.62        ( ( B
% 0.32/0.62          = ( plus_plus_int @ B @ A ) )
% 0.32/0.62        = ( A = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % add_0_iff
% 0.32/0.62  thf(fact_6487_crossproduct__eq,axiom,
% 0.32/0.62      ! [W: real,Y: real,X: real,Z: real] :
% 0.32/0.62        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 0.32/0.62          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 0.32/0.62        = ( ( W = X )
% 0.32/0.62          | ( Y = Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_eq
% 0.32/0.62  thf(fact_6488_crossproduct__eq,axiom,
% 0.32/0.62      ! [W: rat,Y: rat,X: rat,Z: rat] :
% 0.32/0.62        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 0.32/0.62          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 0.32/0.62        = ( ( W = X )
% 0.32/0.62          | ( Y = Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_eq
% 0.32/0.62  thf(fact_6489_crossproduct__eq,axiom,
% 0.32/0.62      ! [W: nat,Y: nat,X: nat,Z: nat] :
% 0.32/0.62        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 0.32/0.62          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 0.32/0.62        = ( ( W = X )
% 0.32/0.62          | ( Y = Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_eq
% 0.32/0.62  thf(fact_6490_crossproduct__eq,axiom,
% 0.32/0.62      ! [W: int,Y: int,X: int,Z: int] :
% 0.32/0.62        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 0.32/0.62          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 0.32/0.62        = ( ( W = X )
% 0.32/0.62          | ( Y = Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_eq
% 0.32/0.62  thf(fact_6491_crossproduct__noteq,axiom,
% 0.32/0.62      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.62        ( ( ( A != B )
% 0.32/0.62          & ( C != D ) )
% 0.32/0.62        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 0.32/0.62         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_noteq
% 0.32/0.62  thf(fact_6492_crossproduct__noteq,axiom,
% 0.32/0.62      ! [A: rat,B: rat,C: rat,D: rat] :
% 0.32/0.62        ( ( ( A != B )
% 0.32/0.62          & ( C != D ) )
% 0.32/0.62        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 0.32/0.62         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_noteq
% 0.32/0.62  thf(fact_6493_crossproduct__noteq,axiom,
% 0.32/0.62      ! [A: nat,B: nat,C: nat,D: nat] :
% 0.32/0.62        ( ( ( A != B )
% 0.32/0.62          & ( C != D ) )
% 0.32/0.62        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 0.32/0.62         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_noteq
% 0.32/0.62  thf(fact_6494_crossproduct__noteq,axiom,
% 0.32/0.62      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.62        ( ( ( A != B )
% 0.32/0.62          & ( C != D ) )
% 0.32/0.62        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 0.32/0.62         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % crossproduct_noteq
% 0.32/0.62  thf(fact_6495_option_Osize__gen_I1_J,axiom,
% 0.32/0.62      ! [X: nat > nat] :
% 0.32/0.62        ( ( size_option_nat @ X @ none_nat )
% 0.32/0.62        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(1)
% 0.32/0.62  thf(fact_6496_option_Osize__gen_I1_J,axiom,
% 0.32/0.62      ! [X: product_prod_nat_nat > nat] :
% 0.32/0.62        ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 0.32/0.62        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(1)
% 0.32/0.62  thf(fact_6497_option_Osize__gen_I1_J,axiom,
% 0.32/0.62      ! [X: num > nat] :
% 0.32/0.62        ( ( size_option_num @ X @ none_num )
% 0.32/0.62        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % option.size_gen(1)
% 0.32/0.62  thf(fact_6498_set__decode__def,axiom,
% 0.32/0.62      ( nat_set_decode
% 0.32/0.62      = ( ^ [X3: nat] :
% 0.32/0.62            ( collect_nat
% 0.32/0.62            @ ^ [N2: nat] :
% 0.32/0.62                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % set_decode_def
% 0.32/0.62  thf(fact_6499_signed__take__bit__Suc__minus__bit1,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.62        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_Suc_minus_bit1
% 0.32/0.62  thf(fact_6500_infinite__int__iff__unbounded__le,axiom,
% 0.32/0.62      ! [S2: set_int] :
% 0.32/0.62        ( ( ~ ( finite_finite_int @ S2 ) )
% 0.32/0.62        = ( ! [M3: int] :
% 0.32/0.62            ? [N2: int] :
% 0.32/0.62              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N2 ) )
% 0.32/0.62              & ( member_int @ N2 @ S2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % infinite_int_iff_unbounded_le
% 0.32/0.62  thf(fact_6501_of__int__code__if,axiom,
% 0.32/0.62      ( ring_1_of_int_real
% 0.32/0.62      = ( ^ [K2: int] :
% 0.32/0.62            ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 0.32/0.62            @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.62              @ ( if_real
% 0.32/0.62                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62                  = zero_zero_int )
% 0.32/0.62                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_code_if
% 0.32/0.62  thf(fact_6502_of__int__code__if,axiom,
% 0.32/0.62      ( ring_1_of_int_int
% 0.32/0.62      = ( ^ [K2: int] :
% 0.32/0.62            ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 0.32/0.62            @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.62              @ ( if_int
% 0.32/0.62                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62                  = zero_zero_int )
% 0.32/0.62                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_code_if
% 0.32/0.62  thf(fact_6503_of__int__code__if,axiom,
% 0.32/0.62      ( ring_17405671764205052669omplex
% 0.32/0.62      = ( ^ [K2: int] :
% 0.32/0.62            ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 0.32/0.62            @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.62              @ ( if_complex
% 0.32/0.62                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62                  = zero_zero_int )
% 0.32/0.62                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_code_if
% 0.32/0.62  thf(fact_6504_of__int__code__if,axiom,
% 0.32/0.62      ( ring_18347121197199848620nteger
% 0.32/0.62      = ( ^ [K2: int] :
% 0.32/0.62            ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.32/0.62            @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.62              @ ( if_Code_integer
% 0.32/0.62                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62                  = zero_zero_int )
% 0.32/0.62                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_code_if
% 0.32/0.62  thf(fact_6505_of__int__code__if,axiom,
% 0.32/0.62      ( ring_1_of_int_rat
% 0.32/0.62      = ( ^ [K2: int] :
% 0.32/0.62            ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 0.32/0.62            @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.62              @ ( if_rat
% 0.32/0.62                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62                  = zero_zero_int )
% 0.32/0.62                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_code_if
% 0.32/0.62  thf(fact_6506_one__div__minus__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % one_div_minus_numeral
% 0.32/0.62  thf(fact_6507_minus__one__div__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % minus_one_div_numeral
% 0.32/0.62  thf(fact_6508_semiring__norm_I90_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( bit1 @ M )
% 0.32/0.62          = ( bit1 @ N ) )
% 0.32/0.62        = ( M = N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(90)
% 0.32/0.62  thf(fact_6509_semiring__norm_I88_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( bit0 @ M )
% 0.32/0.62       != ( bit1 @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(88)
% 0.32/0.62  thf(fact_6510_semiring__norm_I89_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( bit1 @ M )
% 0.32/0.62       != ( bit0 @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(89)
% 0.32/0.62  thf(fact_6511_semiring__norm_I84_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( one
% 0.32/0.62       != ( bit1 @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(84)
% 0.32/0.62  thf(fact_6512_semiring__norm_I86_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( bit1 @ M )
% 0.32/0.62       != one ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(86)
% 0.32/0.62  thf(fact_6513_semiring__norm_I80_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( ord_less_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(80)
% 0.32/0.62  thf(fact_6514_semiring__norm_I73_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(73)
% 0.32/0.62  thf(fact_6515_of__int__eq__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ Z )
% 0.32/0.62          = zero_zero_int )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_0_iff
% 0.32/0.62  thf(fact_6516_of__int__eq__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ Z )
% 0.32/0.62          = zero_zero_real )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_0_iff
% 0.32/0.62  thf(fact_6517_of__int__eq__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.32/0.62          = zero_zero_complex )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_0_iff
% 0.32/0.62  thf(fact_6518_of__int__eq__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ Z )
% 0.32/0.62          = zero_zero_rat )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_0_iff
% 0.32/0.62  thf(fact_6519_of__int__0__eq__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( zero_zero_int
% 0.32/0.62          = ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_eq_iff
% 0.32/0.62  thf(fact_6520_of__int__0__eq__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( zero_zero_real
% 0.32/0.62          = ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_eq_iff
% 0.32/0.62  thf(fact_6521_of__int__0__eq__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( zero_zero_complex
% 0.32/0.62          = ( ring_17405671764205052669omplex @ Z ) )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_eq_iff
% 0.32/0.62  thf(fact_6522_of__int__0__eq__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( zero_zero_rat
% 0.32/0.62          = ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( Z = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_eq_iff
% 0.32/0.62  thf(fact_6523_of__int__0,axiom,
% 0.32/0.62      ( ( ring_1_of_int_int @ zero_zero_int )
% 0.32/0.62      = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0
% 0.32/0.62  thf(fact_6524_of__int__0,axiom,
% 0.32/0.62      ( ( ring_1_of_int_real @ zero_zero_int )
% 0.32/0.62      = zero_zero_real ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0
% 0.32/0.62  thf(fact_6525_of__int__0,axiom,
% 0.32/0.62      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 0.32/0.62      = zero_zero_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0
% 0.32/0.62  thf(fact_6526_of__int__0,axiom,
% 0.32/0.62      ( ( ring_1_of_int_rat @ zero_zero_int )
% 0.32/0.62      = zero_zero_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0
% 0.32/0.62  thf(fact_6527_of__int__eq__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.32/0.62          = ( numera6690914467698888265omplex @ N ) )
% 0.32/0.62        = ( Z
% 0.32/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_iff
% 0.32/0.62  thf(fact_6528_of__int__eq__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ Z )
% 0.32/0.62          = ( numeral_numeral_real @ N ) )
% 0.32/0.62        = ( Z
% 0.32/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_iff
% 0.32/0.62  thf(fact_6529_of__int__eq__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ Z )
% 0.32/0.62          = ( numeral_numeral_rat @ N ) )
% 0.32/0.62        = ( Z
% 0.32/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_iff
% 0.32/0.62  thf(fact_6530_of__int__eq__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ Z )
% 0.32/0.62          = ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( Z
% 0.32/0.62          = ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_iff
% 0.32/0.62  thf(fact_6531_of__int__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numera6690914467698888265omplex @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral
% 0.32/0.62  thf(fact_6532_of__int__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numeral_numeral_real @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral
% 0.32/0.62  thf(fact_6533_of__int__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numeral_numeral_rat @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral
% 0.32/0.62  thf(fact_6534_of__int__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numeral_numeral_int @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral
% 0.32/0.62  thf(fact_6535_of__int__le__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_iff
% 0.32/0.62  thf(fact_6536_of__int__le__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_iff
% 0.32/0.62  thf(fact_6537_of__int__le__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_iff
% 0.32/0.62  thf(fact_6538_of__int__less__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_iff
% 0.32/0.62  thf(fact_6539_of__int__less__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_iff
% 0.32/0.62  thf(fact_6540_of__int__less__iff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_int @ W @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_iff
% 0.32/0.62  thf(fact_6541_of__int__eq__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ Z )
% 0.32/0.62          = one_one_int )
% 0.32/0.62        = ( Z = one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_1_iff
% 0.32/0.62  thf(fact_6542_of__int__eq__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ Z )
% 0.32/0.62          = one_one_real )
% 0.32/0.62        = ( Z = one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_1_iff
% 0.32/0.62  thf(fact_6543_of__int__eq__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ Z )
% 0.32/0.62          = one_one_complex )
% 0.32/0.62        = ( Z = one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_1_iff
% 0.32/0.62  thf(fact_6544_of__int__eq__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ Z )
% 0.32/0.62          = one_one_rat )
% 0.32/0.62        = ( Z = one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_1_iff
% 0.32/0.62  thf(fact_6545_of__int__1,axiom,
% 0.32/0.62      ( ( ring_1_of_int_int @ one_one_int )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1
% 0.32/0.62  thf(fact_6546_of__int__1,axiom,
% 0.32/0.62      ( ( ring_1_of_int_real @ one_one_int )
% 0.32/0.62      = one_one_real ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1
% 0.32/0.62  thf(fact_6547_of__int__1,axiom,
% 0.32/0.62      ( ( ring_17405671764205052669omplex @ one_one_int )
% 0.32/0.62      = one_one_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1
% 0.32/0.62  thf(fact_6548_of__int__1,axiom,
% 0.32/0.62      ( ( ring_1_of_int_rat @ one_one_int )
% 0.32/0.62      = one_one_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1
% 0.32/0.62  thf(fact_6549_of__int__mult,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 0.32/0.62        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_mult
% 0.32/0.62  thf(fact_6550_of__int__mult,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 0.32/0.62        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_mult
% 0.32/0.62  thf(fact_6551_of__int__mult,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 0.32/0.62        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_mult
% 0.32/0.62  thf(fact_6552_of__int__mult,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 0.32/0.62        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_mult
% 0.32/0.62  thf(fact_6553_of__int__add,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 0.32/0.62        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_add
% 0.32/0.62  thf(fact_6554_of__int__add,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 0.32/0.62        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_add
% 0.32/0.62  thf(fact_6555_of__int__add,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 0.32/0.62        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_add
% 0.32/0.62  thf(fact_6556_of__int__add,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 0.32/0.62        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_add
% 0.32/0.62  thf(fact_6557_of__int__diff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 0.32/0.62        = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_diff
% 0.32/0.62  thf(fact_6558_of__int__diff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 0.32/0.62        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_diff
% 0.32/0.62  thf(fact_6559_of__int__diff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 0.32/0.62        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_diff
% 0.32/0.62  thf(fact_6560_of__int__diff,axiom,
% 0.32/0.62      ! [W: int,Z: int] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 0.32/0.62        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_diff
% 0.32/0.62  thf(fact_6561_semiring__norm_I9_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(9)
% 0.32/0.62  thf(fact_6562_semiring__norm_I7_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(7)
% 0.32/0.62  thf(fact_6563_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ X )
% 0.32/0.62          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.32/0.62        = ( X
% 0.32/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6564_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ X )
% 0.32/0.62          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.32/0.62        = ( X
% 0.32/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6565_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ X )
% 0.32/0.62          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.32/0.62        = ( X
% 0.32/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6566_of__int__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ X )
% 0.32/0.62          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 0.32/0.62        = ( X
% 0.32/0.62          = ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6567_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 0.32/0.62          = ( ring_1_of_int_rat @ X ) )
% 0.32/0.62        = ( ( power_power_int @ B @ W )
% 0.32/0.62          = X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6568_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 0.32/0.62          = ( ring_1_of_int_real @ X ) )
% 0.32/0.62        = ( ( power_power_int @ B @ W )
% 0.32/0.62          = X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6569_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 0.32/0.62          = ( ring_1_of_int_int @ X ) )
% 0.32/0.62        = ( ( power_power_int @ B @ W )
% 0.32/0.62          = X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6570_of__int__eq__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 0.32/0.62          = ( ring_17405671764205052669omplex @ X ) )
% 0.32/0.62        = ( ( power_power_int @ B @ W )
% 0.32/0.62          = X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6571_of__int__power,axiom,
% 0.32/0.62      ! [Z: int,N: nat] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 0.32/0.62        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power
% 0.32/0.62  thf(fact_6572_of__int__power,axiom,
% 0.32/0.62      ! [Z: int,N: nat] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 0.32/0.62        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power
% 0.32/0.62  thf(fact_6573_of__int__power,axiom,
% 0.32/0.62      ! [Z: int,N: nat] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 0.32/0.62        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power
% 0.32/0.62  thf(fact_6574_of__int__power,axiom,
% 0.32/0.62      ! [Z: int,N: nat] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 0.32/0.62        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power
% 0.32/0.62  thf(fact_6575_semiring__norm_I15_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(15)
% 0.32/0.62  thf(fact_6576_semiring__norm_I14_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(14)
% 0.32/0.62  thf(fact_6577_semiring__norm_I81_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( ord_less_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(81)
% 0.32/0.62  thf(fact_6578_semiring__norm_I72_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(72)
% 0.32/0.62  thf(fact_6579_semiring__norm_I77_J,axiom,
% 0.32/0.62      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(77)
% 0.32/0.62  thf(fact_6580_semiring__norm_I70_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(70)
% 0.32/0.62  thf(fact_6581_zdiv__numeral__Bit1,axiom,
% 0.32/0.62      ! [V: num,W: num] :
% 0.32/0.62        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.32/0.62        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % zdiv_numeral_Bit1
% 0.32/0.62  thf(fact_6582_semiring__norm_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 0.32/0.62        = ( bit1 @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(3)
% 0.32/0.62  thf(fact_6583_semiring__norm_I4_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(4)
% 0.32/0.62  thf(fact_6584_semiring__norm_I5_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 0.32/0.62        = ( bit1 @ M ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(5)
% 0.32/0.62  thf(fact_6585_semiring__norm_I8_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 0.32/0.62        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(8)
% 0.32/0.62  thf(fact_6586_semiring__norm_I10_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(10)
% 0.32/0.62  thf(fact_6587_semiring__norm_I16_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(16)
% 0.32/0.62  thf(fact_6588_semiring__norm_I79_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62        = ( ord_less_eq_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(79)
% 0.32/0.62  thf(fact_6589_semiring__norm_I74_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( ord_less_num @ M @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(74)
% 0.32/0.62  thf(fact_6590_of__int__0__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_le_iff
% 0.32/0.62  thf(fact_6591_of__int__0__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_le_iff
% 0.32/0.62  thf(fact_6592_of__int__0__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_le_iff
% 0.32/0.62  thf(fact_6593_of__int__le__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_0_iff
% 0.32/0.62  thf(fact_6594_of__int__le__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_0_iff
% 0.32/0.62  thf(fact_6595_of__int__le__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_0_iff
% 0.32/0.62  thf(fact_6596_of__int__0__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_less_iff
% 0.32/0.62  thf(fact_6597_of__int__0__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_less_iff
% 0.32/0.62  thf(fact_6598_of__int__0__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_0_less_iff
% 0.32/0.62  thf(fact_6599_of__int__less__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 0.32/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_0_iff
% 0.32/0.62  thf(fact_6600_of__int__less__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 0.32/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_0_iff
% 0.32/0.62  thf(fact_6601_of__int__less__0__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 0.32/0.62        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_0_iff
% 0.32/0.62  thf(fact_6602_of__int__le__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_iff
% 0.32/0.62  thf(fact_6603_of__int__le__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_iff
% 0.32/0.62  thf(fact_6604_of__int__le__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_iff
% 0.32/0.62  thf(fact_6605_of__int__numeral__le__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_le_iff
% 0.32/0.62  thf(fact_6606_of__int__numeral__le__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_le_iff
% 0.32/0.62  thf(fact_6607_of__int__numeral__le__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_le_iff
% 0.32/0.62  thf(fact_6608_of__int__numeral__less__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_less_iff
% 0.32/0.62  thf(fact_6609_of__int__numeral__less__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_less_iff
% 0.32/0.62  thf(fact_6610_of__int__numeral__less__iff,axiom,
% 0.32/0.62      ! [N: num,Z: int] :
% 0.32/0.62        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_numeral_less_iff
% 0.32/0.62  thf(fact_6611_of__int__less__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_iff
% 0.32/0.62  thf(fact_6612_of__int__less__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 0.32/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_iff
% 0.32/0.62  thf(fact_6613_of__int__less__numeral__iff,axiom,
% 0.32/0.62      ! [Z: int,N: num] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_iff
% 0.32/0.62  thf(fact_6614_of__int__1__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_le_iff
% 0.32/0.62  thf(fact_6615_of__int__1__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_le_iff
% 0.32/0.62  thf(fact_6616_of__int__1__le__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_le_iff
% 0.32/0.62  thf(fact_6617_of__int__le__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_1_iff
% 0.32/0.62  thf(fact_6618_of__int__le__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_1_iff
% 0.32/0.62  thf(fact_6619_of__int__le__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.32/0.62        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_1_iff
% 0.32/0.62  thf(fact_6620_of__int__less__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 0.32/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_1_iff
% 0.32/0.62  thf(fact_6621_of__int__less__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.32/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_1_iff
% 0.32/0.62  thf(fact_6622_of__int__less__1__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.32/0.62        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_1_iff
% 0.32/0.62  thf(fact_6623_of__int__1__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 0.32/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_less_iff
% 0.32/0.62  thf(fact_6624_of__int__1__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.32/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_less_iff
% 0.32/0.62  thf(fact_6625_of__int__1__less__iff,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.32/0.62        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_1_less_iff
% 0.32/0.62  thf(fact_6626_dvd__numeral__simp,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dvd_numeral_simp
% 0.32/0.62  thf(fact_6627_dvd__numeral__simp,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.62        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dvd_numeral_simp
% 0.32/0.62  thf(fact_6628_dvd__numeral__simp,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.62        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dvd_numeral_simp
% 0.32/0.62  thf(fact_6629_divmod__algorithm__code_I2_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ M @ one )
% 0.32/0.62        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(2)
% 0.32/0.62  thf(fact_6630_divmod__algorithm__code_I2_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.32/0.62        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(2)
% 0.32/0.62  thf(fact_6631_divmod__algorithm__code_I2_J,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( unique3479559517661332726nteger @ M @ one )
% 0.32/0.62        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(2)
% 0.32/0.62  thf(fact_6632_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.32/0.62          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6633_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ Y )
% 0.32/0.62          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6634_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ Y )
% 0.32/0.62          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6635_of__int__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ Y )
% 0.32/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6636_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 0.32/0.62          = ( ring_17405671764205052669omplex @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6637_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 0.32/0.62          = ( ring_1_of_int_real @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6638_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 0.32/0.62          = ( ring_1_of_int_rat @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6639_numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.62          = ( ring_1_of_int_int @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6640_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6641_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6642_of__int__le__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6643_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6644_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6645_of__int__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6646_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6647_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6648_of__int__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: int,B: int,W: nat] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 0.32/0.62        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6649_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6650_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6651_of__int__less__of__int__power__cancel__iff,axiom,
% 0.32/0.62      ! [B: int,W: nat,X: int] :
% 0.32/0.62        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_of_int_power_cancel_iff
% 0.32/0.62  thf(fact_6652_div__Suc__eq__div__add3,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.32/0.62        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % div_Suc_eq_div_add3
% 0.32/0.62  thf(fact_6653_Suc__div__eq__add3__div__numeral,axiom,
% 0.32/0.62      ! [M: nat,V: num] :
% 0.32/0.62        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.32/0.62        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc_div_eq_add3_div_numeral
% 0.32/0.62  thf(fact_6654_divmod__algorithm__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 0.32/0.62        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(3)
% 0.32/0.62  thf(fact_6655_divmod__algorithm__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 0.32/0.62        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(3)
% 0.32/0.62  thf(fact_6656_divmod__algorithm__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(3)
% 0.32/0.62  thf(fact_6657_mod__Suc__eq__mod__add3,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.32/0.62        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mod_Suc_eq_mod_add3
% 0.32/0.62  thf(fact_6658_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.32/0.62      ! [M: nat,V: num] :
% 0.32/0.62        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 0.32/0.62        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc_mod_eq_add3_mod_numeral
% 0.32/0.62  thf(fact_6659_divmod__algorithm__code_I4_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 0.32/0.62        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(4)
% 0.32/0.62  thf(fact_6660_divmod__algorithm__code_I4_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 0.32/0.62        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(4)
% 0.32/0.62  thf(fact_6661_divmod__algorithm__code_I4_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 0.32/0.62        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(4)
% 0.32/0.62  thf(fact_6662_minus__numeral__div__numeral,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % minus_numeral_div_numeral
% 0.32/0.62  thf(fact_6663_numeral__div__minus__numeral,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_div_minus_numeral
% 0.32/0.62  thf(fact_6664_of__int__le__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6665_of__int__le__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6666_of__int__le__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6667_numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6668_numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6669_numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6670_of__int__less__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6671_of__int__less__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6672_of__int__less__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6673_numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6674_numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6675_numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6676_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_real @ Y )
% 0.32/0.62          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6677_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_int @ Y )
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6678_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_17405671764205052669omplex @ Y )
% 0.32/0.62          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6679_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.32/0.62          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6680_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [Y: int,X: num,N: nat] :
% 0.32/0.62        ( ( ( ring_1_of_int_rat @ Y )
% 0.32/0.62          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.32/0.62        = ( Y
% 0.32/0.62          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_eq_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6681_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 0.32/0.62          = ( ring_1_of_int_real @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6682_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = ( ring_1_of_int_int @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6683_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 0.32/0.62          = ( ring_17405671764205052669omplex @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6684_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 0.32/0.62          = ( ring_18347121197199848620nteger @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6685_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,Y: int] :
% 0.32/0.62        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 0.32/0.62          = ( ring_1_of_int_rat @ Y ) )
% 0.32/0.62        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.32/0.62          = Y ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_eq_of_int_cancel_iff
% 0.32/0.62  thf(fact_6686_zmod__numeral__Bit1,axiom,
% 0.32/0.62      ! [V: num,W: num] :
% 0.32/0.62        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.32/0.62        = ( 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 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % zmod_numeral_Bit1
% 0.32/0.62  thf(fact_6687_divmod__algorithm__code_I8_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(8)
% 0.32/0.62  thf(fact_6688_divmod__algorithm__code_I8_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(8)
% 0.32/0.62  thf(fact_6689_divmod__algorithm__code_I8_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_num @ M @ N )
% 0.32/0.62         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(8)
% 0.32/0.62  thf(fact_6690_divmod__algorithm__code_I7_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(7)
% 0.32/0.62  thf(fact_6691_divmod__algorithm__code_I7_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(7)
% 0.32/0.62  thf(fact_6692_divmod__algorithm__code_I7_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.32/0.62        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.32/0.62         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/0.62            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(7)
% 0.32/0.62  thf(fact_6693_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6694_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6695_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6696_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.32/0.62        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_le_of_int_cancel_iff
% 0.32/0.62  thf(fact_6697_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6698_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6699_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6700_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_le_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6701_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6702_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6703_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6704_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.32/0.62      ! [A: int,X: num,N: nat] :
% 0.32/0.62        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.32/0.62        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_less_neg_numeral_power_cancel_iff
% 0.32/0.62  thf(fact_6705_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6706_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6707_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6708_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.32/0.62      ! [X: num,N: nat,A: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.32/0.62        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % neg_numeral_power_less_of_int_cancel_iff
% 0.32/0.62  thf(fact_6709_signed__take__bit__Suc__bit1,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_Suc_bit1
% 0.32/0.62  thf(fact_6710_mult__of__int__commute,axiom,
% 0.32/0.62      ! [X: int,Y: complex] :
% 0.32/0.62        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 0.32/0.62        = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mult_of_int_commute
% 0.32/0.62  thf(fact_6711_mult__of__int__commute,axiom,
% 0.32/0.62      ! [X: int,Y: real] :
% 0.32/0.62        ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 0.32/0.62        = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mult_of_int_commute
% 0.32/0.62  thf(fact_6712_mult__of__int__commute,axiom,
% 0.32/0.62      ! [X: int,Y: rat] :
% 0.32/0.62        ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 0.32/0.62        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mult_of_int_commute
% 0.32/0.62  thf(fact_6713_mult__of__int__commute,axiom,
% 0.32/0.62      ! [X: int,Y: int] :
% 0.32/0.62        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 0.32/0.62        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mult_of_int_commute
% 0.32/0.62  thf(fact_6714_verit__eq__simplify_I14_J,axiom,
% 0.32/0.62      ! [X22: num,X32: num] :
% 0.32/0.62        ( ( bit0 @ X22 )
% 0.32/0.62       != ( bit1 @ X32 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % verit_eq_simplify(14)
% 0.32/0.62  thf(fact_6715_verit__eq__simplify_I12_J,axiom,
% 0.32/0.62      ! [X32: num] :
% 0.32/0.62        ( one
% 0.32/0.62       != ( bit1 @ X32 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % verit_eq_simplify(12)
% 0.32/0.62  thf(fact_6716_num_Oexhaust,axiom,
% 0.32/0.62      ! [Y: num] :
% 0.32/0.62        ( ( Y != one )
% 0.32/0.62       => ( ! [X23: num] :
% 0.32/0.62              ( Y
% 0.32/0.62             != ( bit0 @ X23 ) )
% 0.32/0.62         => ~ ! [X33: num] :
% 0.32/0.62                ( Y
% 0.32/0.62               != ( bit1 @ X33 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % num.exhaust
% 0.32/0.62  thf(fact_6717_xor__num_Ocases,axiom,
% 0.32/0.62      ! [X: product_prod_num_num] :
% 0.32/0.62        ( ( X
% 0.32/0.62         != ( product_Pair_num_num @ one @ one ) )
% 0.32/0.62       => ( ! [N3: num] :
% 0.32/0.62              ( X
% 0.32/0.62             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 0.32/0.62         => ( ! [N3: num] :
% 0.32/0.62                ( X
% 0.32/0.62               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 0.32/0.62           => ( ! [M4: num] :
% 0.32/0.62                  ( X
% 0.32/0.62                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 0.32/0.62             => ( ! [M4: num,N3: num] :
% 0.32/0.62                    ( X
% 0.32/0.62                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 0.32/0.62               => ( ! [M4: num,N3: num] :
% 0.32/0.62                      ( X
% 0.32/0.62                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 0.32/0.62                 => ( ! [M4: num] :
% 0.32/0.62                        ( X
% 0.32/0.62                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 0.32/0.62                   => ( ! [M4: num,N3: num] :
% 0.32/0.62                          ( X
% 0.32/0.62                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 0.32/0.62                     => ~ ! [M4: num,N3: num] :
% 0.32/0.62                            ( X
% 0.32/0.62                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % xor_num.cases
% 0.32/0.62  thf(fact_6718_numeral__Bit1,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1
% 0.32/0.62  thf(fact_6719_numeral__Bit1,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1
% 0.32/0.62  thf(fact_6720_numeral__Bit1,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1
% 0.32/0.62  thf(fact_6721_numeral__Bit1,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1
% 0.32/0.62  thf(fact_6722_numeral__Bit1,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1
% 0.32/0.62  thf(fact_6723_eval__nat__numeral_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.32/0.62        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % eval_nat_numeral(3)
% 0.32/0.62  thf(fact_6724_cong__exp__iff__simps_I10_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(10)
% 0.32/0.62  thf(fact_6725_cong__exp__iff__simps_I10_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(10)
% 0.32/0.62  thf(fact_6726_cong__exp__iff__simps_I10_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(10)
% 0.32/0.62  thf(fact_6727_cong__exp__iff__simps_I12_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(12)
% 0.32/0.62  thf(fact_6728_cong__exp__iff__simps_I12_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(12)
% 0.32/0.62  thf(fact_6729_cong__exp__iff__simps_I12_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(12)
% 0.32/0.62  thf(fact_6730_cong__exp__iff__simps_I13_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.32/0.62          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(13)
% 0.32/0.62  thf(fact_6731_cong__exp__iff__simps_I13_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.32/0.62          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(13)
% 0.32/0.62  thf(fact_6732_cong__exp__iff__simps_I13_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.32/0.62          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(13)
% 0.32/0.62  thf(fact_6733_power__minus__Bit1,axiom,
% 0.32/0.62      ! [X: real,K: num] :
% 0.32/0.62        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_minus_Bit1
% 0.32/0.62  thf(fact_6734_power__minus__Bit1,axiom,
% 0.32/0.62      ! [X: int,K: num] :
% 0.32/0.62        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_minus_Bit1
% 0.32/0.62  thf(fact_6735_power__minus__Bit1,axiom,
% 0.32/0.62      ! [X: complex,K: num] :
% 0.32/0.62        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_minus_Bit1
% 0.32/0.62  thf(fact_6736_power__minus__Bit1,axiom,
% 0.32/0.62      ! [X: code_integer,K: num] :
% 0.32/0.62        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_minus_Bit1
% 0.32/0.62  thf(fact_6737_power__minus__Bit1,axiom,
% 0.32/0.62      ! [X: rat,K: num] :
% 0.32/0.62        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_minus_Bit1
% 0.32/0.62  thf(fact_6738_real__of__int__div4,axiom,
% 0.32/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % real_of_int_div4
% 0.32/0.62  thf(fact_6739_real__of__int__div,axiom,
% 0.32/0.62      ! [D: int,N: int] :
% 0.32/0.62        ( ( dvd_dvd_int @ D @ N )
% 0.32/0.62       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 0.32/0.62          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % real_of_int_div
% 0.32/0.62  thf(fact_6740_numeral__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_code(3)
% 0.32/0.62  thf(fact_6741_numeral__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_code(3)
% 0.32/0.62  thf(fact_6742_numeral__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_code(3)
% 0.32/0.62  thf(fact_6743_numeral__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_code(3)
% 0.32/0.62  thf(fact_6744_numeral__code_I3_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.32/0.62        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_code(3)
% 0.32/0.62  thf(fact_6745_power__numeral__odd,axiom,
% 0.32/0.62      ! [Z: complex,W: num] :
% 0.32/0.62        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.32/0.62        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_numeral_odd
% 0.32/0.62  thf(fact_6746_power__numeral__odd,axiom,
% 0.32/0.62      ! [Z: real,W: num] :
% 0.32/0.62        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.32/0.62        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_numeral_odd
% 0.32/0.62  thf(fact_6747_power__numeral__odd,axiom,
% 0.32/0.62      ! [Z: rat,W: num] :
% 0.32/0.62        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.32/0.62        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_numeral_odd
% 0.32/0.62  thf(fact_6748_power__numeral__odd,axiom,
% 0.32/0.62      ! [Z: nat,W: num] :
% 0.32/0.62        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.32/0.62        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_numeral_odd
% 0.32/0.62  thf(fact_6749_power__numeral__odd,axiom,
% 0.32/0.62      ! [Z: int,W: num] :
% 0.32/0.62        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.32/0.62        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power_numeral_odd
% 0.32/0.62  thf(fact_6750_of__int__nonneg,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_nonneg
% 0.32/0.62  thf(fact_6751_of__int__nonneg,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_nonneg
% 0.32/0.62  thf(fact_6752_of__int__nonneg,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_nonneg
% 0.32/0.62  thf(fact_6753_of__int__leD,axiom,
% 0.32/0.62      ! [N: int,X: code_integer] :
% 0.32/0.62        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_leD
% 0.32/0.62  thf(fact_6754_of__int__leD,axiom,
% 0.32/0.62      ! [N: int,X: real] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_leD
% 0.32/0.62  thf(fact_6755_of__int__leD,axiom,
% 0.32/0.62      ! [N: int,X: rat] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_leD
% 0.32/0.62  thf(fact_6756_of__int__leD,axiom,
% 0.32/0.62      ! [N: int,X: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_leD
% 0.32/0.62  thf(fact_6757_of__int__pos,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_pos
% 0.32/0.62  thf(fact_6758_of__int__pos,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_pos
% 0.32/0.62  thf(fact_6759_of__int__pos,axiom,
% 0.32/0.62      ! [Z: int] :
% 0.32/0.62        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.62       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_pos
% 0.32/0.62  thf(fact_6760_of__int__lessD,axiom,
% 0.32/0.62      ! [N: int,X: code_integer] :
% 0.32/0.62        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_lessD
% 0.32/0.62  thf(fact_6761_of__int__lessD,axiom,
% 0.32/0.62      ! [N: int,X: real] :
% 0.32/0.62        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_lessD
% 0.32/0.62  thf(fact_6762_of__int__lessD,axiom,
% 0.32/0.62      ! [N: int,X: rat] :
% 0.32/0.62        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_lessD
% 0.32/0.62  thf(fact_6763_of__int__lessD,axiom,
% 0.32/0.62      ! [N: int,X: int] :
% 0.32/0.62        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.32/0.62       => ( ( N = zero_zero_int )
% 0.32/0.62          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_lessD
% 0.32/0.62  thf(fact_6764_of__int__neg__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_neg_numeral
% 0.32/0.62  thf(fact_6765_of__int__neg__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_neg_numeral
% 0.32/0.62  thf(fact_6766_of__int__neg__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_neg_numeral
% 0.32/0.62  thf(fact_6767_of__int__neg__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_neg_numeral
% 0.32/0.62  thf(fact_6768_of__int__neg__numeral,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_neg_numeral
% 0.32/0.62  thf(fact_6769_numeral__Bit1__div__2,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.62        = ( numeral_numeral_nat @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1_div_2
% 0.32/0.62  thf(fact_6770_numeral__Bit1__div__2,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_Bit1_div_2
% 0.32/0.62  thf(fact_6771_odd__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % odd_numeral
% 0.32/0.62  thf(fact_6772_odd__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % odd_numeral
% 0.32/0.62  thf(fact_6773_odd__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % odd_numeral
% 0.32/0.62  thf(fact_6774_cong__exp__iff__simps_I3_J,axiom,
% 0.32/0.62      ! [N: num,Q2: num] :
% 0.32/0.62        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(3)
% 0.32/0.62  thf(fact_6775_cong__exp__iff__simps_I3_J,axiom,
% 0.32/0.62      ! [N: num,Q2: num] :
% 0.32/0.62        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(3)
% 0.32/0.62  thf(fact_6776_cong__exp__iff__simps_I3_J,axiom,
% 0.32/0.62      ! [N: num,Q2: num] :
% 0.32/0.62        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62       != zero_z3403309356797280102nteger ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(3)
% 0.32/0.62  thf(fact_6777_power3__eq__cube,axiom,
% 0.32/0.62      ! [A: complex] :
% 0.32/0.62        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power3_eq_cube
% 0.32/0.62  thf(fact_6778_power3__eq__cube,axiom,
% 0.32/0.62      ! [A: real] :
% 0.32/0.62        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power3_eq_cube
% 0.32/0.62  thf(fact_6779_power3__eq__cube,axiom,
% 0.32/0.62      ! [A: rat] :
% 0.32/0.62        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power3_eq_cube
% 0.32/0.62  thf(fact_6780_power3__eq__cube,axiom,
% 0.32/0.62      ! [A: nat] :
% 0.32/0.62        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power3_eq_cube
% 0.32/0.62  thf(fact_6781_power3__eq__cube,axiom,
% 0.32/0.62      ! [A: int] :
% 0.32/0.62        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % power3_eq_cube
% 0.32/0.62  thf(fact_6782_numeral__3__eq__3,axiom,
% 0.32/0.62      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.32/0.62      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_3_eq_3
% 0.32/0.62  thf(fact_6783_Suc3__eq__add__3,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.32/0.62        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc3_eq_add_3
% 0.32/0.62  thf(fact_6784_int__le__real__less,axiom,
% 0.32/0.62      ( ord_less_eq_int
% 0.32/0.62      = ( ^ [N2: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % int_le_real_less
% 0.32/0.62  thf(fact_6785_int__less__real__le,axiom,
% 0.32/0.62      ( ord_less_int
% 0.32/0.62      = ( ^ [N2: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % int_less_real_le
% 0.32/0.62  thf(fact_6786_real__of__int__div__aux,axiom,
% 0.32/0.62      ! [X: int,D: int] :
% 0.32/0.62        ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 0.32/0.62        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % real_of_int_div_aux
% 0.32/0.62  thf(fact_6787_num_Osize_I6_J,axiom,
% 0.32/0.62      ! [X32: num] :
% 0.32/0.62        ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.32/0.62        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % num.size(6)
% 0.32/0.62  thf(fact_6788_cong__exp__iff__simps_I7_J,axiom,
% 0.32/0.62      ! [Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.32/0.62          = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(7)
% 0.32/0.62  thf(fact_6789_cong__exp__iff__simps_I7_J,axiom,
% 0.32/0.62      ! [Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.32/0.62          = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(7)
% 0.32/0.62  thf(fact_6790_cong__exp__iff__simps_I7_J,axiom,
% 0.32/0.62      ! [Q2: num,N: num] :
% 0.32/0.62        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.32/0.62          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(7)
% 0.32/0.62  thf(fact_6791_cong__exp__iff__simps_I11_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num] :
% 0.32/0.62        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.32/0.62          = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(11)
% 0.32/0.62  thf(fact_6792_cong__exp__iff__simps_I11_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num] :
% 0.32/0.62        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 0.32/0.62          = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(11)
% 0.32/0.62  thf(fact_6793_cong__exp__iff__simps_I11_J,axiom,
% 0.32/0.62      ! [M: num,Q2: num] :
% 0.32/0.62        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 0.32/0.62          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 0.32/0.62        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 0.32/0.62          = zero_z3403309356797280102nteger ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cong_exp_iff_simps(11)
% 0.32/0.62  thf(fact_6794_Suc__div__eq__add3__div,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.32/0.62        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc_div_eq_add3_div
% 0.32/0.62  thf(fact_6795_real__of__int__div2,axiom,
% 0.32/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % real_of_int_div2
% 0.32/0.62  thf(fact_6796_Suc__mod__eq__add3__mod,axiom,
% 0.32/0.62      ! [M: nat,N: nat] :
% 0.32/0.62        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.32/0.62        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc_mod_eq_add3_mod
% 0.32/0.62  thf(fact_6797_real__of__int__div3,axiom,
% 0.32/0.62      ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 0.32/0.62  
% 0.32/0.62  % real_of_int_div3
% 0.32/0.62  thf(fact_6798_divmod__int__def,axiom,
% 0.32/0.62      ( unique5052692396658037445od_int
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_int_def
% 0.32/0.62  thf(fact_6799_divmod__def,axiom,
% 0.32/0.62      ( unique5052692396658037445od_int
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_def
% 0.32/0.62  thf(fact_6800_divmod__def,axiom,
% 0.32/0.62      ( unique5055182867167087721od_nat
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_def
% 0.32/0.62  thf(fact_6801_divmod__def,axiom,
% 0.32/0.62      ( unique3479559517661332726nteger
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_def
% 0.32/0.62  thf(fact_6802_even__of__int__iff,axiom,
% 0.32/0.62      ! [K: int] :
% 0.32/0.62        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 0.32/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % even_of_int_iff
% 0.32/0.62  thf(fact_6803_even__of__int__iff,axiom,
% 0.32/0.62      ! [K: int] :
% 0.32/0.62        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 0.32/0.62        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 0.32/0.62  
% 0.32/0.62  % even_of_int_iff
% 0.32/0.62  thf(fact_6804_mod__exhaust__less__4,axiom,
% 0.32/0.62      ! [M: nat] :
% 0.32/0.62        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.62          = zero_zero_nat )
% 0.32/0.62        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.62          = one_one_nat )
% 0.32/0.62        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.62          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.62        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.62          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mod_exhaust_less_4
% 0.32/0.62  thf(fact_6805_infinite__nat__iff__unbounded,axiom,
% 0.32/0.62      ! [S2: set_nat] :
% 0.32/0.62        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.32/0.62        = ( ! [M3: nat] :
% 0.32/0.62            ? [N2: nat] :
% 0.32/0.62              ( ( ord_less_nat @ M3 @ N2 )
% 0.32/0.62              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % infinite_nat_iff_unbounded
% 0.32/0.62  thf(fact_6806_unbounded__k__infinite,axiom,
% 0.32/0.62      ! [K: nat,S2: set_nat] :
% 0.32/0.62        ( ! [M4: nat] :
% 0.32/0.62            ( ( ord_less_nat @ K @ M4 )
% 0.32/0.62           => ? [N7: nat] :
% 0.32/0.62                ( ( ord_less_nat @ M4 @ N7 )
% 0.32/0.62                & ( member_nat @ N7 @ S2 ) ) )
% 0.32/0.62       => ~ ( finite_finite_nat @ S2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % unbounded_k_infinite
% 0.32/0.62  thf(fact_6807_infinite__nat__iff__unbounded__le,axiom,
% 0.32/0.62      ! [S2: set_nat] :
% 0.32/0.62        ( ( ~ ( finite_finite_nat @ S2 ) )
% 0.32/0.62        = ( ! [M3: nat] :
% 0.32/0.62            ? [N2: nat] :
% 0.32/0.62              ( ( ord_less_eq_nat @ M3 @ N2 )
% 0.32/0.62              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % infinite_nat_iff_unbounded_le
% 0.32/0.62  thf(fact_6808_odd__mod__4__div__2,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.62          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.32/0.62       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % odd_mod_4_div_2
% 0.32/0.62  thf(fact_6809_divmod__divmod__step,axiom,
% 0.32/0.62      ( unique5055182867167087721od_nat
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_divmod_step
% 0.32/0.62  thf(fact_6810_divmod__divmod__step,axiom,
% 0.32/0.62      ( unique5052692396658037445od_int
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_divmod_step
% 0.32/0.62  thf(fact_6811_divmod__divmod__step,axiom,
% 0.32/0.62      ( unique3479559517661332726nteger
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_divmod_step
% 0.32/0.62  thf(fact_6812_floor__exists,axiom,
% 0.32/0.62      ! [X: real] :
% 0.32/0.62      ? [Z5: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 0.32/0.62        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % floor_exists
% 0.32/0.62  thf(fact_6813_floor__exists,axiom,
% 0.32/0.62      ! [X: rat] :
% 0.32/0.62      ? [Z5: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 0.32/0.62        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % floor_exists
% 0.32/0.62  thf(fact_6814_floor__exists1,axiom,
% 0.32/0.62      ! [X: real] :
% 0.32/0.62      ? [X6: int] :
% 0.32/0.62        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X6 ) @ X )
% 0.32/0.62        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 0.32/0.62        & ! [Y2: int] :
% 0.32/0.62            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ X )
% 0.32/0.62              & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 0.32/0.62           => ( Y2 = X6 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % floor_exists1
% 0.32/0.62  thf(fact_6815_floor__exists1,axiom,
% 0.32/0.62      ! [X: rat] :
% 0.32/0.62      ? [X6: int] :
% 0.32/0.62        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X6 ) @ X )
% 0.32/0.62        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 0.32/0.62        & ! [Y2: int] :
% 0.32/0.62            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ X )
% 0.32/0.62              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 0.32/0.62           => ( Y2 = X6 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % floor_exists1
% 0.32/0.62  thf(fact_6816_signed__take__bit__numeral__minus__bit1,axiom,
% 0.32/0.62      ! [L2: num,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.62        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_numeral_minus_bit1
% 0.32/0.62  thf(fact_6817_dbl__dec__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.62      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(4)
% 0.32/0.62  thf(fact_6818_dbl__dec__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.62      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(4)
% 0.32/0.62  thf(fact_6819_dbl__dec__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.62      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(4)
% 0.32/0.62  thf(fact_6820_dbl__dec__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.62      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(4)
% 0.32/0.62  thf(fact_6821_dbl__dec__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.62      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(4)
% 0.32/0.62  thf(fact_6822_signed__take__bit__numeral__bit1,axiom,
% 0.32/0.62      ! [L2: num,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.32/0.62        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_numeral_bit1
% 0.32/0.62  thf(fact_6823_dbl__inc__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.32/0.62      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(3)
% 0.32/0.62  thf(fact_6824_dbl__inc__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.32/0.62      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(3)
% 0.32/0.62  thf(fact_6825_dbl__inc__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.32/0.62      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(3)
% 0.32/0.62  thf(fact_6826_dbl__inc__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.32/0.62      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(3)
% 0.32/0.62  thf(fact_6827_dbl__dec__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.32/0.62      = one_one_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(3)
% 0.32/0.62  thf(fact_6828_dbl__dec__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.32/0.62      = one_one_real ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(3)
% 0.32/0.62  thf(fact_6829_dbl__dec__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.32/0.62      = one_one_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(3)
% 0.32/0.62  thf(fact_6830_dbl__dec__simps_I3_J,axiom,
% 0.32/0.62      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(3)
% 0.32/0.62  thf(fact_6831_pred__numeral__simps_I1_J,axiom,
% 0.32/0.62      ( ( pred_numeral @ one )
% 0.32/0.62      = zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % pred_numeral_simps(1)
% 0.32/0.62  thf(fact_6832_Suc__eq__numeral,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( ( suc @ N )
% 0.32/0.62          = ( numeral_numeral_nat @ K ) )
% 0.32/0.62        = ( N
% 0.32/0.62          = ( pred_numeral @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Suc_eq_numeral
% 0.32/0.62  thf(fact_6833_eq__numeral__Suc,axiom,
% 0.32/0.62      ! [K: num,N: nat] :
% 0.32/0.62        ( ( ( numeral_numeral_nat @ K )
% 0.32/0.62          = ( suc @ N ) )
% 0.32/0.62        = ( ( pred_numeral @ K )
% 0.32/0.62          = N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % eq_numeral_Suc
% 0.32/0.62  thf(fact_6834_dbl__inc__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.32/0.62      = one_one_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(2)
% 0.32/0.62  thf(fact_6835_dbl__inc__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.32/0.62      = one_one_real ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(2)
% 0.32/0.62  thf(fact_6836_dbl__inc__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.32/0.62      = one_one_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(2)
% 0.32/0.62  thf(fact_6837_dbl__inc__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(2)
% 0.32/0.62  thf(fact_6838_dbl__inc__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.62      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(4)
% 0.32/0.62  thf(fact_6839_dbl__inc__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.62      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(4)
% 0.32/0.62  thf(fact_6840_dbl__inc__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.62      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(4)
% 0.32/0.62  thf(fact_6841_dbl__inc__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.62      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(4)
% 0.32/0.62  thf(fact_6842_dbl__inc__simps_I4_J,axiom,
% 0.32/0.62      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.62      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(4)
% 0.32/0.62  thf(fact_6843_dbl__inc__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.32/0.62        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(5)
% 0.32/0.62  thf(fact_6844_dbl__inc__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 0.32/0.62        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(5)
% 0.32/0.62  thf(fact_6845_dbl__inc__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 0.32/0.62        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(5)
% 0.32/0.62  thf(fact_6846_dbl__inc__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(5)
% 0.32/0.62  thf(fact_6847_less__Suc__numeral,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.62        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % less_Suc_numeral
% 0.32/0.62  thf(fact_6848_less__numeral__Suc,axiom,
% 0.32/0.62      ! [K: num,N: nat] :
% 0.32/0.62        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.32/0.62        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % less_numeral_Suc
% 0.32/0.62  thf(fact_6849_pred__numeral__simps_I3_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( pred_numeral @ ( bit1 @ K ) )
% 0.32/0.62        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % pred_numeral_simps(3)
% 0.32/0.62  thf(fact_6850_le__numeral__Suc,axiom,
% 0.32/0.62      ! [K: num,N: nat] :
% 0.32/0.62        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.32/0.62        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % le_numeral_Suc
% 0.32/0.62  thf(fact_6851_le__Suc__numeral,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.62        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % le_Suc_numeral
% 0.32/0.62  thf(fact_6852_diff__numeral__Suc,axiom,
% 0.32/0.62      ! [K: num,N: nat] :
% 0.32/0.62        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.32/0.62        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % diff_numeral_Suc
% 0.32/0.62  thf(fact_6853_diff__Suc__numeral,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.62        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % diff_Suc_numeral
% 0.32/0.62  thf(fact_6854_max__numeral__Suc,axiom,
% 0.32/0.62      ! [K: num,N: nat] :
% 0.32/0.62        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 0.32/0.62        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % max_numeral_Suc
% 0.32/0.62  thf(fact_6855_max__Suc__numeral,axiom,
% 0.32/0.62      ! [N: nat,K: num] :
% 0.32/0.62        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.62        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % max_Suc_numeral
% 0.32/0.62  thf(fact_6856_dbl__dec__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.32/0.62      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(2)
% 0.32/0.62  thf(fact_6857_dbl__dec__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.32/0.62      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(2)
% 0.32/0.62  thf(fact_6858_dbl__dec__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.32/0.62      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(2)
% 0.32/0.62  thf(fact_6859_dbl__dec__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.32/0.62      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(2)
% 0.32/0.62  thf(fact_6860_dbl__dec__simps_I2_J,axiom,
% 0.32/0.62      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.32/0.62      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(2)
% 0.32/0.62  thf(fact_6861_dbl__dec__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(1)
% 0.32/0.62  thf(fact_6862_dbl__dec__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(1)
% 0.32/0.62  thf(fact_6863_dbl__dec__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.32/0.62        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(1)
% 0.32/0.62  thf(fact_6864_dbl__dec__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.32/0.62        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(1)
% 0.32/0.62  thf(fact_6865_dbl__dec__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(1)
% 0.32/0.62  thf(fact_6866_dbl__inc__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(1)
% 0.32/0.62  thf(fact_6867_dbl__inc__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(1)
% 0.32/0.62  thf(fact_6868_dbl__inc__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 0.32/0.62        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(1)
% 0.32/0.62  thf(fact_6869_dbl__inc__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.32/0.62        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(1)
% 0.32/0.62  thf(fact_6870_dbl__inc__simps_I1_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.32/0.62        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_simps(1)
% 0.32/0.62  thf(fact_6871_signed__take__bit__numeral__bit0,axiom,
% 0.32/0.62      ! [L2: num,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.32/0.62        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_numeral_bit0
% 0.32/0.62  thf(fact_6872_signed__take__bit__numeral__minus__bit0,axiom,
% 0.32/0.62      ! [L2: num,K: num] :
% 0.32/0.62        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.62        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % signed_take_bit_numeral_minus_bit0
% 0.32/0.62  thf(fact_6873_numeral__eq__Suc,axiom,
% 0.32/0.62      ( numeral_numeral_nat
% 0.32/0.62      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % numeral_eq_Suc
% 0.32/0.62  thf(fact_6874_pred__numeral__def,axiom,
% 0.32/0.62      ( pred_numeral
% 0.32/0.62      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % pred_numeral_def
% 0.32/0.62  thf(fact_6875_dbl__inc__def,axiom,
% 0.32/0.62      ( neg_nu8557863876264182079omplex
% 0.32/0.62      = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_def
% 0.32/0.62  thf(fact_6876_dbl__inc__def,axiom,
% 0.32/0.62      ( neg_nu8295874005876285629c_real
% 0.32/0.62      = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_def
% 0.32/0.62  thf(fact_6877_dbl__inc__def,axiom,
% 0.32/0.62      ( neg_nu5219082963157363817nc_rat
% 0.32/0.62      = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_def
% 0.32/0.62  thf(fact_6878_dbl__inc__def,axiom,
% 0.32/0.62      ( neg_nu5851722552734809277nc_int
% 0.32/0.62      = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_inc_def
% 0.32/0.62  thf(fact_6879_divmod_H__nat__def,axiom,
% 0.32/0.62      ( unique5055182867167087721od_nat
% 0.32/0.62      = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod'_nat_def
% 0.32/0.62  thf(fact_6880_dbl__dec__def,axiom,
% 0.32/0.62      ( neg_nu6511756317524482435omplex
% 0.32/0.62      = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_def
% 0.32/0.62  thf(fact_6881_dbl__dec__def,axiom,
% 0.32/0.62      ( neg_nu6075765906172075777c_real
% 0.32/0.62      = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_def
% 0.32/0.62  thf(fact_6882_dbl__dec__def,axiom,
% 0.32/0.62      ( neg_nu3179335615603231917ec_rat
% 0.32/0.62      = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_def
% 0.32/0.62  thf(fact_6883_dbl__dec__def,axiom,
% 0.32/0.62      ( neg_nu3811975205180677377ec_int
% 0.32/0.62      = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_def
% 0.32/0.62  thf(fact_6884_exists__least__lemma,axiom,
% 0.32/0.62      ! [P: nat > $o] :
% 0.32/0.62        ( ~ ( P @ zero_zero_nat )
% 0.32/0.62       => ( ? [X_12: nat] : ( P @ X_12 )
% 0.32/0.62         => ? [N3: nat] :
% 0.32/0.62              ( ~ ( P @ N3 )
% 0.32/0.62              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % exists_least_lemma
% 0.32/0.62  thf(fact_6885_ex__le__of__int,axiom,
% 0.32/0.62      ! [X: real] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_le_of_int
% 0.32/0.62  thf(fact_6886_ex__le__of__int,axiom,
% 0.32/0.62      ! [X: rat] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_le_of_int
% 0.32/0.62  thf(fact_6887_ex__of__int__less,axiom,
% 0.32/0.62      ! [X: real] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z5 ) @ X ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_of_int_less
% 0.32/0.62  thf(fact_6888_ex__of__int__less,axiom,
% 0.32/0.62      ! [X: rat] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z5 ) @ X ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_of_int_less
% 0.32/0.62  thf(fact_6889_ex__less__of__int,axiom,
% 0.32/0.62      ! [X: real] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_less_of_int
% 0.32/0.62  thf(fact_6890_ex__less__of__int,axiom,
% 0.32/0.62      ! [X: rat] :
% 0.32/0.62      ? [Z5: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % ex_less_of_int
% 0.32/0.62  thf(fact_6891_round__unique,axiom,
% 0.32/0.62      ! [X: real,Y: int] :
% 0.32/0.62        ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 0.32/0.62       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62         => ( ( archim8280529875227126926d_real @ X )
% 0.32/0.62            = Y ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_unique
% 0.32/0.62  thf(fact_6892_round__unique,axiom,
% 0.32/0.62      ! [X: rat,Y: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 0.32/0.62       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.62         => ( ( archim7778729529865785530nd_rat @ X )
% 0.32/0.62            = Y ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_unique
% 0.32/0.62  thf(fact_6893_round__unique_H,axiom,
% 0.32/0.62      ! [X: real,N: int] :
% 0.32/0.62        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.62       => ( ( archim8280529875227126926d_real @ X )
% 0.32/0.62          = N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_unique'
% 0.32/0.62  thf(fact_6894_round__unique_H,axiom,
% 0.32/0.62      ! [X: rat,N: int] :
% 0.32/0.62        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.32/0.62       => ( ( archim7778729529865785530nd_rat @ X )
% 0.32/0.62          = N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_unique'
% 0.32/0.62  thf(fact_6895_of__int__round__abs__le,axiom,
% 0.32/0.62      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_abs_le
% 0.32/0.62  thf(fact_6896_of__int__round__abs__le,axiom,
% 0.32/0.62      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_abs_le
% 0.32/0.62  thf(fact_6897_of__int__round__gt,axiom,
% 0.32/0.62      ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_gt
% 0.32/0.62  thf(fact_6898_of__int__round__gt,axiom,
% 0.32/0.62      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_gt
% 0.32/0.62  thf(fact_6899_of__int__round__ge,axiom,
% 0.32/0.62      ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_ge
% 0.32/0.62  thf(fact_6900_of__int__round__ge,axiom,
% 0.32/0.62      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_ge
% 0.32/0.62  thf(fact_6901_of__int__round__le,axiom,
% 0.32/0.62      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_le
% 0.32/0.62  thf(fact_6902_of__int__round__le,axiom,
% 0.32/0.62      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_round_le
% 0.32/0.62  thf(fact_6903_round__0,axiom,
% 0.32/0.62      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 0.32/0.62      = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % round_0
% 0.32/0.62  thf(fact_6904_round__0,axiom,
% 0.32/0.62      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 0.32/0.62      = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % round_0
% 0.32/0.62  thf(fact_6905_round__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 0.32/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_numeral
% 0.32/0.62  thf(fact_6906_round__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 0.32/0.62        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_numeral
% 0.32/0.62  thf(fact_6907_round__1,axiom,
% 0.32/0.62      ( ( archim8280529875227126926d_real @ one_one_real )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % round_1
% 0.32/0.62  thf(fact_6908_round__1,axiom,
% 0.32/0.62      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % round_1
% 0.32/0.62  thf(fact_6909_round__neg__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_neg_numeral
% 0.32/0.62  thf(fact_6910_round__neg__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.62        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_neg_numeral
% 0.32/0.62  thf(fact_6911_round__mono,axiom,
% 0.32/0.62      ! [X: rat,Y: rat] :
% 0.32/0.62        ( ( ord_less_eq_rat @ X @ Y )
% 0.32/0.62       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_mono
% 0.32/0.62  thf(fact_6912_round__diff__minimal,axiom,
% 0.32/0.62      ! [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 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_diff_minimal
% 0.32/0.62  thf(fact_6913_round__diff__minimal,axiom,
% 0.32/0.62      ! [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 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % round_diff_minimal
% 0.32/0.62  thf(fact_6914_divmod__BitM__2__eq,axiom,
% 0.32/0.62      ! [M: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.32/0.62        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_BitM_2_eq
% 0.32/0.62  thf(fact_6915_divmod__algorithm__code_I6_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc4245557441103728435nt_int
% 0.32/0.62          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 0.32/0.62          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(6)
% 0.32/0.62  thf(fact_6916_divmod__algorithm__code_I6_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc2626176000494625587at_nat
% 0.32/0.62          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 0.32/0.62          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(6)
% 0.32/0.62  thf(fact_6917_divmod__algorithm__code_I6_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc6916734918728496179nteger
% 0.32/0.62          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 0.32/0.62          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(6)
% 0.32/0.62  thf(fact_6918_Sum__Icc__int,axiom,
% 0.32/0.62      ! [M: int,N: int] :
% 0.32/0.62        ( ( ord_less_eq_int @ M @ N )
% 0.32/0.62       => ( ( groups4538972089207619220nt_int
% 0.32/0.62            @ ^ [X3: int] : X3
% 0.32/0.62            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.32/0.62          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % Sum_Icc_int
% 0.32/0.62  thf(fact_6919_divmod__step__def,axiom,
% 0.32/0.62      ( unique5026877609467782581ep_nat
% 0.32/0.62      = ( ^ [L: num] :
% 0.32/0.62            ( produc2626176000494625587at_nat
% 0.32/0.62            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_step_def
% 0.32/0.62  thf(fact_6920_divmod__step__def,axiom,
% 0.32/0.62      ( unique5024387138958732305ep_int
% 0.32/0.62      = ( ^ [L: num] :
% 0.32/0.62            ( produc4245557441103728435nt_int
% 0.32/0.62            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_step_def
% 0.32/0.62  thf(fact_6921_divmod__step__def,axiom,
% 0.32/0.62      ( unique4921790084139445826nteger
% 0.32/0.62      = ( ^ [L: num] :
% 0.32/0.62            ( produc6916734918728496179nteger
% 0.32/0.62            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_step_def
% 0.32/0.62  thf(fact_6922_even__set__encode__iff,axiom,
% 0.32/0.62      ! [A2: set_nat] :
% 0.32/0.62        ( ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 0.32/0.62          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % even_set_encode_iff
% 0.32/0.62  thf(fact_6923_mask__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 0.32/0.62        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_numeral
% 0.32/0.62  thf(fact_6924_mask__numeral,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 0.32/0.62        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_numeral
% 0.32/0.62  thf(fact_6925_mask__nat__positive__iff,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.32/0.62        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_nat_positive_iff
% 0.32/0.62  thf(fact_6926_sum_Oneutral__const,axiom,
% 0.32/0.62      ! [A2: set_int] :
% 0.32/0.62        ( ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [Uu3: int] : zero_zero_int
% 0.32/0.62          @ A2 )
% 0.32/0.62        = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral_const
% 0.32/0.62  thf(fact_6927_sum_Oneutral__const,axiom,
% 0.32/0.62      ! [A2: set_complex] :
% 0.32/0.62        ( ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [Uu3: complex] : zero_zero_complex
% 0.32/0.62          @ A2 )
% 0.32/0.62        = zero_zero_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral_const
% 0.32/0.62  thf(fact_6928_sum_Oneutral__const,axiom,
% 0.32/0.62      ! [A2: set_nat] :
% 0.32/0.62        ( ( groups3542108847815614940at_nat
% 0.32/0.62          @ ^ [Uu3: nat] : zero_zero_nat
% 0.32/0.62          @ A2 )
% 0.32/0.62        = zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral_const
% 0.32/0.62  thf(fact_6929_sum_Oneutral__const,axiom,
% 0.32/0.62      ! [A2: set_nat] :
% 0.32/0.62        ( ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [Uu3: nat] : zero_zero_real
% 0.32/0.62          @ A2 )
% 0.32/0.62        = zero_zero_real ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral_const
% 0.32/0.62  thf(fact_6930_case__prod__conv,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 0.32/0.62        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.32/0.62        = ( F @ A @ B ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_conv
% 0.32/0.62  thf(fact_6931_case__prod__conv,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.32/0.62        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 0.32/0.62        = ( F @ A @ B ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_conv
% 0.32/0.62  thf(fact_6932_case__prod__conv,axiom,
% 0.32/0.62      ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 0.32/0.62        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.32/0.62        = ( F @ A @ B ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_conv
% 0.32/0.62  thf(fact_6933_case__prod__conv,axiom,
% 0.32/0.62      ! [F: int > int > $o,A: int,B: int] :
% 0.32/0.62        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.32/0.62        = ( F @ A @ B ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_conv
% 0.32/0.62  thf(fact_6934_case__prod__conv,axiom,
% 0.32/0.62      ! [F: int > int > int,A: int,B: int] :
% 0.32/0.62        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.32/0.62        = ( F @ A @ B ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_conv
% 0.32/0.62  thf(fact_6935_sum_Oempty,axiom,
% 0.32/0.62      ! [G: nat > complex] :
% 0.32/0.62        ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 0.32/0.62        = zero_zero_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6936_sum_Oempty,axiom,
% 0.32/0.62      ! [G: nat > rat] :
% 0.32/0.62        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 0.32/0.62        = zero_zero_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6937_sum_Oempty,axiom,
% 0.32/0.62      ! [G: nat > int] :
% 0.32/0.62        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 0.32/0.62        = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6938_sum_Oempty,axiom,
% 0.32/0.62      ! [G: int > complex] :
% 0.32/0.62        ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 0.32/0.62        = zero_zero_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6939_sum_Oempty,axiom,
% 0.32/0.62      ! [G: int > real] :
% 0.32/0.62        ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 0.32/0.62        = zero_zero_real ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6940_sum_Oempty,axiom,
% 0.32/0.62      ! [G: int > rat] :
% 0.32/0.62        ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 0.32/0.62        = zero_zero_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6941_sum_Oempty,axiom,
% 0.32/0.62      ! [G: int > nat] :
% 0.32/0.62        ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 0.32/0.62        = zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6942_sum_Oempty,axiom,
% 0.32/0.62      ! [G: real > complex] :
% 0.32/0.62        ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 0.32/0.62        = zero_zero_complex ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6943_sum_Oempty,axiom,
% 0.32/0.62      ! [G: real > real] :
% 0.32/0.62        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 0.32/0.62        = zero_zero_real ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6944_sum_Oempty,axiom,
% 0.32/0.62      ! [G: real > rat] :
% 0.32/0.62        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 0.32/0.62        = zero_zero_rat ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.empty
% 0.32/0.62  thf(fact_6945_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > complex] :
% 0.32/0.62        ( ~ ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.32/0.62          = zero_zero_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6946_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > complex] :
% 0.32/0.62        ( ~ ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.32/0.62          = zero_zero_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6947_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > real] :
% 0.32/0.62        ( ~ ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.32/0.62          = zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6948_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > real] :
% 0.32/0.62        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.62          = zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6949_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > rat] :
% 0.32/0.62        ( ~ ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.32/0.62          = zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6950_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > rat] :
% 0.32/0.62        ( ~ ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.32/0.62          = zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6951_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > rat] :
% 0.32/0.62        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.62          = zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6952_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > nat] :
% 0.32/0.62        ( ~ ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.32/0.62          = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6953_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > nat] :
% 0.32/0.62        ( ~ ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.32/0.62          = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6954_sum_Oinfinite,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > int] :
% 0.32/0.62        ( ~ ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.32/0.62          = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.infinite
% 0.32/0.62  thf(fact_6955_sum__eq__0__iff,axiom,
% 0.32/0.62      ! [F3: set_int,F: int > nat] :
% 0.32/0.62        ( ( finite_finite_int @ F3 )
% 0.32/0.62       => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 0.32/0.62            = zero_zero_nat )
% 0.32/0.62          = ( ! [X3: int] :
% 0.32/0.62                ( ( member_int @ X3 @ F3 )
% 0.32/0.62               => ( ( F @ X3 )
% 0.32/0.62                  = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_eq_0_iff
% 0.32/0.62  thf(fact_6956_sum__eq__0__iff,axiom,
% 0.32/0.62      ! [F3: set_complex,F: complex > nat] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ F3 )
% 0.32/0.62       => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 0.32/0.62            = zero_zero_nat )
% 0.32/0.62          = ( ! [X3: complex] :
% 0.32/0.62                ( ( member_complex @ X3 @ F3 )
% 0.32/0.62               => ( ( F @ X3 )
% 0.32/0.62                  = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_eq_0_iff
% 0.32/0.62  thf(fact_6957_sum__eq__0__iff,axiom,
% 0.32/0.62      ! [F3: set_nat,F: nat > nat] :
% 0.32/0.62        ( ( finite_finite_nat @ F3 )
% 0.32/0.62       => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 0.32/0.62            = zero_zero_nat )
% 0.32/0.62          = ( ! [X3: nat] :
% 0.32/0.62                ( ( member_nat @ X3 @ F3 )
% 0.32/0.62               => ( ( F @ X3 )
% 0.32/0.62                  = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_eq_0_iff
% 0.32/0.62  thf(fact_6958_mask__eq__0__iff,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( ( bit_se2002935070580805687sk_nat @ N )
% 0.32/0.62          = zero_zero_nat )
% 0.32/0.62        = ( N = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_eq_0_iff
% 0.32/0.62  thf(fact_6959_mask__eq__0__iff,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( ( bit_se2000444600071755411sk_int @ N )
% 0.32/0.62          = zero_zero_int )
% 0.32/0.62        = ( N = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_eq_0_iff
% 0.32/0.62  thf(fact_6960_mask__0,axiom,
% 0.32/0.62      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 0.32/0.62      = zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_0
% 0.32/0.62  thf(fact_6961_mask__0,axiom,
% 0.32/0.62      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 0.32/0.62      = zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_0
% 0.32/0.62  thf(fact_6962_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > complex] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups5754745047067104278omplex
% 0.32/0.62                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups5754745047067104278omplex
% 0.32/0.62                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6963_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.32/0.62        ( ( finite_finite_nat @ S2 )
% 0.32/0.62       => ( ( ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2073611262835488442omplex
% 0.32/0.62                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2073611262835488442omplex
% 0.32/0.62                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6964_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > complex] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3049146728041665814omplex
% 0.32/0.62                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3049146728041665814omplex
% 0.32/0.62                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6965_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > real] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups8097168146408367636l_real
% 0.32/0.62                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups8097168146408367636l_real
% 0.32/0.62                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6966_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > real] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups8778361861064173332t_real
% 0.32/0.62                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups8778361861064173332t_real
% 0.32/0.62                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6967_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.62       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5808333547571424918x_real
% 0.32/0.62                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5808333547571424918x_real
% 0.32/0.62                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6968_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > rat] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups1300246762558778688al_rat
% 0.32/0.62                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups1300246762558778688al_rat
% 0.32/0.62                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6969_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ S2 )
% 0.32/0.62       => ( ( ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2906978787729119204at_rat
% 0.32/0.62                @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2906978787729119204at_rat
% 0.32/0.62                @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6970_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > rat] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3906332499630173760nt_rat
% 0.32/0.62                @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3906332499630173760nt_rat
% 0.32/0.62                @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6971_sum_Odelta_H,axiom,
% 0.32/0.62      ! [S2: set_complex,A: complex,B: complex > rat] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.62       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5058264527183730370ex_rat
% 0.32/0.62                @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5058264527183730370ex_rat
% 0.32/0.62                @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta'
% 0.32/0.62  thf(fact_6972_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > complex] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups5754745047067104278omplex
% 0.32/0.62                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups5754745047067104278omplex
% 0.32/0.62                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6973_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_nat,A: nat,B: nat > complex] :
% 0.32/0.62        ( ( finite_finite_nat @ S2 )
% 0.32/0.62       => ( ( ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2073611262835488442omplex
% 0.32/0.62                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2073611262835488442omplex
% 0.32/0.62                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6974_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > complex] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3049146728041665814omplex
% 0.32/0.62                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3049146728041665814omplex
% 0.32/0.62                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_complex ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6975_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > real] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups8097168146408367636l_real
% 0.32/0.62                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups8097168146408367636l_real
% 0.32/0.62                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6976_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > real] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups8778361861064173332t_real
% 0.32/0.62                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups8778361861064173332t_real
% 0.32/0.62                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6977_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_complex,A: complex,B: complex > real] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.62       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5808333547571424918x_real
% 0.32/0.62                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5808333547571424918x_real
% 0.32/0.62                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_real ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6978_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_real,A: real,B: real > rat] :
% 0.32/0.62        ( ( finite_finite_real @ S2 )
% 0.32/0.62       => ( ( ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups1300246762558778688al_rat
% 0.32/0.62                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.62           => ( ( groups1300246762558778688al_rat
% 0.32/0.62                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6979_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_nat,A: nat,B: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ S2 )
% 0.32/0.62       => ( ( ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2906978787729119204at_rat
% 0.32/0.62                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_nat @ A @ S2 )
% 0.32/0.62           => ( ( groups2906978787729119204at_rat
% 0.32/0.62                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6980_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_int,A: int,B: int > rat] :
% 0.32/0.62        ( ( finite_finite_int @ S2 )
% 0.32/0.62       => ( ( ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3906332499630173760nt_rat
% 0.32/0.62                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.62           => ( ( groups3906332499630173760nt_rat
% 0.32/0.62                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6981_sum_Odelta,axiom,
% 0.32/0.62      ! [S2: set_complex,A: complex,B: complex > rat] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.62       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5058264527183730370ex_rat
% 0.32/0.62                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = ( B @ A ) ) )
% 0.32/0.62          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.62           => ( ( groups5058264527183730370ex_rat
% 0.32/0.62                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 0.32/0.62                @ S2 )
% 0.32/0.62              = zero_zero_rat ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.delta
% 0.32/0.62  thf(fact_6982_sum__abs,axiom,
% 0.32/0.62      ! [F: int > int,A2: set_int] :
% 0.32/0.62        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.32/0.62        @ ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_abs
% 0.32/0.62  thf(fact_6983_sum__abs,axiom,
% 0.32/0.62      ! [F: nat > real,A2: set_nat] :
% 0.32/0.62        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.32/0.62        @ ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_abs
% 0.32/0.62  thf(fact_6984_set__encode__empty,axiom,
% 0.32/0.62      ( ( nat_set_encode @ bot_bot_set_nat )
% 0.32/0.62      = zero_zero_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % set_encode_empty
% 0.32/0.62  thf(fact_6985_dbl__dec__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 0.32/0.62        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(5)
% 0.32/0.62  thf(fact_6986_dbl__dec__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 0.32/0.62        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(5)
% 0.32/0.62  thf(fact_6987_dbl__dec__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 0.32/0.62        = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(5)
% 0.32/0.62  thf(fact_6988_dbl__dec__simps_I5_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 0.32/0.62        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % dbl_dec_simps(5)
% 0.32/0.62  thf(fact_6989_mask__Suc__0,axiom,
% 0.32/0.62      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 0.32/0.62      = one_one_nat ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_Suc_0
% 0.32/0.62  thf(fact_6990_mask__Suc__0,axiom,
% 0.32/0.62      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 0.32/0.62      = one_one_int ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_Suc_0
% 0.32/0.62  thf(fact_6991_sum__abs__ge__zero,axiom,
% 0.32/0.62      ! [F: int > int,A2: set_int] :
% 0.32/0.62        ( ord_less_eq_int @ zero_zero_int
% 0.32/0.62        @ ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_abs_ge_zero
% 0.32/0.62  thf(fact_6992_sum__abs__ge__zero,axiom,
% 0.32/0.62      ! [F: nat > real,A2: set_nat] :
% 0.32/0.62        ( ord_less_eq_real @ zero_zero_real
% 0.32/0.62        @ ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_abs_ge_zero
% 0.32/0.62  thf(fact_6993_pred__numeral__simps_I2_J,axiom,
% 0.32/0.62      ! [K: num] :
% 0.32/0.62        ( ( pred_numeral @ ( bit0 @ K ) )
% 0.32/0.62        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % pred_numeral_simps(2)
% 0.32/0.62  thf(fact_6994_divmod__algorithm__code_I5_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc4245557441103728435nt_int
% 0.32/0.62          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 0.32/0.62          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(5)
% 0.32/0.62  thf(fact_6995_divmod__algorithm__code_I5_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc2626176000494625587at_nat
% 0.32/0.62          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 0.32/0.62          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(5)
% 0.32/0.62  thf(fact_6996_divmod__algorithm__code_I5_J,axiom,
% 0.32/0.62      ! [M: num,N: num] :
% 0.32/0.62        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/0.62        = ( produc6916734918728496179nteger
% 0.32/0.62          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 0.32/0.62          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % divmod_algorithm_code(5)
% 0.32/0.62  thf(fact_6997_sum_Oneutral,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > int] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ( G @ X6 )
% 0.32/0.62              = zero_zero_int ) )
% 0.32/0.62       => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 0.32/0.62          = zero_zero_int ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral
% 0.32/0.62  thf(fact_6998_sum_Oneutral,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > complex] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ( G @ X6 )
% 0.32/0.62              = zero_zero_complex ) )
% 0.32/0.62       => ( ( groups7754918857620584856omplex @ G @ A2 )
% 0.32/0.62          = zero_zero_complex ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral
% 0.32/0.62  thf(fact_6999_sum_Oneutral,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > nat] :
% 0.32/0.62        ( ! [X6: nat] :
% 0.32/0.62            ( ( member_nat @ X6 @ A2 )
% 0.32/0.62           => ( ( G @ X6 )
% 0.32/0.62              = zero_zero_nat ) )
% 0.32/0.62       => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 0.32/0.62          = zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral
% 0.32/0.62  thf(fact_7000_sum_Oneutral,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > real] :
% 0.32/0.62        ( ! [X6: nat] :
% 0.32/0.62            ( ( member_nat @ X6 @ A2 )
% 0.32/0.62           => ( ( G @ X6 )
% 0.32/0.62              = zero_zero_real ) )
% 0.32/0.62       => ( ( groups6591440286371151544t_real @ G @ A2 )
% 0.32/0.62          = zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.neutral
% 0.32/0.62  thf(fact_7001_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: real > complex,A2: set_real] :
% 0.32/0.62        ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.32/0.62         != zero_zero_complex )
% 0.32/0.62       => ~ ! [A5: real] :
% 0.32/0.62              ( ( member_real @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_complex ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7002_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: nat > complex,A2: set_nat] :
% 0.32/0.62        ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.32/0.62         != zero_zero_complex )
% 0.32/0.62       => ~ ! [A5: nat] :
% 0.32/0.62              ( ( member_nat @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_complex ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7003_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: int > complex,A2: set_int] :
% 0.32/0.62        ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 0.32/0.62         != zero_zero_complex )
% 0.32/0.62       => ~ ! [A5: int] :
% 0.32/0.62              ( ( member_int @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_complex ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7004_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: complex > real,A2: set_complex] :
% 0.32/0.62        ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.62         != zero_zero_real )
% 0.32/0.62       => ~ ! [A5: complex] :
% 0.32/0.62              ( ( member_complex @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_real ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7005_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: real > real,A2: set_real] :
% 0.32/0.62        ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.32/0.62         != zero_zero_real )
% 0.32/0.62       => ~ ! [A5: real] :
% 0.32/0.62              ( ( member_real @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_real ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7006_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: int > real,A2: set_int] :
% 0.32/0.62        ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.32/0.62         != zero_zero_real )
% 0.32/0.62       => ~ ! [A5: int] :
% 0.32/0.62              ( ( member_int @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_real ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7007_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: complex > rat,A2: set_complex] :
% 0.32/0.62        ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.62         != zero_zero_rat )
% 0.32/0.62       => ~ ! [A5: complex] :
% 0.32/0.62              ( ( member_complex @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7008_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: real > rat,A2: set_real] :
% 0.32/0.62        ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.32/0.62         != zero_zero_rat )
% 0.32/0.62       => ~ ! [A5: real] :
% 0.32/0.62              ( ( member_real @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7009_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: nat > rat,A2: set_nat] :
% 0.32/0.62        ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.32/0.62         != zero_zero_rat )
% 0.32/0.62       => ~ ! [A5: nat] :
% 0.32/0.62              ( ( member_nat @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7010_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.32/0.62      ! [G: int > rat,A2: set_int] :
% 0.32/0.62        ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.32/0.62         != zero_zero_rat )
% 0.32/0.62       => ~ ! [A5: int] :
% 0.32/0.62              ( ( member_int @ A5 @ A2 )
% 0.32/0.62             => ( ( G @ A5 )
% 0.32/0.62                = zero_zero_rat ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.not_neutral_contains_not_neutral
% 0.32/0.62  thf(fact_7011_of__int__mask__eq,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.32/0.62        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % of_int_mask_eq
% 0.32/0.62  thf(fact_7012_old_Oprod_Ocase,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 0.32/0.62        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.32/0.62        = ( F @ X1 @ X22 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % old.prod.case
% 0.32/0.62  thf(fact_7013_old_Oprod_Ocase,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 0.32/0.62        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.32/0.62        = ( F @ X1 @ X22 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % old.prod.case
% 0.32/0.62  thf(fact_7014_old_Oprod_Ocase,axiom,
% 0.32/0.62      ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 0.32/0.62        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.32/0.62        = ( F @ X1 @ X22 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % old.prod.case
% 0.32/0.62  thf(fact_7015_old_Oprod_Ocase,axiom,
% 0.32/0.62      ! [F: int > int > $o,X1: int,X22: int] :
% 0.32/0.62        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.32/0.62        = ( F @ X1 @ X22 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % old.prod.case
% 0.32/0.62  thf(fact_7016_old_Oprod_Ocase,axiom,
% 0.32/0.62      ! [F: int > int > int,X1: int,X22: int] :
% 0.32/0.62        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.32/0.62        = ( F @ X1 @ X22 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % old.prod.case
% 0.32/0.62  thf(fact_7017_less__eq__mask,axiom,
% 0.32/0.62      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % less_eq_mask
% 0.32/0.62  thf(fact_7018_semiring__norm_I26_J,axiom,
% 0.32/0.62      ( ( bitM @ one )
% 0.32/0.62      = one ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(26)
% 0.32/0.62  thf(fact_7019_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 0.32/0.62        ( ! [I4: complex] :
% 0.32/0.62            ( ( member_complex @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7020_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_real,F: real > rat,G: real > rat] :
% 0.32/0.62        ( ! [I4: real] :
% 0.32/0.62            ( ( member_real @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7021_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 0.32/0.62        ( ! [I4: nat] :
% 0.32/0.62            ( ( member_nat @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7022_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_int,F: int > rat,G: int > rat] :
% 0.32/0.62        ( ! [I4: int] :
% 0.32/0.62            ( ( member_int @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7023_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 0.32/0.62        ( ! [I4: complex] :
% 0.32/0.62            ( ( member_complex @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7024_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_real,F: real > nat,G: real > nat] :
% 0.32/0.62        ( ! [I4: real] :
% 0.32/0.62            ( ( member_real @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7025_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_int,F: int > nat,G: int > nat] :
% 0.32/0.62        ( ! [I4: int] :
% 0.32/0.62            ( ( member_int @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7026_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 0.32/0.62        ( ! [I4: complex] :
% 0.32/0.62            ( ( member_complex @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7027_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_real,F: real > int,G: real > int] :
% 0.32/0.62        ( ! [I4: real] :
% 0.32/0.62            ( ( member_real @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7028_sum__mono,axiom,
% 0.32/0.62      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 0.32/0.62        ( ! [I4: nat] :
% 0.32/0.62            ( ( member_nat @ I4 @ K5 )
% 0.32/0.62           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono
% 0.32/0.62  thf(fact_7029_sum__distrib__left,axiom,
% 0.32/0.62      ! [R: int,F: int > int,A2: set_int] :
% 0.32/0.62        ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 0.32/0.62        = ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_left
% 0.32/0.62  thf(fact_7030_sum__distrib__left,axiom,
% 0.32/0.62      ! [R: complex,F: complex > complex,A2: set_complex] :
% 0.32/0.62        ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 0.32/0.62        = ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_left
% 0.32/0.62  thf(fact_7031_sum__distrib__left,axiom,
% 0.32/0.62      ! [R: nat,F: nat > nat,A2: set_nat] :
% 0.32/0.62        ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 0.32/0.62        = ( groups3542108847815614940at_nat
% 0.32/0.62          @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_left
% 0.32/0.62  thf(fact_7032_sum__distrib__left,axiom,
% 0.32/0.62      ! [R: real,F: nat > real,A2: set_nat] :
% 0.32/0.62        ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.32/0.62        = ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_left
% 0.32/0.62  thf(fact_7033_sum__distrib__right,axiom,
% 0.32/0.62      ! [F: int > int,A2: set_int,R: int] :
% 0.32/0.62        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_right
% 0.32/0.62  thf(fact_7034_sum__distrib__right,axiom,
% 0.32/0.62      ! [F: complex > complex,A2: set_complex,R: complex] :
% 0.32/0.62        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_right
% 0.32/0.62  thf(fact_7035_sum__distrib__right,axiom,
% 0.32/0.62      ! [F: nat > nat,A2: set_nat,R: nat] :
% 0.32/0.62        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups3542108847815614940at_nat
% 0.32/0.62          @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_right
% 0.32/0.62  thf(fact_7036_sum__distrib__right,axiom,
% 0.32/0.62      ! [F: nat > real,A2: set_nat,R: real] :
% 0.32/0.62        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_distrib_right
% 0.32/0.62  thf(fact_7037_sum__product,axiom,
% 0.32/0.62      ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 0.32/0.62        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 0.32/0.62        = ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [I5: int] :
% 0.32/0.62              ( groups4538972089207619220nt_int
% 0.32/0.62              @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 0.32/0.62              @ B3 )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_product
% 0.32/0.62  thf(fact_7038_sum__product,axiom,
% 0.32/0.62      ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 0.32/0.62        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 0.32/0.62        = ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [I5: complex] :
% 0.32/0.62              ( groups7754918857620584856omplex
% 0.32/0.62              @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 0.32/0.62              @ B3 )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_product
% 0.32/0.62  thf(fact_7039_sum__product,axiom,
% 0.32/0.62      ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 0.32/0.62        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 0.32/0.62        = ( groups3542108847815614940at_nat
% 0.32/0.62          @ ^ [I5: nat] :
% 0.32/0.62              ( groups3542108847815614940at_nat
% 0.32/0.62              @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 0.32/0.62              @ B3 )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_product
% 0.32/0.62  thf(fact_7040_sum__product,axiom,
% 0.32/0.62      ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 0.32/0.62        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 0.32/0.62        = ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [I5: nat] :
% 0.32/0.62              ( groups6591440286371151544t_real
% 0.32/0.62              @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 0.32/0.62              @ B3 )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_product
% 0.32/0.62  thf(fact_7041_sum_Odistrib,axiom,
% 0.32/0.62      ! [G: int > int,H2: int > int,A2: set_int] :
% 0.32/0.62        ( ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.distrib
% 0.32/0.62  thf(fact_7042_sum_Odistrib,axiom,
% 0.32/0.62      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 0.32/0.62        ( ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [X3: complex] : ( plus_plus_complex @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.distrib
% 0.32/0.62  thf(fact_7043_sum_Odistrib,axiom,
% 0.32/0.62      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 0.32/0.62        ( ( groups3542108847815614940at_nat
% 0.32/0.62          @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.distrib
% 0.32/0.62  thf(fact_7044_sum_Odistrib,axiom,
% 0.32/0.62      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 0.32/0.62        ( ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [X3: nat] : ( plus_plus_real @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.distrib
% 0.32/0.62  thf(fact_7045_sum__subtractf,axiom,
% 0.32/0.62      ! [F: int > int,G: int > int,A2: set_int] :
% 0.32/0.62        ( ( groups4538972089207619220nt_int
% 0.32/0.62          @ ^ [X3: int] : ( minus_minus_int @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_subtractf
% 0.32/0.62  thf(fact_7046_sum__subtractf,axiom,
% 0.32/0.62      ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 0.32/0.62        ( ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [X3: complex] : ( minus_minus_complex @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_subtractf
% 0.32/0.62  thf(fact_7047_sum__subtractf,axiom,
% 0.32/0.62      ! [F: nat > real,G: nat > real,A2: set_nat] :
% 0.32/0.62        ( ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [X3: nat] : ( minus_minus_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.62          @ A2 )
% 0.32/0.62        = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_subtractf
% 0.32/0.62  thf(fact_7048_sum__divide__distrib,axiom,
% 0.32/0.62      ! [F: complex > complex,A2: set_complex,R: complex] :
% 0.32/0.62        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups7754918857620584856omplex
% 0.32/0.62          @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_divide_distrib
% 0.32/0.62  thf(fact_7049_sum__divide__distrib,axiom,
% 0.32/0.62      ! [F: nat > real,A2: set_nat,R: real] :
% 0.32/0.62        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 0.32/0.62        = ( groups6591440286371151544t_real
% 0.32/0.62          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 0.32/0.62          @ A2 ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_divide_distrib
% 0.32/0.62  thf(fact_7050_mod__sum__eq,axiom,
% 0.32/0.62      ! [F: int > int,A: int,A2: set_int] :
% 0.32/0.62        ( ( modulo_modulo_int
% 0.32/0.62          @ ( groups4538972089207619220nt_int
% 0.32/0.62            @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 0.32/0.62            @ A2 )
% 0.32/0.62          @ A )
% 0.32/0.62        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mod_sum_eq
% 0.32/0.62  thf(fact_7051_mod__sum__eq,axiom,
% 0.32/0.62      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.32/0.62        ( ( modulo_modulo_nat
% 0.32/0.62          @ ( groups3542108847815614940at_nat
% 0.32/0.62            @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 0.32/0.62            @ A2 )
% 0.32/0.62          @ A )
% 0.32/0.62        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mod_sum_eq
% 0.32/0.62  thf(fact_7052_case__prodE2,axiom,
% 0.32/0.62      ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.32/0.62        ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 0.32/0.62       => ~ ! [X6: nat,Y5: nat] :
% 0.32/0.62              ( ( Z
% 0.32/0.62                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 0.32/0.62             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prodE2
% 0.32/0.62  thf(fact_7053_case__prodE2,axiom,
% 0.32/0.62      ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 0.32/0.62        ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 0.32/0.62       => ~ ! [X6: nat,Y5: nat] :
% 0.32/0.62              ( ( Z
% 0.32/0.62                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 0.32/0.62             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prodE2
% 0.32/0.62  thf(fact_7054_case__prodE2,axiom,
% 0.32/0.62      ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 0.32/0.62        ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 0.32/0.62       => ~ ! [X6: int,Y5: int] :
% 0.32/0.62              ( ( Z
% 0.32/0.62                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.62             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prodE2
% 0.32/0.62  thf(fact_7055_case__prodE2,axiom,
% 0.32/0.62      ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 0.32/0.62        ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 0.32/0.62       => ~ ! [X6: int,Y5: int] :
% 0.32/0.62              ( ( Z
% 0.32/0.62                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.62             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prodE2
% 0.32/0.62  thf(fact_7056_case__prodE2,axiom,
% 0.32/0.62      ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 0.32/0.62        ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 0.32/0.62       => ~ ! [X6: int,Y5: int] :
% 0.32/0.62              ( ( Z
% 0.32/0.62                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.62             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prodE2
% 0.32/0.62  thf(fact_7057_case__prod__eta,axiom,
% 0.32/0.62      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.32/0.62        ( ( produc27273713700761075at_nat
% 0.32/0.62          @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.32/0.62        = F ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_eta
% 0.32/0.62  thf(fact_7058_case__prod__eta,axiom,
% 0.32/0.62      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.32/0.62        ( ( produc8739625826339149834_nat_o
% 0.32/0.62          @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.32/0.62        = F ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_eta
% 0.32/0.62  thf(fact_7059_case__prod__eta,axiom,
% 0.32/0.62      ! [F: product_prod_int_int > product_prod_int_int] :
% 0.32/0.62        ( ( produc4245557441103728435nt_int
% 0.32/0.62          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.32/0.62        = F ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_eta
% 0.32/0.62  thf(fact_7060_case__prod__eta,axiom,
% 0.32/0.62      ! [F: product_prod_int_int > $o] :
% 0.32/0.62        ( ( produc4947309494688390418_int_o
% 0.32/0.62          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.32/0.62        = F ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_eta
% 0.32/0.62  thf(fact_7061_case__prod__eta,axiom,
% 0.32/0.62      ! [F: product_prod_int_int > int] :
% 0.32/0.62        ( ( produc8211389475949308722nt_int
% 0.32/0.62          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.32/0.62        = F ) ).
% 0.32/0.62  
% 0.32/0.62  % case_prod_eta
% 0.32/0.62  thf(fact_7062_cond__case__prod__eta,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.32/0.62        ( ! [X6: nat,Y5: nat] :
% 0.32/0.62            ( ( F @ X6 @ Y5 )
% 0.32/0.62            = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 0.32/0.62       => ( ( produc27273713700761075at_nat @ F )
% 0.32/0.62          = G ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cond_case_prod_eta
% 0.32/0.62  thf(fact_7063_cond__case__prod__eta,axiom,
% 0.32/0.62      ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.32/0.62        ( ! [X6: nat,Y5: nat] :
% 0.32/0.62            ( ( F @ X6 @ Y5 )
% 0.32/0.62            = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 0.32/0.62       => ( ( produc8739625826339149834_nat_o @ F )
% 0.32/0.62          = G ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cond_case_prod_eta
% 0.32/0.62  thf(fact_7064_cond__case__prod__eta,axiom,
% 0.32/0.62      ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 0.32/0.62        ( ! [X6: int,Y5: int] :
% 0.32/0.62            ( ( F @ X6 @ Y5 )
% 0.32/0.62            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 0.32/0.62       => ( ( produc4245557441103728435nt_int @ F )
% 0.32/0.62          = G ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cond_case_prod_eta
% 0.32/0.62  thf(fact_7065_cond__case__prod__eta,axiom,
% 0.32/0.62      ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 0.32/0.62        ( ! [X6: int,Y5: int] :
% 0.32/0.62            ( ( F @ X6 @ Y5 )
% 0.32/0.62            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 0.32/0.62       => ( ( produc4947309494688390418_int_o @ F )
% 0.32/0.62          = G ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cond_case_prod_eta
% 0.32/0.62  thf(fact_7066_cond__case__prod__eta,axiom,
% 0.32/0.62      ! [F: int > int > int,G: product_prod_int_int > int] :
% 0.32/0.62        ( ! [X6: int,Y5: int] :
% 0.32/0.62            ( ( F @ X6 @ Y5 )
% 0.32/0.62            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 0.32/0.62       => ( ( produc8211389475949308722nt_int @ F )
% 0.32/0.62          = G ) ) ).
% 0.32/0.62  
% 0.32/0.62  % cond_case_prod_eta
% 0.32/0.62  thf(fact_7067_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > real] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 0.32/0.62       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7068_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > real] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 0.32/0.62       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7069_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > real] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 0.32/0.62       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7070_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > rat] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7071_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > rat] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7072_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_nat,F: nat > rat] :
% 0.32/0.62        ( ! [X6: nat] :
% 0.32/0.62            ( ( member_nat @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7073_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > rat] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 0.32/0.62       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7074_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > nat] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7075_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > nat] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7076_sum__nonpos,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > nat] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 0.32/0.62       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonpos
% 0.32/0.62  thf(fact_7077_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > real] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7078_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > real] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7079_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > real] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7080_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > rat] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7081_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > rat] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7082_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_nat,F: nat > rat] :
% 0.32/0.62        ( ! [X6: nat] :
% 0.32/0.62            ( ( member_nat @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7083_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > rat] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7084_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > nat] :
% 0.32/0.62        ( ! [X6: complex] :
% 0.32/0.62            ( ( member_complex @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7085_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > nat] :
% 0.32/0.62        ( ! [X6: real] :
% 0.32/0.62            ( ( member_real @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7086_sum__nonneg,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > nat] :
% 0.32/0.62        ( ! [X6: int] :
% 0.32/0.62            ( ( member_int @ X6 @ A2 )
% 0.32/0.62           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg
% 0.32/0.62  thf(fact_7087_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 0.32/0.62        ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 0.32/0.62          = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: real] :
% 0.32/0.62              ( ( member_real @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_real @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_real @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7088_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 0.32/0.62        ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 0.32/0.62          = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: nat] :
% 0.32/0.62              ( ( member_nat @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_nat @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_nat @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7089_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 0.32/0.62        ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 0.32/0.62          = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: int] :
% 0.32/0.62              ( ( member_int @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_int @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_int @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7090_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 0.32/0.62        ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 0.32/0.62          = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: complex] :
% 0.32/0.62              ( ( member_complex @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_complex @ I @ I6 )
% 0.32/0.62           => ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7091_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 0.32/0.62        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 0.32/0.62          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: real] :
% 0.32/0.62              ( ( member_real @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_real @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_real @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7092_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 0.32/0.62        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 0.32/0.62          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: int] :
% 0.32/0.62              ( ( member_int @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_int @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_int @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7093_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 0.32/0.62        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 0.32/0.62          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: complex] :
% 0.32/0.62              ( ( member_complex @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_complex @ I @ I6 )
% 0.32/0.62           => ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7094_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: real > int,I6: set_real,G: real > int,I: real] :
% 0.32/0.62        ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 0.32/0.62          = ( groups1932886352136224148al_int @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: real] :
% 0.32/0.62              ( ( member_real @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_real @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_real @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7095_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: nat > int,I6: set_nat,G: nat > int,I: nat] :
% 0.32/0.62        ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 0.32/0.62          = ( groups3539618377306564664at_int @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: nat] :
% 0.32/0.62              ( ( member_nat @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_nat @ I @ I6 )
% 0.32/0.62           => ( ( finite_finite_nat @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7096_sum__mono__inv,axiom,
% 0.32/0.62      ! [F: complex > int,I6: set_complex,G: complex > int,I: complex] :
% 0.32/0.62        ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 0.32/0.62          = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 0.32/0.62       => ( ! [I4: complex] :
% 0.32/0.62              ( ( member_complex @ I4 @ I6 )
% 0.32/0.62             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 0.32/0.62         => ( ( member_complex @ I @ I6 )
% 0.32/0.62           => ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.62             => ( ( F @ I )
% 0.32/0.62                = ( G @ I ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_mono_inv
% 0.32/0.62  thf(fact_7097_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_real,G: real > complex,P: real > $o] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ( groups5754745047067104278omplex @ G
% 0.32/0.62            @ ( collect_real
% 0.32/0.62              @ ^ [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups5754745047067104278omplex
% 0.32/0.62            @ ^ [X3: real] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7098_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 0.32/0.62        ( ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( groups2073611262835488442omplex @ G
% 0.32/0.62            @ ( collect_nat
% 0.32/0.62              @ ^ [X3: nat] :
% 0.32/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups2073611262835488442omplex
% 0.32/0.62            @ ^ [X3: nat] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7099_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > complex,P: int > $o] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups3049146728041665814omplex @ G
% 0.32/0.62            @ ( collect_int
% 0.32/0.62              @ ^ [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups3049146728041665814omplex
% 0.32/0.62            @ ^ [X3: int] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7100_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_real,G: real > real,P: real > $o] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ( groups8097168146408367636l_real @ G
% 0.32/0.62            @ ( collect_real
% 0.32/0.62              @ ^ [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups8097168146408367636l_real
% 0.32/0.62            @ ^ [X3: real] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7101_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > real,P: int > $o] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups8778361861064173332t_real @ G
% 0.32/0.62            @ ( collect_int
% 0.32/0.62              @ ^ [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups8778361861064173332t_real
% 0.32/0.62            @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7102_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ( groups5808333547571424918x_real @ G
% 0.32/0.62            @ ( collect_complex
% 0.32/0.62              @ ^ [X3: complex] :
% 0.32/0.62                  ( ( member_complex @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups5808333547571424918x_real
% 0.32/0.62            @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7103_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_real,G: real > rat,P: real > $o] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ( groups1300246762558778688al_rat @ G
% 0.32/0.62            @ ( collect_real
% 0.32/0.62              @ ^ [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups1300246762558778688al_rat
% 0.32/0.62            @ ^ [X3: real] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7104_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 0.32/0.62        ( ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ( groups2906978787729119204at_rat @ G
% 0.32/0.62            @ ( collect_nat
% 0.32/0.62              @ ^ [X3: nat] :
% 0.32/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups2906978787729119204at_rat
% 0.32/0.62            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7105_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_int,G: int > rat,P: int > $o] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ( groups3906332499630173760nt_rat @ G
% 0.32/0.62            @ ( collect_int
% 0.32/0.62              @ ^ [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups3906332499630173760nt_rat
% 0.32/0.62            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7106_sum_Ointer__filter,axiom,
% 0.32/0.62      ! [A2: set_complex,G: complex > rat,P: complex > $o] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ( groups5058264527183730370ex_rat @ G
% 0.32/0.62            @ ( collect_complex
% 0.32/0.62              @ ^ [X3: complex] :
% 0.32/0.62                  ( ( member_complex @ X3 @ A2 )
% 0.32/0.62                  & ( P @ X3 ) ) ) )
% 0.32/0.62          = ( groups5058264527183730370ex_rat
% 0.32/0.62            @ ^ [X3: complex] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 0.32/0.62            @ A2 ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum.inter_filter
% 0.32/0.62  thf(fact_7107_mask__nonnegative__int,axiom,
% 0.32/0.62      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.32/0.62  
% 0.32/0.62  % mask_nonnegative_int
% 0.32/0.62  thf(fact_7108_not__mask__negative__int,axiom,
% 0.32/0.62      ! [N: nat] :
% 0.32/0.62        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 0.32/0.62  
% 0.32/0.62  % not_mask_negative_int
% 0.32/0.62  thf(fact_7109_semiring__norm_I28_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( bitM @ ( bit1 @ N ) )
% 0.32/0.62        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(28)
% 0.32/0.62  thf(fact_7110_semiring__norm_I27_J,axiom,
% 0.32/0.62      ! [N: num] :
% 0.32/0.62        ( ( bitM @ ( bit0 @ N ) )
% 0.32/0.62        = ( bit1 @ ( bitM @ N ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % semiring_norm(27)
% 0.32/0.62  thf(fact_7111_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > real] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ! [X6: real] :
% 0.32/0.62              ( ( member_real @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 0.32/0.62              = zero_zero_real )
% 0.32/0.62            = ( ! [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7112_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > real] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ! [X6: int] :
% 0.32/0.62              ( ( member_int @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 0.32/0.62              = zero_zero_real )
% 0.32/0.62            = ( ! [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7113_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > real] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ! [X6: complex] :
% 0.32/0.62              ( ( member_complex @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 0.32/0.62              = zero_zero_real )
% 0.32/0.62            = ( ! [X3: complex] :
% 0.32/0.62                  ( ( member_complex @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_real ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7114_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > rat] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ! [X6: real] :
% 0.32/0.62              ( ( member_real @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 0.32/0.62              = zero_zero_rat )
% 0.32/0.62            = ( ! [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7115_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_nat,F: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ A2 )
% 0.32/0.62       => ( ! [X6: nat] :
% 0.32/0.62              ( ( member_nat @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 0.32/0.62              = zero_zero_rat )
% 0.32/0.62            = ( ! [X3: nat] :
% 0.32/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7116_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > rat] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ! [X6: int] :
% 0.32/0.62              ( ( member_int @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 0.32/0.62              = zero_zero_rat )
% 0.32/0.62            = ( ! [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7117_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > rat] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ! [X6: complex] :
% 0.32/0.62              ( ( member_complex @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 0.32/0.62              = zero_zero_rat )
% 0.32/0.62            = ( ! [X3: complex] :
% 0.32/0.62                  ( ( member_complex @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_rat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7118_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_real,F: real > nat] :
% 0.32/0.62        ( ( finite_finite_real @ A2 )
% 0.32/0.62       => ( ! [X6: real] :
% 0.32/0.62              ( ( member_real @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 0.32/0.62              = zero_zero_nat )
% 0.32/0.62            = ( ! [X3: real] :
% 0.32/0.62                  ( ( member_real @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7119_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_int,F: int > nat] :
% 0.32/0.62        ( ( finite_finite_int @ A2 )
% 0.32/0.62       => ( ! [X6: int] :
% 0.32/0.62              ( ( member_int @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.32/0.62              = zero_zero_nat )
% 0.32/0.62            = ( ! [X3: int] :
% 0.32/0.62                  ( ( member_int @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7120_sum__nonneg__eq__0__iff,axiom,
% 0.32/0.62      ! [A2: set_complex,F: complex > nat] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.62       => ( ! [X6: complex] :
% 0.32/0.62              ( ( member_complex @ X6 @ A2 )
% 0.32/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.62         => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.32/0.62              = zero_zero_nat )
% 0.32/0.62            = ( ! [X3: complex] :
% 0.32/0.62                  ( ( member_complex @ X3 @ A2 )
% 0.32/0.62                 => ( ( F @ X3 )
% 0.32/0.62                    = zero_zero_nat ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_nonneg_eq_0_iff
% 0.32/0.62  thf(fact_7121_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 0.32/0.62        ( ( finite_finite_int @ S )
% 0.32/0.62       => ( ( finite_finite_int @ T )
% 0.32/0.62         => ( ! [X6: int] :
% 0.32/0.62                ( ( member_int @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: int] :
% 0.32/0.62                  ( ( member_int @ X6 @ S )
% 0.32/0.62                 => ? [Xa: int] :
% 0.32/0.62                      ( ( member_int @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7122_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 0.32/0.62        ( ( finite_finite_int @ S )
% 0.32/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.32/0.62         => ( ! [X6: complex] :
% 0.32/0.62                ( ( member_complex @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: int] :
% 0.32/0.62                  ( ( member_int @ X6 @ S )
% 0.32/0.62                 => ? [Xa: complex] :
% 0.32/0.62                      ( ( member_complex @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7123_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.62       => ( ( finite_finite_int @ T )
% 0.32/0.62         => ( ! [X6: int] :
% 0.32/0.62                ( ( member_int @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: complex] :
% 0.32/0.62                  ( ( member_complex @ X6 @ S )
% 0.32/0.62                 => ? [Xa: int] :
% 0.32/0.62                      ( ( member_int @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7124_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 0.32/0.62        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.32/0.62         => ( ! [X6: complex] :
% 0.32/0.62                ( ( member_complex @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: complex] :
% 0.32/0.62                  ( ( member_complex @ X6 @ S )
% 0.32/0.62                 => ? [Xa: complex] :
% 0.32/0.62                      ( ( member_complex @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7125_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ S )
% 0.32/0.62       => ( ( finite_finite_nat @ T )
% 0.32/0.62         => ( ! [X6: nat] :
% 0.32/0.62                ( ( member_nat @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: nat] :
% 0.32/0.62                  ( ( member_nat @ X6 @ S )
% 0.32/0.62                 => ? [Xa: nat] :
% 0.32/0.62                      ( ( member_nat @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7126_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ S )
% 0.32/0.62       => ( ( finite_finite_int @ T )
% 0.32/0.62         => ( ! [X6: int] :
% 0.32/0.62                ( ( member_int @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: nat] :
% 0.32/0.62                  ( ( member_nat @ X6 @ S )
% 0.32/0.62                 => ? [Xa: int] :
% 0.32/0.62                      ( ( member_int @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7127_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 0.32/0.62        ( ( finite_finite_nat @ S )
% 0.32/0.62       => ( ( finite3207457112153483333omplex @ T )
% 0.32/0.62         => ( ! [X6: complex] :
% 0.32/0.62                ( ( member_complex @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: nat] :
% 0.32/0.62                  ( ( member_nat @ X6 @ S )
% 0.32/0.62                 => ? [Xa: complex] :
% 0.32/0.62                      ( ( member_complex @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7128_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 0.32/0.62        ( ( finite_finite_int @ S )
% 0.32/0.62       => ( ( finite_finite_nat @ T )
% 0.32/0.62         => ( ! [X6: nat] :
% 0.32/0.62                ( ( member_nat @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: int] :
% 0.32/0.62                  ( ( member_int @ X6 @ S )
% 0.32/0.62                 => ? [Xa: nat] :
% 0.32/0.62                      ( ( member_nat @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.62  
% 0.32/0.62  % sum_le_included
% 0.32/0.62  thf(fact_7129_sum__le__included,axiom,
% 0.32/0.62      ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 0.32/0.62        ( ( finite_finite_int @ S )
% 0.32/0.62       => ( ( finite_finite_int @ T )
% 0.32/0.62         => ( ! [X6: int] :
% 0.32/0.62                ( ( member_int @ X6 @ T )
% 0.32/0.62               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.62           => ( ! [X6: int] :
% 0.32/0.62                  ( ( member_int @ X6 @ S )
% 0.32/0.62                 => ? [Xa: int] :
% 0.32/0.62                      ( ( member_int @ Xa @ T )
% 0.32/0.62                      & ( ( I @ Xa )
% 0.32/0.62                        = X6 )
% 0.32/0.62                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.62             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_le_included
% 0.32/0.63  thf(fact_7130_sum__le__included,axiom,
% 0.32/0.63      ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ T )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ T )
% 0.32/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ! [X6: int] :
% 0.32/0.63                  ( ( member_int @ X6 @ S )
% 0.32/0.63                 => ? [Xa: complex] :
% 0.32/0.63                      ( ( member_complex @ Xa @ T )
% 0.32/0.63                      & ( ( I @ Xa )
% 0.32/0.63                        = X6 )
% 0.32/0.63                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 0.32/0.63             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_le_included
% 0.32/0.63  thf(fact_7131_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > real,G: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ! [X6: int] :
% 0.32/0.63              ( ( member_int @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: int] :
% 0.32/0.63                ( ( member_int @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7132_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ! [X6: complex] :
% 0.32/0.63              ( ( member_complex @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: complex] :
% 0.32/0.63                ( ( member_complex @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7133_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ! [X6: nat] :
% 0.32/0.63              ( ( member_nat @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: nat] :
% 0.32/0.63                ( ( member_nat @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7134_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ! [X6: int] :
% 0.32/0.63              ( ( member_int @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: int] :
% 0.32/0.63                ( ( member_int @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7135_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ! [X6: complex] :
% 0.32/0.63              ( ( member_complex @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: complex] :
% 0.32/0.63                ( ( member_complex @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7136_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ! [X6: int] :
% 0.32/0.63              ( ( member_int @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: int] :
% 0.32/0.63                ( ( member_int @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7137_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ! [X6: complex] :
% 0.32/0.63              ( ( member_complex @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: complex] :
% 0.32/0.63                ( ( member_complex @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7138_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ! [X6: nat] :
% 0.32/0.63              ( ( member_nat @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: nat] :
% 0.32/0.63                ( ( member_nat @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7139_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ! [X6: complex] :
% 0.32/0.63              ( ( member_complex @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: complex] :
% 0.32/0.63                ( ( member_complex @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7140_sum__strict__mono__ex1,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > int,G: int > int] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ! [X6: int] :
% 0.32/0.63              ( ( member_int @ X6 @ A2 )
% 0.32/0.63             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63         => ( ? [X4: int] :
% 0.32/0.63                ( ( member_int @ X4 @ A2 )
% 0.32/0.63                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 0.32/0.63           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono_ex1
% 0.32/0.63  thf(fact_7141_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.32/0.63        ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 0.32/0.63       => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_nat @ S2 )
% 0.32/0.63           => ( ! [X6: nat] :
% 0.32/0.63                  ( ( member_nat @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7142_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 0.32/0.63        ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 0.32/0.63       => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_int @ S2 )
% 0.32/0.63           => ( ! [X6: int] :
% 0.32/0.63                  ( ( member_int @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7143_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 0.32/0.63        ( ( R4 @ zero_zero_real @ zero_zero_real )
% 0.32/0.63       => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_int @ S2 )
% 0.32/0.63           => ( ! [X6: int] :
% 0.32/0.63                  ( ( member_int @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7144_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.32/0.63        ( ( R4 @ zero_zero_real @ zero_zero_real )
% 0.32/0.63       => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7145_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 0.32/0.63        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.32/0.63       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_nat @ S2 )
% 0.32/0.63           => ( ! [X6: nat] :
% 0.32/0.63                  ( ( member_nat @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7146_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 0.32/0.63        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.32/0.63       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_int @ S2 )
% 0.32/0.63           => ( ! [X6: int] :
% 0.32/0.63                  ( ( member_int @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7147_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.32/0.63        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 0.32/0.63       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7148_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 0.32/0.63        ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.32/0.63       => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_int @ S2 )
% 0.32/0.63           => ( ! [X6: int] :
% 0.32/0.63                  ( ( member_int @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7149_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.32/0.63        ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 0.32/0.63       => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7150_sum_Orelated,axiom,
% 0.32/0.63      ! [R4: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 0.32/0.63        ( ( R4 @ zero_zero_int @ zero_zero_int )
% 0.32/0.63       => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 0.32/0.63              ( ( ( R4 @ X15 @ X23 )
% 0.32/0.63                & ( R4 @ Y15 @ Y23 ) )
% 0.32/0.63             => ( R4 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 0.32/0.63         => ( ( finite_finite_nat @ S2 )
% 0.32/0.63           => ( ! [X6: nat] :
% 0.32/0.63                  ( ( member_nat @ X6 @ S2 )
% 0.32/0.63                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63             => ( R4 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.related
% 0.32/0.63  thf(fact_7151_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7152_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > real,G: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_int )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7153_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_real,F: real > real,G: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_real )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7154_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7155_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_nat )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7156_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > rat,G: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_int )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7157_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_real,F: real > rat,G: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_real )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7158_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7159_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > nat,G: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_int )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7160_sum__strict__mono,axiom,
% 0.32/0.63      ! [A2: set_real,F: real > nat,G: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ A2 )
% 0.32/0.63       => ( ( A2 != bot_bot_set_real )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ A2 )
% 0.32/0.63               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 0.32/0.63           => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono
% 0.32/0.63  thf(fact_7161_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 0.32/0.63        ( ( finite_finite_real @ S4 )
% 0.32/0.63       => ( ( finite_finite_real @ T4 )
% 0.32/0.63         => ( ! [A5: real] :
% 0.32/0.63                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: real] :
% 0.32/0.63                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: real] :
% 0.32/0.63                        ( ( member_real @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_complex ) )
% 0.32/0.63                   => ( ! [B5: real] :
% 0.32/0.63                          ( ( member_real @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_complex ) )
% 0.32/0.63                     => ( ! [A5: real] :
% 0.32/0.63                            ( ( member_real @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.32/0.63                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7162_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 0.32/0.63        ( ( finite_finite_real @ S4 )
% 0.32/0.63       => ( ( finite_finite_int @ T4 )
% 0.32/0.63         => ( ! [A5: real] :
% 0.32/0.63                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: int] :
% 0.32/0.63                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: int] :
% 0.32/0.63                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: real] :
% 0.32/0.63                        ( ( member_real @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_complex ) )
% 0.32/0.63                   => ( ! [B5: int] :
% 0.32/0.63                          ( ( member_int @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_complex ) )
% 0.32/0.63                     => ( ! [A5: real] :
% 0.32/0.63                            ( ( member_real @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.32/0.63                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7163_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 0.32/0.63        ( ( finite_finite_int @ S4 )
% 0.32/0.63       => ( ( finite_finite_real @ T4 )
% 0.32/0.63         => ( ! [A5: int] :
% 0.32/0.63                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: int] :
% 0.32/0.63                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: real] :
% 0.32/0.63                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: int] :
% 0.32/0.63                        ( ( member_int @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_complex ) )
% 0.32/0.63                   => ( ! [B5: real] :
% 0.32/0.63                          ( ( member_real @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_complex ) )
% 0.32/0.63                     => ( ! [A5: int] :
% 0.32/0.63                            ( ( member_int @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.32/0.63                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7164_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 0.32/0.63        ( ( finite_finite_int @ S4 )
% 0.32/0.63       => ( ( finite_finite_int @ T4 )
% 0.32/0.63         => ( ! [A5: int] :
% 0.32/0.63                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: int] :
% 0.32/0.63                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: int] :
% 0.32/0.63                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: int] :
% 0.32/0.63                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: int] :
% 0.32/0.63                        ( ( member_int @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_complex ) )
% 0.32/0.63                   => ( ! [B5: int] :
% 0.32/0.63                          ( ( member_int @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_complex ) )
% 0.32/0.63                     => ( ! [A5: int] :
% 0.32/0.63                            ( ( member_int @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.32/0.63                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7165_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > real,H2: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ S4 )
% 0.32/0.63       => ( ( finite_finite_real @ T4 )
% 0.32/0.63         => ( ! [A5: real] :
% 0.32/0.63                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: real] :
% 0.32/0.63                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: real] :
% 0.32/0.63                        ( ( member_real @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: real] :
% 0.32/0.63                          ( ( member_real @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: real] :
% 0.32/0.63                            ( ( member_real @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.32/0.63                          = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7166_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > real,H2: int > real] :
% 0.32/0.63        ( ( finite_finite_real @ S4 )
% 0.32/0.63       => ( ( finite_finite_int @ T4 )
% 0.32/0.63         => ( ! [A5: real] :
% 0.32/0.63                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: int] :
% 0.32/0.63                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: int] :
% 0.32/0.63                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: real] :
% 0.32/0.63                        ( ( member_real @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: int] :
% 0.32/0.63                          ( ( member_int @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: real] :
% 0.32/0.63                            ( ( member_real @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.32/0.63                          = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7167_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > real,H2: complex > real] :
% 0.32/0.63        ( ( finite_finite_real @ S4 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ T4 )
% 0.32/0.63         => ( ! [A5: real] :
% 0.32/0.63                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: complex] :
% 0.32/0.63                      ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: real] :
% 0.32/0.63                        ( ( member_real @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: complex] :
% 0.32/0.63                          ( ( member_complex @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: real] :
% 0.32/0.63                            ( ( member_real @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.32/0.63                          = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7168_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > real,H2: real > real] :
% 0.32/0.63        ( ( finite_finite_int @ S4 )
% 0.32/0.63       => ( ( finite_finite_real @ T4 )
% 0.32/0.63         => ( ! [A5: int] :
% 0.32/0.63                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: int] :
% 0.32/0.63                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: real] :
% 0.32/0.63                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: int] :
% 0.32/0.63                        ( ( member_int @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: real] :
% 0.32/0.63                          ( ( member_real @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: int] :
% 0.32/0.63                            ( ( member_int @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.32/0.63                          = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7169_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > real,H2: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ S4 )
% 0.32/0.63       => ( ( finite_finite_int @ T4 )
% 0.32/0.63         => ( ! [A5: int] :
% 0.32/0.63                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: int] :
% 0.32/0.63                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: int] :
% 0.32/0.63                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: int] :
% 0.32/0.63                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: int] :
% 0.32/0.63                        ( ( member_int @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: int] :
% 0.32/0.63                          ( ( member_int @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: int] :
% 0.32/0.63                            ( ( member_int @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.32/0.63                          = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7170_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.32/0.63      ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > real,H2: complex > real] :
% 0.32/0.63        ( ( finite_finite_int @ S4 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ T4 )
% 0.32/0.63         => ( ! [A5: int] :
% 0.32/0.63                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63               => ( ( I @ ( J @ A5 ) )
% 0.32/0.63                  = A5 ) )
% 0.32/0.63           => ( ! [A5: int] :
% 0.32/0.63                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 0.32/0.63                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.32/0.63                   => ( ( J @ ( I @ B5 ) )
% 0.32/0.63                      = B5 ) )
% 0.32/0.63               => ( ! [B5: complex] :
% 0.32/0.63                      ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 0.32/0.63                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 0.32/0.63                 => ( ! [A5: int] :
% 0.32/0.63                        ( ( member_int @ A5 @ S4 )
% 0.32/0.63                       => ( ( G @ A5 )
% 0.32/0.63                          = zero_zero_real ) )
% 0.32/0.63                   => ( ! [B5: complex] :
% 0.32/0.63                          ( ( member_complex @ B5 @ T4 )
% 0.32/0.63                         => ( ( H2 @ B5 )
% 0.32/0.63                            = zero_zero_real ) )
% 0.32/0.63                     => ( ! [A5: int] :
% 0.32/0.63                            ( ( member_int @ A5 @ S2 )
% 0.32/0.63                           => ( ( H2 @ ( J @ A5 ) )
% 0.32/0.63                              = ( G @ A5 ) ) )
% 0.32/0.63                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.32/0.63                          = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.reindex_bij_witness_not_neutral
% 0.32/0.63  thf(fact_7171_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_real,F: real > real,B3: real,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7172_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_int,F: int > real,B3: real,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7173_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > real,B3: real,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7174_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_real,F: real > rat,B3: rat,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7175_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_nat,F: nat > rat,B3: rat,I: nat] :
% 0.32/0.63        ( ( finite_finite_nat @ S )
% 0.32/0.63       => ( ! [I4: nat] :
% 0.32/0.63              ( ( member_nat @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_nat @ I @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7176_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_int,F: int > rat,B3: rat,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7177_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > rat,B3: rat,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7178_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_real,F: real > nat,B3: nat,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7179_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_int,F: int > nat,B3: nat,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7180_sum__nonneg__leq__bound,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > nat,B3: nat,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 0.32/0.63              = B3 )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_leq_bound
% 0.32/0.63  thf(fact_7181_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_real,F: real > real,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.32/0.63              = zero_zero_real )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7182_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_int,F: int > real,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.32/0.63              = zero_zero_real )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7183_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > real,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.32/0.63              = zero_zero_real )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_real ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7184_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_real,F: real > rat,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.32/0.63              = zero_zero_rat )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7185_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_nat,F: nat > rat,I: nat] :
% 0.32/0.63        ( ( finite_finite_nat @ S )
% 0.32/0.63       => ( ! [I4: nat] :
% 0.32/0.63              ( ( member_nat @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.32/0.63              = zero_zero_rat )
% 0.32/0.63           => ( ( member_nat @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7186_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_int,F: int > rat,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.32/0.63              = zero_zero_rat )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7187_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > rat,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.32/0.63              = zero_zero_rat )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_rat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7188_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_real,F: real > nat,I: real] :
% 0.32/0.63        ( ( finite_finite_real @ S )
% 0.32/0.63       => ( ! [I4: real] :
% 0.32/0.63              ( ( member_real @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 0.32/0.63              = zero_zero_nat )
% 0.32/0.63           => ( ( member_real @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7189_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_int,F: int > nat,I: int] :
% 0.32/0.63        ( ( finite_finite_int @ S )
% 0.32/0.63       => ( ! [I4: int] :
% 0.32/0.63              ( ( member_int @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 0.32/0.63              = zero_zero_nat )
% 0.32/0.63           => ( ( member_int @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7190_sum__nonneg__0,axiom,
% 0.32/0.63      ! [S: set_complex,F: complex > nat,I: complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ S )
% 0.32/0.63       => ( ! [I4: complex] :
% 0.32/0.63              ( ( member_complex @ I4 @ S )
% 0.32/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63         => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 0.32/0.63              = zero_zero_nat )
% 0.32/0.63           => ( ( member_complex @ I @ S )
% 0.32/0.63             => ( ( F @ I )
% 0.32/0.63                = zero_zero_nat ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nonneg_0
% 0.32/0.63  thf(fact_7191_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_int,G: int > complex] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( groups3049146728041665814omplex @ G
% 0.32/0.63            @ ( minus_minus_set_int @ A2
% 0.32/0.63              @ ( collect_int
% 0.32/0.63                @ ^ [X3: int] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_complex ) ) ) )
% 0.32/0.63          = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7192_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_int,G: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( groups8778361861064173332t_real @ G
% 0.32/0.63            @ ( minus_minus_set_int @ A2
% 0.32/0.63              @ ( collect_int
% 0.32/0.63                @ ^ [X3: int] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_real ) ) ) )
% 0.32/0.63          = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7193_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_complex,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( groups5808333547571424918x_real @ G
% 0.32/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.32/0.63              @ ( collect_complex
% 0.32/0.63                @ ^ [X3: complex] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_real ) ) ) )
% 0.32/0.63          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7194_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_int,G: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( groups3906332499630173760nt_rat @ G
% 0.32/0.63            @ ( minus_minus_set_int @ A2
% 0.32/0.63              @ ( collect_int
% 0.32/0.63                @ ^ [X3: int] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_rat ) ) ) )
% 0.32/0.63          = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7195_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_complex,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( groups5058264527183730370ex_rat @ G
% 0.32/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.32/0.63              @ ( collect_complex
% 0.32/0.63                @ ^ [X3: complex] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_rat ) ) ) )
% 0.32/0.63          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7196_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_int,G: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( groups4541462559716669496nt_nat @ G
% 0.32/0.63            @ ( minus_minus_set_int @ A2
% 0.32/0.63              @ ( collect_int
% 0.32/0.63                @ ^ [X3: int] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_nat ) ) ) )
% 0.32/0.63          = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7197_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_complex,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( groups5693394587270226106ex_nat @ G
% 0.32/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.32/0.63              @ ( collect_complex
% 0.32/0.63                @ ^ [X3: complex] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_nat ) ) ) )
% 0.32/0.63          = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7198_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_complex,G: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( groups5690904116761175830ex_int @ G
% 0.32/0.63            @ ( minus_811609699411566653omplex @ A2
% 0.32/0.63              @ ( collect_complex
% 0.32/0.63                @ ^ [X3: complex] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_int ) ) ) )
% 0.32/0.63          = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7199_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_nat,G: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( groups2073611262835488442omplex @ G
% 0.32/0.63            @ ( minus_minus_set_nat @ A2
% 0.32/0.63              @ ( collect_nat
% 0.32/0.63                @ ^ [X3: nat] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_complex ) ) ) )
% 0.32/0.63          = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7200_sum_Osetdiff__irrelevant,axiom,
% 0.32/0.63      ! [A2: set_nat,G: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( groups2906978787729119204at_rat @ G
% 0.32/0.63            @ ( minus_minus_set_nat @ A2
% 0.32/0.63              @ ( collect_nat
% 0.32/0.63                @ ^ [X3: nat] :
% 0.32/0.63                    ( ( G @ X3 )
% 0.32/0.63                    = zero_zero_rat ) ) ) )
% 0.32/0.63          = ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.setdiff_irrelevant
% 0.32/0.63  thf(fact_7201_less__mask,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.63       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % less_mask
% 0.32/0.63  thf(fact_7202_eval__nat__numeral_I2_J,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.32/0.63        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % eval_nat_numeral(2)
% 0.32/0.63  thf(fact_7203_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_real,I: real,F: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( member_real @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: real] :
% 0.32/0.63                  ( ( member_real @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7204_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_int,I: int,F: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( member_int @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: int] :
% 0.32/0.63                  ( ( member_int @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7205_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_complex,I: complex,F: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( member_complex @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: complex] :
% 0.32/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7206_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_real,I: real,F: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( member_real @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: real] :
% 0.32/0.63                  ( ( member_real @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7207_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_nat,I: nat,F: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ I6 )
% 0.32/0.63       => ( ( member_nat @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: nat] :
% 0.32/0.63                  ( ( member_nat @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7208_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_int,I: int,F: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( member_int @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: int] :
% 0.32/0.63                  ( ( member_int @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7209_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_complex,I: complex,F: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( member_complex @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: complex] :
% 0.32/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7210_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_real,I: real,F: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( member_real @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: real] :
% 0.32/0.63                  ( ( member_real @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7211_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_int,I: int,F: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( member_int @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: int] :
% 0.32/0.63                  ( ( member_int @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7212_sum__pos2,axiom,
% 0.32/0.63      ! [I6: set_complex,I: complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( member_complex @ I @ I6 )
% 0.32/0.63         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 0.32/0.63           => ( ! [I4: complex] :
% 0.32/0.63                  ( ( member_complex @ I4 @ I6 )
% 0.32/0.63                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63             => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos2
% 0.32/0.63  thf(fact_7213_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_complex,F: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7214_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_int,F: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_int )
% 0.32/0.63         => ( ! [I4: int] :
% 0.32/0.63                ( ( member_int @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7215_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_real,F: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_real )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7216_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_complex,F: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7217_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_nat,F: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_nat )
% 0.32/0.63         => ( ! [I4: nat] :
% 0.32/0.63                ( ( member_nat @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7218_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_int,F: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_int )
% 0.32/0.63         => ( ! [I4: int] :
% 0.32/0.63                ( ( member_int @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7219_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_real,F: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_real )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7220_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_complex )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7221_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_int,F: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_int )
% 0.32/0.63         => ( ! [I4: int] :
% 0.32/0.63                ( ( member_int @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7222_sum__pos,axiom,
% 0.32/0.63      ! [I6: set_real,F: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ I6 )
% 0.32/0.63       => ( ( I6 != bot_bot_set_real )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 0.32/0.63           => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_pos
% 0.32/0.63  thf(fact_7223_set__encode__inf,axiom,
% 0.32/0.63      ! [A2: set_nat] :
% 0.32/0.63        ( ~ ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( nat_set_encode @ A2 )
% 0.32/0.63          = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % set_encode_inf
% 0.32/0.63  thf(fact_7224_BitM__plus__one,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 0.32/0.63        = ( bit0 @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % BitM_plus_one
% 0.32/0.63  thf(fact_7225_one__plus__BitM,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 0.32/0.63        = ( bit0 @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % one_plus_BitM
% 0.32/0.63  thf(fact_7226_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5754745047067104278omplex @ G @ T3 )
% 0.32/0.63                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7227_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups8097168146408367636l_real @ G @ T3 )
% 0.32/0.63                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7228_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.32/0.63                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7229_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 0.32/0.63                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7230_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 0.32/0.63                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7231_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 0.32/0.63                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7232_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 0.32/0.63                = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7233_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,G: real > int,H2: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1932886352136224148al_int @ G @ T3 )
% 0.32/0.63                = ( groups1932886352136224148al_int @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7234_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 0.32/0.63                = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7235_sum_Omono__neutral__cong__right,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > complex,H2: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ! [X6: nat] :
% 0.32/0.63                  ( ( member_nat @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups2073611262835488442omplex @ G @ T3 )
% 0.32/0.63                = ( groups2073611262835488442omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_right
% 0.32/0.63  thf(fact_7236_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 0.32/0.63                = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7237_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 0.32/0.63                = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7238_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.32/0.63                = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7239_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 0.32/0.63                = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7240_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.32/0.63                = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7241_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 0.32/0.63                = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7242_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.32/0.63                = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7243_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_real,S2: set_real,H2: real > int,G: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: real] :
% 0.32/0.63                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ! [X6: real] :
% 0.32/0.63                  ( ( member_real @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups1932886352136224148al_int @ G @ S2 )
% 0.32/0.63                = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7244_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ! [X6: complex] :
% 0.32/0.63                  ( ( member_complex @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.32/0.63                = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7245_sum_Omono__neutral__cong__left,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( H2 @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ! [X6: nat] :
% 0.32/0.63                  ( ( member_nat @ X6 @ S2 )
% 0.32/0.63                 => ( ( G @ X6 )
% 0.32/0.63                    = ( H2 @ X6 ) ) )
% 0.32/0.63             => ( ( groups2073611262835488442omplex @ G @ S2 )
% 0.32/0.63                = ( groups2073611262835488442omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_cong_left
% 0.32/0.63  thf(fact_7246_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.32/0.63              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7247_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 0.32/0.63              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7248_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 0.32/0.63              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7249_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 0.32/0.63              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7250_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ( groups2073611262835488442omplex @ G @ T3 )
% 0.32/0.63              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7251_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 0.32/0.63              = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7252_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ( groups3539618377306564664at_int @ G @ T3 )
% 0.32/0.63              = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7253_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ( groups3049146728041665814omplex @ G @ T3 )
% 0.32/0.63              = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7254_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ( groups8778361861064173332t_real @ G @ T3 )
% 0.32/0.63              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7255_sum_Omono__neutral__right,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 0.32/0.63              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_right
% 0.32/0.63  thf(fact_7256_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 0.32/0.63              = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7257_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 0.32/0.63              = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7258_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_nat ) )
% 0.32/0.63           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 0.32/0.63              = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7259_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ T3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: complex] :
% 0.32/0.63                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 0.32/0.63              = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7260_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 0.32/0.63              = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7261_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 0.32/0.63              = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7262_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: nat] :
% 0.32/0.63                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_int ) )
% 0.32/0.63           => ( ( groups3539618377306564664at_int @ G @ S2 )
% 0.32/0.63              = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7263_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > complex] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_complex ) )
% 0.32/0.63           => ( ( groups3049146728041665814omplex @ G @ S2 )
% 0.32/0.63              = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7264_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_real ) )
% 0.32/0.63           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 0.32/0.63              = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7265_sum_Omono__neutral__left,axiom,
% 0.32/0.63      ! [T3: set_int,S2: set_int,G: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ T3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 0.32/0.63         => ( ! [X6: int] :
% 0.32/0.63                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 0.32/0.63               => ( ( G @ X6 )
% 0.32/0.63                  = zero_zero_rat ) )
% 0.32/0.63           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 0.32/0.63              = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.mono_neutral_left
% 0.32/0.63  thf(fact_7266_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_complex ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_complex ) )
% 0.32/0.63               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.32/0.63                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.32/0.63                    = ( groups5754745047067104278omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7267_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_real ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_real ) )
% 0.32/0.63               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.32/0.63                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.32/0.63                    = ( groups8097168146408367636l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7268_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_real ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_real ) )
% 0.32/0.63               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.32/0.63                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.63                    = ( groups5808333547571424918x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7269_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_rat ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_rat ) )
% 0.32/0.63               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.32/0.63                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.32/0.63                    = ( groups1300246762558778688al_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7270_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_rat ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_rat ) )
% 0.32/0.63               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.32/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7271_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_nat ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_nat ) )
% 0.32/0.63               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.32/0.63                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.32/0.63                    = ( groups1935376822645274424al_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7272_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_nat ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_nat ) )
% 0.32/0.63               => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 0.32/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.32/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7273_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_int ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_int ) )
% 0.32/0.63               => ( ( ( groups1932886352136224148al_int @ G @ C4 )
% 0.32/0.63                    = ( groups1932886352136224148al_int @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 0.32/0.63                    = ( groups1932886352136224148al_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7274_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_int ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_int ) )
% 0.32/0.63               => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 0.32/0.63                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.32/0.63                    = ( groups5690904116761175830ex_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7275_sum_Osame__carrierI,axiom,
% 0.32/0.63      ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: nat] :
% 0.32/0.63                  ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_complex ) )
% 0.32/0.63             => ( ! [B5: nat] :
% 0.32/0.63                    ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_complex ) )
% 0.32/0.63               => ( ( ( groups2073611262835488442omplex @ G @ C4 )
% 0.32/0.63                    = ( groups2073611262835488442omplex @ H2 @ C4 ) )
% 0.32/0.63                 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.32/0.63                    = ( groups2073611262835488442omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrierI
% 0.32/0.63  thf(fact_7276_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_complex ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_complex ) )
% 0.32/0.63               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 0.32/0.63                    = ( groups5754745047067104278omplex @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 0.32/0.63                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7277_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_real ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_real ) )
% 0.32/0.63               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.32/0.63                    = ( groups8097168146408367636l_real @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 0.32/0.63                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7278_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_real ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_real ) )
% 0.32/0.63               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.63                    = ( groups5808333547571424918x_real @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 0.32/0.63                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7279_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_rat ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_rat ) )
% 0.32/0.63               => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.32/0.63                    = ( groups1300246762558778688al_rat @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 0.32/0.63                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7280_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_rat ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_rat ) )
% 0.32/0.63               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 0.32/0.63                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7281_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_nat ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_nat ) )
% 0.32/0.63               => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.32/0.63                    = ( groups1935376822645274424al_nat @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 0.32/0.63                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7282_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_nat ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_nat ) )
% 0.32/0.63               => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.32/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 0.32/0.63                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7283_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: real] :
% 0.32/0.63                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_int ) )
% 0.32/0.63             => ( ! [B5: real] :
% 0.32/0.63                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_int ) )
% 0.32/0.63               => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 0.32/0.63                    = ( groups1932886352136224148al_int @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups1932886352136224148al_int @ G @ C4 )
% 0.32/0.63                    = ( groups1932886352136224148al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7284_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ C4 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: complex] :
% 0.32/0.63                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_int ) )
% 0.32/0.63             => ( ! [B5: complex] :
% 0.32/0.63                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_int ) )
% 0.32/0.63               => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.32/0.63                    = ( groups5690904116761175830ex_int @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 0.32/0.63                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7285_sum_Osame__carrier,axiom,
% 0.32/0.63      ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 0.32/0.63        ( ( finite_finite_nat @ C4 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 0.32/0.63         => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 0.32/0.63           => ( ! [A5: nat] :
% 0.32/0.63                  ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 0.32/0.63                 => ( ( G @ A5 )
% 0.32/0.63                    = zero_zero_complex ) )
% 0.32/0.63             => ( ! [B5: nat] :
% 0.32/0.63                    ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 0.32/0.63                   => ( ( H2 @ B5 )
% 0.32/0.63                      = zero_zero_complex ) )
% 0.32/0.63               => ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 0.32/0.63                    = ( groups2073611262835488442omplex @ H2 @ B3 ) )
% 0.32/0.63                  = ( ( groups2073611262835488442omplex @ G @ C4 )
% 0.32/0.63                    = ( groups2073611262835488442omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.same_carrier
% 0.32/0.63  thf(fact_7286_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 0.32/0.63        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.63            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7287_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 0.32/0.63        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.63            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7288_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 0.32/0.63        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.32/0.63            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7289_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 0.32/0.63        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63       => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.32/0.63            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7290_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 0.32/0.63        ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_nat @ A2 )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 0.32/0.63            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7291_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 0.32/0.63        ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_nat @ A2 )
% 0.32/0.63         => ( ( groups3539618377306564664at_int @ G @ A2 )
% 0.32/0.63            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7292_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_int,A2: set_int,G: int > real] :
% 0.32/0.63        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_int @ A2 )
% 0.32/0.63         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.32/0.63            = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7293_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_int,A2: set_int,G: int > rat] :
% 0.32/0.63        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_int @ A2 )
% 0.32/0.63         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.32/0.63            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7294_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_int,A2: set_int,G: int > nat] :
% 0.32/0.63        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_int @ A2 )
% 0.32/0.63         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.32/0.63            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7295_sum_Osubset__diff,axiom,
% 0.32/0.63      ! [B3: set_int,A2: set_int,G: int > int] :
% 0.32/0.63        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63       => ( ( finite_finite_int @ A2 )
% 0.32/0.63         => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 0.32/0.63            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.subset_diff
% 0.32/0.63  thf(fact_7296_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_complex,B3: set_complex,F: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63         => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7297_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7298_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7299_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7300_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7301_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_int,B3: set_int,F: int > real] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63         => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7302_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_int,B3: set_int,F: int > rat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63         => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7303_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_int,B3: set_int,F: int > int] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7304_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7305_sum__diff,axiom,
% 0.32/0.63      ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff
% 0.32/0.63  thf(fact_7306_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,F: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: real] :
% 0.32/0.63                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7307_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: complex] :
% 0.32/0.63                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7308_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,F: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: real] :
% 0.32/0.63                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7309_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: complex] :
% 0.32/0.63                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7310_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,F: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: nat] :
% 0.32/0.63                ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7311_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,F: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: real] :
% 0.32/0.63                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7312_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: complex] :
% 0.32/0.63                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7313_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,F: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: real] :
% 0.32/0.63                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7314_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,F: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: complex] :
% 0.32/0.63                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7315_sum__mono2,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,F: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.63         => ( ! [B5: nat] :
% 0.32/0.63                ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 0.32/0.63               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 0.32/0.63           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_mono2
% 0.32/0.63  thf(fact_7316_numeral__BitM,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 0.32/0.63        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 0.32/0.63  
% 0.32/0.63  % numeral_BitM
% 0.32/0.63  thf(fact_7317_numeral__BitM,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( numeral_numeral_real @ ( bitM @ N ) )
% 0.32/0.63        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 0.32/0.63  
% 0.32/0.63  % numeral_BitM
% 0.32/0.63  thf(fact_7318_numeral__BitM,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 0.32/0.63        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % numeral_BitM
% 0.32/0.63  thf(fact_7319_numeral__BitM,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 0.32/0.63        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 0.32/0.63  
% 0.32/0.63  % numeral_BitM
% 0.32/0.63  thf(fact_7320_odd__numeral__BitM,axiom,
% 0.32/0.63      ! [W: num] :
% 0.32/0.63        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % odd_numeral_BitM
% 0.32/0.63  thf(fact_7321_odd__numeral__BitM,axiom,
% 0.32/0.63      ! [W: num] :
% 0.32/0.63        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % odd_numeral_BitM
% 0.32/0.63  thf(fact_7322_odd__numeral__BitM,axiom,
% 0.32/0.63      ! [W: num] :
% 0.32/0.63        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % odd_numeral_BitM
% 0.32/0.63  thf(fact_7323_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: real] :
% 0.32/0.63                    ( ( member_real @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7324_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: complex] :
% 0.32/0.63                    ( ( member_complex @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7325_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: real] :
% 0.32/0.63                    ( ( member_real @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7326_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: complex] :
% 0.32/0.63                    ( ( member_complex @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7327_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 0.32/0.63        ( ( finite_finite_nat @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.63         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: nat] :
% 0.32/0.63                    ( ( member_nat @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7328_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: real] :
% 0.32/0.63                    ( ( member_real @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7329_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: complex] :
% 0.32/0.63                    ( ( member_complex @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7330_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 0.32/0.63        ( ( finite_finite_real @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.63         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: real] :
% 0.32/0.63                    ( ( member_real @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7331_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 0.32/0.63         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: complex] :
% 0.32/0.63                    ( ( member_complex @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7332_sum__strict__mono2,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 0.32/0.63        ( ( finite_finite_nat @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.63         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 0.32/0.63           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 0.32/0.63             => ( ! [X6: nat] :
% 0.32/0.63                    ( ( member_nat @ X6 @ B3 )
% 0.32/0.63                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 0.32/0.63               => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_strict_mono2
% 0.32/0.63  thf(fact_7333_Suc__mask__eq__exp,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.32/0.63        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % Suc_mask_eq_exp
% 0.32/0.63  thf(fact_7334_mask__nat__less__exp,axiom,
% 0.32/0.63      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_nat_less_exp
% 0.32/0.63  thf(fact_7335_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 0.32/0.63        ( ! [I4: complex] :
% 0.32/0.63            ( ( member_complex @ I4 @ I6 )
% 0.32/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 0.32/0.63            = one_one_Code_integer )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_le3102999989581377725nteger
% 0.32/0.63              @ ( abs_abs_Code_integer
% 0.32/0.63                @ ( minus_8373710615458151222nteger
% 0.32/0.63                  @ ( groups6621422865394947399nteger
% 0.32/0.63                    @ ^ [I5: complex] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7336_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.32/0.63        ( ! [I4: real] :
% 0.32/0.63            ( ( member_real @ I4 @ I6 )
% 0.32/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 0.32/0.63            = one_one_Code_integer )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_le3102999989581377725nteger
% 0.32/0.63              @ ( abs_abs_Code_integer
% 0.32/0.63                @ ( minus_8373710615458151222nteger
% 0.32/0.63                  @ ( groups7713935264441627589nteger
% 0.32/0.63                    @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7337_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.32/0.63        ( ! [I4: nat] :
% 0.32/0.63            ( ( member_nat @ I4 @ I6 )
% 0.32/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 0.32/0.63            = one_one_Code_integer )
% 0.32/0.63         => ( ! [I4: nat] :
% 0.32/0.63                ( ( member_nat @ I4 @ I6 )
% 0.32/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_le3102999989581377725nteger
% 0.32/0.63              @ ( abs_abs_Code_integer
% 0.32/0.63                @ ( minus_8373710615458151222nteger
% 0.32/0.63                  @ ( groups7501900531339628137nteger
% 0.32/0.63                    @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7338_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.32/0.63        ( ! [I4: int] :
% 0.32/0.63            ( ( member_int @ I4 @ I6 )
% 0.32/0.63           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 0.32/0.63            = one_one_Code_integer )
% 0.32/0.63         => ( ! [I4: int] :
% 0.32/0.63                ( ( member_int @ I4 @ I6 )
% 0.32/0.63               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_le3102999989581377725nteger
% 0.32/0.63              @ ( abs_abs_Code_integer
% 0.32/0.63                @ ( minus_8373710615458151222nteger
% 0.32/0.63                  @ ( groups7873554091576472773nteger
% 0.32/0.63                    @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7339_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 0.32/0.63        ( ! [I4: complex] :
% 0.32/0.63            ( ( member_complex @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 0.32/0.63            = one_one_real )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_real
% 0.32/0.63              @ ( abs_abs_real
% 0.32/0.63                @ ( minus_minus_real
% 0.32/0.63                  @ ( groups5808333547571424918x_real
% 0.32/0.63                    @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7340_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 0.32/0.63        ( ! [I4: real] :
% 0.32/0.63            ( ( member_real @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 0.32/0.63            = one_one_real )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_real
% 0.32/0.63              @ ( abs_abs_real
% 0.32/0.63                @ ( minus_minus_real
% 0.32/0.63                  @ ( groups8097168146408367636l_real
% 0.32/0.63                    @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7341_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 0.32/0.63        ( ! [I4: int] :
% 0.32/0.63            ( ( member_int @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 0.32/0.63            = one_one_real )
% 0.32/0.63         => ( ! [I4: int] :
% 0.32/0.63                ( ( member_int @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_real
% 0.32/0.63              @ ( abs_abs_real
% 0.32/0.63                @ ( minus_minus_real
% 0.32/0.63                  @ ( groups8778361861064173332t_real
% 0.32/0.63                    @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7342_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 0.32/0.63        ( ! [I4: complex] :
% 0.32/0.63            ( ( member_complex @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 0.32/0.63            = one_one_rat )
% 0.32/0.63         => ( ! [I4: complex] :
% 0.32/0.63                ( ( member_complex @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_rat
% 0.32/0.63              @ ( abs_abs_rat
% 0.32/0.63                @ ( minus_minus_rat
% 0.32/0.63                  @ ( groups5058264527183730370ex_rat
% 0.32/0.63                    @ ^ [I5: complex] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7343_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 0.32/0.63        ( ! [I4: real] :
% 0.32/0.63            ( ( member_real @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 0.32/0.63            = one_one_rat )
% 0.32/0.63         => ( ! [I4: real] :
% 0.32/0.63                ( ( member_real @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_rat
% 0.32/0.63              @ ( abs_abs_rat
% 0.32/0.63                @ ( minus_minus_rat
% 0.32/0.63                  @ ( groups1300246762558778688al_rat
% 0.32/0.63                    @ ^ [I5: real] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7344_convex__sum__bound__le,axiom,
% 0.32/0.63      ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.32/0.63        ( ! [I4: nat] :
% 0.32/0.63            ( ( member_nat @ I4 @ I6 )
% 0.32/0.63           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 0.32/0.63       => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 0.32/0.63            = one_one_rat )
% 0.32/0.63         => ( ! [I4: nat] :
% 0.32/0.63                ( ( member_nat @ I4 @ I6 )
% 0.32/0.63               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 0.32/0.63           => ( ord_less_eq_rat
% 0.32/0.63              @ ( abs_abs_rat
% 0.32/0.63                @ ( minus_minus_rat
% 0.32/0.63                  @ ( groups2906978787729119204at_rat
% 0.32/0.63                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 0.32/0.63                    @ I6 )
% 0.32/0.63                  @ B ) )
% 0.32/0.63              @ Delta ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % convex_sum_bound_le
% 0.32/0.63  thf(fact_7345_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 0.32/0.63        = ( N = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % semiring_bit_operations_class.even_mask_iff
% 0.32/0.63  thf(fact_7346_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.32/0.63        = ( N = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % semiring_bit_operations_class.even_mask_iff
% 0.32/0.63  thf(fact_7347_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.32/0.63        = ( N = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % semiring_bit_operations_class.even_mask_iff
% 0.32/0.63  thf(fact_7348_mask__nat__def,axiom,
% 0.32/0.63      ( bit_se2002935070580805687sk_nat
% 0.32/0.63      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_nat_def
% 0.32/0.63  thf(fact_7349_mask__half__int,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.63        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_half_int
% 0.32/0.63  thf(fact_7350_mask__int__def,axiom,
% 0.32/0.63      ( bit_se2000444600071755411sk_int
% 0.32/0.63      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_int_def
% 0.32/0.63  thf(fact_7351_mask__eq__exp__minus__1,axiom,
% 0.32/0.63      ( bit_se2002935070580805687sk_nat
% 0.32/0.63      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_eq_exp_minus_1
% 0.32/0.63  thf(fact_7352_mask__eq__exp__minus__1,axiom,
% 0.32/0.63      ( bit_se2000444600071755411sk_int
% 0.32/0.63      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mask_eq_exp_minus_1
% 0.32/0.63  thf(fact_7353_divmod__step__nat__def,axiom,
% 0.32/0.63      ( unique5026877609467782581ep_nat
% 0.32/0.63      = ( ^ [L: num] :
% 0.32/0.63            ( produc2626176000494625587at_nat
% 0.32/0.63            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % divmod_step_nat_def
% 0.32/0.63  thf(fact_7354_divmod__step__int__def,axiom,
% 0.32/0.63      ( unique5024387138958732305ep_int
% 0.32/0.63      = ( ^ [L: num] :
% 0.32/0.63            ( produc4245557441103728435nt_int
% 0.32/0.63            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % divmod_step_int_def
% 0.32/0.63  thf(fact_7355_divmod__nat__if,axiom,
% 0.32/0.63      ( divmod_nat
% 0.32/0.63      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.63            ( if_Pro6206227464963214023at_nat
% 0.32/0.63            @ ( ( N2 = zero_zero_nat )
% 0.32/0.63              | ( ord_less_nat @ M3 @ N2 ) )
% 0.32/0.63            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 0.32/0.63            @ ( produc2626176000494625587at_nat
% 0.32/0.63              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.32/0.63              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % divmod_nat_if
% 0.32/0.63  thf(fact_7356_num_Osize__gen_I3_J,axiom,
% 0.32/0.63      ! [X32: num] :
% 0.32/0.63        ( ( size_num @ ( bit1 @ X32 ) )
% 0.32/0.63        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % num.size_gen(3)
% 0.32/0.63  thf(fact_7357_take__bit__rec,axiom,
% 0.32/0.63      ( bit_se1745604003318907178nteger
% 0.32/0.63      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_rec
% 0.32/0.63  thf(fact_7358_take__bit__rec,axiom,
% 0.32/0.63      ( bit_se2923211474154528505it_int
% 0.32/0.63      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_rec
% 0.32/0.63  thf(fact_7359_take__bit__rec,axiom,
% 0.32/0.63      ( bit_se2925701944663578781it_nat
% 0.32/0.63      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_rec
% 0.32/0.63  thf(fact_7360_num_Osize__gen_I2_J,axiom,
% 0.32/0.63      ! [X22: num] :
% 0.32/0.63        ( ( size_num @ ( bit0 @ X22 ) )
% 0.32/0.63        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % num.size_gen(2)
% 0.32/0.63  thf(fact_7361_tanh__real__altdef,axiom,
% 0.32/0.63      ( tanh_real
% 0.32/0.63      = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % tanh_real_altdef
% 0.32/0.63  thf(fact_7362_and__int__unfold,axiom,
% 0.32/0.63      ( bit_se725231765392027082nd_int
% 0.32/0.63      = ( ^ [K2: int,L: int] :
% 0.32/0.63            ( if_int
% 0.32/0.63            @ ( ( K2 = zero_zero_int )
% 0.32/0.63              | ( L = zero_zero_int ) )
% 0.32/0.63            @ zero_zero_int
% 0.32/0.63            @ ( if_int
% 0.32/0.63              @ ( K2
% 0.32/0.63                = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63              @ L
% 0.32/0.63              @ ( if_int
% 0.32/0.63                @ ( L
% 0.32/0.63                  = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63                @ K2
% 0.32/0.63                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_int_unfold
% 0.32/0.63  thf(fact_7363_and_Oidem,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ A @ A )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.idem
% 0.32/0.63  thf(fact_7364_and_Oidem,axiom,
% 0.32/0.63      ! [A: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.idem
% 0.32/0.63  thf(fact_7365_and_Oleft__idem,axiom,
% 0.32/0.63      ! [A: int,B: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_idem
% 0.32/0.63  thf(fact_7366_and_Oleft__idem,axiom,
% 0.32/0.63      ! [A: nat,B: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.32/0.63        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_idem
% 0.32/0.63  thf(fact_7367_and_Oright__idem,axiom,
% 0.32/0.63      ! [A: int,B: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.right_idem
% 0.32/0.63  thf(fact_7368_and_Oright__idem,axiom,
% 0.32/0.63      ! [A: nat,B: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 0.32/0.63        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.right_idem
% 0.32/0.63  thf(fact_7369_case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc8763457246119570046nteger,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.32/0.63        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( C @ A5 @ B5 ) )
% 0.32/0.63       => ( produc127349428274296955eger_o @ C @ P5 ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2
% 0.32/0.63  thf(fact_7370_case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.32/0.63        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( C @ A5 @ B5 ) )
% 0.32/0.63       => ( produc6253627499356882019eger_o @ C @ P5 ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2
% 0.32/0.63  thf(fact_7371_case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.32/0.63        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 0.32/0.63           => ( C @ A5 @ B5 ) )
% 0.32/0.63       => ( produc1573362020775583542_int_o @ C @ P5 ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2
% 0.32/0.63  thf(fact_7372_case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.32/0.63        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 0.32/0.63           => ( C @ A5 @ B5 ) )
% 0.32/0.63       => ( produc2558449545302689196_int_o @ C @ P5 ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2
% 0.32/0.63  thf(fact_7373_case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,C: int > int > $o] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( C @ A5 @ B5 ) )
% 0.32/0.63       => ( produc4947309494688390418_int_o @ C @ P5 ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2
% 0.32/0.63  thf(fact_7374_case__prodI,axiom,
% 0.32/0.63      ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( F @ A @ B )
% 0.32/0.63       => ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI
% 0.32/0.63  thf(fact_7375_case__prodI,axiom,
% 0.32/0.63      ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( F @ A @ B )
% 0.32/0.63       => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI
% 0.32/0.63  thf(fact_7376_case__prodI,axiom,
% 0.32/0.63      ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.32/0.63        ( ( F @ A @ B )
% 0.32/0.63       => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI
% 0.32/0.63  thf(fact_7377_case__prodI,axiom,
% 0.32/0.63      ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.32/0.63        ( ( F @ A @ B )
% 0.32/0.63       => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI
% 0.32/0.63  thf(fact_7378_case__prodI,axiom,
% 0.32/0.63      ! [F: int > int > $o,A: int,B: int] :
% 0.32/0.63        ( ( F @ A @ B )
% 0.32/0.63       => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI
% 0.32/0.63  thf(fact_7379_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,Z: complex,C: int > int > set_complex] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7380_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,Z: real,C: int > int > set_real] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7381_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,Z: nat,C: int > int > set_nat] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7382_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,Z: int,C: int > int > set_int] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7383_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: product_prod_int_int,Z: set_nat,C: int > int > set_set_nat] :
% 0.32/0.63        ( ! [A5: int,B5: int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( product_Pair_int_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_set_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7384_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc8763457246119570046nteger,Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex] :
% 0.32/0.63        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7385_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc8763457246119570046nteger,Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real] :
% 0.32/0.63        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7386_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc8763457246119570046nteger,Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 0.32/0.63        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7387_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc8763457246119570046nteger,Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 0.32/0.63        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 0.32/0.63           => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7388_mem__case__prodI2,axiom,
% 0.32/0.63      ! [P5: produc7773217078559923341nt_int,Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex] :
% 0.32/0.63        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.32/0.63            ( ( P5
% 0.32/0.63              = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 0.32/0.63           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI2
% 0.32/0.63  thf(fact_7389_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: complex,C: int > int > set_complex,A: int,B: int] :
% 0.32/0.63        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7390_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: real,C: int > int > set_real,A: int,B: int] :
% 0.32/0.63        ( ( member_real @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7391_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: nat,C: int > int > set_nat,A: int,B: int] :
% 0.32/0.63        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7392_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: int,C: int > int > set_int,A: int,B: int] :
% 0.32/0.63        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7393_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: set_nat,C: int > int > set_set_nat,A: int,B: int] :
% 0.32/0.63        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7394_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7395_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( member_real @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7396_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7397_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7398_mem__case__prodI,axiom,
% 0.32/0.63      ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.32/0.63        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 0.32/0.63       => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodI
% 0.32/0.63  thf(fact_7399_case__prodI2_H,axiom,
% 0.32/0.63      ! [P5: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.32/0.63        ( ! [A5: nat,B5: nat] :
% 0.32/0.63            ( ( ( product_Pair_nat_nat @ A5 @ B5 )
% 0.32/0.63              = P5 )
% 0.32/0.63           => ( C @ A5 @ B5 @ X ) )
% 0.32/0.63       => ( produc8739625826339149834_nat_o @ C @ P5 @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodI2'
% 0.32/0.63  thf(fact_7400_take__bit__of__0,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_0
% 0.32/0.63  thf(fact_7401_take__bit__of__0,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_0
% 0.32/0.63  thf(fact_7402_and__zero__eq,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_zero_eq
% 0.32/0.63  thf(fact_7403_and__zero__eq,axiom,
% 0.32/0.63      ! [A: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % and_zero_eq
% 0.32/0.63  thf(fact_7404_zero__and__eq,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % zero_and_eq
% 0.32/0.63  thf(fact_7405_zero__and__eq,axiom,
% 0.32/0.63      ! [A: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % zero_and_eq
% 0.32/0.63  thf(fact_7406_bit_Oconj__zero__left,axiom,
% 0.32/0.63      ! [X: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % bit.conj_zero_left
% 0.32/0.63  thf(fact_7407_bit_Oconj__zero__right,axiom,
% 0.32/0.63      ! [X: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % bit.conj_zero_right
% 0.32/0.63  thf(fact_7408_take__bit__and,axiom,
% 0.32/0.63      ! [N: nat,A: int,B: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_and
% 0.32/0.63  thf(fact_7409_take__bit__and,axiom,
% 0.32/0.63      ! [N: nat,A: nat,B: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.32/0.63        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_and
% 0.32/0.63  thf(fact_7410_exp__le__cancel__iff,axiom,
% 0.32/0.63      ! [X: real,Y: real] :
% 0.32/0.63        ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 0.32/0.63        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_le_cancel_iff
% 0.32/0.63  thf(fact_7411_concat__bit__of__zero__2,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 0.32/0.63        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.32/0.63  
% 0.32/0.63  % concat_bit_of_zero_2
% 0.32/0.63  thf(fact_7412_take__bit__0,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_0
% 0.32/0.63  thf(fact_7413_take__bit__0,axiom,
% 0.32/0.63      ! [A: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_0
% 0.32/0.63  thf(fact_7414_exp__zero,axiom,
% 0.32/0.63      ( ( exp_complex @ zero_zero_complex )
% 0.32/0.63      = one_one_complex ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_zero
% 0.32/0.63  thf(fact_7415_exp__zero,axiom,
% 0.32/0.63      ( ( exp_real @ zero_zero_real )
% 0.32/0.63      = one_one_real ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_zero
% 0.32/0.63  thf(fact_7416_take__bit__Suc__1,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_Suc_1
% 0.32/0.63  thf(fact_7417_take__bit__Suc__1,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 0.32/0.63        = one_one_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_Suc_1
% 0.32/0.63  thf(fact_7418_and_Oleft__neutral,axiom,
% 0.32/0.63      ! [A: code_integer] :
% 0.32/0.63        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_neutral
% 0.32/0.63  thf(fact_7419_and_Oleft__neutral,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_neutral
% 0.32/0.63  thf(fact_7420_and_Oright__neutral,axiom,
% 0.32/0.63      ! [A: code_integer] :
% 0.32/0.63        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.right_neutral
% 0.32/0.63  thf(fact_7421_and_Oright__neutral,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63        = A ) ).
% 0.32/0.63  
% 0.32/0.63  % and.right_neutral
% 0.32/0.63  thf(fact_7422_bit_Oconj__one__right,axiom,
% 0.32/0.63      ! [X: code_integer] :
% 0.32/0.63        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.63        = X ) ).
% 0.32/0.63  
% 0.32/0.63  % bit.conj_one_right
% 0.32/0.63  thf(fact_7423_bit_Oconj__one__right,axiom,
% 0.32/0.63      ! [X: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63        = X ) ).
% 0.32/0.63  
% 0.32/0.63  % bit.conj_one_right
% 0.32/0.63  thf(fact_7424_take__bit__numeral__1,axiom,
% 0.32/0.63      ! [L2: num] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_numeral_1
% 0.32/0.63  thf(fact_7425_take__bit__numeral__1,axiom,
% 0.32/0.63      ! [L2: num] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 0.32/0.63        = one_one_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_numeral_1
% 0.32/0.63  thf(fact_7426_exp__eq__one__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ( exp_real @ X )
% 0.32/0.63          = one_one_real )
% 0.32/0.63        = ( X = zero_zero_real ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_eq_one_iff
% 0.32/0.63  thf(fact_7427_and__nonnegative__int__iff,axiom,
% 0.32/0.63      ! [K: int,L2: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.32/0.63        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.63          | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_nonnegative_int_iff
% 0.32/0.63  thf(fact_7428_and__negative__int__iff,axiom,
% 0.32/0.63      ! [K: int,L2: int] :
% 0.32/0.63        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 0.32/0.63        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.63          & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_negative_int_iff
% 0.32/0.63  thf(fact_7429_take__bit__of__1__eq__0__iff,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.32/0.63          = zero_zero_int )
% 0.32/0.63        = ( N = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_1_eq_0_iff
% 0.32/0.63  thf(fact_7430_take__bit__of__1__eq__0__iff,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.32/0.63          = zero_zero_nat )
% 0.32/0.63        = ( N = zero_zero_nat ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_1_eq_0_iff
% 0.32/0.63  thf(fact_7431_and__numerals_I2_J,axiom,
% 0.32/0.63      ! [Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(2)
% 0.32/0.63  thf(fact_7432_and__numerals_I2_J,axiom,
% 0.32/0.63      ! [Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.63        = one_one_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(2)
% 0.32/0.63  thf(fact_7433_and__numerals_I8_J,axiom,
% 0.32/0.63      ! [X: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(8)
% 0.32/0.63  thf(fact_7434_and__numerals_I8_J,axiom,
% 0.32/0.63      ! [X: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.32/0.63        = one_one_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(8)
% 0.32/0.63  thf(fact_7435_one__less__exp__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 0.32/0.63        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % one_less_exp_iff
% 0.32/0.63  thf(fact_7436_exp__less__one__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 0.32/0.63        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_less_one_iff
% 0.32/0.63  thf(fact_7437_exp__le__one__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 0.32/0.63        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_le_one_iff
% 0.32/0.63  thf(fact_7438_one__le__exp__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 0.32/0.63        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % one_le_exp_iff
% 0.32/0.63  thf(fact_7439_take__bit__minus__one__eq__mask,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.63        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_minus_one_eq_mask
% 0.32/0.63  thf(fact_7440_take__bit__minus__one__eq__mask,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_minus_one_eq_mask
% 0.32/0.63  thf(fact_7441_exp__ln,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.63       => ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.32/0.63          = X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_ln
% 0.32/0.63  thf(fact_7442_exp__ln__iff,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.32/0.63          = X )
% 0.32/0.63        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_ln_iff
% 0.32/0.63  thf(fact_7443_take__bit__of__Suc__0,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.63        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_Suc_0
% 0.32/0.63  thf(fact_7444_and__numerals_I1_J,axiom,
% 0.32/0.63      ! [Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(1)
% 0.32/0.63  thf(fact_7445_and__numerals_I1_J,axiom,
% 0.32/0.63      ! [Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(1)
% 0.32/0.63  thf(fact_7446_and__numerals_I5_J,axiom,
% 0.32/0.63      ! [X: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(5)
% 0.32/0.63  thf(fact_7447_and__numerals_I5_J,axiom,
% 0.32/0.63      ! [X: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.32/0.63        = zero_zero_nat ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(5)
% 0.32/0.63  thf(fact_7448_and__numerals_I3_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.32/0.63        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(3)
% 0.32/0.63  thf(fact_7449_and__numerals_I3_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.63        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(3)
% 0.32/0.63  thf(fact_7450_sum_Ocl__ivl__Suc,axiom,
% 0.32/0.63      ! [N: nat,M: nat,G: nat > complex] :
% 0.32/0.63        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = zero_zero_complex ) )
% 0.32/0.63        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.cl_ivl_Suc
% 0.32/0.63  thf(fact_7451_sum_Ocl__ivl__Suc,axiom,
% 0.32/0.63      ! [N: nat,M: nat,G: nat > rat] :
% 0.32/0.63        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = zero_zero_rat ) )
% 0.32/0.63        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.cl_ivl_Suc
% 0.32/0.63  thf(fact_7452_sum_Ocl__ivl__Suc,axiom,
% 0.32/0.63      ! [N: nat,M: nat,G: nat > int] :
% 0.32/0.63        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = zero_zero_int ) )
% 0.32/0.63        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.cl_ivl_Suc
% 0.32/0.63  thf(fact_7453_sum_Ocl__ivl__Suc,axiom,
% 0.32/0.63      ! [N: nat,M: nat,G: nat > nat] :
% 0.32/0.63        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = zero_zero_nat ) )
% 0.32/0.63        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.cl_ivl_Suc
% 0.32/0.63  thf(fact_7454_sum_Ocl__ivl__Suc,axiom,
% 0.32/0.63      ! [N: nat,M: nat,G: nat > real] :
% 0.32/0.63        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = zero_zero_real ) )
% 0.32/0.63        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.32/0.63         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.cl_ivl_Suc
% 0.32/0.63  thf(fact_7455_take__bit__of__1,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 0.32/0.63        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_1
% 0.32/0.63  thf(fact_7456_take__bit__of__1,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.32/0.63        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_1
% 0.32/0.63  thf(fact_7457_take__bit__of__1,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.32/0.63        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_1
% 0.32/0.63  thf(fact_7458_and__minus__numerals_I6_J,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_minus_numerals(6)
% 0.32/0.63  thf(fact_7459_and__minus__numerals_I2_J,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.63        = one_one_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_minus_numerals(2)
% 0.32/0.63  thf(fact_7460_sum__zero__power,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > complex] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2073611262835488442omplex
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( C @ zero_zero_nat ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2073611262835488442omplex
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_complex ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power
% 0.32/0.63  thf(fact_7461_sum__zero__power,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > rat] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( C @ zero_zero_nat ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_rat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power
% 0.32/0.63  thf(fact_7462_sum__zero__power,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > real] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups6591440286371151544t_real
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( C @ zero_zero_nat ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups6591440286371151544t_real
% 0.32/0.63              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_real ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power
% 0.32/0.63  thf(fact_7463_and__numerals_I4_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.32/0.63        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(4)
% 0.32/0.63  thf(fact_7464_and__numerals_I4_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.63        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(4)
% 0.32/0.63  thf(fact_7465_and__numerals_I6_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.32/0.63        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(6)
% 0.32/0.63  thf(fact_7466_and__numerals_I6_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.63        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(6)
% 0.32/0.63  thf(fact_7467_even__take__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,A: code_integer] :
% 0.32/0.63        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 0.32/0.63        = ( ( N = zero_zero_nat )
% 0.32/0.63          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_take_bit_eq
% 0.32/0.63  thf(fact_7468_even__take__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,A: int] :
% 0.32/0.63        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.32/0.63        = ( ( N = zero_zero_nat )
% 0.32/0.63          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_take_bit_eq
% 0.32/0.63  thf(fact_7469_even__take__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,A: nat] :
% 0.32/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 0.32/0.63        = ( ( N = zero_zero_nat )
% 0.32/0.63          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_take_bit_eq
% 0.32/0.63  thf(fact_7470_and__minus__numerals_I1_J,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_minus_numerals(1)
% 0.32/0.63  thf(fact_7471_and__minus__numerals_I5_J,axiom,
% 0.32/0.63      ! [N: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.32/0.63        = zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % and_minus_numerals(5)
% 0.32/0.63  thf(fact_7472_sum__zero__power_H,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2073611262835488442omplex
% 0.32/0.63              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2073611262835488442omplex
% 0.32/0.63              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_complex ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power'
% 0.32/0.63  thf(fact_7473_sum__zero__power_H,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat
% 0.32/0.63              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups2906978787729119204at_rat
% 0.32/0.63              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_rat ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power'
% 0.32/0.63  thf(fact_7474_sum__zero__power_H,axiom,
% 0.32/0.63      ! [A2: set_nat,C: nat > real,D: nat > real] :
% 0.32/0.63        ( ( ( ( finite_finite_nat @ A2 )
% 0.32/0.63            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups6591440286371151544t_real
% 0.32/0.63              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.32/0.63        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.32/0.63              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.32/0.63         => ( ( groups6591440286371151544t_real
% 0.32/0.63              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 0.32/0.63              @ A2 )
% 0.32/0.63            = zero_zero_real ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_zero_power'
% 0.32/0.63  thf(fact_7475_take__bit__Suc__0,axiom,
% 0.32/0.63      ! [A: code_integer] :
% 0.32/0.63        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 0.32/0.63        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_Suc_0
% 0.32/0.63  thf(fact_7476_take__bit__Suc__0,axiom,
% 0.32/0.63      ! [A: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 0.32/0.63        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_Suc_0
% 0.32/0.63  thf(fact_7477_take__bit__Suc__0,axiom,
% 0.32/0.63      ! [A: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 0.32/0.63        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_Suc_0
% 0.32/0.63  thf(fact_7478_and__numerals_I7_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.32/0.63        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(7)
% 0.32/0.63  thf(fact_7479_and__numerals_I7_J,axiom,
% 0.32/0.63      ! [X: num,Y: num] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.63        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_numerals(7)
% 0.32/0.63  thf(fact_7480_take__bit__of__exp,axiom,
% 0.32/0.63      ! [M: nat,N: nat] :
% 0.32/0.63        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.63        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_exp
% 0.32/0.63  thf(fact_7481_take__bit__of__exp,axiom,
% 0.32/0.63      ! [M: nat,N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.63        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_exp
% 0.32/0.63  thf(fact_7482_take__bit__of__exp,axiom,
% 0.32/0.63      ! [M: nat,N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.63        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_exp
% 0.32/0.63  thf(fact_7483_take__bit__of__2,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.63        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_2
% 0.32/0.63  thf(fact_7484_take__bit__of__2,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.63        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_2
% 0.32/0.63  thf(fact_7485_take__bit__of__2,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.63        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_2
% 0.32/0.63  thf(fact_7486_take__bit__eq__mask,axiom,
% 0.32/0.63      ( bit_se2923211474154528505it_int
% 0.32/0.63      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_eq_mask
% 0.32/0.63  thf(fact_7487_take__bit__eq__mask,axiom,
% 0.32/0.63      ( bit_se2925701944663578781it_nat
% 0.32/0.63      = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_eq_mask
% 0.32/0.63  thf(fact_7488_of__int__and__eq,axiom,
% 0.32/0.63      ! [K: int,L2: int] :
% 0.32/0.63        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % of_int_and_eq
% 0.32/0.63  thf(fact_7489_take__bit__of__int,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 0.32/0.63        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_of_int
% 0.32/0.63  thf(fact_7490_and_Oassoc,axiom,
% 0.32/0.63      ! [A: int,B: int,C: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.assoc
% 0.32/0.63  thf(fact_7491_and_Oassoc,axiom,
% 0.32/0.63      ! [A: nat,B: nat,C: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 0.32/0.63        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.assoc
% 0.32/0.63  thf(fact_7492_and_Ocommute,axiom,
% 0.32/0.63      ( bit_se725231765392027082nd_int
% 0.32/0.63      = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.commute
% 0.32/0.63  thf(fact_7493_and_Ocommute,axiom,
% 0.32/0.63      ( bit_se727722235901077358nd_nat
% 0.32/0.63      = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.commute
% 0.32/0.63  thf(fact_7494_and_Oleft__commute,axiom,
% 0.32/0.63      ! [B: int,A: int,C: int] :
% 0.32/0.63        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 0.32/0.63        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_commute
% 0.32/0.63  thf(fact_7495_and_Oleft__commute,axiom,
% 0.32/0.63      ! [B: nat,A: nat,C: nat] :
% 0.32/0.63        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 0.32/0.63        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and.left_commute
% 0.32/0.63  thf(fact_7496_take__bit__add,axiom,
% 0.32/0.63      ! [N: nat,A: int,B: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 0.32/0.63        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_add
% 0.32/0.63  thf(fact_7497_take__bit__add,axiom,
% 0.32/0.63      ! [N: nat,A: nat,B: nat] :
% 0.32/0.63        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 0.32/0.63        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_add
% 0.32/0.63  thf(fact_7498_take__bit__tightened,axiom,
% 0.32/0.63      ! [N: nat,A: int,B: int,M: nat] :
% 0.32/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.32/0.63          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.32/0.63       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 0.32/0.63            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_tightened
% 0.32/0.63  thf(fact_7499_take__bit__tightened,axiom,
% 0.32/0.63      ! [N: nat,A: nat,B: nat,M: nat] :
% 0.32/0.63        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.32/0.63          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 0.32/0.63       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 0.32/0.63            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_tightened
% 0.32/0.63  thf(fact_7500_take__bit__tightened__less__eq__nat,axiom,
% 0.32/0.63      ! [M: nat,N: nat,Q2: nat] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_tightened_less_eq_nat
% 0.32/0.63  thf(fact_7501_take__bit__nat__less__eq__self,axiom,
% 0.32/0.63      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_nat_less_eq_self
% 0.32/0.63  thf(fact_7502_exp__not__eq__zero,axiom,
% 0.32/0.63      ! [X: complex] :
% 0.32/0.63        ( ( exp_complex @ X )
% 0.32/0.63       != zero_zero_complex ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_not_eq_zero
% 0.32/0.63  thf(fact_7503_exp__not__eq__zero,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( exp_real @ X )
% 0.32/0.63       != zero_zero_real ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_not_eq_zero
% 0.32/0.63  thf(fact_7504_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: complex,C: int > int > set_complex,P5: product_prod_int_int] :
% 0.32/0.63        ( ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7505_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: real,C: int > int > set_real,P5: product_prod_int_int] :
% 0.32/0.63        ( ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7506_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: nat,C: int > int > set_nat,P5: product_prod_int_int] :
% 0.32/0.63        ( ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7507_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: int,C: int > int > set_int,P5: product_prod_int_int] :
% 0.32/0.63        ( ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7508_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: set_nat,C: int > int > set_set_nat,P5: product_prod_int_int] :
% 0.32/0.63        ( ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_set_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7509_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,P5: produc8763457246119570046nteger] :
% 0.32/0.63        ( ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7510_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,P5: produc8763457246119570046nteger] :
% 0.32/0.63        ( ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7511_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P5: produc8763457246119570046nteger] :
% 0.32/0.63        ( ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7512_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P5: produc8763457246119570046nteger] :
% 0.32/0.63        ( ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7513_mem__case__prodE,axiom,
% 0.32/0.63      ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,P5: produc7773217078559923341nt_int] :
% 0.32/0.63        ( ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) )
% 0.32/0.63       => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mem_case_prodE
% 0.32/0.63  thf(fact_7514_take__bit__minus,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.32/0.63        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_minus
% 0.32/0.63  thf(fact_7515_exp__times__arg__commute,axiom,
% 0.32/0.63      ! [A2: complex] :
% 0.32/0.63        ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 0.32/0.63        = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_times_arg_commute
% 0.32/0.63  thf(fact_7516_exp__times__arg__commute,axiom,
% 0.32/0.63      ! [A2: real] :
% 0.32/0.63        ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 0.32/0.63        = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_times_arg_commute
% 0.32/0.63  thf(fact_7517_take__bit__mult,axiom,
% 0.32/0.63      ! [N: nat,K: int,L2: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 0.32/0.63        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_mult
% 0.32/0.63  thf(fact_7518_take__bit__diff,axiom,
% 0.32/0.63      ! [N: nat,K: int,L2: int] :
% 0.32/0.63        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 0.32/0.63        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_diff
% 0.32/0.63  thf(fact_7519_concat__bit__eq__iff,axiom,
% 0.32/0.63      ! [N: nat,K: int,L2: int,R: int,S: int] :
% 0.32/0.63        ( ( ( bit_concat_bit @ N @ K @ L2 )
% 0.32/0.63          = ( bit_concat_bit @ N @ R @ S ) )
% 0.32/0.63        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.63            = ( bit_se2923211474154528505it_int @ N @ R ) )
% 0.32/0.63          & ( L2 = S ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % concat_bit_eq_iff
% 0.32/0.63  thf(fact_7520_concat__bit__take__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,B: int] :
% 0.32/0.63        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 0.32/0.63        = ( bit_concat_bit @ N @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % concat_bit_take_bit_eq
% 0.32/0.63  thf(fact_7521_case__prodE,axiom,
% 0.32/0.63      ! [C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc8763457246119570046nteger] :
% 0.32/0.63        ( ( produc127349428274296955eger_o @ C @ P5 )
% 0.32/0.63       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE
% 0.32/0.63  thf(fact_7522_case__prodE,axiom,
% 0.32/0.63      ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc1908205239877642774nteger] :
% 0.32/0.63        ( ( produc6253627499356882019eger_o @ C @ P5 )
% 0.32/0.63       => ~ ! [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc8603105652947943368nteger @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE
% 0.32/0.63  thf(fact_7523_case__prodE,axiom,
% 0.32/0.63      ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc2285326912895808259nt_int] :
% 0.32/0.63        ( ( produc1573362020775583542_int_o @ C @ P5 )
% 0.32/0.63       => ~ ! [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc5700946648718959541nt_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE
% 0.32/0.63  thf(fact_7524_case__prodE,axiom,
% 0.32/0.63      ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc7773217078559923341nt_int] :
% 0.32/0.63        ( ( produc2558449545302689196_int_o @ C @ P5 )
% 0.32/0.63       => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE
% 0.32/0.63  thf(fact_7525_case__prodE,axiom,
% 0.32/0.63      ! [C: int > int > $o,P5: product_prod_int_int] :
% 0.32/0.63        ( ( produc4947309494688390418_int_o @ C @ P5 )
% 0.32/0.63       => ~ ! [X6: int,Y5: int] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE
% 0.32/0.63  thf(fact_7526_case__prodD,axiom,
% 0.32/0.63      ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) )
% 0.32/0.63       => ( F @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD
% 0.32/0.63  thf(fact_7527_case__prodD,axiom,
% 0.32/0.63      ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.32/0.63        ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 0.32/0.63       => ( F @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD
% 0.32/0.63  thf(fact_7528_case__prodD,axiom,
% 0.32/0.63      ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.32/0.63        ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 0.32/0.63       => ( F @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD
% 0.32/0.63  thf(fact_7529_case__prodD,axiom,
% 0.32/0.63      ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.32/0.63        ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 0.32/0.63       => ( F @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD
% 0.32/0.63  thf(fact_7530_case__prodD,axiom,
% 0.32/0.63      ! [F: int > int > $o,A: int,B: int] :
% 0.32/0.63        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 0.32/0.63       => ( F @ A @ B ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD
% 0.32/0.63  thf(fact_7531_case__prodE_H,axiom,
% 0.32/0.63      ! [C: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.32/0.63        ( ( produc8739625826339149834_nat_o @ C @ P5 @ Z )
% 0.32/0.63       => ~ ! [X6: nat,Y5: nat] :
% 0.32/0.63              ( ( P5
% 0.32/0.63                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 0.32/0.63             => ~ ( C @ X6 @ Y5 @ Z ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodE'
% 0.32/0.63  thf(fact_7532_case__prodD_H,axiom,
% 0.32/0.63      ! [R4: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 0.32/0.63        ( ( produc8739625826339149834_nat_o @ R4 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 0.32/0.63       => ( R4 @ A @ B @ C ) ) ).
% 0.32/0.63  
% 0.32/0.63  % case_prodD'
% 0.32/0.63  thf(fact_7533_and__eq__minus__1__iff,axiom,
% 0.32/0.63      ! [A: code_integer,B: code_integer] :
% 0.32/0.63        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 0.32/0.63          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.63        = ( ( A
% 0.32/0.63            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.63          & ( B
% 0.32/0.63            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_eq_minus_1_iff
% 0.32/0.63  thf(fact_7534_and__eq__minus__1__iff,axiom,
% 0.32/0.63      ! [A: int,B: int] :
% 0.32/0.63        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 0.32/0.63          = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63        = ( ( A
% 0.32/0.63            = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.63          & ( B
% 0.32/0.63            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_eq_minus_1_iff
% 0.32/0.63  thf(fact_7535_not__exp__less__zero,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.32/0.63  
% 0.32/0.63  % not_exp_less_zero
% 0.32/0.63  thf(fact_7536_exp__gt__zero,axiom,
% 0.32/0.63      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_gt_zero
% 0.32/0.63  thf(fact_7537_exp__total,axiom,
% 0.32/0.63      ! [Y: real] :
% 0.32/0.63        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.63       => ? [X6: real] :
% 0.32/0.63            ( ( exp_real @ X6 )
% 0.32/0.63            = Y ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_total
% 0.32/0.63  thf(fact_7538_exp__ge__zero,axiom,
% 0.32/0.63      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_ge_zero
% 0.32/0.63  thf(fact_7539_not__exp__le__zero,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.32/0.63  
% 0.32/0.63  % not_exp_le_zero
% 0.32/0.63  thf(fact_7540_sum__cong__Suc,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.32/0.63        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.32/0.63       => ( ! [X6: nat] :
% 0.32/0.63              ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 0.32/0.63             => ( ( F @ ( suc @ X6 ) )
% 0.32/0.63                = ( G @ ( suc @ X6 ) ) ) )
% 0.32/0.63         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.32/0.63            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_cong_Suc
% 0.32/0.63  thf(fact_7541_sum__cong__Suc,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 0.32/0.63        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 0.32/0.63       => ( ! [X6: nat] :
% 0.32/0.63              ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 0.32/0.63             => ( ( F @ ( suc @ X6 ) )
% 0.32/0.63                = ( G @ ( suc @ X6 ) ) ) )
% 0.32/0.63         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 0.32/0.63            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_cong_Suc
% 0.32/0.63  thf(fact_7542_take__bit__tightened__less__eq__int,axiom,
% 0.32/0.63      ! [M: nat,N: nat,K: int] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_tightened_less_eq_int
% 0.32/0.63  thf(fact_7543_AND__upper2_H,axiom,
% 0.32/0.63      ! [Y: int,Z: int,X: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.63       => ( ( ord_less_eq_int @ Y @ Z )
% 0.32/0.63         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper2'
% 0.32/0.63  thf(fact_7544_AND__upper1_H,axiom,
% 0.32/0.63      ! [Y: int,Z: int,Ya: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.63       => ( ( ord_less_eq_int @ Y @ Z )
% 0.32/0.63         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper1'
% 0.32/0.63  thf(fact_7545_AND__upper2,axiom,
% 0.32/0.63      ! [Y: int,X: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.63       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper2
% 0.32/0.63  thf(fact_7546_AND__upper1,axiom,
% 0.32/0.63      ! [X: int,Y: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.63       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper1
% 0.32/0.63  thf(fact_7547_AND__lower,axiom,
% 0.32/0.63      ! [X: int,Y: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.63       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_lower
% 0.32/0.63  thf(fact_7548_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,A: int,B: int] :
% 0.32/0.63        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 0.32/0.63          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 0.32/0.63        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.32/0.63          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % signed_take_bit_eq_iff_take_bit_eq
% 0.32/0.63  thf(fact_7549_take__bit__int__less__eq__self__iff,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.32/0.63        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_int_less_eq_self_iff
% 0.32/0.63  thf(fact_7550_take__bit__nonnegative,axiom,
% 0.32/0.63      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_nonnegative
% 0.32/0.63  thf(fact_7551_not__take__bit__negative,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 0.32/0.63  
% 0.32/0.63  % not_take_bit_negative
% 0.32/0.63  thf(fact_7552_take__bit__int__greater__self__iff,axiom,
% 0.32/0.63      ! [K: int,N: nat] :
% 0.32/0.63        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.32/0.63        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_int_greater_self_iff
% 0.32/0.63  thf(fact_7553_signed__take__bit__take__bit,axiom,
% 0.32/0.63      ! [M: nat,N: nat,A: int] :
% 0.32/0.63        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 0.32/0.63        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 0.32/0.63  
% 0.32/0.63  % signed_take_bit_take_bit
% 0.32/0.63  thf(fact_7554_mult__exp__exp,axiom,
% 0.32/0.63      ! [X: complex,Y: complex] :
% 0.32/0.63        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 0.32/0.63        = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mult_exp_exp
% 0.32/0.63  thf(fact_7555_mult__exp__exp,axiom,
% 0.32/0.63      ! [X: real,Y: real] :
% 0.32/0.63        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 0.32/0.63        = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % mult_exp_exp
% 0.32/0.63  thf(fact_7556_exp__add__commuting,axiom,
% 0.32/0.63      ! [X: complex,Y: complex] :
% 0.32/0.63        ( ( ( times_times_complex @ X @ Y )
% 0.32/0.63          = ( times_times_complex @ Y @ X ) )
% 0.32/0.63       => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 0.32/0.63          = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_add_commuting
% 0.32/0.63  thf(fact_7557_exp__add__commuting,axiom,
% 0.32/0.63      ! [X: real,Y: real] :
% 0.32/0.63        ( ( ( times_times_real @ X @ Y )
% 0.32/0.63          = ( times_times_real @ Y @ X ) )
% 0.32/0.63       => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 0.32/0.63          = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_add_commuting
% 0.32/0.63  thf(fact_7558_exp__diff,axiom,
% 0.32/0.63      ! [X: complex,Y: complex] :
% 0.32/0.63        ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 0.32/0.63        = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_diff
% 0.32/0.63  thf(fact_7559_exp__diff,axiom,
% 0.32/0.63      ! [X: real,Y: real] :
% 0.32/0.63        ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 0.32/0.63        = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_diff
% 0.32/0.63  thf(fact_7560_take__bit__unset__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: int] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_unset_bit_eq
% 0.32/0.63  thf(fact_7561_take__bit__unset__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: nat] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_unset_bit_eq
% 0.32/0.63  thf(fact_7562_take__bit__set__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: int] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_set_bit_eq
% 0.32/0.63  thf(fact_7563_take__bit__set__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: nat] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_set_bit_eq
% 0.32/0.63  thf(fact_7564_take__bit__flip__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: int] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 0.32/0.63            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_flip_bit_eq
% 0.32/0.63  thf(fact_7565_take__bit__flip__bit__eq,axiom,
% 0.32/0.63      ! [N: nat,M: nat,A: nat] :
% 0.32/0.63        ( ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 0.32/0.63        & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.32/0.63         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 0.32/0.63            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_flip_bit_eq
% 0.32/0.63  thf(fact_7566_sum__subtractf__nat,axiom,
% 0.32/0.63      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 0.32/0.63        ( ! [X6: complex] :
% 0.32/0.63            ( ( member_complex @ X6 @ A2 )
% 0.32/0.63           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 0.32/0.63       => ( ( groups5693394587270226106ex_nat
% 0.32/0.63            @ ^ [X3: complex] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.63            @ A2 )
% 0.32/0.63          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_subtractf_nat
% 0.32/0.63  thf(fact_7567_sum__subtractf__nat,axiom,
% 0.32/0.63      ! [A2: set_real,G: real > nat,F: real > nat] :
% 0.32/0.63        ( ! [X6: real] :
% 0.32/0.63            ( ( member_real @ X6 @ A2 )
% 0.32/0.63           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 0.32/0.63       => ( ( groups1935376822645274424al_nat
% 0.32/0.63            @ ^ [X3: real] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.63            @ A2 )
% 0.32/0.63          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_subtractf_nat
% 0.32/0.63  thf(fact_7568_sum__subtractf__nat,axiom,
% 0.32/0.63      ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 0.32/0.63        ( ! [X6: set_nat] :
% 0.32/0.63            ( ( member_set_nat @ X6 @ A2 )
% 0.32/0.63           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 0.32/0.63       => ( ( groups8294997508430121362at_nat
% 0.32/0.63            @ ^ [X3: set_nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.63            @ A2 )
% 0.32/0.63          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_subtractf_nat
% 0.32/0.63  thf(fact_7569_sum__subtractf__nat,axiom,
% 0.32/0.63      ! [A2: set_int,G: int > nat,F: int > nat] :
% 0.32/0.63        ( ! [X6: int] :
% 0.32/0.63            ( ( member_int @ X6 @ A2 )
% 0.32/0.63           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 0.32/0.63       => ( ( groups4541462559716669496nt_nat
% 0.32/0.63            @ ^ [X3: int] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.63            @ A2 )
% 0.32/0.63          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_subtractf_nat
% 0.32/0.63  thf(fact_7570_sum__subtractf__nat,axiom,
% 0.32/0.63      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.32/0.63        ( ! [X6: nat] :
% 0.32/0.63            ( ( member_nat @ X6 @ A2 )
% 0.32/0.63           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 0.32/0.63       => ( ( groups3542108847815614940at_nat
% 0.32/0.63            @ ^ [X3: nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.63            @ A2 )
% 0.32/0.63          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_subtractf_nat
% 0.32/0.63  thf(fact_7571_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.32/0.63      ! [G: nat > nat,M: nat,N: nat] :
% 0.32/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.32/0.63        = ( groups3542108847815614940at_nat
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.shift_bounds_cl_Suc_ivl
% 0.32/0.63  thf(fact_7572_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.32/0.63      ! [G: nat > real,M: nat,N: nat] :
% 0.32/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.32/0.63        = ( groups6591440286371151544t_real
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.shift_bounds_cl_Suc_ivl
% 0.32/0.63  thf(fact_7573_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.32/0.63      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 0.32/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.32/0.63        = ( groups3542108847815614940at_nat
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.shift_bounds_cl_nat_ivl
% 0.32/0.63  thf(fact_7574_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.32/0.63      ! [G: nat > real,M: nat,K: nat,N: nat] :
% 0.32/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.32/0.63        = ( groups6591440286371151544t_real
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.shift_bounds_cl_nat_ivl
% 0.32/0.63  thf(fact_7575_sum__eq__Suc0__iff,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.32/0.63            = ( suc @ zero_zero_nat ) )
% 0.32/0.63          = ( ? [X3: int] :
% 0.32/0.63                ( ( member_int @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = ( suc @ zero_zero_nat ) )
% 0.32/0.63                & ! [Y3: int] :
% 0.32/0.63                    ( ( member_int @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_Suc0_iff
% 0.32/0.63  thf(fact_7576_sum__eq__Suc0__iff,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.32/0.63            = ( suc @ zero_zero_nat ) )
% 0.32/0.63          = ( ? [X3: complex] :
% 0.32/0.63                ( ( member_complex @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = ( suc @ zero_zero_nat ) )
% 0.32/0.63                & ! [Y3: complex] :
% 0.32/0.63                    ( ( member_complex @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_Suc0_iff
% 0.32/0.63  thf(fact_7577_sum__eq__Suc0__iff,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > nat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.32/0.63            = ( suc @ zero_zero_nat ) )
% 0.32/0.63          = ( ? [X3: nat] :
% 0.32/0.63                ( ( member_nat @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = ( suc @ zero_zero_nat ) )
% 0.32/0.63                & ! [Y3: nat] :
% 0.32/0.63                    ( ( member_nat @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_Suc0_iff
% 0.32/0.63  thf(fact_7578_sum__SucD,axiom,
% 0.32/0.63      ! [F: nat > nat,A2: set_nat,N: nat] :
% 0.32/0.63        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.32/0.63          = ( suc @ N ) )
% 0.32/0.63       => ? [X6: nat] :
% 0.32/0.63            ( ( member_nat @ X6 @ A2 )
% 0.32/0.63            & ( ord_less_nat @ zero_zero_nat @ ( F @ X6 ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_SucD
% 0.32/0.63  thf(fact_7579_exp__gt__one,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.63       => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_gt_one
% 0.32/0.63  thf(fact_7580_sum__eq__1__iff,axiom,
% 0.32/0.63      ! [A2: set_int,F: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ A2 )
% 0.32/0.63       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 0.32/0.63            = one_one_nat )
% 0.32/0.63          = ( ? [X3: int] :
% 0.32/0.63                ( ( member_int @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = one_one_nat )
% 0.32/0.63                & ! [Y3: int] :
% 0.32/0.63                    ( ( member_int @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_1_iff
% 0.32/0.63  thf(fact_7581_sum__eq__1__iff,axiom,
% 0.32/0.63      ! [A2: set_complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.63       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 0.32/0.63            = one_one_nat )
% 0.32/0.63          = ( ? [X3: complex] :
% 0.32/0.63                ( ( member_complex @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = one_one_nat )
% 0.32/0.63                & ! [Y3: complex] :
% 0.32/0.63                    ( ( member_complex @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_1_iff
% 0.32/0.63  thf(fact_7582_sum__eq__1__iff,axiom,
% 0.32/0.63      ! [A2: set_nat,F: nat > nat] :
% 0.32/0.63        ( ( finite_finite_nat @ A2 )
% 0.32/0.63       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 0.32/0.63            = one_one_nat )
% 0.32/0.63          = ( ? [X3: nat] :
% 0.32/0.63                ( ( member_nat @ X3 @ A2 )
% 0.32/0.63                & ( ( F @ X3 )
% 0.32/0.63                  = one_one_nat )
% 0.32/0.63                & ! [Y3: nat] :
% 0.32/0.63                    ( ( member_nat @ Y3 @ A2 )
% 0.32/0.63                   => ( ( X3 != Y3 )
% 0.32/0.63                     => ( ( F @ Y3 )
% 0.32/0.63                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_eq_1_iff
% 0.32/0.63  thf(fact_7583_take__bit__signed__take__bit,axiom,
% 0.32/0.63      ! [M: nat,N: nat,A: int] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.63       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 0.32/0.63          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_signed_take_bit
% 0.32/0.63  thf(fact_7584_exp__ge__add__one__self,axiom,
% 0.32/0.63      ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_ge_add_one_self
% 0.32/0.63  thf(fact_7585_and__less__eq,axiom,
% 0.32/0.63      ! [L2: int,K: int] :
% 0.32/0.63        ( ( ord_less_int @ L2 @ zero_zero_int )
% 0.32/0.63       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 0.32/0.63  
% 0.32/0.63  % and_less_eq
% 0.32/0.63  thf(fact_7586_AND__upper1_H_H,axiom,
% 0.32/0.63      ! [Y: int,Z: int,Ya: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.63       => ( ( ord_less_int @ Y @ Z )
% 0.32/0.63         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper1''
% 0.32/0.63  thf(fact_7587_AND__upper2_H_H,axiom,
% 0.32/0.63      ! [Y: int,Z: int,X: int] :
% 0.32/0.63        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.63       => ( ( ord_less_int @ Y @ Z )
% 0.32/0.63         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % AND_upper2''
% 0.32/0.63  thf(fact_7588_take__bit__eq__mask__iff,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.63          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.32/0.63        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.32/0.63          = zero_zero_int ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_eq_mask_iff
% 0.32/0.63  thf(fact_7589_exp__minus__inverse,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 0.32/0.63        = one_one_real ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_minus_inverse
% 0.32/0.63  thf(fact_7590_exp__minus__inverse,axiom,
% 0.32/0.63      ! [X: complex] :
% 0.32/0.63        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 0.32/0.63        = one_one_complex ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_minus_inverse
% 0.32/0.63  thf(fact_7591_take__bit__decr__eq,axiom,
% 0.32/0.63      ! [N: nat,K: int] :
% 0.32/0.63        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.63         != zero_zero_int )
% 0.32/0.63       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 0.32/0.63          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % take_bit_decr_eq
% 0.32/0.63  thf(fact_7592_sum__power__add,axiom,
% 0.32/0.63      ! [X: complex,M: nat,I6: set_nat] :
% 0.32/0.63        ( ( groups2073611262835488442omplex
% 0.32/0.63          @ ^ [I5: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I5 ) )
% 0.32/0.63          @ I6 )
% 0.32/0.63        = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_power_add
% 0.32/0.63  thf(fact_7593_sum__power__add,axiom,
% 0.32/0.63      ! [X: rat,M: nat,I6: set_nat] :
% 0.32/0.63        ( ( groups2906978787729119204at_rat
% 0.32/0.63          @ ^ [I5: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I5 ) )
% 0.32/0.63          @ I6 )
% 0.32/0.63        = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I6 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_power_add
% 0.32/0.63  thf(fact_7594_sum__power__add,axiom,
% 0.32/0.63      ! [X: int,M: nat,I6: set_nat] :
% 0.32/0.63        ( ( groups3539618377306564664at_int
% 0.32/0.63          @ ^ [I5: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I5 ) )
% 0.32/0.63          @ I6 )
% 0.32/0.63        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_power_add
% 0.32/0.63  thf(fact_7595_sum__power__add,axiom,
% 0.32/0.63      ! [X: real,M: nat,I6: set_nat] :
% 0.32/0.63        ( ( groups6591440286371151544t_real
% 0.32/0.63          @ ^ [I5: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I5 ) )
% 0.32/0.63          @ I6 )
% 0.32/0.63        = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_power_add
% 0.32/0.63  thf(fact_7596_sum_OatLeastAtMost__rev,axiom,
% 0.32/0.63      ! [G: nat > nat,N: nat,M: nat] :
% 0.32/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.32/0.63        = ( groups3542108847815614940at_nat
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeastAtMost_rev
% 0.32/0.63  thf(fact_7597_sum_OatLeastAtMost__rev,axiom,
% 0.32/0.63      ! [G: nat > real,N: nat,M: nat] :
% 0.32/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.32/0.63        = ( groups6591440286371151544t_real
% 0.32/0.63          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 0.32/0.63          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeastAtMost_rev
% 0.32/0.63  thf(fact_7598_sum__nth__roots,axiom,
% 0.32/0.63      ! [N: nat,C: complex] :
% 0.32/0.63        ( ( ord_less_nat @ one_one_nat @ N )
% 0.32/0.63       => ( ( groups7754918857620584856omplex
% 0.32/0.63            @ ^ [X3: complex] : X3
% 0.32/0.63            @ ( collect_complex
% 0.32/0.63              @ ^ [Z3: complex] :
% 0.32/0.63                  ( ( power_power_complex @ Z3 @ N )
% 0.32/0.63                  = C ) ) )
% 0.32/0.63          = zero_zero_complex ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_nth_roots
% 0.32/0.63  thf(fact_7599_sum__roots__unity,axiom,
% 0.32/0.63      ! [N: nat] :
% 0.32/0.63        ( ( ord_less_nat @ one_one_nat @ N )
% 0.32/0.63       => ( ( groups7754918857620584856omplex
% 0.32/0.63            @ ^ [X3: complex] : X3
% 0.32/0.63            @ ( collect_complex
% 0.32/0.63              @ ^ [Z3: complex] :
% 0.32/0.63                  ( ( power_power_complex @ Z3 @ N )
% 0.32/0.63                  = one_one_complex ) ) )
% 0.32/0.63          = zero_zero_complex ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_roots_unity
% 0.32/0.63  thf(fact_7600_even__and__iff,axiom,
% 0.32/0.63      ! [A: code_integer,B: code_integer] :
% 0.32/0.63        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 0.32/0.63        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.63          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_and_iff
% 0.32/0.63  thf(fact_7601_even__and__iff,axiom,
% 0.32/0.63      ! [A: int,B: int] :
% 0.32/0.63        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 0.32/0.63        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.63          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_and_iff
% 0.32/0.63  thf(fact_7602_even__and__iff,axiom,
% 0.32/0.63      ! [A: nat,B: nat] :
% 0.32/0.63        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 0.32/0.63        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.63          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_and_iff
% 0.32/0.63  thf(fact_7603_sum__diff__nat,axiom,
% 0.32/0.63      ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 0.32/0.63        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.63       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 0.32/0.63         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff_nat
% 0.32/0.63  thf(fact_7604_sum__diff__nat,axiom,
% 0.32/0.63      ! [B3: set_int,A2: set_int,F: int > nat] :
% 0.32/0.63        ( ( finite_finite_int @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 0.32/0.63         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff_nat
% 0.32/0.63  thf(fact_7605_sum__diff__nat,axiom,
% 0.32/0.63      ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 0.32/0.63        ( ( finite_finite_nat @ B3 )
% 0.32/0.63       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 0.32/0.63         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 0.32/0.63            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_diff_nat
% 0.32/0.63  thf(fact_7606_exp__ge__add__one__self__aux,axiom,
% 0.32/0.63      ! [X: real] :
% 0.32/0.63        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.63       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % exp_ge_add_one_self_aux
% 0.32/0.63  thf(fact_7607_sum__shift__lb__Suc0__0,axiom,
% 0.32/0.63      ! [F: nat > complex,K: nat] :
% 0.32/0.63        ( ( ( F @ zero_zero_nat )
% 0.32/0.63          = zero_zero_complex )
% 0.32/0.63       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.32/0.63          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_shift_lb_Suc0_0
% 0.32/0.63  thf(fact_7608_sum__shift__lb__Suc0__0,axiom,
% 0.32/0.63      ! [F: nat > rat,K: nat] :
% 0.32/0.63        ( ( ( F @ zero_zero_nat )
% 0.32/0.63          = zero_zero_rat )
% 0.32/0.63       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.32/0.63          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_shift_lb_Suc0_0
% 0.32/0.63  thf(fact_7609_sum__shift__lb__Suc0__0,axiom,
% 0.32/0.63      ! [F: nat > int,K: nat] :
% 0.32/0.63        ( ( ( F @ zero_zero_nat )
% 0.32/0.63          = zero_zero_int )
% 0.32/0.63       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.32/0.63          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_shift_lb_Suc0_0
% 0.32/0.63  thf(fact_7610_sum__shift__lb__Suc0__0,axiom,
% 0.32/0.63      ! [F: nat > nat,K: nat] :
% 0.32/0.63        ( ( ( F @ zero_zero_nat )
% 0.32/0.63          = zero_zero_nat )
% 0.32/0.63       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.32/0.63          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_shift_lb_Suc0_0
% 0.32/0.63  thf(fact_7611_sum__shift__lb__Suc0__0,axiom,
% 0.32/0.63      ! [F: nat > real,K: nat] :
% 0.32/0.63        ( ( ( F @ zero_zero_nat )
% 0.32/0.63          = zero_zero_real )
% 0.32/0.63       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.32/0.63          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum_shift_lb_Suc0_0
% 0.32/0.63  thf(fact_7612_even__and__iff__int,axiom,
% 0.32/0.63      ! [K: int,L2: int] :
% 0.32/0.63        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 0.32/0.63        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.32/0.63          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % even_and_iff_int
% 0.32/0.63  thf(fact_7613_sum_OatLeast0__atMost__Suc,axiom,
% 0.32/0.63      ! [G: nat > rat,N: nat] :
% 0.32/0.63        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.32/0.63        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast0_atMost_Suc
% 0.32/0.63  thf(fact_7614_sum_OatLeast0__atMost__Suc,axiom,
% 0.32/0.63      ! [G: nat > int,N: nat] :
% 0.32/0.63        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.32/0.63        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast0_atMost_Suc
% 0.32/0.63  thf(fact_7615_sum_OatLeast0__atMost__Suc,axiom,
% 0.32/0.63      ! [G: nat > nat,N: nat] :
% 0.32/0.63        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.32/0.63        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast0_atMost_Suc
% 0.32/0.63  thf(fact_7616_sum_OatLeast0__atMost__Suc,axiom,
% 0.32/0.63      ! [G: nat > real,N: nat] :
% 0.32/0.63        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.32/0.63        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast0_atMost_Suc
% 0.32/0.63  thf(fact_7617_lemma__exp__total,axiom,
% 0.32/0.63      ! [Y: real] :
% 0.32/0.63        ( ( ord_less_eq_real @ one_one_real @ Y )
% 0.32/0.63       => ? [X6: real] :
% 0.32/0.63            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 0.32/0.63            & ( ord_less_eq_real @ X6 @ ( minus_minus_real @ Y @ one_one_real ) )
% 0.32/0.63            & ( ( exp_real @ X6 )
% 0.32/0.63              = Y ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % lemma_exp_total
% 0.32/0.63  thf(fact_7618_sum_OatLeast__Suc__atMost,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > rat] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.63          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast_Suc_atMost
% 0.32/0.63  thf(fact_7619_sum_OatLeast__Suc__atMost,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > int] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.63          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast_Suc_atMost
% 0.32/0.63  thf(fact_7620_sum_OatLeast__Suc__atMost,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > nat] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.63          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast_Suc_atMost
% 0.32/0.63  thf(fact_7621_sum_OatLeast__Suc__atMost,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > real] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.63       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.63          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.atLeast_Suc_atMost
% 0.32/0.63  thf(fact_7622_sum_Onat__ivl__Suc_H,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > rat] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.63       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.63          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.63  
% 0.32/0.63  % sum.nat_ivl_Suc'
% 0.32/0.63  thf(fact_7623_sum_Onat__ivl__Suc_H,axiom,
% 0.32/0.63      ! [M: nat,N: nat,G: nat > int] :
% 0.32/0.63        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.63       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.nat_ivl_Suc'
% 0.32/0.64  thf(fact_7624_sum_Onat__ivl__Suc_H,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.nat_ivl_Suc'
% 0.32/0.64  thf(fact_7625_sum_Onat__ivl__Suc_H,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > real] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.nat_ivl_Suc'
% 0.32/0.64  thf(fact_7626_ln__ge__iff,axiom,
% 0.32/0.64      ! [X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 0.32/0.64          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % ln_ge_iff
% 0.32/0.64  thf(fact_7627_ln__x__over__x__mono,axiom,
% 0.32/0.64      ! [X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 0.32/0.64       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.64         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % ln_x_over_x_mono
% 0.32/0.64  thf(fact_7628_sum_OSuc__reindex__ivl,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > rat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_rat @ ( G @ M )
% 0.32/0.64            @ ( groups2906978787729119204at_rat
% 0.32/0.64              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.Suc_reindex_ivl
% 0.32/0.64  thf(fact_7629_sum_OSuc__reindex__ivl,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > int] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_int @ ( G @ M )
% 0.32/0.64            @ ( groups3539618377306564664at_int
% 0.32/0.64              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.Suc_reindex_ivl
% 0.32/0.64  thf(fact_7630_sum_OSuc__reindex__ivl,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_nat @ ( G @ M )
% 0.32/0.64            @ ( groups3542108847815614940at_nat
% 0.32/0.64              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.Suc_reindex_ivl
% 0.32/0.64  thf(fact_7631_sum_OSuc__reindex__ivl,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > real] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 0.32/0.64          = ( plus_plus_real @ ( G @ M )
% 0.32/0.64            @ ( groups6591440286371151544t_real
% 0.32/0.64              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.Suc_reindex_ivl
% 0.32/0.64  thf(fact_7632_sum__Suc__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.64       => ( ( groups2906978787729119204at_rat
% 0.32/0.64            @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_Suc_diff
% 0.32/0.64  thf(fact_7633_sum__Suc__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.64       => ( ( groups3539618377306564664at_int
% 0.32/0.64            @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_Suc_diff
% 0.32/0.64  thf(fact_7634_sum__Suc__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.64       => ( ( groups6591440286371151544t_real
% 0.32/0.64            @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_Suc_diff
% 0.32/0.64  thf(fact_7635_take__bit__Suc__bit0,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.32/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_bit0
% 0.32/0.64  thf(fact_7636_take__bit__Suc__bit0,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.64        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_bit0
% 0.32/0.64  thf(fact_7637_take__bit__eq__mod,axiom,
% 0.32/0.64      ( bit_se1745604003318907178nteger
% 0.32/0.64      = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_mod
% 0.32/0.64  thf(fact_7638_take__bit__eq__mod,axiom,
% 0.32/0.64      ( bit_se2923211474154528505it_int
% 0.32/0.64      = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_mod
% 0.32/0.64  thf(fact_7639_take__bit__eq__mod,axiom,
% 0.32/0.64      ( bit_se2925701944663578781it_nat
% 0.32/0.64      = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_mod
% 0.32/0.64  thf(fact_7640_one__and__eq,axiom,
% 0.32/0.64      ! [A: code_integer] :
% 0.32/0.64        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 0.32/0.64        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % one_and_eq
% 0.32/0.64  thf(fact_7641_one__and__eq,axiom,
% 0.32/0.64      ! [A: int] :
% 0.32/0.64        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 0.32/0.64        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % one_and_eq
% 0.32/0.64  thf(fact_7642_one__and__eq,axiom,
% 0.32/0.64      ! [A: nat] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 0.32/0.64        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % one_and_eq
% 0.32/0.64  thf(fact_7643_and__one__eq,axiom,
% 0.32/0.64      ! [A: code_integer] :
% 0.32/0.64        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 0.32/0.64        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_one_eq
% 0.32/0.64  thf(fact_7644_and__one__eq,axiom,
% 0.32/0.64      ! [A: int] :
% 0.32/0.64        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 0.32/0.64        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_one_eq
% 0.32/0.64  thf(fact_7645_and__one__eq,axiom,
% 0.32/0.64      ! [A: nat] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 0.32/0.64        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_one_eq
% 0.32/0.64  thf(fact_7646_take__bit__nat__eq__self__iff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.32/0.64          = M )
% 0.32/0.64        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_nat_eq_self_iff
% 0.32/0.64  thf(fact_7647_take__bit__nat__less__exp,axiom,
% 0.32/0.64      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_nat_less_exp
% 0.32/0.64  thf(fact_7648_take__bit__nat__eq__self,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.32/0.64          = M ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_nat_eq_self
% 0.32/0.64  thf(fact_7649_take__bit__nat__def,axiom,
% 0.32/0.64      ( bit_se2925701944663578781it_nat
% 0.32/0.64      = ( ^ [N2: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_nat_def
% 0.32/0.64  thf(fact_7650_exp__le,axiom,
% 0.32/0.64      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_le
% 0.32/0.64  thf(fact_7651_take__bit__int__less__exp,axiom,
% 0.32/0.64      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_less_exp
% 0.32/0.64  thf(fact_7652_sum_Oub__add__nat,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > rat,P5: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.32/0.64       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 0.32/0.64          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.ub_add_nat
% 0.32/0.64  thf(fact_7653_sum_Oub__add__nat,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > int,P5: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.32/0.64       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 0.32/0.64          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.ub_add_nat
% 0.32/0.64  thf(fact_7654_sum_Oub__add__nat,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > nat,P5: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.32/0.64       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 0.32/0.64          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.ub_add_nat
% 0.32/0.64  thf(fact_7655_sum_Oub__add__nat,axiom,
% 0.32/0.64      ! [M: nat,N: nat,G: nat > real,P5: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.32/0.64       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 0.32/0.64          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.ub_add_nat
% 0.32/0.64  thf(fact_7656_take__bit__int__def,axiom,
% 0.32/0.64      ( bit_se2923211474154528505it_int
% 0.32/0.64      = ( ^ [N2: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_def
% 0.32/0.64  thf(fact_7657_set__encode__def,axiom,
% 0.32/0.64      ( nat_set_encode
% 0.32/0.64      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_encode_def
% 0.32/0.64  thf(fact_7658_tanh__altdef,axiom,
% 0.32/0.64      ( tanh_real
% 0.32/0.64      = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % tanh_altdef
% 0.32/0.64  thf(fact_7659_tanh__altdef,axiom,
% 0.32/0.64      ( tanh_complex
% 0.32/0.64      = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % tanh_altdef
% 0.32/0.64  thf(fact_7660_num_Osize__gen_I1_J,axiom,
% 0.32/0.64      ( ( size_num @ one )
% 0.32/0.64      = zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % num.size_gen(1)
% 0.32/0.64  thf(fact_7661_take__bit__eq__0__iff,axiom,
% 0.32/0.64      ! [N: nat,A: code_integer] :
% 0.32/0.64        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.32/0.64          = zero_z3403309356797280102nteger )
% 0.32/0.64        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_0_iff
% 0.32/0.64  thf(fact_7662_take__bit__eq__0__iff,axiom,
% 0.32/0.64      ! [N: nat,A: int] :
% 0.32/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.32/0.64          = zero_zero_int )
% 0.32/0.64        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_0_iff
% 0.32/0.64  thf(fact_7663_take__bit__eq__0__iff,axiom,
% 0.32/0.64      ! [N: nat,A: nat] :
% 0.32/0.64        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.32/0.64          = zero_zero_nat )
% 0.32/0.64        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_0_iff
% 0.32/0.64  thf(fact_7664_Divides_Oadjust__div__def,axiom,
% 0.32/0.64      ( adjust_div
% 0.32/0.64      = ( produc8211389475949308722nt_int
% 0.32/0.64        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Divides.adjust_div_def
% 0.32/0.64  thf(fact_7665_take__bit__numeral__bit0,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.32/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_bit0
% 0.32/0.64  thf(fact_7666_take__bit__numeral__bit0,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.32/0.64        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_bit0
% 0.32/0.64  thf(fact_7667_take__bit__nat__less__self__iff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_nat_less_self_iff
% 0.32/0.64  thf(fact_7668_exp__half__le2,axiom,
% 0.32/0.64      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_half_le2
% 0.32/0.64  thf(fact_7669_take__bit__Suc__minus__bit0,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_minus_bit0
% 0.32/0.64  thf(fact_7670_take__bit__int__less__self__iff,axiom,
% 0.32/0.64      ! [N: nat,K: int] :
% 0.32/0.64        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.32/0.64        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_less_self_iff
% 0.32/0.64  thf(fact_7671_take__bit__int__greater__eq__self__iff,axiom,
% 0.32/0.64      ! [K: int,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.32/0.64        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_greater_eq_self_iff
% 0.32/0.64  thf(fact_7672_exp__double,axiom,
% 0.32/0.64      ! [Z: complex] :
% 0.32/0.64        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 0.32/0.64        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_double
% 0.32/0.64  thf(fact_7673_exp__double,axiom,
% 0.32/0.64      ! [Z: real] :
% 0.32/0.64        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 0.32/0.64        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_double
% 0.32/0.64  thf(fact_7674_sum__natinterval__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > complex] :
% 0.32/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups2073611262835488442omplex
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.32/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups2073611262835488442omplex
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_complex ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_natinterval_diff
% 0.32/0.64  thf(fact_7675_sum__natinterval__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.32/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups2906978787729119204at_rat
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.32/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups2906978787729119204at_rat
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_rat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_natinterval_diff
% 0.32/0.64  thf(fact_7676_sum__natinterval__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.32/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups3539618377306564664at_int
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.32/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups3539618377306564664at_int
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_natinterval_diff
% 0.32/0.64  thf(fact_7677_sum__natinterval__diff,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.32/0.64        ( ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups6591440286371151544t_real
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.32/0.64        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.64         => ( ( groups6591440286371151544t_real
% 0.32/0.64              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_natinterval_diff
% 0.32/0.64  thf(fact_7678_sum__telescope_H_H,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > rat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( groups2906978787729119204at_rat
% 0.32/0.64            @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.32/0.64          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_telescope''
% 0.32/0.64  thf(fact_7679_sum__telescope_H_H,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > int] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( groups3539618377306564664at_int
% 0.32/0.64            @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.32/0.64          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_telescope''
% 0.32/0.64  thf(fact_7680_sum__telescope_H_H,axiom,
% 0.32/0.64      ! [M: nat,N: nat,F: nat > real] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( groups6591440286371151544t_real
% 0.32/0.64            @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 0.32/0.64            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.32/0.64          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_telescope''
% 0.32/0.64  thf(fact_7681_take__bit__int__eq__self__iff,axiom,
% 0.32/0.64      ! [N: nat,K: int] :
% 0.32/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.64          = K )
% 0.32/0.64        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.64          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_eq_self_iff
% 0.32/0.64  thf(fact_7682_take__bit__int__eq__self,axiom,
% 0.32/0.64      ! [K: int,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.64       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.64            = K ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_eq_self
% 0.32/0.64  thf(fact_7683_take__bit__numeral__minus__bit0,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.64        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_minus_bit0
% 0.32/0.64  thf(fact_7684_take__bit__incr__eq,axiom,
% 0.32/0.64      ! [N: nat,K: int] :
% 0.32/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.64         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.32/0.64       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.32/0.64          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_incr_eq
% 0.32/0.64  thf(fact_7685_divmod__nat__def,axiom,
% 0.32/0.64      ( divmod_nat
% 0.32/0.64      = ( ^ [M3: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N2 ) @ ( modulo_modulo_nat @ M3 @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % divmod_nat_def
% 0.32/0.64  thf(fact_7686_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.32/0.64      ! [N: nat,K: int] :
% 0.32/0.64        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.32/0.64          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.32/0.64        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_eq_mask_iff_exp_dvd
% 0.32/0.64  thf(fact_7687_mask__eq__sum__exp,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 0.32/0.64        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.64          @ ( collect_nat
% 0.32/0.64            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mask_eq_sum_exp
% 0.32/0.64  thf(fact_7688_mask__eq__sum__exp,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 0.32/0.64        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.64          @ ( collect_nat
% 0.32/0.64            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mask_eq_sum_exp
% 0.32/0.64  thf(fact_7689_sum__gp__multiplied,axiom,
% 0.32/0.64      ! [M: nat,N: nat,X: complex] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.32/0.64          = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp_multiplied
% 0.32/0.64  thf(fact_7690_sum__gp__multiplied,axiom,
% 0.32/0.64      ! [M: nat,N: nat,X: rat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.32/0.64          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp_multiplied
% 0.32/0.64  thf(fact_7691_sum__gp__multiplied,axiom,
% 0.32/0.64      ! [M: nat,N: nat,X: int] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.32/0.64          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp_multiplied
% 0.32/0.64  thf(fact_7692_sum__gp__multiplied,axiom,
% 0.32/0.64      ! [M: nat,N: nat,X: real] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.64       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.32/0.64          = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp_multiplied
% 0.32/0.64  thf(fact_7693_sum_Oin__pairs,axiom,
% 0.32/0.64      ! [G: nat > rat,M: nat,N: nat] :
% 0.32/0.64        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.64        = ( groups2906978787729119204at_rat
% 0.32/0.64          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.in_pairs
% 0.32/0.64  thf(fact_7694_sum_Oin__pairs,axiom,
% 0.32/0.64      ! [G: nat > int,M: nat,N: nat] :
% 0.32/0.64        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.64        = ( groups3539618377306564664at_int
% 0.32/0.64          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.in_pairs
% 0.32/0.64  thf(fact_7695_sum_Oin__pairs,axiom,
% 0.32/0.64      ! [G: nat > nat,M: nat,N: nat] :
% 0.32/0.64        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.64        = ( groups3542108847815614940at_nat
% 0.32/0.64          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.in_pairs
% 0.32/0.64  thf(fact_7696_sum_Oin__pairs,axiom,
% 0.32/0.64      ! [G: nat > real,M: nat,N: nat] :
% 0.32/0.64        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.32/0.64        = ( groups6591440286371151544t_real
% 0.32/0.64          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.in_pairs
% 0.32/0.64  thf(fact_7697_take__bit__Suc__minus__1__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.64        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_minus_1_eq
% 0.32/0.64  thf(fact_7698_take__bit__Suc__minus__1__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.64        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_minus_1_eq
% 0.32/0.64  thf(fact_7699_take__bit__Suc__bit1,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_bit1
% 0.32/0.64  thf(fact_7700_take__bit__Suc__bit1,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_bit1
% 0.32/0.64  thf(fact_7701_take__bit__numeral__minus__1__eq,axiom,
% 0.32/0.64      ! [K: num] :
% 0.32/0.64        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.64        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_minus_1_eq
% 0.32/0.64  thf(fact_7702_take__bit__numeral__minus__1__eq,axiom,
% 0.32/0.64      ! [K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.64        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_minus_1_eq
% 0.32/0.64  thf(fact_7703_take__bit__Suc,axiom,
% 0.32/0.64      ! [N: nat,A: code_integer] :
% 0.32/0.64        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 0.32/0.64        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc
% 0.32/0.64  thf(fact_7704_take__bit__Suc,axiom,
% 0.32/0.64      ! [N: nat,A: int] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc
% 0.32/0.64  thf(fact_7705_take__bit__Suc,axiom,
% 0.32/0.64      ! [N: nat,A: nat] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 0.32/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc
% 0.32/0.64  thf(fact_7706_exp__bound,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.64         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_bound
% 0.32/0.64  thf(fact_7707_take__bit__int__less__eq,axiom,
% 0.32/0.64      ! [N: nat,K: int] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.32/0.64       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.64         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_less_eq
% 0.32/0.64  thf(fact_7708_take__bit__int__greater__eq,axiom,
% 0.32/0.64      ! [K: int,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.64       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_int_greater_eq
% 0.32/0.64  thf(fact_7709_signed__take__bit__eq__take__bit__shift,axiom,
% 0.32/0.64      ( bit_ri631733984087533419it_int
% 0.32/0.64      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % signed_take_bit_eq_take_bit_shift
% 0.32/0.64  thf(fact_7710_mask__eq__sum__exp__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.64        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.64          @ ( collect_nat
% 0.32/0.64            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mask_eq_sum_exp_nat
% 0.32/0.64  thf(fact_7711_and__int__rec,axiom,
% 0.32/0.64      ( bit_se725231765392027082nd_int
% 0.32/0.64      = ( ^ [K2: int,L: int] :
% 0.32/0.64            ( plus_plus_int
% 0.32/0.64            @ ( zero_n2684676970156552555ol_int
% 0.32/0.64              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.32/0.64                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.32/0.64            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_int_rec
% 0.32/0.64  thf(fact_7712_stable__imp__take__bit__eq,axiom,
% 0.32/0.64      ! [A: code_integer,N: nat] :
% 0.32/0.64        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.64          = A )
% 0.32/0.64       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.32/0.64              = zero_z3403309356797280102nteger ) )
% 0.32/0.64          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.32/0.64              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % stable_imp_take_bit_eq
% 0.32/0.64  thf(fact_7713_stable__imp__take__bit__eq,axiom,
% 0.32/0.64      ! [A: int,N: nat] :
% 0.32/0.64        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.64          = A )
% 0.32/0.64       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.32/0.64              = zero_zero_int ) )
% 0.32/0.64          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.32/0.64              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % stable_imp_take_bit_eq
% 0.32/0.64  thf(fact_7714_stable__imp__take__bit__eq,axiom,
% 0.32/0.64      ! [A: nat,N: nat] :
% 0.32/0.64        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.64          = A )
% 0.32/0.64       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.32/0.64              = zero_zero_nat ) )
% 0.32/0.64          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.32/0.64           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.32/0.64              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % stable_imp_take_bit_eq
% 0.32/0.64  thf(fact_7715_gauss__sum__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( groups3542108847815614940at_nat
% 0.32/0.64          @ ^ [X3: nat] : X3
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.64        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % gauss_sum_nat
% 0.32/0.64  thf(fact_7716_take__bit__numeral__bit1,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_bit1
% 0.32/0.64  thf(fact_7717_take__bit__numeral__bit1,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.32/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_bit1
% 0.32/0.64  thf(fact_7718_real__exp__bound__lemma,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.64         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_exp_bound_lemma
% 0.32/0.64  thf(fact_7719_take__bit__minus__small__eq,axiom,
% 0.32/0.64      ! [K: int,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.64       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.32/0.64            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_minus_small_eq
% 0.32/0.64  thf(fact_7720_arith__series__nat,axiom,
% 0.32/0.64      ! [A: nat,D: nat,N: nat] :
% 0.32/0.64        ( ( groups3542108847815614940at_nat
% 0.32/0.64          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.64        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % arith_series_nat
% 0.32/0.64  thf(fact_7721_Sum__Icc__nat,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( groups3542108847815614940at_nat
% 0.32/0.64          @ ^ [X3: nat] : X3
% 0.32/0.64          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Sum_Icc_nat
% 0.32/0.64  thf(fact_7722_exp__lower__Taylor__quadratic,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_lower_Taylor_quadratic
% 0.32/0.64  thf(fact_7723_take__bit__numeral__minus__bit1,axiom,
% 0.32/0.64      ! [L2: num,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_numeral_minus_bit1
% 0.32/0.64  thf(fact_7724_and__int_Oelims,axiom,
% 0.32/0.64      ! [X: int,Xa2: int,Y: int] :
% 0.32/0.64        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.32/0.64          = Y )
% 0.32/0.64       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.64              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.64           => ( Y
% 0.32/0.64              = ( uminus_uminus_int
% 0.32/0.64                @ ( zero_n2684676970156552555ol_int
% 0.32/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.32/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.32/0.64          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.64                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.64           => ( Y
% 0.32/0.64              = ( plus_plus_int
% 0.32/0.64                @ ( zero_n2684676970156552555ol_int
% 0.32/0.64                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.32/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.32/0.64                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_int.elims
% 0.32/0.64  thf(fact_7725_and__int_Osimps,axiom,
% 0.32/0.64      ( bit_se725231765392027082nd_int
% 0.32/0.64      = ( ^ [K2: int,L: int] :
% 0.32/0.64            ( if_int
% 0.32/0.64            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.64              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.64            @ ( uminus_uminus_int
% 0.32/0.64              @ ( zero_n2684676970156552555ol_int
% 0.32/0.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.32/0.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 0.32/0.64            @ ( plus_plus_int
% 0.32/0.64              @ ( zero_n2684676970156552555ol_int
% 0.32/0.64                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.32/0.64                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.32/0.64              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_int.simps
% 0.32/0.64  thf(fact_7726_take__bit__Suc__minus__bit1,axiom,
% 0.32/0.64      ! [N: nat,K: num] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_Suc_minus_bit1
% 0.32/0.64  thf(fact_7727_sum__gp,axiom,
% 0.32/0.64      ! [N: nat,M: nat,X: complex] :
% 0.32/0.64        ( ( ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_complex ) )
% 0.32/0.64        & ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( ( X = one_one_complex )
% 0.32/0.64             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.32/0.64            & ( ( X != one_one_complex )
% 0.32/0.64             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp
% 0.32/0.64  thf(fact_7728_sum__gp,axiom,
% 0.32/0.64      ! [N: nat,M: nat,X: rat] :
% 0.32/0.64        ( ( ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_rat ) )
% 0.32/0.64        & ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( ( X = one_one_rat )
% 0.32/0.64             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.32/0.64            & ( ( X != one_one_rat )
% 0.32/0.64             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp
% 0.32/0.64  thf(fact_7729_sum__gp,axiom,
% 0.32/0.64      ! [N: nat,M: nat,X: real] :
% 0.32/0.64        ( ( ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64            = zero_zero_real ) )
% 0.32/0.64        & ( ~ ( ord_less_nat @ N @ M )
% 0.32/0.64         => ( ( ( X = one_one_real )
% 0.32/0.64             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.32/0.64            & ( ( X != one_one_real )
% 0.32/0.64             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.32/0.64                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_gp
% 0.32/0.64  thf(fact_7730_log__base__10__eq1,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.64          = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_base_10_eq1
% 0.32/0.64  thf(fact_7731_of__nat__eq__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ( semiri8010041392384452111omplex @ M )
% 0.32/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.32/0.64        = ( M = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_iff
% 0.32/0.64  thf(fact_7732_of__nat__eq__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ M )
% 0.32/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( M = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_iff
% 0.32/0.64  thf(fact_7733_of__nat__eq__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ( semiri681578069525770553at_rat @ M )
% 0.32/0.64          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( M = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_iff
% 0.32/0.64  thf(fact_7734_of__nat__eq__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.32/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( M = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_iff
% 0.32/0.64  thf(fact_7735_of__nat__eq__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( M = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_iff
% 0.32/0.64  thf(fact_7736_insert__subset,axiom,
% 0.32/0.64      ! [X: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.64        ( ( ord_le211207098394363844omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 0.32/0.64        = ( ( member_complex @ X @ B3 )
% 0.32/0.64          & ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_subset
% 0.32/0.64  thf(fact_7737_insert__subset,axiom,
% 0.32/0.64      ! [X: real,A2: set_real,B3: set_real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 0.32/0.64        = ( ( member_real @ X @ B3 )
% 0.32/0.64          & ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_subset
% 0.32/0.64  thf(fact_7738_insert__subset,axiom,
% 0.32/0.64      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.64        ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 0.32/0.64        = ( ( member_set_nat @ X @ B3 )
% 0.32/0.64          & ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_subset
% 0.32/0.64  thf(fact_7739_insert__subset,axiom,
% 0.32/0.64      ! [X: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 0.32/0.64        = ( ( member_nat @ X @ B3 )
% 0.32/0.64          & ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_subset
% 0.32/0.64  thf(fact_7740_insert__subset,axiom,
% 0.32/0.64      ! [X: int,A2: set_int,B3: set_int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 0.32/0.64        = ( ( member_int @ X @ B3 )
% 0.32/0.64          & ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_subset
% 0.32/0.64  thf(fact_7741_int__eq__iff__numeral,axiom,
% 0.32/0.64      ! [M: nat,V: num] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.64          = ( numeral_numeral_int @ V ) )
% 0.32/0.64        = ( M
% 0.32/0.64          = ( numeral_numeral_nat @ V ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_eq_iff_numeral
% 0.32/0.64  thf(fact_7742_abs__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.64        = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % abs_of_nat
% 0.32/0.64  thf(fact_7743_abs__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % abs_of_nat
% 0.32/0.64  thf(fact_7744_abs__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % abs_of_nat
% 0.32/0.64  thf(fact_7745_abs__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % abs_of_nat
% 0.32/0.64  thf(fact_7746_negative__eq__positive,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64          = ( semiri1314217659103216013at_int @ M ) )
% 0.32/0.64        = ( ( N = zero_zero_nat )
% 0.32/0.64          & ( M = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % negative_eq_positive
% 0.32/0.64  thf(fact_7747_Diff__insert0,axiom,
% 0.32/0.64      ! [X: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.64        ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64       => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 0.32/0.64          = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert0
% 0.32/0.64  thf(fact_7748_Diff__insert0,axiom,
% 0.32/0.64      ! [X: real,A2: set_real,B3: set_real] :
% 0.32/0.64        ( ~ ( member_real @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 0.32/0.64          = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert0
% 0.32/0.64  thf(fact_7749_Diff__insert0,axiom,
% 0.32/0.64      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.64        ( ~ ( member_set_nat @ X @ A2 )
% 0.32/0.64       => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 0.32/0.64          = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert0
% 0.32/0.64  thf(fact_7750_Diff__insert0,axiom,
% 0.32/0.64      ! [X: int,A2: set_int,B3: set_int] :
% 0.32/0.64        ( ~ ( member_int @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 0.32/0.64          = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert0
% 0.32/0.64  thf(fact_7751_Diff__insert0,axiom,
% 0.32/0.64      ! [X: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.64        ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 0.32/0.64          = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert0
% 0.32/0.64  thf(fact_7752_insert__Diff1,axiom,
% 0.32/0.64      ! [X: complex,B3: set_complex,A2: set_complex] :
% 0.32/0.64        ( ( member_complex @ X @ B3 )
% 0.32/0.64       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 0.32/0.64          = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff1
% 0.32/0.64  thf(fact_7753_insert__Diff1,axiom,
% 0.32/0.64      ! [X: real,B3: set_real,A2: set_real] :
% 0.32/0.64        ( ( member_real @ X @ B3 )
% 0.32/0.64       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 0.32/0.64          = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff1
% 0.32/0.64  thf(fact_7754_insert__Diff1,axiom,
% 0.32/0.64      ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 0.32/0.64        ( ( member_set_nat @ X @ B3 )
% 0.32/0.64       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 0.32/0.64          = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff1
% 0.32/0.64  thf(fact_7755_insert__Diff1,axiom,
% 0.32/0.64      ! [X: int,B3: set_int,A2: set_int] :
% 0.32/0.64        ( ( member_int @ X @ B3 )
% 0.32/0.64       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 0.32/0.64          = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff1
% 0.32/0.64  thf(fact_7756_insert__Diff1,axiom,
% 0.32/0.64      ! [X: nat,B3: set_nat,A2: set_nat] :
% 0.32/0.64        ( ( member_nat @ X @ B3 )
% 0.32/0.64       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 0.32/0.64          = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff1
% 0.32/0.64  thf(fact_7757_negative__zle,axiom,
% 0.32/0.64      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.32/0.64  
% 0.32/0.64  % negative_zle
% 0.32/0.64  thf(fact_7758_of__nat__eq__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ( semiri8010041392384452111omplex @ M )
% 0.32/0.64          = zero_zero_complex )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_0_iff
% 0.32/0.64  thf(fact_7759_of__nat__eq__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ M )
% 0.32/0.64          = zero_zero_real )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_0_iff
% 0.32/0.64  thf(fact_7760_of__nat__eq__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ( semiri681578069525770553at_rat @ M )
% 0.32/0.64          = zero_zero_rat )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_0_iff
% 0.32/0.64  thf(fact_7761_of__nat__eq__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ( semiri1316708129612266289at_nat @ M )
% 0.32/0.64          = zero_zero_nat )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_0_iff
% 0.32/0.64  thf(fact_7762_of__nat__eq__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.64          = zero_zero_int )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_0_iff
% 0.32/0.64  thf(fact_7763_of__nat__0__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( zero_zero_complex
% 0.32/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.32/0.64        = ( zero_zero_nat = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_eq_iff
% 0.32/0.64  thf(fact_7764_of__nat__0__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( zero_zero_real
% 0.32/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( zero_zero_nat = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_eq_iff
% 0.32/0.64  thf(fact_7765_of__nat__0__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( zero_zero_rat
% 0.32/0.64          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( zero_zero_nat = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_eq_iff
% 0.32/0.64  thf(fact_7766_of__nat__0__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( zero_zero_nat
% 0.32/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( zero_zero_nat = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_eq_iff
% 0.32/0.64  thf(fact_7767_of__nat__0__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( zero_zero_int
% 0.32/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( zero_zero_nat = N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_eq_iff
% 0.32/0.64  thf(fact_7768_of__nat__0,axiom,
% 0.32/0.64      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.32/0.64      = zero_zero_complex ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0
% 0.32/0.64  thf(fact_7769_of__nat__0,axiom,
% 0.32/0.64      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.32/0.64      = zero_zero_real ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0
% 0.32/0.64  thf(fact_7770_of__nat__0,axiom,
% 0.32/0.64      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.32/0.64      = zero_zero_rat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0
% 0.32/0.64  thf(fact_7771_of__nat__0,axiom,
% 0.32/0.64      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.32/0.64      = zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0
% 0.32/0.64  thf(fact_7772_of__nat__0,axiom,
% 0.32/0.64      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.32/0.64      = zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0
% 0.32/0.64  thf(fact_7773_of__nat__less__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_iff
% 0.32/0.64  thf(fact_7774_of__nat__less__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_iff
% 0.32/0.64  thf(fact_7775_of__nat__less__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_iff
% 0.32/0.64  thf(fact_7776_of__nat__less__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_iff
% 0.32/0.64  thf(fact_7777_of__nat__numeral,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numera6690914467698888265omplex @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_numeral
% 0.32/0.64  thf(fact_7778_of__nat__numeral,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numeral_numeral_real @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_numeral
% 0.32/0.64  thf(fact_7779_of__nat__numeral,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numeral_numeral_rat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_numeral
% 0.32/0.64  thf(fact_7780_of__nat__numeral,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numeral_numeral_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_numeral
% 0.32/0.64  thf(fact_7781_of__nat__numeral,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_numeral
% 0.32/0.64  thf(fact_7782_of__nat__le__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_iff
% 0.32/0.64  thf(fact_7783_of__nat__le__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_iff
% 0.32/0.64  thf(fact_7784_of__nat__le__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_iff
% 0.32/0.64  thf(fact_7785_of__nat__le__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_iff
% 0.32/0.64  thf(fact_7786_singleton__insert__inj__eq,axiom,
% 0.32/0.64      ! [B: nat,A: nat,A2: set_nat] :
% 0.32/0.64        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.32/0.64          = ( insert_nat @ A @ A2 ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq
% 0.32/0.64  thf(fact_7787_singleton__insert__inj__eq,axiom,
% 0.32/0.64      ! [B: real,A: real,A2: set_real] :
% 0.32/0.64        ( ( ( insert_real @ B @ bot_bot_set_real )
% 0.32/0.64          = ( insert_real @ A @ A2 ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq
% 0.32/0.64  thf(fact_7788_singleton__insert__inj__eq,axiom,
% 0.32/0.64      ! [B: int,A: int,A2: set_int] :
% 0.32/0.64        ( ( ( insert_int @ B @ bot_bot_set_int )
% 0.32/0.64          = ( insert_int @ A @ A2 ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq
% 0.32/0.64  thf(fact_7789_singleton__insert__inj__eq_H,axiom,
% 0.32/0.64      ! [A: nat,A2: set_nat,B: nat] :
% 0.32/0.64        ( ( ( insert_nat @ A @ A2 )
% 0.32/0.64          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq'
% 0.32/0.64  thf(fact_7790_singleton__insert__inj__eq_H,axiom,
% 0.32/0.64      ! [A: real,A2: set_real,B: real] :
% 0.32/0.64        ( ( ( insert_real @ A @ A2 )
% 0.32/0.64          = ( insert_real @ B @ bot_bot_set_real ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq'
% 0.32/0.64  thf(fact_7791_singleton__insert__inj__eq_H,axiom,
% 0.32/0.64      ! [A: int,A2: set_int,B: int] :
% 0.32/0.64        ( ( ( insert_int @ A @ A2 )
% 0.32/0.64          = ( insert_int @ B @ bot_bot_set_int ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % singleton_insert_inj_eq'
% 0.32/0.64  thf(fact_7792_of__nat__add,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.64        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_add
% 0.32/0.64  thf(fact_7793_of__nat__add,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.64        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_add
% 0.32/0.64  thf(fact_7794_of__nat__add,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.64        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_add
% 0.32/0.64  thf(fact_7795_of__nat__add,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.64        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_add
% 0.32/0.64  thf(fact_7796_of__nat__add,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_add
% 0.32/0.64  thf(fact_7797_of__nat__mult,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 0.32/0.64        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mult
% 0.32/0.64  thf(fact_7798_of__nat__mult,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 0.32/0.64        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mult
% 0.32/0.64  thf(fact_7799_of__nat__mult,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 0.32/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mult
% 0.32/0.64  thf(fact_7800_of__nat__mult,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.32/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mult
% 0.32/0.64  thf(fact_7801_of__nat__mult,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.32/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mult
% 0.32/0.64  thf(fact_7802_of__nat__1,axiom,
% 0.32/0.64      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.32/0.64      = one_one_complex ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1
% 0.32/0.64  thf(fact_7803_of__nat__1,axiom,
% 0.32/0.64      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.32/0.64      = one_one_real ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1
% 0.32/0.64  thf(fact_7804_of__nat__1,axiom,
% 0.32/0.64      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.32/0.64      = one_one_rat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1
% 0.32/0.64  thf(fact_7805_of__nat__1,axiom,
% 0.32/0.64      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.32/0.64      = one_one_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1
% 0.32/0.64  thf(fact_7806_of__nat__1,axiom,
% 0.32/0.64      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.32/0.64      = one_one_int ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1
% 0.32/0.64  thf(fact_7807_of__nat__1__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( one_one_complex
% 0.32/0.64          = ( semiri8010041392384452111omplex @ N ) )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1_eq_iff
% 0.32/0.64  thf(fact_7808_of__nat__1__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( one_one_real
% 0.32/0.64          = ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1_eq_iff
% 0.32/0.64  thf(fact_7809_of__nat__1__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( one_one_rat
% 0.32/0.64          = ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1_eq_iff
% 0.32/0.64  thf(fact_7810_of__nat__1__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( one_one_nat
% 0.32/0.64          = ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1_eq_iff
% 0.32/0.64  thf(fact_7811_of__nat__1__eq__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( one_one_int
% 0.32/0.64          = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_1_eq_iff
% 0.32/0.64  thf(fact_7812_of__nat__eq__1__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ( semiri8010041392384452111omplex @ N )
% 0.32/0.64          = one_one_complex )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_1_iff
% 0.32/0.64  thf(fact_7813_of__nat__eq__1__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ N )
% 0.32/0.64          = one_one_real )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_1_iff
% 0.32/0.64  thf(fact_7814_of__nat__eq__1__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ( semiri681578069525770553at_rat @ N )
% 0.32/0.64          = one_one_rat )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_1_iff
% 0.32/0.64  thf(fact_7815_of__nat__eq__1__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ( semiri1316708129612266289at_nat @ N )
% 0.32/0.64          = one_one_nat )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_1_iff
% 0.32/0.64  thf(fact_7816_of__nat__eq__1__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ N )
% 0.32/0.64          = one_one_int )
% 0.32/0.64        = ( N = one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_1_iff
% 0.32/0.64  thf(fact_7817_atLeastAtMost__singleton,axiom,
% 0.32/0.64      ! [A: nat] :
% 0.32/0.64        ( ( set_or1269000886237332187st_nat @ A @ A )
% 0.32/0.64        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton
% 0.32/0.64  thf(fact_7818_atLeastAtMost__singleton,axiom,
% 0.32/0.64      ! [A: int] :
% 0.32/0.64        ( ( set_or1266510415728281911st_int @ A @ A )
% 0.32/0.64        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton
% 0.32/0.64  thf(fact_7819_atLeastAtMost__singleton,axiom,
% 0.32/0.64      ! [A: real] :
% 0.32/0.64        ( ( set_or1222579329274155063t_real @ A @ A )
% 0.32/0.64        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton
% 0.32/0.64  thf(fact_7820_atLeastAtMost__singleton__iff,axiom,
% 0.32/0.64      ! [A: nat,B: nat,C: nat] :
% 0.32/0.64        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.32/0.64          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( B = C ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton_iff
% 0.32/0.64  thf(fact_7821_atLeastAtMost__singleton__iff,axiom,
% 0.32/0.64      ! [A: int,B: int,C: int] :
% 0.32/0.64        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.32/0.64          = ( insert_int @ C @ bot_bot_set_int ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( B = C ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton_iff
% 0.32/0.64  thf(fact_7822_atLeastAtMost__singleton__iff,axiom,
% 0.32/0.64      ! [A: real,B: real,C: real] :
% 0.32/0.64        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.32/0.64          = ( insert_real @ C @ bot_bot_set_real ) )
% 0.32/0.64        = ( ( A = B )
% 0.32/0.64          & ( B = C ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton_iff
% 0.32/0.64  thf(fact_7823_insert__Diff__single,axiom,
% 0.32/0.64      ! [A: int,A2: set_int] :
% 0.32/0.64        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.64        = ( insert_int @ A @ A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_single
% 0.32/0.64  thf(fact_7824_insert__Diff__single,axiom,
% 0.32/0.64      ! [A: real,A2: set_real] :
% 0.32/0.64        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.64        = ( insert_real @ A @ A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_single
% 0.32/0.64  thf(fact_7825_insert__Diff__single,axiom,
% 0.32/0.64      ! [A: nat,A2: set_nat] :
% 0.32/0.64        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.64        = ( insert_nat @ A @ A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_single
% 0.32/0.64  thf(fact_7826_finite__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_real,A: real,B3: set_real] :
% 0.32/0.64        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) ) )
% 0.32/0.64        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_Diff_insert
% 0.32/0.64  thf(fact_7827_finite__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_int,A: int,B3: set_int] :
% 0.32/0.64        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) ) )
% 0.32/0.64        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_Diff_insert
% 0.32/0.64  thf(fact_7828_finite__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_complex,A: complex,B3: set_complex] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B3 ) ) )
% 0.32/0.64        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_Diff_insert
% 0.32/0.64  thf(fact_7829_finite__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_nat,A: nat,B3: set_nat] :
% 0.32/0.64        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) ) )
% 0.32/0.64        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_Diff_insert
% 0.32/0.64  thf(fact_7830_of__nat__power,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 0.32/0.64        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power
% 0.32/0.64  thf(fact_7831_of__nat__power,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 0.32/0.64        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power
% 0.32/0.64  thf(fact_7832_of__nat__power,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 0.32/0.64        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power
% 0.32/0.64  thf(fact_7833_of__nat__power,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 0.32/0.64        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power
% 0.32/0.64  thf(fact_7834_of__nat__power,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 0.32/0.64        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power
% 0.32/0.64  thf(fact_7835_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 0.32/0.64          = ( semiri8010041392384452111omplex @ X ) )
% 0.32/0.64        = ( ( power_power_nat @ B @ W )
% 0.32/0.64          = X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7836_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 0.32/0.64          = ( semiri5074537144036343181t_real @ X ) )
% 0.32/0.64        = ( ( power_power_nat @ B @ W )
% 0.32/0.64          = X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7837_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 0.32/0.64          = ( semiri681578069525770553at_rat @ X ) )
% 0.32/0.64        = ( ( power_power_nat @ B @ W )
% 0.32/0.64          = X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7838_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 0.32/0.64          = ( semiri1316708129612266289at_nat @ X ) )
% 0.32/0.64        = ( ( power_power_nat @ B @ W )
% 0.32/0.64          = X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7839_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 0.32/0.64          = ( semiri1314217659103216013at_int @ X ) )
% 0.32/0.64        = ( ( power_power_nat @ B @ W )
% 0.32/0.64          = X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_eq_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7840_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ( semiri8010041392384452111omplex @ X )
% 0.32/0.64          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 0.32/0.64        = ( X
% 0.32/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7841_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ X )
% 0.32/0.64          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.32/0.64        = ( X
% 0.32/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7842_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ( semiri681578069525770553at_rat @ X )
% 0.32/0.64          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.32/0.64        = ( X
% 0.32/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7843_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ( semiri1316708129612266289at_nat @ X )
% 0.32/0.64          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.32/0.64        = ( X
% 0.32/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7844_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ X )
% 0.32/0.64          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.32/0.64        = ( X
% 0.32/0.64          = ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7845_log__one,axiom,
% 0.32/0.64      ! [A: real] :
% 0.32/0.64        ( ( log @ A @ one_one_real )
% 0.32/0.64        = zero_zero_real ) ).
% 0.32/0.64  
% 0.32/0.64  % log_one
% 0.32/0.64  thf(fact_7846_pred__numeral__inc,axiom,
% 0.32/0.64      ! [K: num] :
% 0.32/0.64        ( ( pred_numeral @ ( inc @ K ) )
% 0.32/0.64        = ( numeral_numeral_nat @ K ) ) ).
% 0.32/0.64  
% 0.32/0.64  % pred_numeral_inc
% 0.32/0.64  thf(fact_7847_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n1201886186963655149omplex @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7848_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7849_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7850_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7851_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7852_of__nat__of__bool,axiom,
% 0.32/0.64      ! [P: $o] :
% 0.32/0.64        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.32/0.64        = ( zero_n356916108424825756nteger @ P ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_of_bool
% 0.32/0.64  thf(fact_7853_of__nat__le__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_0_iff
% 0.32/0.64  thf(fact_7854_of__nat__le__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_0_iff
% 0.32/0.64  thf(fact_7855_of__nat__le__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_0_iff
% 0.32/0.64  thf(fact_7856_of__nat__le__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.32/0.64        = ( M = zero_zero_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_0_iff
% 0.32/0.64  thf(fact_7857_and__nat__numerals_I3_J,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.64        = zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % and_nat_numerals(3)
% 0.32/0.64  thf(fact_7858_and__nat__numerals_I1_J,axiom,
% 0.32/0.64      ! [Y: num] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.64        = zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % and_nat_numerals(1)
% 0.32/0.64  thf(fact_7859_of__nat__Suc,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 0.32/0.64        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_Suc
% 0.32/0.64  thf(fact_7860_of__nat__Suc,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.32/0.64        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_Suc
% 0.32/0.64  thf(fact_7861_of__nat__Suc,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.32/0.64        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_Suc
% 0.32/0.64  thf(fact_7862_of__nat__Suc,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.32/0.64        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_Suc
% 0.32/0.64  thf(fact_7863_of__nat__Suc,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.32/0.64        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_Suc
% 0.32/0.64  thf(fact_7864_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > real] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ~ ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7865_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > real] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ~ ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7866_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7867_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > rat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ~ ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7868_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.32/0.64        ( ( finite_finite_nat @ A2 )
% 0.32/0.64       => ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7869_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > rat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ~ ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7870_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7871_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > nat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ~ ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7872_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > nat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ~ ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7873_sum_Oinsert,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > nat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert
% 0.32/0.64  thf(fact_7874_numeral__less__real__of__nat__iff,axiom,
% 0.32/0.64      ! [W: num,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_less_real_of_nat_iff
% 0.32/0.64  thf(fact_7875_real__of__nat__less__numeral__iff,axiom,
% 0.32/0.64      ! [N: nat,W: num] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 0.32/0.64        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_less_numeral_iff
% 0.32/0.64  thf(fact_7876_numeral__le__real__of__nat__iff,axiom,
% 0.32/0.64      ! [N: num,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_le_real_of_nat_iff
% 0.32/0.64  thf(fact_7877_subset__Compl__singleton,axiom,
% 0.32/0.64      ! [A2: set_complex,B: complex] :
% 0.32/0.64        ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 0.32/0.64        = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Compl_singleton
% 0.32/0.64  thf(fact_7878_subset__Compl__singleton,axiom,
% 0.32/0.64      ! [A2: set_set_nat,B: set_nat] :
% 0.32/0.64        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 0.32/0.64        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Compl_singleton
% 0.32/0.64  thf(fact_7879_subset__Compl__singleton,axiom,
% 0.32/0.64      ! [A2: set_nat,B: nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.32/0.64        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Compl_singleton
% 0.32/0.64  thf(fact_7880_subset__Compl__singleton,axiom,
% 0.32/0.64      ! [A2: set_real,B: real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 0.32/0.64        = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Compl_singleton
% 0.32/0.64  thf(fact_7881_subset__Compl__singleton,axiom,
% 0.32/0.64      ! [A2: set_int,B: int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.32/0.64        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Compl_singleton
% 0.32/0.64  thf(fact_7882_log__eq__one,axiom,
% 0.32/0.64      ! [A: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( A != one_one_real )
% 0.32/0.64         => ( ( log @ A @ A )
% 0.32/0.64            = one_one_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_eq_one
% 0.32/0.64  thf(fact_7883_log__less__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.64           => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 0.32/0.64              = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_less_cancel_iff
% 0.32/0.64  thf(fact_7884_log__less__one__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 0.32/0.64            = ( ord_less_real @ X @ A ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_less_one_cancel_iff
% 0.32/0.64  thf(fact_7885_one__less__log__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 0.32/0.64            = ( ord_less_real @ A @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % one_less_log_cancel_iff
% 0.32/0.64  thf(fact_7886_log__less__zero__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.32/0.64            = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_less_zero_cancel_iff
% 0.32/0.64  thf(fact_7887_zero__less__log__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.32/0.64            = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zero_less_log_cancel_iff
% 0.32/0.64  thf(fact_7888_of__nat__0__less__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_less_iff
% 0.32/0.64  thf(fact_7889_of__nat__0__less__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_less_iff
% 0.32/0.64  thf(fact_7890_of__nat__0__less__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_less_iff
% 0.32/0.64  thf(fact_7891_of__nat__0__less__iff,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_less_iff
% 0.32/0.64  thf(fact_7892_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7893_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7894_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7895_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7896_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7897_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7898_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7899_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7900_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: num,N: nat,Y: nat] :
% 0.32/0.64        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 0.32/0.64          = ( semiri8010041392384452111omplex @ Y ) )
% 0.32/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = Y ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7901_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: num,N: nat,Y: nat] :
% 0.32/0.64        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 0.32/0.64          = ( semiri5074537144036343181t_real @ Y ) )
% 0.32/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = Y ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7902_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: num,N: nat,Y: nat] :
% 0.32/0.64        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 0.32/0.64          = ( semiri681578069525770553at_rat @ Y ) )
% 0.32/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = Y ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7903_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: num,N: nat,Y: nat] :
% 0.32/0.64        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = ( semiri1316708129612266289at_nat @ Y ) )
% 0.32/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = Y ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7904_numeral__power__eq__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: num,N: nat,Y: nat] :
% 0.32/0.64        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.64          = ( semiri1314217659103216013at_int @ Y ) )
% 0.32/0.64        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.64          = Y ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_eq_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7905_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [Y: nat,X: num,N: nat] :
% 0.32/0.64        ( ( ( semiri8010041392384452111omplex @ Y )
% 0.32/0.64          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 0.32/0.64        = ( Y
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7906_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [Y: nat,X: num,N: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ Y )
% 0.32/0.64          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 0.32/0.64        = ( Y
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7907_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [Y: nat,X: num,N: nat] :
% 0.32/0.64        ( ( ( semiri681578069525770553at_rat @ Y )
% 0.32/0.64          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 0.32/0.64        = ( Y
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7908_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [Y: nat,X: num,N: nat] :
% 0.32/0.64        ( ( ( semiri1316708129612266289at_nat @ Y )
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.32/0.64        = ( Y
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7909_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [Y: nat,X: num,N: nat] :
% 0.32/0.64        ( ( ( semiri1314217659103216013at_int @ Y )
% 0.32/0.64          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 0.32/0.64        = ( Y
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_eq_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7910_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7911_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7912_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7913_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.32/0.64      ! [B: nat,W: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_of_nat_power_cancel_iff
% 0.32/0.64  thf(fact_7914_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7915_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7916_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7917_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,B: nat,W: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7918_and__nat__numerals_I4_J,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.64        = one_one_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % and_nat_numerals(4)
% 0.32/0.64  thf(fact_7919_and__nat__numerals_I2_J,axiom,
% 0.32/0.64      ! [Y: num] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.64        = one_one_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % and_nat_numerals(2)
% 0.32/0.64  thf(fact_7920_set__replicate,axiom,
% 0.32/0.64      ! [N: nat,X: vEBT_VEBT] :
% 0.32/0.64        ( ( N != zero_zero_nat )
% 0.32/0.64       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.32/0.64          = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate
% 0.32/0.64  thf(fact_7921_set__replicate,axiom,
% 0.32/0.64      ! [N: nat,X: nat] :
% 0.32/0.64        ( ( N != zero_zero_nat )
% 0.32/0.64       => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.32/0.64          = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate
% 0.32/0.64  thf(fact_7922_set__replicate,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( N != zero_zero_nat )
% 0.32/0.64       => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.32/0.64          = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate
% 0.32/0.64  thf(fact_7923_set__replicate,axiom,
% 0.32/0.64      ! [N: nat,X: real] :
% 0.32/0.64        ( ( N != zero_zero_nat )
% 0.32/0.64       => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.32/0.64          = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate
% 0.32/0.64  thf(fact_7924_log__le__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.64           => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 0.32/0.64              = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_le_cancel_iff
% 0.32/0.64  thf(fact_7925_log__le__one__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 0.32/0.64            = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_le_one_cancel_iff
% 0.32/0.64  thf(fact_7926_one__le__log__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 0.32/0.64            = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % one_le_log_cancel_iff
% 0.32/0.64  thf(fact_7927_log__le__zero__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.32/0.64            = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_le_zero_cancel_iff
% 0.32/0.64  thf(fact_7928_zero__le__log__cancel__iff,axiom,
% 0.32/0.64      ! [A: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.64       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.32/0.64            = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zero_le_log_cancel_iff
% 0.32/0.64  thf(fact_7929_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(5)
% 0.32/0.64  thf(fact_7930_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(5)
% 0.32/0.64  thf(fact_7931_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.32/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(5)
% 0.32/0.64  thf(fact_7932_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.32/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(5)
% 0.32/0.64  thf(fact_7933_add__neg__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.32/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(5)
% 0.32/0.64  thf(fact_7934_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(6)
% 0.32/0.64  thf(fact_7935_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(6)
% 0.32/0.64  thf(fact_7936_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(6)
% 0.32/0.64  thf(fact_7937_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(6)
% 0.32/0.64  thf(fact_7938_add__neg__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_neg_numeral_special(6)
% 0.32/0.64  thf(fact_7939_diff__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.64        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(6)
% 0.32/0.64  thf(fact_7940_diff__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.64        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(6)
% 0.32/0.64  thf(fact_7941_diff__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.64        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(6)
% 0.32/0.64  thf(fact_7942_diff__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.32/0.64        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(6)
% 0.32/0.64  thf(fact_7943_diff__numeral__special_I6_J,axiom,
% 0.32/0.64      ! [M: num] :
% 0.32/0.64        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.64        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(6)
% 0.32/0.64  thf(fact_7944_diff__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.64        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(5)
% 0.32/0.64  thf(fact_7945_diff__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(5)
% 0.32/0.64  thf(fact_7946_diff__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 0.32/0.64        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(5)
% 0.32/0.64  thf(fact_7947_diff__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.32/0.64        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(5)
% 0.32/0.64  thf(fact_7948_diff__numeral__special_I5_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.32/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % diff_numeral_special(5)
% 0.32/0.64  thf(fact_7949_log__pow__cancel,axiom,
% 0.32/0.64      ! [A: real,B: nat] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( A != one_one_real )
% 0.32/0.64         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.32/0.64            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_pow_cancel
% 0.32/0.64  thf(fact_7950_of__nat__zero__less__power__iff,axiom,
% 0.32/0.64      ! [X: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 0.32/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.32/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_zero_less_power_iff
% 0.32/0.64  thf(fact_7951_of__nat__zero__less__power__iff,axiom,
% 0.32/0.64      ! [X: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 0.32/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.32/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_zero_less_power_iff
% 0.32/0.64  thf(fact_7952_of__nat__zero__less__power__iff,axiom,
% 0.32/0.64      ! [X: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 0.32/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.32/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_zero_less_power_iff
% 0.32/0.64  thf(fact_7953_of__nat__zero__less__power__iff,axiom,
% 0.32/0.64      ! [X: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 0.32/0.64        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.32/0.64          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_zero_less_power_iff
% 0.32/0.64  thf(fact_7954_Suc__0__and__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.64        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Suc_0_and_eq
% 0.32/0.64  thf(fact_7955_and__Suc__0__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.64        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % and_Suc_0_eq
% 0.32/0.64  thf(fact_7956_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7957_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7958_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7959_numeral__power__less__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.32/0.64        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_less_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7960_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7961_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7962_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7963_of__nat__less__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7964_even__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % even_of_nat
% 0.32/0.64  thf(fact_7965_even__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % even_of_nat
% 0.32/0.64  thf(fact_7966_even__of__nat,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % even_of_nat
% 0.32/0.64  thf(fact_7967_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7968_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7969_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7970_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.32/0.64      ! [I: num,N: nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.32/0.64        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_power_le_of_nat_cancel_iff
% 0.32/0.64  thf(fact_7971_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7972_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7973_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7974_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.32/0.64      ! [X: nat,I: num,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_le_numeral_power_cancel_iff
% 0.32/0.64  thf(fact_7975_Collect__case__prod__mono,axiom,
% 0.32/0.64      ! [A2: int > int > $o,B3: int > int > $o] :
% 0.32/0.64        ( ( ord_le6741204236512500942_int_o @ A2 @ B3 )
% 0.32/0.64       => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Collect_case_prod_mono
% 0.32/0.64  thf(fact_7976_real__arch__simple,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64      ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_arch_simple
% 0.32/0.64  thf(fact_7977_real__arch__simple,axiom,
% 0.32/0.64      ! [X: rat] :
% 0.32/0.64      ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_arch_simple
% 0.32/0.64  thf(fact_7978_reals__Archimedean2,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64      ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % reals_Archimedean2
% 0.32/0.64  thf(fact_7979_reals__Archimedean2,axiom,
% 0.32/0.64      ! [X: rat] :
% 0.32/0.64      ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % reals_Archimedean2
% 0.32/0.64  thf(fact_7980_mult__of__nat__commute,axiom,
% 0.32/0.64      ! [X: nat,Y: complex] :
% 0.32/0.64        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 0.32/0.64        = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_of_nat_commute
% 0.32/0.64  thf(fact_7981_mult__of__nat__commute,axiom,
% 0.32/0.64      ! [X: nat,Y: real] :
% 0.32/0.64        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 0.32/0.64        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_of_nat_commute
% 0.32/0.64  thf(fact_7982_mult__of__nat__commute,axiom,
% 0.32/0.64      ! [X: nat,Y: rat] :
% 0.32/0.64        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 0.32/0.64        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_of_nat_commute
% 0.32/0.64  thf(fact_7983_mult__of__nat__commute,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 0.32/0.64        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_of_nat_commute
% 0.32/0.64  thf(fact_7984_mult__of__nat__commute,axiom,
% 0.32/0.64      ! [X: nat,Y: int] :
% 0.32/0.64        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 0.32/0.64        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_of_nat_commute
% 0.32/0.64  thf(fact_7985_insert__mono,axiom,
% 0.32/0.64      ! [C4: set_nat,D4: set_nat,A: nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ C4 @ D4 )
% 0.32/0.64       => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_mono
% 0.32/0.64  thf(fact_7986_insert__mono,axiom,
% 0.32/0.64      ! [C4: set_real,D4: set_real,A: real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ C4 @ D4 )
% 0.32/0.64       => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_mono
% 0.32/0.64  thf(fact_7987_insert__mono,axiom,
% 0.32/0.64      ! [C4: set_int,D4: set_int,A: int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ C4 @ D4 )
% 0.32/0.64       => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_mono
% 0.32/0.64  thf(fact_7988_subset__insert,axiom,
% 0.32/0.64      ! [X: complex,A2: set_complex,B3: set_complex] :
% 0.32/0.64        ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64       => ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 0.32/0.64          = ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert
% 0.32/0.64  thf(fact_7989_subset__insert,axiom,
% 0.32/0.64      ! [X: real,A2: set_real,B3: set_real] :
% 0.32/0.64        ( ~ ( member_real @ X @ A2 )
% 0.32/0.64       => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 0.32/0.64          = ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert
% 0.32/0.64  thf(fact_7990_subset__insert,axiom,
% 0.32/0.64      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 0.32/0.64        ( ~ ( member_set_nat @ X @ A2 )
% 0.32/0.64       => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 0.32/0.64          = ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert
% 0.32/0.64  thf(fact_7991_subset__insert,axiom,
% 0.32/0.64      ! [X: nat,A2: set_nat,B3: set_nat] :
% 0.32/0.64        ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64       => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 0.32/0.64          = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert
% 0.32/0.64  thf(fact_7992_subset__insert,axiom,
% 0.32/0.64      ! [X: int,A2: set_int,B3: set_int] :
% 0.32/0.64        ( ~ ( member_int @ X @ A2 )
% 0.32/0.64       => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 0.32/0.64          = ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert
% 0.32/0.64  thf(fact_7993_subset__insertI,axiom,
% 0.32/0.64      ! [B3: set_nat,A: nat] : ( ord_less_eq_set_nat @ B3 @ ( insert_nat @ A @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI
% 0.32/0.64  thf(fact_7994_subset__insertI,axiom,
% 0.32/0.64      ! [B3: set_real,A: real] : ( ord_less_eq_set_real @ B3 @ ( insert_real @ A @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI
% 0.32/0.64  thf(fact_7995_subset__insertI,axiom,
% 0.32/0.64      ! [B3: set_int,A: int] : ( ord_less_eq_set_int @ B3 @ ( insert_int @ A @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI
% 0.32/0.64  thf(fact_7996_subset__insertI2,axiom,
% 0.32/0.64      ! [A2: set_nat,B3: set_nat,B: nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI2
% 0.32/0.64  thf(fact_7997_subset__insertI2,axiom,
% 0.32/0.64      ! [A2: set_real,B3: set_real,B: real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI2
% 0.32/0.64  thf(fact_7998_subset__insertI2,axiom,
% 0.32/0.64      ! [A2: set_int,B3: set_int,B: int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insertI2
% 0.32/0.64  thf(fact_7999_take__bit__of__nat,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 0.32/0.64        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_of_nat
% 0.32/0.64  thf(fact_8000_take__bit__of__nat,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 0.32/0.64        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % take_bit_of_nat
% 0.32/0.64  thf(fact_8001_of__nat__and__eq,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 0.32/0.64        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_and_eq
% 0.32/0.64  thf(fact_8002_of__nat__and__eq,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 0.32/0.64        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_and_eq
% 0.32/0.64  thf(fact_8003_insert__Diff__if,axiom,
% 0.32/0.64      ! [X: complex,B3: set_complex,A2: set_complex] :
% 0.32/0.64        ( ( ( member_complex @ X @ B3 )
% 0.32/0.64         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( minus_811609699411566653omplex @ A2 @ B3 ) ) )
% 0.32/0.64        & ( ~ ( member_complex @ X @ B3 )
% 0.32/0.64         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_if
% 0.32/0.64  thf(fact_8004_insert__Diff__if,axiom,
% 0.32/0.64      ! [X: real,B3: set_real,A2: set_real] :
% 0.32/0.64        ( ( ( member_real @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( minus_minus_set_real @ A2 @ B3 ) ) )
% 0.32/0.64        & ( ~ ( member_real @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_if
% 0.32/0.64  thf(fact_8005_insert__Diff__if,axiom,
% 0.32/0.64      ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 0.32/0.64        ( ( ( member_set_nat @ X @ B3 )
% 0.32/0.64         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) )
% 0.32/0.64        & ( ~ ( member_set_nat @ X @ B3 )
% 0.32/0.64         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_if
% 0.32/0.64  thf(fact_8006_insert__Diff__if,axiom,
% 0.32/0.64      ! [X: int,B3: set_int,A2: set_int] :
% 0.32/0.64        ( ( ( member_int @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( minus_minus_set_int @ A2 @ B3 ) ) )
% 0.32/0.64        & ( ~ ( member_int @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_if
% 0.32/0.64  thf(fact_8007_insert__Diff__if,axiom,
% 0.32/0.64      ! [X: nat,B3: set_nat,A2: set_nat] :
% 0.32/0.64        ( ( ( member_nat @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( minus_minus_set_nat @ A2 @ B3 ) ) )
% 0.32/0.64        & ( ~ ( member_nat @ X @ B3 )
% 0.32/0.64         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 0.32/0.64            = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff_if
% 0.32/0.64  thf(fact_8008_int__diff__cases,axiom,
% 0.32/0.64      ! [Z: int] :
% 0.32/0.64        ~ ! [M4: nat,N3: nat] :
% 0.32/0.64            ( Z
% 0.32/0.64           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_diff_cases
% 0.32/0.64  thf(fact_8009_log__of__power__eq,axiom,
% 0.32/0.64      ! [M: nat,B: real,N: nat] :
% 0.32/0.64        ( ( ( semiri5074537144036343181t_real @ M )
% 0.32/0.64          = ( power_power_real @ B @ N ) )
% 0.32/0.64       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.64         => ( ( semiri5074537144036343181t_real @ N )
% 0.32/0.64            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_of_power_eq
% 0.32/0.64  thf(fact_8010_less__log__of__power,axiom,
% 0.32/0.64      ! [B: real,N: nat,M: real] :
% 0.32/0.64        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 0.32/0.64       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.64         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_log_of_power
% 0.32/0.64  thf(fact_8011_of__nat__less__of__int__iff,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 0.32/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_int_iff
% 0.32/0.64  thf(fact_8012_of__nat__less__of__int__iff,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 0.32/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_int_iff
% 0.32/0.64  thf(fact_8013_of__nat__less__of__int__iff,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 0.32/0.64        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_of_int_iff
% 0.32/0.64  thf(fact_8014_num__induct,axiom,
% 0.32/0.64      ! [P: num > $o,X: num] :
% 0.32/0.64        ( ( P @ one )
% 0.32/0.64       => ( ! [X6: num] :
% 0.32/0.64              ( ( P @ X6 )
% 0.32/0.64             => ( P @ ( inc @ X6 ) ) )
% 0.32/0.64         => ( P @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % num_induct
% 0.32/0.64  thf(fact_8015_add__inc,axiom,
% 0.32/0.64      ! [X: num,Y: num] :
% 0.32/0.64        ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 0.32/0.64        = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_inc
% 0.32/0.64  thf(fact_8016_le__log__of__power,axiom,
% 0.32/0.64      ! [B: real,N: nat,M: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 0.32/0.64       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.64         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % le_log_of_power
% 0.32/0.64  thf(fact_8017_log__base__pow,axiom,
% 0.32/0.64      ! [A: real,N: nat,X: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 0.32/0.64          = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_base_pow
% 0.32/0.64  thf(fact_8018_log__nat__power,axiom,
% 0.32/0.64      ! [X: real,B: real,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 0.32/0.64          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_nat_power
% 0.32/0.64  thf(fact_8019_of__nat__0__le__iff,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_le_iff
% 0.32/0.64  thf(fact_8020_of__nat__0__le__iff,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_le_iff
% 0.32/0.64  thf(fact_8021_of__nat__0__le__iff,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_le_iff
% 0.32/0.64  thf(fact_8022_of__nat__0__le__iff,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_0_le_iff
% 0.32/0.64  thf(fact_8023_of__nat__less__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_0_iff
% 0.32/0.64  thf(fact_8024_of__nat__less__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_0_iff
% 0.32/0.64  thf(fact_8025_of__nat__less__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_0_iff
% 0.32/0.64  thf(fact_8026_of__nat__less__0__iff,axiom,
% 0.32/0.64      ! [M: nat] :
% 0.32/0.64        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_0_iff
% 0.32/0.64  thf(fact_8027_of__nat__neq__0,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 0.32/0.64       != zero_zero_complex ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_neq_0
% 0.32/0.64  thf(fact_8028_of__nat__neq__0,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 0.32/0.64       != zero_zero_real ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_neq_0
% 0.32/0.64  thf(fact_8029_of__nat__neq__0,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.32/0.64       != zero_zero_rat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_neq_0
% 0.32/0.64  thf(fact_8030_of__nat__neq__0,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.32/0.64       != zero_zero_nat ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_neq_0
% 0.32/0.64  thf(fact_8031_of__nat__neq__0,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.32/0.64       != zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_neq_0
% 0.32/0.64  thf(fact_8032_div__mult2__eq_H,axiom,
% 0.32/0.64      ! [A: nat,M: nat,N: nat] :
% 0.32/0.64        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.32/0.64        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % div_mult2_eq'
% 0.32/0.64  thf(fact_8033_div__mult2__eq_H,axiom,
% 0.32/0.64      ! [A: int,M: nat,N: nat] :
% 0.32/0.64        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.64        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % div_mult2_eq'
% 0.32/0.64  thf(fact_8034_less__imp__of__nat__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ N )
% 0.32/0.64       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_imp_of_nat_less
% 0.32/0.64  thf(fact_8035_less__imp__of__nat__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ N )
% 0.32/0.64       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_imp_of_nat_less
% 0.32/0.64  thf(fact_8036_less__imp__of__nat__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ N )
% 0.32/0.64       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_imp_of_nat_less
% 0.32/0.64  thf(fact_8037_less__imp__of__nat__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ N )
% 0.32/0.64       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_imp_of_nat_less
% 0.32/0.64  thf(fact_8038_of__nat__less__imp__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_imp_less
% 0.32/0.64  thf(fact_8039_of__nat__less__imp__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.32/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_imp_less
% 0.32/0.64  thf(fact_8040_of__nat__less__imp__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_imp_less
% 0.32/0.64  thf(fact_8041_of__nat__less__imp__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64       => ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_imp_less
% 0.32/0.64  thf(fact_8042_of__nat__mono,axiom,
% 0.32/0.64      ! [I: nat,J: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.64       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mono
% 0.32/0.64  thf(fact_8043_of__nat__mono,axiom,
% 0.32/0.64      ! [I: nat,J: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.64       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mono
% 0.32/0.64  thf(fact_8044_of__nat__mono,axiom,
% 0.32/0.64      ! [I: nat,J: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.64       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mono
% 0.32/0.64  thf(fact_8045_of__nat__mono,axiom,
% 0.32/0.64      ! [I: nat,J: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.64       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mono
% 0.32/0.64  thf(fact_8046_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.64        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.64  thf(fact_8047_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.64        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % unique_euclidean_semiring_with_nat_class.of_nat_div
% 0.32/0.64  thf(fact_8048_of__nat__dvd__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_dvd_iff
% 0.32/0.64  thf(fact_8049_of__nat__dvd__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_dvd_iff
% 0.32/0.64  thf(fact_8050_of__nat__dvd__iff,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( dvd_dvd_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_dvd_iff
% 0.32/0.64  thf(fact_8051_subset__singletonD,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.32/0.64       => ( ( A2 = bot_bot_set_nat )
% 0.32/0.64          | ( A2
% 0.32/0.64            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singletonD
% 0.32/0.64  thf(fact_8052_subset__singletonD,axiom,
% 0.32/0.64      ! [A2: set_real,X: real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.32/0.64       => ( ( A2 = bot_bot_set_real )
% 0.32/0.64          | ( A2
% 0.32/0.64            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singletonD
% 0.32/0.64  thf(fact_8053_subset__singletonD,axiom,
% 0.32/0.64      ! [A2: set_int,X: int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.32/0.64       => ( ( A2 = bot_bot_set_int )
% 0.32/0.64          | ( A2
% 0.32/0.64            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singletonD
% 0.32/0.64  thf(fact_8054_subset__singleton__iff,axiom,
% 0.32/0.64      ! [X8: set_nat,A: nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.32/0.64        = ( ( X8 = bot_bot_set_nat )
% 0.32/0.64          | ( X8
% 0.32/0.64            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singleton_iff
% 0.32/0.64  thf(fact_8055_subset__singleton__iff,axiom,
% 0.32/0.64      ! [X8: set_real,A: real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.32/0.64        = ( ( X8 = bot_bot_set_real )
% 0.32/0.64          | ( X8
% 0.32/0.64            = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singleton_iff
% 0.32/0.64  thf(fact_8056_subset__singleton__iff,axiom,
% 0.32/0.64      ! [X8: set_int,A: int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.32/0.64        = ( ( X8 = bot_bot_set_int )
% 0.32/0.64          | ( X8
% 0.32/0.64            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_singleton_iff
% 0.32/0.64  thf(fact_8057_int__ops_I1_J,axiom,
% 0.32/0.64      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.32/0.64      = zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(1)
% 0.32/0.64  thf(fact_8058_int__ops_I3_J,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.32/0.64        = ( numeral_numeral_int @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(3)
% 0.32/0.64  thf(fact_8059_nat__int__comparison_I2_J,axiom,
% 0.32/0.64      ( ord_less_nat
% 0.32/0.64      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_int_comparison(2)
% 0.32/0.64  thf(fact_8060_atLeastAtMost__singleton_H,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( A = B )
% 0.32/0.64       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.32/0.64          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton'
% 0.32/0.64  thf(fact_8061_atLeastAtMost__singleton_H,axiom,
% 0.32/0.64      ! [A: int,B: int] :
% 0.32/0.64        ( ( A = B )
% 0.32/0.64       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.32/0.64          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton'
% 0.32/0.64  thf(fact_8062_atLeastAtMost__singleton_H,axiom,
% 0.32/0.64      ! [A: real,B: real] :
% 0.32/0.64        ( ( A = B )
% 0.32/0.64       => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.32/0.64          = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMost_singleton'
% 0.32/0.64  thf(fact_8063_Diff__insert__absorb,axiom,
% 0.32/0.64      ! [X: complex,A2: set_complex] :
% 0.32/0.64        ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert_absorb
% 0.32/0.64  thf(fact_8064_Diff__insert__absorb,axiom,
% 0.32/0.64      ! [X: set_nat,A2: set_set_nat] :
% 0.32/0.64        ( ~ ( member_set_nat @ X @ A2 )
% 0.32/0.64       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert_absorb
% 0.32/0.64  thf(fact_8065_Diff__insert__absorb,axiom,
% 0.32/0.64      ! [X: int,A2: set_int] :
% 0.32/0.64        ( ~ ( member_int @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert_absorb
% 0.32/0.64  thf(fact_8066_Diff__insert__absorb,axiom,
% 0.32/0.64      ! [X: real,A2: set_real] :
% 0.32/0.64        ( ~ ( member_real @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert_absorb
% 0.32/0.64  thf(fact_8067_Diff__insert__absorb,axiom,
% 0.32/0.64      ! [X: nat,A2: set_nat] :
% 0.32/0.64        ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert_absorb
% 0.32/0.64  thf(fact_8068_Diff__insert2,axiom,
% 0.32/0.64      ! [A2: set_int,A: int,B3: set_int] :
% 0.32/0.64        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert2
% 0.32/0.64  thf(fact_8069_Diff__insert2,axiom,
% 0.32/0.64      ! [A2: set_real,A: real,B3: set_real] :
% 0.32/0.64        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert2
% 0.32/0.64  thf(fact_8070_Diff__insert2,axiom,
% 0.32/0.64      ! [A2: set_nat,A: nat,B3: set_nat] :
% 0.32/0.64        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B3 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert2
% 0.32/0.64  thf(fact_8071_insert__Diff,axiom,
% 0.32/0.64      ! [A: complex,A2: set_complex] :
% 0.32/0.64        ( ( member_complex @ A @ A2 )
% 0.32/0.64       => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff
% 0.32/0.64  thf(fact_8072_insert__Diff,axiom,
% 0.32/0.64      ! [A: set_nat,A2: set_set_nat] :
% 0.32/0.64        ( ( member_set_nat @ A @ A2 )
% 0.32/0.64       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff
% 0.32/0.64  thf(fact_8073_insert__Diff,axiom,
% 0.32/0.64      ! [A: int,A2: set_int] :
% 0.32/0.64        ( ( member_int @ A @ A2 )
% 0.32/0.64       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff
% 0.32/0.64  thf(fact_8074_insert__Diff,axiom,
% 0.32/0.64      ! [A: real,A2: set_real] :
% 0.32/0.64        ( ( member_real @ A @ A2 )
% 0.32/0.64       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff
% 0.32/0.64  thf(fact_8075_insert__Diff,axiom,
% 0.32/0.64      ! [A: nat,A2: set_nat] :
% 0.32/0.64        ( ( member_nat @ A @ A2 )
% 0.32/0.64       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.64          = A2 ) ) ).
% 0.32/0.64  
% 0.32/0.64  % insert_Diff
% 0.32/0.64  thf(fact_8076_Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_int,A: int,B3: set_int] :
% 0.32/0.64        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert
% 0.32/0.64  thf(fact_8077_Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_real,A: real,B3: set_real] :
% 0.32/0.64        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B3 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert
% 0.32/0.64  thf(fact_8078_Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_nat,A: nat,B3: set_nat] :
% 0.32/0.64        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 0.32/0.64        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_insert
% 0.32/0.64  thf(fact_8079_zle__int,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zle_int
% 0.32/0.64  thf(fact_8080_nat__int__comparison_I3_J,axiom,
% 0.32/0.64      ( ord_less_eq_nat
% 0.32/0.64      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_int_comparison(3)
% 0.32/0.64  thf(fact_8081_subset__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_complex,B3: set_complex,X: complex,C4: set_complex] :
% 0.32/0.64        ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ ( insert_complex @ X @ C4 ) ) )
% 0.32/0.64        = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ C4 ) )
% 0.32/0.64          & ~ ( member_complex @ X @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Diff_insert
% 0.32/0.64  thf(fact_8082_subset__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_real,B3: set_real,X: real,C4: set_real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ ( insert_real @ X @ C4 ) ) )
% 0.32/0.64        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ C4 ) )
% 0.32/0.64          & ~ ( member_real @ X @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Diff_insert
% 0.32/0.64  thf(fact_8083_subset__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_set_nat,B3: set_set_nat,X: set_nat,C4: set_set_nat] :
% 0.32/0.64        ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ ( insert_set_nat @ X @ C4 ) ) )
% 0.32/0.64        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ C4 ) )
% 0.32/0.64          & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Diff_insert
% 0.32/0.64  thf(fact_8084_subset__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_nat,B3: set_nat,X: nat,C4: set_nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ ( insert_nat @ X @ C4 ) ) )
% 0.32/0.64        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ C4 ) )
% 0.32/0.64          & ~ ( member_nat @ X @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Diff_insert
% 0.32/0.64  thf(fact_8085_subset__Diff__insert,axiom,
% 0.32/0.64      ! [A2: set_int,B3: set_int,X: int,C4: set_int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ ( insert_int @ X @ C4 ) ) )
% 0.32/0.64        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ C4 ) )
% 0.32/0.64          & ~ ( member_int @ X @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_Diff_insert
% 0.32/0.64  thf(fact_8086_nonneg__int__cases,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ( K
% 0.32/0.64             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nonneg_int_cases
% 0.32/0.64  thf(fact_8087_zero__le__imp__eq__int,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.64       => ? [N3: nat] :
% 0.32/0.64            ( K
% 0.32/0.64            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zero_le_imp_eq_int
% 0.32/0.64  thf(fact_8088_of__nat__mod,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.64        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mod
% 0.32/0.64  thf(fact_8089_of__nat__mod,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.64        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mod
% 0.32/0.64  thf(fact_8090_of__nat__mod,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 0.32/0.64        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mod
% 0.32/0.64  thf(fact_8091_zadd__int__left,axiom,
% 0.32/0.64      ! [M: nat,N: nat,Z: int] :
% 0.32/0.64        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zadd_int_left
% 0.32/0.64  thf(fact_8092_int__plus,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_plus
% 0.32/0.64  thf(fact_8093_int__ops_I5_J,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(5)
% 0.32/0.64  thf(fact_8094_int__ops_I7_J,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.32/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(7)
% 0.32/0.64  thf(fact_8095_int__ops_I2_J,axiom,
% 0.32/0.64      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.32/0.64      = one_one_int ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(2)
% 0.32/0.64  thf(fact_8096_zle__iff__zadd,axiom,
% 0.32/0.64      ( ord_less_eq_int
% 0.32/0.64      = ( ^ [W3: int,Z3: int] :
% 0.32/0.64          ? [N2: nat] :
% 0.32/0.64            ( Z3
% 0.32/0.64            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zle_iff_zadd
% 0.32/0.64  thf(fact_8097_zdiv__int,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.32/0.64        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zdiv_int
% 0.32/0.64  thf(fact_8098_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8099_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8100_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8101_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8102_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8103_of__nat__max,axiom,
% 0.32/0.64      ! [X: nat,Y: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 0.32/0.64        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_max
% 0.32/0.64  thf(fact_8104_zmod__int,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.32/0.64        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zmod_int
% 0.32/0.64  thf(fact_8105_log2__of__power__eq,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( M
% 0.32/0.64          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64       => ( ( semiri5074537144036343181t_real @ N )
% 0.32/0.64          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log2_of_power_eq
% 0.32/0.64  thf(fact_8106_log__of__power__less,axiom,
% 0.32/0.64      ! [M: nat,B: real,N: nat] :
% 0.32/0.64        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.32/0.64       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.64         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.64           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_of_power_less
% 0.32/0.64  thf(fact_8107_nat__less__as__int,axiom,
% 0.32/0.64      ( ord_less_nat
% 0.32/0.64      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_less_as_int
% 0.32/0.64  thf(fact_8108_nat__leq__as__int,axiom,
% 0.32/0.64      ( ord_less_eq_nat
% 0.32/0.64      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_leq_as_int
% 0.32/0.64  thf(fact_8109_of__nat__mask__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.32/0.64        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mask_eq
% 0.32/0.64  thf(fact_8110_of__nat__mask__eq,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.32/0.64        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_mask_eq
% 0.32/0.64  thf(fact_8111_inc_Osimps_I1_J,axiom,
% 0.32/0.64      ( ( inc @ one )
% 0.32/0.64      = ( bit0 @ one ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inc.simps(1)
% 0.32/0.64  thf(fact_8112_inc_Osimps_I3_J,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( inc @ ( bit1 @ X ) )
% 0.32/0.64        = ( bit0 @ ( inc @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inc.simps(3)
% 0.32/0.64  thf(fact_8113_inc_Osimps_I2_J,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( inc @ ( bit0 @ X ) )
% 0.32/0.64        = ( bit1 @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inc.simps(2)
% 0.32/0.64  thf(fact_8114_log__of__power__le,axiom,
% 0.32/0.64      ! [M: nat,B: real,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.32/0.64       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.64         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.64           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_of_power_le
% 0.32/0.64  thf(fact_8115_ex__less__of__nat__mult,axiom,
% 0.32/0.64      ! [X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % ex_less_of_nat_mult
% 0.32/0.64  thf(fact_8116_ex__less__of__nat__mult,axiom,
% 0.32/0.64      ! [X: rat,Y: rat] :
% 0.32/0.64        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.32/0.64       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % ex_less_of_nat_mult
% 0.32/0.64  thf(fact_8117_add__One,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( plus_plus_num @ X @ one )
% 0.32/0.64        = ( inc @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % add_One
% 0.32/0.64  thf(fact_8118_inc__BitM__eq,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( inc @ ( bitM @ N ) )
% 0.32/0.64        = ( bit0 @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inc_BitM_eq
% 0.32/0.64  thf(fact_8119_of__nat__diff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_diff
% 0.32/0.64  thf(fact_8120_of__nat__diff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_diff
% 0.32/0.64  thf(fact_8121_of__nat__diff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_diff
% 0.32/0.64  thf(fact_8122_of__nat__diff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_diff
% 0.32/0.64  thf(fact_8123_of__nat__diff,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.64          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_diff
% 0.32/0.64  thf(fact_8124_BitM__inc__eq,axiom,
% 0.32/0.64      ! [N: num] :
% 0.32/0.64        ( ( bitM @ ( inc @ N ) )
% 0.32/0.64        = ( bit1 @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % BitM_inc_eq
% 0.32/0.64  thf(fact_8125_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_complex )
% 0.32/0.64         => ( ! [X6: complex,S5: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ S5 )
% 0.32/0.64               => ( ! [Y2: complex] :
% 0.32/0.64                      ( ( member_complex @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8126_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 0.32/0.64        ( ( finite_finite_nat @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [X6: nat,S5: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ S5 )
% 0.32/0.64               => ( ! [Y2: nat] :
% 0.32/0.64                      ( ( member_nat @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8127_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 0.32/0.64        ( ( finite_finite_int @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [X6: int,S5: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ S5 )
% 0.32/0.64               => ( ! [Y2: int] :
% 0.32/0.64                      ( ( member_int @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8128_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 0.32/0.64        ( ( finite_finite_real @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [X6: real,S5: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ S5 )
% 0.32/0.64               => ( ! [Y2: real] :
% 0.32/0.64                      ( ( member_real @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8129_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_complex )
% 0.32/0.64         => ( ! [X6: complex,S5: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ S5 )
% 0.32/0.64               => ( ! [Y2: complex] :
% 0.32/0.64                      ( ( member_complex @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8130_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 0.32/0.64        ( ( finite_finite_nat @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [X6: nat,S5: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ S5 )
% 0.32/0.64               => ( ! [Y2: nat] :
% 0.32/0.64                      ( ( member_nat @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8131_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 0.32/0.64        ( ( finite_finite_int @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [X6: int,S5: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ S5 )
% 0.32/0.64               => ( ! [Y2: int] :
% 0.32/0.64                      ( ( member_int @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8132_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 0.32/0.64        ( ( finite_finite_real @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [X6: real,S5: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ S5 )
% 0.32/0.64               => ( ! [Y2: real] :
% 0.32/0.64                      ( ( member_real @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8133_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_complex )
% 0.32/0.64         => ( ! [X6: complex,S5: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ S5 )
% 0.32/0.64               => ( ! [Y2: complex] :
% 0.32/0.64                      ( ( member_complex @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8134_finite__ranking__induct,axiom,
% 0.32/0.64      ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 0.32/0.64        ( ( finite_finite_nat @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [X6: nat,S5: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ S5 )
% 0.32/0.64               => ( ! [Y2: nat] :
% 0.32/0.64                      ( ( member_nat @ Y2 @ S5 )
% 0.32/0.64                     => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 0.32/0.64                 => ( ( P @ S5 )
% 0.32/0.64                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_ranking_induct
% 0.32/0.64  thf(fact_8135_finite__linorder__max__induct,axiom,
% 0.32/0.64      ! [A2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [B5: real,A7: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ A7 )
% 0.32/0.64               => ( ! [X4: real] :
% 0.32/0.64                      ( ( member_real @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_real @ X4 @ B5 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_max_induct
% 0.32/0.64  thf(fact_8136_finite__linorder__max__induct,axiom,
% 0.32/0.64      ! [A2: set_rat,P: set_rat > $o] :
% 0.32/0.64        ( ( finite_finite_rat @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_rat )
% 0.32/0.64         => ( ! [B5: rat,A7: set_rat] :
% 0.32/0.64                ( ( finite_finite_rat @ A7 )
% 0.32/0.64               => ( ! [X4: rat] :
% 0.32/0.64                      ( ( member_rat @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_rat @ X4 @ B5 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_max_induct
% 0.32/0.64  thf(fact_8137_finite__linorder__max__induct,axiom,
% 0.32/0.64      ! [A2: set_num,P: set_num > $o] :
% 0.32/0.64        ( ( finite_finite_num @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_num )
% 0.32/0.64         => ( ! [B5: num,A7: set_num] :
% 0.32/0.64                ( ( finite_finite_num @ A7 )
% 0.32/0.64               => ( ! [X4: num] :
% 0.32/0.64                      ( ( member_num @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_num @ X4 @ B5 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_max_induct
% 0.32/0.64  thf(fact_8138_finite__linorder__max__induct,axiom,
% 0.32/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [B5: nat,A7: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ A7 )
% 0.32/0.64               => ( ! [X4: nat] :
% 0.32/0.64                      ( ( member_nat @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_nat @ X4 @ B5 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_max_induct
% 0.32/0.64  thf(fact_8139_finite__linorder__max__induct,axiom,
% 0.32/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [B5: int,A7: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ A7 )
% 0.32/0.64               => ( ! [X4: int] :
% 0.32/0.64                      ( ( member_int @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_int @ X4 @ B5 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_max_induct
% 0.32/0.64  thf(fact_8140_finite__linorder__min__induct,axiom,
% 0.32/0.64      ! [A2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [B5: real,A7: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ A7 )
% 0.32/0.64               => ( ! [X4: real] :
% 0.32/0.64                      ( ( member_real @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_real @ B5 @ X4 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_min_induct
% 0.32/0.64  thf(fact_8141_finite__linorder__min__induct,axiom,
% 0.32/0.64      ! [A2: set_rat,P: set_rat > $o] :
% 0.32/0.64        ( ( finite_finite_rat @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_rat )
% 0.32/0.64         => ( ! [B5: rat,A7: set_rat] :
% 0.32/0.64                ( ( finite_finite_rat @ A7 )
% 0.32/0.64               => ( ! [X4: rat] :
% 0.32/0.64                      ( ( member_rat @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_rat @ B5 @ X4 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_min_induct
% 0.32/0.64  thf(fact_8142_finite__linorder__min__induct,axiom,
% 0.32/0.64      ! [A2: set_num,P: set_num > $o] :
% 0.32/0.64        ( ( finite_finite_num @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_num )
% 0.32/0.64         => ( ! [B5: num,A7: set_num] :
% 0.32/0.64                ( ( finite_finite_num @ A7 )
% 0.32/0.64               => ( ! [X4: num] :
% 0.32/0.64                      ( ( member_num @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_num @ B5 @ X4 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_min_induct
% 0.32/0.64  thf(fact_8143_finite__linorder__min__induct,axiom,
% 0.32/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [B5: nat,A7: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ A7 )
% 0.32/0.64               => ( ! [X4: nat] :
% 0.32/0.64                      ( ( member_nat @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_nat @ B5 @ X4 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_min_induct
% 0.32/0.64  thf(fact_8144_finite__linorder__min__induct,axiom,
% 0.32/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [B5: int,A7: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ A7 )
% 0.32/0.64               => ( ! [X4: int] :
% 0.32/0.64                      ( ( member_int @ X4 @ A7 )
% 0.32/0.64                     => ( ord_less_int @ B5 @ X4 ) )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_linorder_min_induct
% 0.32/0.64  thf(fact_8145_exp__of__nat2__mult,axiom,
% 0.32/0.64      ! [X: complex,N: nat] :
% 0.32/0.64        ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 0.32/0.64        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_of_nat2_mult
% 0.32/0.64  thf(fact_8146_exp__of__nat2__mult,axiom,
% 0.32/0.64      ! [X: real,N: nat] :
% 0.32/0.64        ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.64        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_of_nat2_mult
% 0.32/0.64  thf(fact_8147_exp__of__nat__mult,axiom,
% 0.32/0.64      ! [N: nat,X: complex] :
% 0.32/0.64        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 0.32/0.64        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_of_nat_mult
% 0.32/0.64  thf(fact_8148_exp__of__nat__mult,axiom,
% 0.32/0.64      ! [N: nat,X: real] :
% 0.32/0.64        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 0.32/0.64        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_of_nat_mult
% 0.32/0.64  thf(fact_8149_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > real] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8150_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > real] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8151_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8152_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > rat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8153_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat,G: nat > rat] :
% 0.32/0.64        ( ( finite_finite_nat @ A2 )
% 0.32/0.64       => ( ( ( member_nat @ X @ A2 )
% 0.32/0.64           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.32/0.64              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8154_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > rat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8155_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8156_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > nat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( groups1935376822645274424al_nat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_real @ X @ A2 )
% 0.32/0.64           => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8157_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > nat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_int @ X @ A2 )
% 0.32/0.64           => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8158_sum_Oinsert__if,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > nat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( groups5693394587270226106ex_nat @ G @ A2 ) ) )
% 0.32/0.64          & ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64              = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_if
% 0.32/0.64  thf(fact_8159_finite__subset__induct,axiom,
% 0.32/0.64      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.32/0.64        ( ( finite1152437895449049373et_nat @ F3 )
% 0.32/0.64       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_set_nat )
% 0.32/0.64           => ( ! [A5: set_nat,F4: set_set_nat] :
% 0.32/0.64                  ( ( finite1152437895449049373et_nat @ F4 )
% 0.32/0.64                 => ( ( member_set_nat @ A5 @ A2 )
% 0.32/0.64                   => ( ~ ( member_set_nat @ A5 @ F4 )
% 0.32/0.64                     => ( ( P @ F4 )
% 0.32/0.64                       => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct
% 0.32/0.64  thf(fact_8160_finite__subset__induct,axiom,
% 0.32/0.64      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ F3 )
% 0.32/0.64       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_complex )
% 0.32/0.64           => ( ! [A5: complex,F4: set_complex] :
% 0.32/0.64                  ( ( finite3207457112153483333omplex @ F4 )
% 0.32/0.64                 => ( ( member_complex @ A5 @ A2 )
% 0.32/0.64                   => ( ~ ( member_complex @ A5 @ F4 )
% 0.32/0.64                     => ( ( P @ F4 )
% 0.32/0.64                       => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct
% 0.32/0.64  thf(fact_8161_finite__subset__induct,axiom,
% 0.32/0.64      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_nat )
% 0.32/0.64           => ( ! [A5: nat,F4: set_nat] :
% 0.32/0.64                  ( ( finite_finite_nat @ F4 )
% 0.32/0.64                 => ( ( member_nat @ A5 @ A2 )
% 0.32/0.64                   => ( ~ ( member_nat @ A5 @ F4 )
% 0.32/0.64                     => ( ( P @ F4 )
% 0.32/0.64                       => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct
% 0.32/0.64  thf(fact_8162_finite__subset__induct,axiom,
% 0.32/0.64      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_real )
% 0.32/0.64           => ( ! [A5: real,F4: set_real] :
% 0.32/0.64                  ( ( finite_finite_real @ F4 )
% 0.32/0.64                 => ( ( member_real @ A5 @ A2 )
% 0.32/0.64                   => ( ~ ( member_real @ A5 @ F4 )
% 0.32/0.64                     => ( ( P @ F4 )
% 0.32/0.64                       => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct
% 0.32/0.64  thf(fact_8163_finite__subset__induct,axiom,
% 0.32/0.64      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_int )
% 0.32/0.64           => ( ! [A5: int,F4: set_int] :
% 0.32/0.64                  ( ( finite_finite_int @ F4 )
% 0.32/0.64                 => ( ( member_int @ A5 @ A2 )
% 0.32/0.64                   => ( ~ ( member_int @ A5 @ F4 )
% 0.32/0.64                     => ( ( P @ F4 )
% 0.32/0.64                       => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct
% 0.32/0.64  thf(fact_8164_finite__subset__induct_H,axiom,
% 0.32/0.64      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.32/0.64        ( ( finite1152437895449049373et_nat @ F3 )
% 0.32/0.64       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_set_nat )
% 0.32/0.64           => ( ! [A5: set_nat,F4: set_set_nat] :
% 0.32/0.64                  ( ( finite1152437895449049373et_nat @ F4 )
% 0.32/0.64                 => ( ( member_set_nat @ A5 @ A2 )
% 0.32/0.64                   => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 0.32/0.64                     => ( ~ ( member_set_nat @ A5 @ F4 )
% 0.32/0.64                       => ( ( P @ F4 )
% 0.32/0.64                         => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct'
% 0.32/0.64  thf(fact_8165_finite__subset__induct_H,axiom,
% 0.32/0.64      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ F3 )
% 0.32/0.64       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_complex )
% 0.32/0.64           => ( ! [A5: complex,F4: set_complex] :
% 0.32/0.64                  ( ( finite3207457112153483333omplex @ F4 )
% 0.32/0.64                 => ( ( member_complex @ A5 @ A2 )
% 0.32/0.64                   => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 0.32/0.64                     => ( ~ ( member_complex @ A5 @ F4 )
% 0.32/0.64                       => ( ( P @ F4 )
% 0.32/0.64                         => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct'
% 0.32/0.64  thf(fact_8166_finite__subset__induct_H,axiom,
% 0.32/0.64      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_nat )
% 0.32/0.64           => ( ! [A5: nat,F4: set_nat] :
% 0.32/0.64                  ( ( finite_finite_nat @ F4 )
% 0.32/0.64                 => ( ( member_nat @ A5 @ A2 )
% 0.32/0.64                   => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 0.32/0.64                     => ( ~ ( member_nat @ A5 @ F4 )
% 0.32/0.64                       => ( ( P @ F4 )
% 0.32/0.64                         => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct'
% 0.32/0.64  thf(fact_8167_finite__subset__induct_H,axiom,
% 0.32/0.64      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_real )
% 0.32/0.64           => ( ! [A5: real,F4: set_real] :
% 0.32/0.64                  ( ( finite_finite_real @ F4 )
% 0.32/0.64                 => ( ( member_real @ A5 @ A2 )
% 0.32/0.64                   => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 0.32/0.64                     => ( ~ ( member_real @ A5 @ F4 )
% 0.32/0.64                       => ( ( P @ F4 )
% 0.32/0.64                         => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct'
% 0.32/0.64  thf(fact_8168_finite__subset__induct_H,axiom,
% 0.32/0.64      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ F3 )
% 0.32/0.64       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 0.32/0.64         => ( ( P @ bot_bot_set_int )
% 0.32/0.64           => ( ! [A5: int,F4: set_int] :
% 0.32/0.64                  ( ( finite_finite_int @ F4 )
% 0.32/0.64                 => ( ( member_int @ A5 @ A2 )
% 0.32/0.64                   => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 0.32/0.64                     => ( ~ ( member_int @ A5 @ F4 )
% 0.32/0.64                       => ( ( P @ F4 )
% 0.32/0.64                         => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) ) )
% 0.32/0.64             => ( P @ F3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_subset_induct'
% 0.32/0.64  thf(fact_8169_reals__Archimedean3,axiom,
% 0.32/0.64      ! [X: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64       => ! [Y2: real] :
% 0.32/0.64          ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % reals_Archimedean3
% 0.32/0.64  thf(fact_8170_log__ln,axiom,
% 0.32/0.64      ( ln_ln_real
% 0.32/0.64      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_ln
% 0.32/0.64  thf(fact_8171_int__cases4,axiom,
% 0.32/0.64      ! [M: int] :
% 0.32/0.64        ( ! [N3: nat] :
% 0.32/0.64            ( M
% 0.32/0.64           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.64             => ( M
% 0.32/0.64               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_cases4
% 0.32/0.64  thf(fact_8172_infinite__remove,axiom,
% 0.32/0.64      ! [S2: set_complex,A: complex] :
% 0.32/0.64        ( ~ ( finite3207457112153483333omplex @ S2 )
% 0.32/0.64       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_remove
% 0.32/0.64  thf(fact_8173_infinite__remove,axiom,
% 0.32/0.64      ! [S2: set_int,A: int] :
% 0.32/0.64        ( ~ ( finite_finite_int @ S2 )
% 0.32/0.64       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_remove
% 0.32/0.64  thf(fact_8174_infinite__remove,axiom,
% 0.32/0.64      ! [S2: set_real,A: real] :
% 0.32/0.64        ( ~ ( finite_finite_real @ S2 )
% 0.32/0.64       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_remove
% 0.32/0.64  thf(fact_8175_infinite__remove,axiom,
% 0.32/0.64      ! [S2: set_nat,A: nat] :
% 0.32/0.64        ( ~ ( finite_finite_nat @ S2 )
% 0.32/0.64       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_remove
% 0.32/0.64  thf(fact_8176_infinite__coinduct,axiom,
% 0.32/0.64      ! [X8: set_complex > $o,A2: set_complex] :
% 0.32/0.64        ( ( X8 @ A2 )
% 0.32/0.64       => ( ! [A7: set_complex] :
% 0.32/0.64              ( ( X8 @ A7 )
% 0.32/0.64             => ? [X4: complex] :
% 0.32/0.64                  ( ( member_complex @ X4 @ A7 )
% 0.32/0.64                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) )
% 0.32/0.64                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.64         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_coinduct
% 0.32/0.64  thf(fact_8177_infinite__coinduct,axiom,
% 0.32/0.64      ! [X8: set_int > $o,A2: set_int] :
% 0.32/0.64        ( ( X8 @ A2 )
% 0.32/0.64       => ( ! [A7: set_int] :
% 0.32/0.64              ( ( X8 @ A7 )
% 0.32/0.64             => ? [X4: int] :
% 0.32/0.64                  ( ( member_int @ X4 @ A7 )
% 0.32/0.64                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) )
% 0.32/0.64                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ) )
% 0.32/0.64         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_coinduct
% 0.32/0.64  thf(fact_8178_infinite__coinduct,axiom,
% 0.32/0.64      ! [X8: set_real > $o,A2: set_real] :
% 0.32/0.64        ( ( X8 @ A2 )
% 0.32/0.64       => ( ! [A7: set_real] :
% 0.32/0.64              ( ( X8 @ A7 )
% 0.32/0.64             => ? [X4: real] :
% 0.32/0.64                  ( ( member_real @ X4 @ A7 )
% 0.32/0.64                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) )
% 0.32/0.64                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ) )
% 0.32/0.64         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_coinduct
% 0.32/0.64  thf(fact_8179_infinite__coinduct,axiom,
% 0.32/0.64      ! [X8: set_nat > $o,A2: set_nat] :
% 0.32/0.64        ( ( X8 @ A2 )
% 0.32/0.64       => ( ! [A7: set_nat] :
% 0.32/0.64              ( ( X8 @ A7 )
% 0.32/0.64             => ? [X4: nat] :
% 0.32/0.64                  ( ( member_nat @ X4 @ A7 )
% 0.32/0.64                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
% 0.32/0.64                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
% 0.32/0.64         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % infinite_coinduct
% 0.32/0.64  thf(fact_8180_finite__empty__induct,axiom,
% 0.32/0.64      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 0.32/0.64        ( ( finite1152437895449049373et_nat @ A2 )
% 0.32/0.64       => ( ( P @ A2 )
% 0.32/0.64         => ( ! [A5: set_nat,A7: set_set_nat] :
% 0.32/0.64                ( ( finite1152437895449049373et_nat @ A7 )
% 0.32/0.64               => ( ( member_set_nat @ A5 @ A7 )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ A5 @ bot_bot_set_set_nat ) ) ) ) ) )
% 0.32/0.64           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_empty_induct
% 0.32/0.64  thf(fact_8181_finite__empty__induct,axiom,
% 0.32/0.64      ! [A2: set_complex,P: set_complex > $o] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( P @ A2 )
% 0.32/0.64         => ( ! [A5: complex,A7: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ A7 )
% 0.32/0.64               => ( ( member_complex @ A5 @ A7 )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A5 @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.64           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_empty_induct
% 0.32/0.64  thf(fact_8182_finite__empty__induct,axiom,
% 0.32/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( P @ A2 )
% 0.32/0.64         => ( ! [A5: int,A7: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ A7 )
% 0.32/0.64               => ( ( member_int @ A5 @ A7 )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ) )
% 0.32/0.64           => ( P @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_empty_induct
% 0.32/0.64  thf(fact_8183_finite__empty__induct,axiom,
% 0.32/0.64      ! [A2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( P @ A2 )
% 0.32/0.64         => ( ! [A5: real,A7: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ A7 )
% 0.32/0.64               => ( ( member_real @ A5 @ A7 )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A5 @ bot_bot_set_real ) ) ) ) ) )
% 0.32/0.64           => ( P @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_empty_induct
% 0.32/0.64  thf(fact_8184_finite__empty__induct,axiom,
% 0.32/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ A2 )
% 0.32/0.64       => ( ( P @ A2 )
% 0.32/0.64         => ( ! [A5: nat,A7: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ A7 )
% 0.32/0.64               => ( ( member_nat @ A5 @ A7 )
% 0.32/0.64                 => ( ( P @ A7 )
% 0.32/0.64                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ) )
% 0.32/0.64           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_empty_induct
% 0.32/0.64  thf(fact_8185_Diff__single__insert,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,B3: set_real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_single_insert
% 0.32/0.64  thf(fact_8186_Diff__single__insert,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat,B3: set_nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_single_insert
% 0.32/0.64  thf(fact_8187_Diff__single__insert,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,B3: set_int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 )
% 0.32/0.64       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Diff_single_insert
% 0.32/0.64  thf(fact_8188_subset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,B3: set_complex] :
% 0.32/0.64        ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 0.32/0.64          & ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64           => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert_iff
% 0.32/0.64  thf(fact_8189_subset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 0.32/0.64        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_set_nat @ X @ A2 )
% 0.32/0.64           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 0.32/0.64          & ( ~ ( member_set_nat @ X @ A2 )
% 0.32/0.64           => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert_iff
% 0.32/0.64  thf(fact_8190_subset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,B3: set_real] :
% 0.32/0.64        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_real @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 0.32/0.64          & ( ~ ( member_real @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert_iff
% 0.32/0.64  thf(fact_8191_subset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat,B3: set_nat] :
% 0.32/0.64        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_nat @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 0.32/0.64          & ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert_iff
% 0.32/0.64  thf(fact_8192_subset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,B3: set_int] :
% 0.32/0.64        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_int @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 0.32/0.64          & ( ~ ( member_int @ X @ A2 )
% 0.32/0.64           => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % subset_insert_iff
% 0.32/0.64  thf(fact_8193_real__of__nat__div4,axiom,
% 0.32/0.64      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_div4
% 0.32/0.64  thf(fact_8194_sum__diff1__nat,axiom,
% 0.32/0.64      ! [A: complex,A2: set_complex,F: complex > nat] :
% 0.32/0.64        ( ( ( member_complex @ A @ A2 )
% 0.32/0.64         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.64            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.64        & ( ~ ( member_complex @ A @ A2 )
% 0.32/0.64         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.64            = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_diff1_nat
% 0.32/0.64  thf(fact_8195_sum__diff1__nat,axiom,
% 0.32/0.64      ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 0.32/0.64        ( ( ( member_set_nat @ A @ A2 )
% 0.32/0.64         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.32/0.64            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.64        & ( ~ ( member_set_nat @ A @ A2 )
% 0.32/0.64         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.32/0.64            = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_diff1_nat
% 0.32/0.64  thf(fact_8196_sum__diff1__nat,axiom,
% 0.32/0.64      ! [A: int,A2: set_int,F: int > nat] :
% 0.32/0.64        ( ( ( member_int @ A @ A2 )
% 0.32/0.64         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.64            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.64        & ( ~ ( member_int @ A @ A2 )
% 0.32/0.64         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.64            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_diff1_nat
% 0.32/0.64  thf(fact_8197_sum__diff1__nat,axiom,
% 0.32/0.64      ! [A: real,A2: set_real,F: real > nat] :
% 0.32/0.64        ( ( ( member_real @ A @ A2 )
% 0.32/0.64         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.64            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.64        & ( ~ ( member_real @ A @ A2 )
% 0.32/0.64         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.64            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_diff1_nat
% 0.32/0.64  thf(fact_8198_sum__diff1__nat,axiom,
% 0.32/0.64      ! [A: nat,A2: set_nat,F: nat > nat] :
% 0.32/0.64        ( ( ( member_nat @ A @ A2 )
% 0.32/0.64         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.64            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.64        & ( ~ ( member_nat @ A @ A2 )
% 0.32/0.64         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.64            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum_diff1_nat
% 0.32/0.64  thf(fact_8199_int__ops_I4_J,axiom,
% 0.32/0.64      ! [A: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(4)
% 0.32/0.64  thf(fact_8200_int__Suc,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.32/0.64        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_Suc
% 0.32/0.64  thf(fact_8201_zless__iff__Suc__zadd,axiom,
% 0.32/0.64      ( ord_less_int
% 0.32/0.64      = ( ^ [W3: int,Z3: int] :
% 0.32/0.64          ? [N2: nat] :
% 0.32/0.64            ( Z3
% 0.32/0.64            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zless_iff_Suc_zadd
% 0.32/0.64  thf(fact_8202_int__zle__neg,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.64        = ( ( N = zero_zero_nat )
% 0.32/0.64          & ( M = zero_zero_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_zle_neg
% 0.32/0.64  thf(fact_8203_real__of__nat__div,axiom,
% 0.32/0.64      ! [D: nat,N: nat] :
% 0.32/0.64        ( ( dvd_dvd_nat @ D @ N )
% 0.32/0.64       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 0.32/0.64          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_div
% 0.32/0.64  thf(fact_8204_negative__zle__0,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % negative_zle_0
% 0.32/0.64  thf(fact_8205_nonpos__int__cases,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ( K
% 0.32/0.64             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nonpos_int_cases
% 0.32/0.64  thf(fact_8206_mult__inc,axiom,
% 0.32/0.64      ! [X: num,Y: num] :
% 0.32/0.64        ( ( times_times_num @ X @ ( inc @ Y ) )
% 0.32/0.64        = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mult_inc
% 0.32/0.64  thf(fact_8207_set__update__subset__insert,axiom,
% 0.32/0.64      ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_update_subset_insert
% 0.32/0.64  thf(fact_8208_set__update__subset__insert,axiom,
% 0.32/0.64      ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_update_subset_insert
% 0.32/0.64  thf(fact_8209_set__update__subset__insert,axiom,
% 0.32/0.64      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_update_subset_insert
% 0.32/0.64  thf(fact_8210_set__update__subset__insert,axiom,
% 0.32/0.64      ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_update_subset_insert
% 0.32/0.64  thf(fact_8211_Compl__insert,axiom,
% 0.32/0.64      ! [X: int,A2: set_int] :
% 0.32/0.64        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 0.32/0.64        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Compl_insert
% 0.32/0.64  thf(fact_8212_Compl__insert,axiom,
% 0.32/0.64      ! [X: real,A2: set_real] :
% 0.32/0.64        ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 0.32/0.64        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Compl_insert
% 0.32/0.64  thf(fact_8213_Compl__insert,axiom,
% 0.32/0.64      ! [X: nat,A2: set_nat] :
% 0.32/0.64        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 0.32/0.64        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % Compl_insert
% 0.32/0.64  thf(fact_8214_less__log2__of__power,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.32/0.64       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % less_log2_of_power
% 0.32/0.64  thf(fact_8215_le__log2__of__power,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.32/0.64       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % le_log2_of_power
% 0.32/0.64  thf(fact_8216_log2__of__power__less,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.64         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log2_of_power_less
% 0.32/0.64  thf(fact_8217_log__base__change,axiom,
% 0.32/0.64      ! [A: real,B: real,X: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( A != one_one_real )
% 0.32/0.64         => ( ( log @ B @ X )
% 0.32/0.64            = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_base_change
% 0.32/0.64  thf(fact_8218_numeral__inc,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 0.32/0.64        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_inc
% 0.32/0.64  thf(fact_8219_numeral__inc,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( numeral_numeral_real @ ( inc @ X ) )
% 0.32/0.64        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_inc
% 0.32/0.64  thf(fact_8220_numeral__inc,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 0.32/0.64        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_inc
% 0.32/0.64  thf(fact_8221_numeral__inc,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 0.32/0.64        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_inc
% 0.32/0.64  thf(fact_8222_numeral__inc,axiom,
% 0.32/0.64      ! [X: num] :
% 0.32/0.64        ( ( numeral_numeral_int @ ( inc @ X ) )
% 0.32/0.64        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % numeral_inc
% 0.32/0.64  thf(fact_8223_mod__mult2__eq_H,axiom,
% 0.32/0.64      ! [A: code_integer,M: nat,N: nat] :
% 0.32/0.64        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.32/0.64        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mod_mult2_eq'
% 0.32/0.64  thf(fact_8224_mod__mult2__eq_H,axiom,
% 0.32/0.64      ! [A: nat,M: nat,N: nat] :
% 0.32/0.64        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.32/0.64        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mod_mult2_eq'
% 0.32/0.64  thf(fact_8225_mod__mult2__eq_H,axiom,
% 0.32/0.64      ! [A: int,M: nat,N: nat] :
% 0.32/0.64        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.64        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % mod_mult2_eq'
% 0.32/0.64  thf(fact_8226_field__char__0__class_Oof__nat__div,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.64        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % field_char_0_class.of_nat_div
% 0.32/0.64  thf(fact_8227_field__char__0__class_Oof__nat__div,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.64        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % field_char_0_class.of_nat_div
% 0.32/0.64  thf(fact_8228_field__char__0__class_Oof__nat__div,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 0.32/0.64        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % field_char_0_class.of_nat_div
% 0.32/0.64  thf(fact_8229_remove__induct,axiom,
% 0.32/0.64      ! [P: set_set_nat > $o,B3: set_set_nat] :
% 0.32/0.64        ( ( P @ bot_bot_set_set_nat )
% 0.32/0.64       => ( ( ~ ( finite1152437895449049373et_nat @ B3 )
% 0.32/0.64           => ( P @ B3 ) )
% 0.32/0.64         => ( ! [A7: set_set_nat] :
% 0.32/0.64                ( ( finite1152437895449049373et_nat @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_set_nat )
% 0.32/0.64                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: set_nat] :
% 0.32/0.64                          ( ( member_set_nat @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % remove_induct
% 0.32/0.64  thf(fact_8230_remove__induct,axiom,
% 0.32/0.64      ! [P: set_complex > $o,B3: set_complex] :
% 0.32/0.64        ( ( P @ bot_bot_set_complex )
% 0.32/0.64       => ( ( ~ ( finite3207457112153483333omplex @ B3 )
% 0.32/0.64           => ( P @ B3 ) )
% 0.32/0.64         => ( ! [A7: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_complex )
% 0.32/0.64                 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: complex] :
% 0.32/0.64                          ( ( member_complex @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % remove_induct
% 0.32/0.64  thf(fact_8231_remove__induct,axiom,
% 0.32/0.64      ! [P: set_real > $o,B3: set_real] :
% 0.32/0.64        ( ( P @ bot_bot_set_real )
% 0.32/0.64       => ( ( ~ ( finite_finite_real @ B3 )
% 0.32/0.64           => ( P @ B3 ) )
% 0.32/0.64         => ( ! [A7: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_real )
% 0.32/0.64                 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: real] :
% 0.32/0.64                          ( ( member_real @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % remove_induct
% 0.32/0.64  thf(fact_8232_remove__induct,axiom,
% 0.32/0.64      ! [P: set_nat > $o,B3: set_nat] :
% 0.32/0.64        ( ( P @ bot_bot_set_nat )
% 0.32/0.64       => ( ( ~ ( finite_finite_nat @ B3 )
% 0.32/0.64           => ( P @ B3 ) )
% 0.32/0.64         => ( ! [A7: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_nat )
% 0.32/0.64                 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: nat] :
% 0.32/0.64                          ( ( member_nat @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % remove_induct
% 0.32/0.64  thf(fact_8233_remove__induct,axiom,
% 0.32/0.64      ! [P: set_int > $o,B3: set_int] :
% 0.32/0.64        ( ( P @ bot_bot_set_int )
% 0.32/0.64       => ( ( ~ ( finite_finite_int @ B3 )
% 0.32/0.64           => ( P @ B3 ) )
% 0.32/0.64         => ( ! [A7: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_int )
% 0.32/0.64                 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: int] :
% 0.32/0.64                          ( ( member_int @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % remove_induct
% 0.32/0.64  thf(fact_8234_finite__remove__induct,axiom,
% 0.32/0.64      ! [B3: set_set_nat,P: set_set_nat > $o] :
% 0.32/0.64        ( ( finite1152437895449049373et_nat @ B3 )
% 0.32/0.64       => ( ( P @ bot_bot_set_set_nat )
% 0.32/0.64         => ( ! [A7: set_set_nat] :
% 0.32/0.64                ( ( finite1152437895449049373et_nat @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_set_nat )
% 0.32/0.64                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: set_nat] :
% 0.32/0.64                          ( ( member_set_nat @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_remove_induct
% 0.32/0.64  thf(fact_8235_finite__remove__induct,axiom,
% 0.32/0.64      ! [B3: set_complex,P: set_complex > $o] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ B3 )
% 0.32/0.64       => ( ( P @ bot_bot_set_complex )
% 0.32/0.64         => ( ! [A7: set_complex] :
% 0.32/0.64                ( ( finite3207457112153483333omplex @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_complex )
% 0.32/0.64                 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: complex] :
% 0.32/0.64                          ( ( member_complex @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_remove_induct
% 0.32/0.64  thf(fact_8236_finite__remove__induct,axiom,
% 0.32/0.64      ! [B3: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ B3 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [A7: set_real] :
% 0.32/0.64                ( ( finite_finite_real @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_real )
% 0.32/0.64                 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: real] :
% 0.32/0.64                          ( ( member_real @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_remove_induct
% 0.32/0.64  thf(fact_8237_finite__remove__induct,axiom,
% 0.32/0.64      ! [B3: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ B3 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [A7: set_nat] :
% 0.32/0.64                ( ( finite_finite_nat @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_nat )
% 0.32/0.64                 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: nat] :
% 0.32/0.64                          ( ( member_nat @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_remove_induct
% 0.32/0.64  thf(fact_8238_finite__remove__induct,axiom,
% 0.32/0.64      ! [B3: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ B3 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [A7: set_int] :
% 0.32/0.64                ( ( finite_finite_int @ A7 )
% 0.32/0.64               => ( ( A7 != bot_bot_set_int )
% 0.32/0.64                 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 0.32/0.64                   => ( ! [X4: int] :
% 0.32/0.64                          ( ( member_int @ X4 @ A7 )
% 0.32/0.64                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 0.32/0.64                     => ( P @ A7 ) ) ) ) )
% 0.32/0.64           => ( P @ B3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_remove_induct
% 0.32/0.64  thf(fact_8239_zero__less__imp__eq__int,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.64       => ? [N3: nat] :
% 0.32/0.64            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.64            & ( K
% 0.32/0.64              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zero_less_imp_eq_int
% 0.32/0.64  thf(fact_8240_pos__int__cases,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ( ( K
% 0.32/0.64                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.32/0.64             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % pos_int_cases
% 0.32/0.64  thf(fact_8241_int__cases3,axiom,
% 0.32/0.64      ! [K: int] :
% 0.32/0.64        ( ( K != zero_zero_int )
% 0.32/0.64       => ( ! [N3: nat] :
% 0.32/0.64              ( ( K
% 0.32/0.64                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.32/0.64             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.32/0.64         => ~ ! [N3: nat] :
% 0.32/0.64                ( ( K
% 0.32/0.64                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.32/0.64               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_cases3
% 0.32/0.64  thf(fact_8242_nat__less__real__le,axiom,
% 0.32/0.64      ( ord_less_nat
% 0.32/0.64      = ( ^ [N2: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_less_real_le
% 0.32/0.64  thf(fact_8243_nat__le__real__less,axiom,
% 0.32/0.64      ( ord_less_eq_nat
% 0.32/0.64      = ( ^ [N2: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_le_real_less
% 0.32/0.64  thf(fact_8244_zmult__zless__mono2__lemma,axiom,
% 0.32/0.64      ! [I: int,J: int,K: nat] :
% 0.32/0.64        ( ( ord_less_int @ I @ J )
% 0.32/0.64       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.64         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % zmult_zless_mono2_lemma
% 0.32/0.64  thf(fact_8245_not__zle__0__negative,axiom,
% 0.32/0.64      ! [N: nat] :
% 0.32/0.64        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % not_zle_0_negative
% 0.32/0.64  thf(fact_8246_negative__zless__0,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.32/0.64  
% 0.32/0.64  % negative_zless_0
% 0.32/0.64  thf(fact_8247_negD,axiom,
% 0.32/0.64      ! [X: int] :
% 0.32/0.64        ( ( ord_less_int @ X @ zero_zero_int )
% 0.32/0.64       => ? [N3: nat] :
% 0.32/0.64            ( X
% 0.32/0.64            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % negD
% 0.32/0.64  thf(fact_8248_finite__induct__select,axiom,
% 0.32/0.64      ! [S2: set_complex,P: set_complex > $o] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_complex )
% 0.32/0.64         => ( ! [T5: set_complex] :
% 0.32/0.64                ( ( ord_less_set_complex @ T5 @ S2 )
% 0.32/0.64               => ( ( P @ T5 )
% 0.32/0.64                 => ? [X4: complex] :
% 0.32/0.64                      ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ S2 @ T5 ) )
% 0.32/0.64                      & ( P @ ( insert_complex @ X4 @ T5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_induct_select
% 0.32/0.64  thf(fact_8249_finite__induct__select,axiom,
% 0.32/0.64      ! [S2: set_int,P: set_int > $o] :
% 0.32/0.64        ( ( finite_finite_int @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_int )
% 0.32/0.64         => ( ! [T5: set_int] :
% 0.32/0.64                ( ( ord_less_set_int @ T5 @ S2 )
% 0.32/0.64               => ( ( P @ T5 )
% 0.32/0.64                 => ? [X4: int] :
% 0.32/0.64                      ( ( member_int @ X4 @ ( minus_minus_set_int @ S2 @ T5 ) )
% 0.32/0.64                      & ( P @ ( insert_int @ X4 @ T5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_induct_select
% 0.32/0.64  thf(fact_8250_finite__induct__select,axiom,
% 0.32/0.64      ! [S2: set_real,P: set_real > $o] :
% 0.32/0.64        ( ( finite_finite_real @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_real )
% 0.32/0.64         => ( ! [T5: set_real] :
% 0.32/0.64                ( ( ord_less_set_real @ T5 @ S2 )
% 0.32/0.64               => ( ( P @ T5 )
% 0.32/0.64                 => ? [X4: real] :
% 0.32/0.64                      ( ( member_real @ X4 @ ( minus_minus_set_real @ S2 @ T5 ) )
% 0.32/0.64                      & ( P @ ( insert_real @ X4 @ T5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_induct_select
% 0.32/0.64  thf(fact_8251_finite__induct__select,axiom,
% 0.32/0.64      ! [S2: set_nat,P: set_nat > $o] :
% 0.32/0.64        ( ( finite_finite_nat @ S2 )
% 0.32/0.64       => ( ( P @ bot_bot_set_nat )
% 0.32/0.64         => ( ! [T5: set_nat] :
% 0.32/0.64                ( ( ord_less_set_nat @ T5 @ S2 )
% 0.32/0.64               => ( ( P @ T5 )
% 0.32/0.64                 => ? [X4: nat] :
% 0.32/0.64                      ( ( member_nat @ X4 @ ( minus_minus_set_nat @ S2 @ T5 ) )
% 0.32/0.64                      & ( P @ ( insert_nat @ X4 @ T5 ) ) ) ) )
% 0.32/0.64           => ( P @ S2 ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % finite_induct_select
% 0.32/0.64  thf(fact_8252_psubset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,B3: set_complex] :
% 0.32/0.64        ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_complex @ X @ B3 )
% 0.32/0.64           => ( ord_less_set_complex @ A2 @ B3 ) )
% 0.32/0.64          & ( ~ ( member_complex @ X @ B3 )
% 0.32/0.64           => ( ( ( member_complex @ X @ A2 )
% 0.32/0.64               => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 0.32/0.64              & ( ~ ( member_complex @ X @ A2 )
% 0.32/0.64               => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % psubset_insert_iff
% 0.32/0.64  thf(fact_8253_psubset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 0.32/0.64        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_set_nat @ X @ B3 )
% 0.32/0.64           => ( ord_less_set_set_nat @ A2 @ B3 ) )
% 0.32/0.64          & ( ~ ( member_set_nat @ X @ B3 )
% 0.32/0.64           => ( ( ( member_set_nat @ X @ A2 )
% 0.32/0.64               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 0.32/0.64              & ( ~ ( member_set_nat @ X @ A2 )
% 0.32/0.64               => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % psubset_insert_iff
% 0.32/0.64  thf(fact_8254_psubset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,B3: set_real] :
% 0.32/0.64        ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_real @ X @ B3 )
% 0.32/0.64           => ( ord_less_set_real @ A2 @ B3 ) )
% 0.32/0.64          & ( ~ ( member_real @ X @ B3 )
% 0.32/0.64           => ( ( ( member_real @ X @ A2 )
% 0.32/0.64               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 0.32/0.64              & ( ~ ( member_real @ X @ A2 )
% 0.32/0.64               => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % psubset_insert_iff
% 0.32/0.64  thf(fact_8255_psubset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_nat,X: nat,B3: set_nat] :
% 0.32/0.64        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_nat @ X @ B3 )
% 0.32/0.64           => ( ord_less_set_nat @ A2 @ B3 ) )
% 0.32/0.64          & ( ~ ( member_nat @ X @ B3 )
% 0.32/0.64           => ( ( ( member_nat @ X @ A2 )
% 0.32/0.64               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 0.32/0.64              & ( ~ ( member_nat @ X @ A2 )
% 0.32/0.64               => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % psubset_insert_iff
% 0.32/0.64  thf(fact_8256_psubset__insert__iff,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,B3: set_int] :
% 0.32/0.64        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 0.32/0.64        = ( ( ( member_int @ X @ B3 )
% 0.32/0.64           => ( ord_less_set_int @ A2 @ B3 ) )
% 0.32/0.64          & ( ~ ( member_int @ X @ B3 )
% 0.32/0.64           => ( ( ( member_int @ X @ A2 )
% 0.32/0.64               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 0.32/0.64              & ( ~ ( member_int @ X @ A2 )
% 0.32/0.64               => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % psubset_insert_iff
% 0.32/0.64  thf(fact_8257_set__replicate__Suc,axiom,
% 0.32/0.64      ! [N: nat,X: vEBT_VEBT] :
% 0.32/0.64        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 0.32/0.64        = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_Suc
% 0.32/0.64  thf(fact_8258_set__replicate__Suc,axiom,
% 0.32/0.64      ! [N: nat,X: nat] :
% 0.32/0.64        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 0.32/0.64        = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_Suc
% 0.32/0.64  thf(fact_8259_set__replicate__Suc,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 0.32/0.64        = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_Suc
% 0.32/0.64  thf(fact_8260_set__replicate__Suc,axiom,
% 0.32/0.64      ! [N: nat,X: real] :
% 0.32/0.64        ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 0.32/0.64        = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_Suc
% 0.32/0.64  thf(fact_8261_log2__of__power__le,axiom,
% 0.32/0.64      ! [M: nat,N: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.64       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.64         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log2_of_power_le
% 0.32/0.64  thf(fact_8262_set__replicate__conv__if,axiom,
% 0.32/0.64      ! [N: nat,X: vEBT_VEBT] :
% 0.32/0.64        ( ( ( N = zero_zero_nat )
% 0.32/0.64         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.32/0.64            = bot_bo8194388402131092736T_VEBT ) )
% 0.32/0.64        & ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.32/0.64            = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_conv_if
% 0.32/0.64  thf(fact_8263_set__replicate__conv__if,axiom,
% 0.32/0.64      ! [N: nat,X: nat] :
% 0.32/0.64        ( ( ( N = zero_zero_nat )
% 0.32/0.64         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.32/0.64            = bot_bot_set_nat ) )
% 0.32/0.64        & ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.32/0.64            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_conv_if
% 0.32/0.64  thf(fact_8264_set__replicate__conv__if,axiom,
% 0.32/0.64      ! [N: nat,X: int] :
% 0.32/0.64        ( ( ( N = zero_zero_nat )
% 0.32/0.64         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.32/0.64            = bot_bot_set_int ) )
% 0.32/0.64        & ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.32/0.64            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_conv_if
% 0.32/0.64  thf(fact_8265_set__replicate__conv__if,axiom,
% 0.32/0.64      ! [N: nat,X: real] :
% 0.32/0.64        ( ( ( N = zero_zero_nat )
% 0.32/0.64         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.32/0.64            = bot_bot_set_real ) )
% 0.32/0.64        & ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.32/0.64            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % set_replicate_conv_if
% 0.32/0.64  thf(fact_8266_int__ops_I6_J,axiom,
% 0.32/0.64      ! [A: nat,B: nat] :
% 0.32/0.64        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.32/0.64         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.64            = zero_zero_int ) )
% 0.32/0.64        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.32/0.64         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.64            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % int_ops(6)
% 0.32/0.64  thf(fact_8267_real__of__nat__div__aux,axiom,
% 0.32/0.64      ! [X: nat,D: nat] :
% 0.32/0.64        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 0.32/0.64        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_of_nat_div_aux
% 0.32/0.64  thf(fact_8268_atLeastAtMostPlus1__int__conv,axiom,
% 0.32/0.64      ! [M: int,N: int] :
% 0.32/0.64        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.32/0.64       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.32/0.64          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % atLeastAtMostPlus1_int_conv
% 0.32/0.64  thf(fact_8269_simp__from__to,axiom,
% 0.32/0.64      ( set_or1266510415728281911st_int
% 0.32/0.64      = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % simp_from_to
% 0.32/0.64  thf(fact_8270_nat__approx__posE,axiom,
% 0.32/0.64      ! [E: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ E )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_approx_posE
% 0.32/0.64  thf(fact_8271_nat__approx__posE,axiom,
% 0.32/0.64      ! [E: rat] :
% 0.32/0.64        ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.32/0.64       => ~ ! [N3: nat] :
% 0.32/0.64              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.32/0.64  
% 0.32/0.64  % nat_approx_posE
% 0.32/0.64  thf(fact_8272_log__mult,axiom,
% 0.32/0.64      ! [A: real,X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( A != one_one_real )
% 0.32/0.64         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.64             => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 0.32/0.64                = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_mult
% 0.32/0.64  thf(fact_8273_of__nat__less__two__power,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_two_power
% 0.32/0.64  thf(fact_8274_of__nat__less__two__power,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_two_power
% 0.32/0.64  thf(fact_8275_of__nat__less__two__power,axiom,
% 0.32/0.64      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.64  
% 0.32/0.64  % of_nat_less_two_power
% 0.32/0.64  thf(fact_8276_log__divide,axiom,
% 0.32/0.64      ! [A: real,X: real,Y: real] :
% 0.32/0.64        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.64       => ( ( A != one_one_real )
% 0.32/0.64         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.64           => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.64             => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 0.32/0.64                = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % log_divide
% 0.32/0.64  thf(fact_8277_inverse__of__nat__le,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inverse_of_nat_le
% 0.32/0.64  thf(fact_8278_inverse__of__nat__le,axiom,
% 0.32/0.64      ! [N: nat,M: nat] :
% 0.32/0.64        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.64       => ( ( N != zero_zero_nat )
% 0.32/0.64         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % inverse_of_nat_le
% 0.32/0.64  thf(fact_8279_exp__divide__power__eq,axiom,
% 0.32/0.64      ! [N: nat,X: complex] :
% 0.32/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.64       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 0.32/0.64          = ( exp_complex @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_divide_power_eq
% 0.32/0.64  thf(fact_8280_exp__divide__power__eq,axiom,
% 0.32/0.64      ! [N: nat,X: real] :
% 0.32/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.64       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 0.32/0.64          = ( exp_real @ X ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % exp_divide_power_eq
% 0.32/0.64  thf(fact_8281_real__archimedian__rdiv__eq__0,axiom,
% 0.32/0.64      ! [X: real,C: real] :
% 0.32/0.64        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.64       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.32/0.64         => ( ! [M4: nat] :
% 0.32/0.64                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 0.32/0.64               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 0.32/0.64           => ( X = zero_zero_real ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % real_archimedian_rdiv_eq_0
% 0.32/0.64  thf(fact_8282_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > real] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8283_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > rat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8284_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > nat] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8285_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_complex,X: complex,G: complex > int] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( member_complex @ X @ A2 )
% 0.32/0.64         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 0.32/0.64            = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8286_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > real] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8287_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > rat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8288_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_int,X: int,G: int > nat] :
% 0.32/0.64        ( ( finite_finite_int @ A2 )
% 0.32/0.64       => ( ( member_int @ X @ A2 )
% 0.32/0.64         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8289_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > real] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 0.32/0.64            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8290_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > rat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8291_sum_Oremove,axiom,
% 0.32/0.64      ! [A2: set_real,X: real,G: real > nat] :
% 0.32/0.64        ( ( finite_finite_real @ A2 )
% 0.32/0.64       => ( ( member_real @ X @ A2 )
% 0.32/0.64         => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 0.32/0.64            = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.remove
% 0.32/0.64  thf(fact_8292_sum_Oinsert__remove,axiom,
% 0.32/0.64      ! [A2: set_complex,G: complex > real,X: complex] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64          = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_remove
% 0.32/0.64  thf(fact_8293_sum_Oinsert__remove,axiom,
% 0.32/0.64      ! [A2: set_complex,G: complex > rat,X: complex] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64          = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.32/0.64  
% 0.32/0.64  % sum.insert_remove
% 0.32/0.64  thf(fact_8294_sum_Oinsert__remove,axiom,
% 0.32/0.64      ! [A2: set_complex,G: complex > nat,X: complex] :
% 0.32/0.64        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.64       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.64          = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8295_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_complex,G: complex > int,X: complex] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8296_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_int,G: int > real,X: int] :
% 0.32/0.65        ( ( finite_finite_int @ A2 )
% 0.32/0.65       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8297_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_int,G: int > rat,X: int] :
% 0.32/0.65        ( ( finite_finite_int @ A2 )
% 0.32/0.65       => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8298_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_int,G: int > nat,X: int] :
% 0.32/0.65        ( ( finite_finite_int @ A2 )
% 0.32/0.65       => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8299_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_real,G: real > real,X: real] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8300_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_real,G: real > rat,X: real] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8301_sum_Oinsert__remove,axiom,
% 0.32/0.65      ! [A2: set_real,G: real > nat,X: real] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 0.32/0.65          = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.insert_remove
% 0.32/0.65  thf(fact_8302_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_complex,A: complex,F: complex > real] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8303_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_int,A: int,F: int > real] :
% 0.32/0.65        ( ( finite_finite_int @ A2 )
% 0.32/0.65       => ( ( ( member_int @ A @ A2 )
% 0.32/0.65           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.65              = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_int @ A @ A2 )
% 0.32/0.65           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.65              = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8304_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_real,A: real,F: real > real] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8305_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_complex,A: complex,F: complex > rat] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8306_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_int,A: int,F: int > rat] :
% 0.32/0.65        ( ( finite_finite_int @ A2 )
% 0.32/0.65       => ( ( ( member_int @ A @ A2 )
% 0.32/0.65           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.65              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_int @ A @ A2 )
% 0.32/0.65           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.32/0.65              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8307_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_real,A: real,F: real > rat] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8308_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_complex,A: complex,F: complex > int] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ A2 )
% 0.32/0.65           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.32/0.65              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8309_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_real,A: real,F: real > int] :
% 0.32/0.65        ( ( finite_finite_real @ A2 )
% 0.32/0.65       => ( ( ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ A2 )
% 0.32/0.65           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.32/0.65              = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8310_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_nat,A: nat,F: nat > rat] :
% 0.32/0.65        ( ( finite_finite_nat @ A2 )
% 0.32/0.65       => ( ( ( member_nat @ A @ A2 )
% 0.32/0.65           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.65              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_nat @ A @ A2 )
% 0.32/0.65           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.65              = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8311_sum__diff1,axiom,
% 0.32/0.65      ! [A2: set_nat,A: nat,F: nat > int] :
% 0.32/0.65        ( ( finite_finite_nat @ A2 )
% 0.32/0.65       => ( ( ( member_nat @ A @ A2 )
% 0.32/0.65           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.65              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 0.32/0.65          & ( ~ ( member_nat @ A @ A2 )
% 0.32/0.65           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.32/0.65              = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff1
% 0.32/0.65  thf(fact_8312_neg__int__cases,axiom,
% 0.32/0.65      ! [K: int] :
% 0.32/0.65        ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.65       => ~ ! [N3: nat] :
% 0.32/0.65              ( ( K
% 0.32/0.65                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.32/0.65             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % neg_int_cases
% 0.32/0.65  thf(fact_8313_zdiff__int__split,axiom,
% 0.32/0.65      ! [P: int > $o,X: nat,Y: nat] :
% 0.32/0.65        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 0.32/0.65        = ( ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.65           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.32/0.65          & ( ( ord_less_nat @ X @ Y )
% 0.32/0.65           => ( P @ zero_zero_int ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % zdiff_int_split
% 0.32/0.65  thf(fact_8314_real__of__nat__div2,axiom,
% 0.32/0.65      ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_of_nat_div2
% 0.32/0.65  thf(fact_8315_real__of__nat__div3,axiom,
% 0.32/0.65      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % real_of_nat_div3
% 0.32/0.65  thf(fact_8316_ln__realpow,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 0.32/0.65          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_realpow
% 0.32/0.65  thf(fact_8317_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5808333547571424918x_real
% 0.32/0.65                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5808333547571424918x_real
% 0.32/0.65                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8318_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5058264527183730370ex_rat
% 0.32/0.65                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5058264527183730370ex_rat
% 0.32/0.65                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8319_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5693394587270226106ex_nat
% 0.32/0.65                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5693394587270226106ex_nat
% 0.32/0.65                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8320_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 0.32/0.65        ( ( finite3207457112153483333omplex @ S2 )
% 0.32/0.65       => ( ( ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5690904116761175830ex_int
% 0.32/0.65                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_complex @ A @ S2 )
% 0.32/0.65           => ( ( groups5690904116761175830ex_int
% 0.32/0.65                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8321_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 0.32/0.65        ( ( finite_finite_int @ S2 )
% 0.32/0.65       => ( ( ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups8778361861064173332t_real
% 0.32/0.65                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups8778361861064173332t_real
% 0.32/0.65                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8322_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 0.32/0.65        ( ( finite_finite_int @ S2 )
% 0.32/0.65       => ( ( ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups3906332499630173760nt_rat
% 0.32/0.65                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups3906332499630173760nt_rat
% 0.32/0.65                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8323_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_int,A: int,B: int > nat,C: int > nat] :
% 0.32/0.65        ( ( finite_finite_int @ S2 )
% 0.32/0.65       => ( ( ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups4541462559716669496nt_nat
% 0.32/0.65                @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_int @ A @ S2 )
% 0.32/0.65           => ( ( groups4541462559716669496nt_nat
% 0.32/0.65                @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8324_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 0.32/0.65        ( ( finite_finite_real @ S2 )
% 0.32/0.65       => ( ( ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups8097168146408367636l_real
% 0.32/0.65                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups8097168146408367636l_real
% 0.32/0.65                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8325_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 0.32/0.65        ( ( finite_finite_real @ S2 )
% 0.32/0.65       => ( ( ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups1300246762558778688al_rat
% 0.32/0.65                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups1300246762558778688al_rat
% 0.32/0.65                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8326_sum_Odelta__remove,axiom,
% 0.32/0.65      ! [S2: set_real,A: real,B: real > nat,C: real > nat] :
% 0.32/0.65        ( ( finite_finite_real @ S2 )
% 0.32/0.65       => ( ( ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups1935376822645274424al_nat
% 0.32/0.65                @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( member_real @ A @ S2 )
% 0.32/0.65           => ( ( groups1935376822645274424al_nat
% 0.32/0.65                @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 0.32/0.65                @ S2 )
% 0.32/0.65              = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.delta_remove
% 0.32/0.65  thf(fact_8327_log__eq__div__ln__mult__log,axiom,
% 0.32/0.65      ! [A: real,B: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( A != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.65           => ( ( B != one_one_real )
% 0.32/0.65             => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65               => ( ( log @ A @ X )
% 0.32/0.65                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_eq_div_ln_mult_log
% 0.32/0.65  thf(fact_8328_member__le__sum,axiom,
% 0.32/0.65      ! [I: complex,A2: set_complex,F: complex > real] :
% 0.32/0.65        ( ( member_complex @ I @ A2 )
% 0.32/0.65       => ( ! [X6: complex] :
% 0.32/0.65              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.32/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8329_member__le__sum,axiom,
% 0.32/0.65      ! [I: int,A2: set_int,F: int > real] :
% 0.32/0.65        ( ( member_int @ I @ A2 )
% 0.32/0.65       => ( ! [X6: int] :
% 0.32/0.65              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.32/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_int @ A2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8330_member__le__sum,axiom,
% 0.32/0.65      ! [I: real,A2: set_real,F: real > real] :
% 0.32/0.65        ( ( member_real @ I @ A2 )
% 0.32/0.65       => ( ! [X6: real] :
% 0.32/0.65              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.32/0.65             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_real @ A2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8331_member__le__sum,axiom,
% 0.32/0.65      ! [I: complex,A2: set_complex,F: complex > rat] :
% 0.32/0.65        ( ( member_complex @ I @ A2 )
% 0.32/0.65       => ( ! [X6: complex] :
% 0.32/0.65              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.32/0.65             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8332_member__le__sum,axiom,
% 0.32/0.65      ! [I: int,A2: set_int,F: int > rat] :
% 0.32/0.65        ( ( member_int @ I @ A2 )
% 0.32/0.65       => ( ! [X6: int] :
% 0.32/0.65              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.32/0.65             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_int @ A2 )
% 0.32/0.65           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8333_member__le__sum,axiom,
% 0.32/0.65      ! [I: real,A2: set_real,F: real > rat] :
% 0.32/0.65        ( ( member_real @ I @ A2 )
% 0.32/0.65       => ( ! [X6: real] :
% 0.32/0.65              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.32/0.65             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_real @ A2 )
% 0.32/0.65           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8334_member__le__sum,axiom,
% 0.32/0.65      ! [I: nat,A2: set_nat,F: nat > rat] :
% 0.32/0.65        ( ( member_nat @ I @ A2 )
% 0.32/0.65       => ( ! [X6: nat] :
% 0.32/0.65              ( ( member_nat @ X6 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.32/0.65             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_nat @ A2 )
% 0.32/0.65           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8335_member__le__sum,axiom,
% 0.32/0.65      ! [I: complex,A2: set_complex,F: complex > nat] :
% 0.32/0.65        ( ( member_complex @ I @ A2 )
% 0.32/0.65       => ( ! [X6: complex] :
% 0.32/0.65              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.32/0.65             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite3207457112153483333omplex @ A2 )
% 0.32/0.65           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8336_member__le__sum,axiom,
% 0.32/0.65      ! [I: int,A2: set_int,F: int > nat] :
% 0.32/0.65        ( ( member_int @ I @ A2 )
% 0.32/0.65       => ( ! [X6: int] :
% 0.32/0.65              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.32/0.65             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_int @ A2 )
% 0.32/0.65           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8337_member__le__sum,axiom,
% 0.32/0.65      ! [I: real,A2: set_real,F: real > nat] :
% 0.32/0.65        ( ( member_real @ I @ A2 )
% 0.32/0.65       => ( ! [X6: real] :
% 0.32/0.65              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.32/0.65             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 0.32/0.65         => ( ( finite_finite_real @ A2 )
% 0.32/0.65           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % member_le_sum
% 0.32/0.65  thf(fact_8338_linear__plus__1__le__power,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % linear_plus_1_le_power
% 0.32/0.65  thf(fact_8339_Bernoulli__inequality,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Bernoulli_inequality
% 0.32/0.65  thf(fact_8340_and__nat__unfold,axiom,
% 0.32/0.65      ( bit_se727722235901077358nd_nat
% 0.32/0.65      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.65            ( if_nat
% 0.32/0.65            @ ( ( M3 = zero_zero_nat )
% 0.32/0.65              | ( N2 = zero_zero_nat ) )
% 0.32/0.65            @ zero_zero_nat
% 0.32/0.65            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % and_nat_unfold
% 0.32/0.65  thf(fact_8341_and__nat__rec,axiom,
% 0.32/0.65      ( bit_se727722235901077358nd_nat
% 0.32/0.65      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.65            ( plus_plus_nat
% 0.32/0.65            @ ( zero_n2687167440665602831ol_nat
% 0.32/0.65              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.32/0.65                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.65            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % and_nat_rec
% 0.32/0.65  thf(fact_8342_double__gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum
% 0.32/0.65  thf(fact_8343_double__gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum
% 0.32/0.65  thf(fact_8344_double__gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum
% 0.32/0.65  thf(fact_8345_double__gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum
% 0.32/0.65  thf(fact_8346_double__gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum
% 0.32/0.65  thf(fact_8347_double__arith__series,axiom,
% 0.32/0.65      ! [A: complex,D: complex,N: nat] :
% 0.32/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.32/0.65          @ ( groups2073611262835488442omplex
% 0.32/0.65            @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 0.32/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_arith_series
% 0.32/0.65  thf(fact_8348_double__arith__series,axiom,
% 0.32/0.65      ! [A: rat,D: rat,N: nat] :
% 0.32/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.32/0.65          @ ( groups2906978787729119204at_rat
% 0.32/0.65            @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 0.32/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_arith_series
% 0.32/0.65  thf(fact_8349_double__arith__series,axiom,
% 0.32/0.65      ! [A: int,D: int,N: nat] :
% 0.32/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.32/0.65          @ ( groups3539618377306564664at_int
% 0.32/0.65            @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 0.32/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_arith_series
% 0.32/0.65  thf(fact_8350_double__arith__series,axiom,
% 0.32/0.65      ! [A: nat,D: nat,N: nat] :
% 0.32/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.32/0.65          @ ( groups3542108847815614940at_nat
% 0.32/0.65            @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 0.32/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_arith_series
% 0.32/0.65  thf(fact_8351_double__arith__series,axiom,
% 0.32/0.65      ! [A: real,D: real,N: nat] :
% 0.32/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 0.32/0.65            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.65        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_arith_series
% 0.32/0.65  thf(fact_8352_gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.65        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % gauss_sum
% 0.32/0.65  thf(fact_8353_gauss__sum,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % gauss_sum
% 0.32/0.65  thf(fact_8354_arith__series,axiom,
% 0.32/0.65      ! [A: int,D: int,N: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 0.32/0.65          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.65        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arith_series
% 0.32/0.65  thf(fact_8355_arith__series,axiom,
% 0.32/0.65      ! [A: nat,D: nat,N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat
% 0.32/0.65          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 0.32/0.65          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.32/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arith_series
% 0.32/0.65  thf(fact_8356_double__gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.32/0.65        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8357_double__gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.32/0.65        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8358_double__gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.32/0.65        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8359_double__gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.32/0.65        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8360_double__gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.32/0.65        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % double_gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8361_Bernoulli__inequality__even,axiom,
% 0.32/0.65      ! [N: nat,X: real] :
% 0.32/0.65        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.65       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Bernoulli_inequality_even
% 0.32/0.65  thf(fact_8362_sum__gp__offset,axiom,
% 0.32/0.65      ! [X: complex,M: nat,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_complex )
% 0.32/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 0.32/0.65        & ( ( X != one_one_complex )
% 0.32/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_offset
% 0.32/0.65  thf(fact_8363_sum__gp__offset,axiom,
% 0.32/0.65      ! [X: rat,M: nat,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_rat )
% 0.32/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 0.32/0.65        & ( ( X != one_one_rat )
% 0.32/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_offset
% 0.32/0.65  thf(fact_8364_sum__gp__offset,axiom,
% 0.32/0.65      ! [X: real,M: nat,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_real )
% 0.32/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 0.32/0.65        & ( ( X != one_one_real )
% 0.32/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.32/0.65            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_offset
% 0.32/0.65  thf(fact_8365_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.32/0.65      ! [N: nat,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_ge_one_plus_x_over_n_power_n
% 0.32/0.65  thf(fact_8366_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_ge_one_minus_x_over_n_power_n
% 0.32/0.65  thf(fact_8367_log__base__10__eq2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_base_10_eq2
% 0.32/0.65  thf(fact_8368_gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.32/0.65        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8369_gauss__sum__from__Suc__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.32/0.65        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % gauss_sum_from_Suc_0
% 0.32/0.65  thf(fact_8370_of__nat__code__if,axiom,
% 0.32/0.65      ( semiri8010041392384452111omplex
% 0.32/0.65      = ( ^ [N2: nat] :
% 0.32/0.65            ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 0.32/0.65            @ ( produc1917071388513777916omplex
% 0.32/0.65              @ ^ [M3: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 0.32/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % of_nat_code_if
% 0.32/0.65  thf(fact_8371_of__nat__code__if,axiom,
% 0.32/0.65      ( semiri5074537144036343181t_real
% 0.32/0.65      = ( ^ [N2: nat] :
% 0.32/0.65            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 0.32/0.65            @ ( produc1703576794950452218t_real
% 0.32/0.65              @ ^ [M3: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 0.32/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % of_nat_code_if
% 0.32/0.65  thf(fact_8372_of__nat__code__if,axiom,
% 0.32/0.65      ( semiri681578069525770553at_rat
% 0.32/0.65      = ( ^ [N2: nat] :
% 0.32/0.65            ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 0.32/0.65            @ ( produc6207742614233964070at_rat
% 0.32/0.65              @ ^ [M3: nat,Q5: nat] : ( if_rat @ ( Q5 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 0.32/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % of_nat_code_if
% 0.32/0.65  thf(fact_8373_of__nat__code__if,axiom,
% 0.32/0.65      ( semiri1316708129612266289at_nat
% 0.32/0.65      = ( ^ [N2: nat] :
% 0.32/0.65            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 0.32/0.65            @ ( produc6842872674320459806at_nat
% 0.32/0.65              @ ^ [M3: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 0.32/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % of_nat_code_if
% 0.32/0.65  thf(fact_8374_of__nat__code__if,axiom,
% 0.32/0.65      ( semiri1314217659103216013at_int
% 0.32/0.65      = ( ^ [N2: nat] :
% 0.32/0.65            ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 0.32/0.65            @ ( produc6840382203811409530at_int
% 0.32/0.65              @ ^ [M3: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 0.32/0.65              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % of_nat_code_if
% 0.32/0.65  thf(fact_8375_monoseq__arctan__series,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( topolo6980174941875973593q_real
% 0.32/0.65          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % monoseq_arctan_series
% 0.32/0.65  thf(fact_8376_lemma__termdiff3,axiom,
% 0.32/0.65      ! [H2: real,Z: real,K5: real,N: nat] :
% 0.32/0.65        ( ( H2 != zero_zero_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff3
% 0.32/0.65  thf(fact_8377_lemma__termdiff3,axiom,
% 0.32/0.65      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 0.32/0.65        ( ( H2 != zero_zero_complex )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff3
% 0.32/0.65  thf(fact_8378_ln__series,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65         => ( ( ln_ln_real @ X )
% 0.32/0.65            = ( suminf_real
% 0.32/0.65              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_series
% 0.32/0.65  thf(fact_8379_lemma__termdiff2,axiom,
% 0.32/0.65      ! [H2: complex,Z: complex,N: nat] :
% 0.32/0.65        ( ( H2 != zero_zero_complex )
% 0.32/0.65       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.32/0.65          = ( times_times_complex @ H2
% 0.32/0.65            @ ( groups2073611262835488442omplex
% 0.32/0.65              @ ^ [P2: nat] :
% 0.32/0.65                  ( groups2073611262835488442omplex
% 0.32/0.65                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.32/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff2
% 0.32/0.65  thf(fact_8380_lemma__termdiff2,axiom,
% 0.32/0.65      ! [H2: rat,Z: rat,N: nat] :
% 0.32/0.65        ( ( H2 != zero_zero_rat )
% 0.32/0.65       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.32/0.65          = ( times_times_rat @ H2
% 0.32/0.65            @ ( groups2906978787729119204at_rat
% 0.32/0.65              @ ^ [P2: nat] :
% 0.32/0.65                  ( groups2906978787729119204at_rat
% 0.32/0.65                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.32/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff2
% 0.32/0.65  thf(fact_8381_lemma__termdiff2,axiom,
% 0.32/0.65      ! [H2: real,Z: real,N: nat] :
% 0.32/0.65        ( ( H2 != zero_zero_real )
% 0.32/0.65       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.32/0.65          = ( times_times_real @ H2
% 0.32/0.65            @ ( groups6591440286371151544t_real
% 0.32/0.65              @ ^ [P2: nat] :
% 0.32/0.65                  ( groups6591440286371151544t_real
% 0.32/0.65                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.32/0.65                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff2
% 0.32/0.65  thf(fact_8382_lessThan__eq__iff,axiom,
% 0.32/0.65      ! [X: nat,Y: nat] :
% 0.32/0.65        ( ( ( set_ord_lessThan_nat @ X )
% 0.32/0.65          = ( set_ord_lessThan_nat @ Y ) )
% 0.32/0.65        = ( X = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_eq_iff
% 0.32/0.65  thf(fact_8383_lessThan__eq__iff,axiom,
% 0.32/0.65      ! [X: int,Y: int] :
% 0.32/0.65        ( ( ( set_ord_lessThan_int @ X )
% 0.32/0.65          = ( set_ord_lessThan_int @ Y ) )
% 0.32/0.65        = ( X = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_eq_iff
% 0.32/0.65  thf(fact_8384_lessThan__eq__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( set_or5984915006950818249n_real @ X )
% 0.32/0.65          = ( set_or5984915006950818249n_real @ Y ) )
% 0.32/0.65        = ( X = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_eq_iff
% 0.32/0.65  thf(fact_8385_lessThan__iff,axiom,
% 0.32/0.65      ! [I: set_nat,K: set_nat] :
% 0.32/0.65        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 0.32/0.65        = ( ord_less_set_nat @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8386_lessThan__iff,axiom,
% 0.32/0.65      ! [I: rat,K: rat] :
% 0.32/0.65        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 0.32/0.65        = ( ord_less_rat @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8387_lessThan__iff,axiom,
% 0.32/0.65      ! [I: num,K: num] :
% 0.32/0.65        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 0.32/0.65        = ( ord_less_num @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8388_lessThan__iff,axiom,
% 0.32/0.65      ! [I: nat,K: nat] :
% 0.32/0.65        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.32/0.65        = ( ord_less_nat @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8389_lessThan__iff,axiom,
% 0.32/0.65      ! [I: int,K: int] :
% 0.32/0.65        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 0.32/0.65        = ( ord_less_int @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8390_lessThan__iff,axiom,
% 0.32/0.65      ! [I: real,K: real] :
% 0.32/0.65        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 0.32/0.65        = ( ord_less_real @ I @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_iff
% 0.32/0.65  thf(fact_8391_finite__lessThan,axiom,
% 0.32/0.65      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % finite_lessThan
% 0.32/0.65  thf(fact_8392_lessThan__subset__iff,axiom,
% 0.32/0.65      ! [X: rat,Y: rat] :
% 0.32/0.65        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.32/0.65        = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_subset_iff
% 0.32/0.65  thf(fact_8393_lessThan__subset__iff,axiom,
% 0.32/0.65      ! [X: num,Y: num] :
% 0.32/0.65        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 0.32/0.65        = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_subset_iff
% 0.32/0.65  thf(fact_8394_lessThan__subset__iff,axiom,
% 0.32/0.65      ! [X: nat,Y: nat] :
% 0.32/0.65        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.32/0.65        = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_subset_iff
% 0.32/0.65  thf(fact_8395_lessThan__subset__iff,axiom,
% 0.32/0.65      ! [X: int,Y: int] :
% 0.32/0.65        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 0.32/0.65        = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_subset_iff
% 0.32/0.65  thf(fact_8396_lessThan__subset__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 0.32/0.65        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_subset_iff
% 0.32/0.65  thf(fact_8397_lessThan__0,axiom,
% 0.32/0.65      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.32/0.65      = bot_bot_set_nat ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_0
% 0.32/0.65  thf(fact_8398_sum_OlessThan__Suc,axiom,
% 0.32/0.65      ! [G: nat > rat,N: nat] :
% 0.32/0.65        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc
% 0.32/0.65  thf(fact_8399_sum_OlessThan__Suc,axiom,
% 0.32/0.65      ! [G: nat > int,N: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc
% 0.32/0.65  thf(fact_8400_sum_OlessThan__Suc,axiom,
% 0.32/0.65      ! [G: nat > nat,N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc
% 0.32/0.65  thf(fact_8401_sum_OlessThan__Suc,axiom,
% 0.32/0.65      ! [G: nat > real,N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc
% 0.32/0.65  thf(fact_8402_single__Diff__lessThan,axiom,
% 0.32/0.65      ! [K: nat] :
% 0.32/0.65        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.32/0.65        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % single_Diff_lessThan
% 0.32/0.65  thf(fact_8403_single__Diff__lessThan,axiom,
% 0.32/0.65      ! [K: int] :
% 0.32/0.65        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.32/0.65        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.32/0.65  
% 0.32/0.65  % single_Diff_lessThan
% 0.32/0.65  thf(fact_8404_single__Diff__lessThan,axiom,
% 0.32/0.65      ! [K: real] :
% 0.32/0.65        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 0.32/0.65        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % single_Diff_lessThan
% 0.32/0.65  thf(fact_8405_powser__zero,axiom,
% 0.32/0.65      ! [F: nat > complex] :
% 0.32/0.65        ( ( suminf_complex
% 0.32/0.65          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 0.32/0.65        = ( F @ zero_zero_nat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powser_zero
% 0.32/0.65  thf(fact_8406_powser__zero,axiom,
% 0.32/0.65      ! [F: nat > real] :
% 0.32/0.65        ( ( suminf_real
% 0.32/0.65          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 0.32/0.65        = ( F @ zero_zero_nat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powser_zero
% 0.32/0.65  thf(fact_8407_set__encode__insert,axiom,
% 0.32/0.65      ! [A2: set_nat,N: nat] :
% 0.32/0.65        ( ( finite_finite_nat @ A2 )
% 0.32/0.65       => ( ~ ( member_nat @ N @ A2 )
% 0.32/0.65         => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 0.32/0.65            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % set_encode_insert
% 0.32/0.65  thf(fact_8408_lessThan__nat__numeral,axiom,
% 0.32/0.65      ! [K: num] :
% 0.32/0.65        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 0.32/0.65        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_nat_numeral
% 0.32/0.65  thf(fact_8409_lessThan__Suc,axiom,
% 0.32/0.65      ! [K: nat] :
% 0.32/0.65        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.32/0.65        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_Suc
% 0.32/0.65  thf(fact_8410_lessThan__non__empty,axiom,
% 0.32/0.65      ! [X: int] :
% 0.32/0.65        ( ( set_ord_lessThan_int @ X )
% 0.32/0.65       != bot_bot_set_int ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_non_empty
% 0.32/0.65  thf(fact_8411_lessThan__non__empty,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( set_or5984915006950818249n_real @ X )
% 0.32/0.65       != bot_bot_set_real ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_non_empty
% 0.32/0.65  thf(fact_8412_infinite__Iio,axiom,
% 0.32/0.65      ! [A: int] :
% 0.32/0.65        ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 0.32/0.65  
% 0.32/0.65  % infinite_Iio
% 0.32/0.65  thf(fact_8413_infinite__Iio,axiom,
% 0.32/0.65      ! [A: real] :
% 0.32/0.65        ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 0.32/0.65  
% 0.32/0.65  % infinite_Iio
% 0.32/0.65  thf(fact_8414_lessThan__def,axiom,
% 0.32/0.65      ( set_or890127255671739683et_nat
% 0.32/0.65      = ( ^ [U2: set_nat] :
% 0.32/0.65            ( collect_set_nat
% 0.32/0.65            @ ^ [X3: set_nat] : ( ord_less_set_nat @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8415_lessThan__def,axiom,
% 0.32/0.65      ( set_ord_lessThan_rat
% 0.32/0.65      = ( ^ [U2: rat] :
% 0.32/0.65            ( collect_rat
% 0.32/0.65            @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8416_lessThan__def,axiom,
% 0.32/0.65      ( set_ord_lessThan_num
% 0.32/0.65      = ( ^ [U2: num] :
% 0.32/0.65            ( collect_num
% 0.32/0.65            @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8417_lessThan__def,axiom,
% 0.32/0.65      ( set_ord_lessThan_nat
% 0.32/0.65      = ( ^ [U2: nat] :
% 0.32/0.65            ( collect_nat
% 0.32/0.65            @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8418_lessThan__def,axiom,
% 0.32/0.65      ( set_ord_lessThan_int
% 0.32/0.65      = ( ^ [U2: int] :
% 0.32/0.65            ( collect_int
% 0.32/0.65            @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8419_lessThan__def,axiom,
% 0.32/0.65      ( set_or5984915006950818249n_real
% 0.32/0.65      = ( ^ [U2: real] :
% 0.32/0.65            ( collect_real
% 0.32/0.65            @ ^ [X3: real] : ( ord_less_real @ X3 @ U2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_def
% 0.32/0.65  thf(fact_8420_Iio__eq__empty__iff,axiom,
% 0.32/0.65      ! [N: extended_enat] :
% 0.32/0.65        ( ( ( set_or8419480210114673929d_enat @ N )
% 0.32/0.65          = bot_bo7653980558646680370d_enat )
% 0.32/0.65        = ( N = bot_bo4199563552545308370d_enat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Iio_eq_empty_iff
% 0.32/0.65  thf(fact_8421_Iio__eq__empty__iff,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( ( set_ord_lessThan_nat @ N )
% 0.32/0.65          = bot_bot_set_nat )
% 0.32/0.65        = ( N = bot_bot_nat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Iio_eq_empty_iff
% 0.32/0.65  thf(fact_8422_lessThan__strict__subset__iff,axiom,
% 0.32/0.65      ! [M: rat,N: rat] :
% 0.32/0.65        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 0.32/0.65        = ( ord_less_rat @ M @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_strict_subset_iff
% 0.32/0.65  thf(fact_8423_lessThan__strict__subset__iff,axiom,
% 0.32/0.65      ! [M: num,N: num] :
% 0.32/0.65        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 0.32/0.65        = ( ord_less_num @ M @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_strict_subset_iff
% 0.32/0.65  thf(fact_8424_lessThan__strict__subset__iff,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65        = ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_strict_subset_iff
% 0.32/0.65  thf(fact_8425_lessThan__strict__subset__iff,axiom,
% 0.32/0.65      ! [M: int,N: int] :
% 0.32/0.65        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 0.32/0.65        = ( ord_less_int @ M @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_strict_subset_iff
% 0.32/0.65  thf(fact_8426_lessThan__strict__subset__iff,axiom,
% 0.32/0.65      ! [M: real,N: real] :
% 0.32/0.65        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 0.32/0.65        = ( ord_less_real @ M @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_strict_subset_iff
% 0.32/0.65  thf(fact_8427_complex__mod__minus__le__complex__mod,axiom,
% 0.32/0.65      ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_mod_minus_le_complex_mod
% 0.32/0.65  thf(fact_8428_complex__mod__triangle__ineq2,axiom,
% 0.32/0.65      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_mod_triangle_ineq2
% 0.32/0.65  thf(fact_8429_lessThan__empty__iff,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( ( set_ord_lessThan_nat @ N )
% 0.32/0.65          = bot_bot_set_nat )
% 0.32/0.65        = ( N = zero_zero_nat ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lessThan_empty_iff
% 0.32/0.65  thf(fact_8430_finite__nat__bounded,axiom,
% 0.32/0.65      ! [S2: set_nat] :
% 0.32/0.65        ( ( finite_finite_nat @ S2 )
% 0.32/0.65       => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % finite_nat_bounded
% 0.32/0.65  thf(fact_8431_finite__nat__iff__bounded,axiom,
% 0.32/0.65      ( finite_finite_nat
% 0.32/0.65      = ( ^ [S6: set_nat] :
% 0.32/0.65          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % finite_nat_iff_bounded
% 0.32/0.65  thf(fact_8432_atLeast0__atMost__Suc,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.32/0.65        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % atLeast0_atMost_Suc
% 0.32/0.65  thf(fact_8433_Icc__eq__insert__lb__nat,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.65       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 0.32/0.65          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Icc_eq_insert_lb_nat
% 0.32/0.65  thf(fact_8434_atLeastAtMostSuc__conv,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.32/0.65       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 0.32/0.65          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % atLeastAtMostSuc_conv
% 0.32/0.65  thf(fact_8435_atLeastAtMost__insertL,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.65       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.32/0.65          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % atLeastAtMost_insertL
% 0.32/0.65  thf(fact_8436_norm__exp,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_exp
% 0.32/0.65  thf(fact_8437_norm__exp,axiom,
% 0.32/0.65      ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_exp
% 0.32/0.65  thf(fact_8438_sum_Onat__diff__reindex,axiom,
% 0.32/0.65      ! [G: nat > nat,N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat
% 0.32/0.65          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.nat_diff_reindex
% 0.32/0.65  thf(fact_8439_sum_Onat__diff__reindex,axiom,
% 0.32/0.65      ! [G: nat > real,N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.nat_diff_reindex
% 0.32/0.65  thf(fact_8440_sum__diff__distrib,axiom,
% 0.32/0.65      ! [Q: int > nat,P: int > nat,N: int] :
% 0.32/0.65        ( ! [X6: int] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 0.32/0.65       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 0.32/0.65          = ( groups4541462559716669496nt_nat
% 0.32/0.65            @ ^ [X3: int] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 0.32/0.65            @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff_distrib
% 0.32/0.65  thf(fact_8441_sum__diff__distrib,axiom,
% 0.32/0.65      ! [Q: real > nat,P: real > nat,N: real] :
% 0.32/0.65        ( ! [X6: real] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 0.32/0.65       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 0.32/0.65          = ( groups1935376822645274424al_nat
% 0.32/0.65            @ ^ [X3: real] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 0.32/0.65            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff_distrib
% 0.32/0.65  thf(fact_8442_sum__diff__distrib,axiom,
% 0.32/0.65      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 0.32/0.65        ( ! [X6: nat] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 0.32/0.65       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 0.32/0.65          = ( groups3542108847815614940at_nat
% 0.32/0.65            @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_diff_distrib
% 0.32/0.65  thf(fact_8443_sum_OlessThan__Suc__shift,axiom,
% 0.32/0.65      ! [G: nat > rat,N: nat] :
% 0.32/0.65        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.32/0.65          @ ( groups2906978787729119204at_rat
% 0.32/0.65            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc_shift
% 0.32/0.65  thf(fact_8444_sum_OlessThan__Suc__shift,axiom,
% 0.32/0.65      ! [G: nat > int,N: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.32/0.65          @ ( groups3539618377306564664at_int
% 0.32/0.65            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc_shift
% 0.32/0.65  thf(fact_8445_sum_OlessThan__Suc__shift,axiom,
% 0.32/0.65      ! [G: nat > nat,N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.32/0.65          @ ( groups3542108847815614940at_nat
% 0.32/0.65            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc_shift
% 0.32/0.65  thf(fact_8446_sum_OlessThan__Suc__shift,axiom,
% 0.32/0.65      ! [G: nat > real,N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.lessThan_Suc_shift
% 0.32/0.65  thf(fact_8447_sum__lessThan__telescope,axiom,
% 0.32/0.65      ! [F: nat > rat,M: nat] :
% 0.32/0.65        ( ( groups2906978787729119204at_rat
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope
% 0.32/0.65  thf(fact_8448_sum__lessThan__telescope,axiom,
% 0.32/0.65      ! [F: nat > int,M: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope
% 0.32/0.65  thf(fact_8449_sum__lessThan__telescope,axiom,
% 0.32/0.65      ! [F: nat > real,M: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope
% 0.32/0.65  thf(fact_8450_sum__lessThan__telescope_H,axiom,
% 0.32/0.65      ! [F: nat > rat,M: nat] :
% 0.32/0.65        ( ( groups2906978787729119204at_rat
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope'
% 0.32/0.65  thf(fact_8451_sum__lessThan__telescope_H,axiom,
% 0.32/0.65      ! [F: nat > int,M: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope'
% 0.32/0.65  thf(fact_8452_sum__lessThan__telescope_H,axiom,
% 0.32/0.65      ! [F: nat > real,M: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_lessThan_telescope'
% 0.32/0.65  thf(fact_8453_sumr__diff__mult__const2,axiom,
% 0.32/0.65      ! [F: nat > complex,N: nat,R: complex] :
% 0.32/0.65        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 0.32/0.65        = ( groups2073611262835488442omplex
% 0.32/0.65          @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ I5 ) @ R )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sumr_diff_mult_const2
% 0.32/0.65  thf(fact_8454_sumr__diff__mult__const2,axiom,
% 0.32/0.65      ! [F: nat > rat,N: nat,R: rat] :
% 0.32/0.65        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 0.32/0.65        = ( groups2906978787729119204at_rat
% 0.32/0.65          @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ R )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sumr_diff_mult_const2
% 0.32/0.65  thf(fact_8455_sumr__diff__mult__const2,axiom,
% 0.32/0.65      ! [F: nat > int,N: nat,R: int] :
% 0.32/0.65        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 0.32/0.65        = ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sumr_diff_mult_const2
% 0.32/0.65  thf(fact_8456_sumr__diff__mult__const2,axiom,
% 0.32/0.65      ! [F: nat > real,N: nat,R: real] :
% 0.32/0.65        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 0.32/0.65        = ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sumr_diff_mult_const2
% 0.32/0.65  thf(fact_8457_sum_OatLeast1__atMost__eq,axiom,
% 0.32/0.65      ! [G: nat > nat,N: nat] :
% 0.32/0.65        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.32/0.65        = ( groups3542108847815614940at_nat
% 0.32/0.65          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.atLeast1_atMost_eq
% 0.32/0.65  thf(fact_8458_sum_OatLeast1__atMost__eq,axiom,
% 0.32/0.65      ! [G: nat > real,N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.32/0.65        = ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum.atLeast1_atMost_eq
% 0.32/0.65  thf(fact_8459_power__diff__1__eq,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 0.32/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_1_eq
% 0.32/0.65  thf(fact_8460_power__diff__1__eq,axiom,
% 0.32/0.65      ! [X: rat,N: nat] :
% 0.32/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 0.32/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_1_eq
% 0.32/0.65  thf(fact_8461_power__diff__1__eq,axiom,
% 0.32/0.65      ! [X: int,N: nat] :
% 0.32/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 0.32/0.65        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_1_eq
% 0.32/0.65  thf(fact_8462_power__diff__1__eq,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 0.32/0.65        = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_1_eq
% 0.32/0.65  thf(fact_8463_one__diff__power__eq,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.32/0.65        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq
% 0.32/0.65  thf(fact_8464_one__diff__power__eq,axiom,
% 0.32/0.65      ! [X: rat,N: nat] :
% 0.32/0.65        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.32/0.65        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq
% 0.32/0.65  thf(fact_8465_one__diff__power__eq,axiom,
% 0.32/0.65      ! [X: int,N: nat] :
% 0.32/0.65        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.32/0.65        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq
% 0.32/0.65  thf(fact_8466_one__diff__power__eq,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.32/0.65        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq
% 0.32/0.65  thf(fact_8467_geometric__sum,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( X != one_one_complex )
% 0.32/0.65       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % geometric_sum
% 0.32/0.65  thf(fact_8468_geometric__sum,axiom,
% 0.32/0.65      ! [X: rat,N: nat] :
% 0.32/0.65        ( ( X != one_one_rat )
% 0.32/0.65       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % geometric_sum
% 0.32/0.65  thf(fact_8469_geometric__sum,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( X != one_one_real )
% 0.32/0.65       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % geometric_sum
% 0.32/0.65  thf(fact_8470_monoseq__realpow,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65         => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % monoseq_realpow
% 0.32/0.65  thf(fact_8471_sum__gp__strict,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_complex )
% 0.32/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( semiri8010041392384452111omplex @ N ) ) )
% 0.32/0.65        & ( ( X != one_one_complex )
% 0.32/0.65         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_strict
% 0.32/0.65  thf(fact_8472_sum__gp__strict,axiom,
% 0.32/0.65      ! [X: rat,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_rat )
% 0.32/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( semiri681578069525770553at_rat @ N ) ) )
% 0.32/0.65        & ( ( X != one_one_rat )
% 0.32/0.65         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_strict
% 0.32/0.65  thf(fact_8473_sum__gp__strict,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ( X = one_one_real )
% 0.32/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.65        & ( ( X != one_one_real )
% 0.32/0.65         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_gp_strict
% 0.32/0.65  thf(fact_8474_lemma__termdiff1,axiom,
% 0.32/0.65      ! [Z: complex,H2: complex,M: nat] :
% 0.32/0.65        ( ( groups2073611262835488442omplex
% 0.32/0.65          @ ^ [P2: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ P2 ) ) @ ( power_power_complex @ Z @ M ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( groups2073611262835488442omplex
% 0.32/0.65          @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P2 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff1
% 0.32/0.65  thf(fact_8475_lemma__termdiff1,axiom,
% 0.32/0.65      ! [Z: rat,H2: rat,M: nat] :
% 0.32/0.65        ( ( groups2906978787729119204at_rat
% 0.32/0.65          @ ^ [P2: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ P2 ) ) @ ( power_power_rat @ Z @ M ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( groups2906978787729119204at_rat
% 0.32/0.65          @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P2 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff1
% 0.32/0.65  thf(fact_8476_lemma__termdiff1,axiom,
% 0.32/0.65      ! [Z: int,H2: int,M: nat] :
% 0.32/0.65        ( ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [P2: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ P2 ) ) @ ( power_power_int @ Z @ M ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( groups3539618377306564664at_int
% 0.32/0.65          @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ Z @ P2 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff1
% 0.32/0.65  thf(fact_8477_lemma__termdiff1,axiom,
% 0.32/0.65      ! [Z: real,H2: real,M: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [P2: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ P2 ) ) @ ( power_power_real @ Z @ M ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) )
% 0.32/0.65        = ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ Z @ P2 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_termdiff1
% 0.32/0.65  thf(fact_8478_power__diff__sumr2,axiom,
% 0.32/0.65      ! [X: complex,N: nat,Y: complex] :
% 0.32/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 0.32/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.32/0.65          @ ( groups2073611262835488442omplex
% 0.32/0.65            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_sumr2
% 0.32/0.65  thf(fact_8479_power__diff__sumr2,axiom,
% 0.32/0.65      ! [X: rat,N: nat,Y: rat] :
% 0.32/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.32/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.32/0.65          @ ( groups2906978787729119204at_rat
% 0.32/0.65            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_sumr2
% 0.32/0.65  thf(fact_8480_power__diff__sumr2,axiom,
% 0.32/0.65      ! [X: int,N: nat,Y: int] :
% 0.32/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.32/0.65        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.32/0.65          @ ( groups3539618377306564664at_int
% 0.32/0.65            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_int @ X @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_sumr2
% 0.32/0.65  thf(fact_8481_power__diff__sumr2,axiom,
% 0.32/0.65      ! [X: real,N: nat,Y: real] :
% 0.32/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 0.32/0.65        = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_real @ X @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_diff_sumr2
% 0.32/0.65  thf(fact_8482_diff__power__eq__sum,axiom,
% 0.32/0.65      ! [X: complex,N: nat,Y: complex] :
% 0.32/0.65        ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 0.32/0.65        = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.32/0.65          @ ( groups2073611262835488442omplex
% 0.32/0.65            @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ X @ P2 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % diff_power_eq_sum
% 0.32/0.65  thf(fact_8483_diff__power__eq__sum,axiom,
% 0.32/0.65      ! [X: rat,N: nat,Y: rat] :
% 0.32/0.65        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 0.32/0.65        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.32/0.65          @ ( groups2906978787729119204at_rat
% 0.32/0.65            @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ X @ P2 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % diff_power_eq_sum
% 0.32/0.65  thf(fact_8484_diff__power__eq__sum,axiom,
% 0.32/0.65      ! [X: int,N: nat,Y: int] :
% 0.32/0.65        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 0.32/0.65        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.32/0.65          @ ( groups3539618377306564664at_int
% 0.32/0.65            @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ X @ P2 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % diff_power_eq_sum
% 0.32/0.65  thf(fact_8485_diff__power__eq__sum,axiom,
% 0.32/0.65      ! [X: real,N: nat,Y: real] :
% 0.32/0.65        ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 0.32/0.65        = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ X @ P2 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % diff_power_eq_sum
% 0.32/0.65  thf(fact_8486_set__decode__plus__power__2,axiom,
% 0.32/0.65      ! [N: nat,Z: nat] :
% 0.32/0.65        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 0.32/0.65       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 0.32/0.65          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % set_decode_plus_power_2
% 0.32/0.65  thf(fact_8487_real__sum__nat__ivl__bounded2,axiom,
% 0.32/0.65      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 0.32/0.65        ( ! [P7: nat] :
% 0.32/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.32/0.65           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 0.32/0.65       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.32/0.65         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sum_nat_ivl_bounded2
% 0.32/0.65  thf(fact_8488_real__sum__nat__ivl__bounded2,axiom,
% 0.32/0.65      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 0.32/0.65        ( ! [P7: nat] :
% 0.32/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.32/0.65           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 0.32/0.65       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.32/0.65         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sum_nat_ivl_bounded2
% 0.32/0.65  thf(fact_8489_real__sum__nat__ivl__bounded2,axiom,
% 0.32/0.65      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 0.32/0.65        ( ! [P7: nat] :
% 0.32/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.32/0.65           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 0.32/0.65       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.32/0.65         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sum_nat_ivl_bounded2
% 0.32/0.65  thf(fact_8490_real__sum__nat__ivl__bounded2,axiom,
% 0.32/0.65      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 0.32/0.65        ( ! [P7: nat] :
% 0.32/0.65            ( ( ord_less_nat @ P7 @ N )
% 0.32/0.65           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.32/0.65         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sum_nat_ivl_bounded2
% 0.32/0.65  thf(fact_8491_exp__bound__half,axiom,
% 0.32/0.65      ! [Z: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_bound_half
% 0.32/0.65  thf(fact_8492_exp__bound__half,axiom,
% 0.32/0.65      ! [Z: complex] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_bound_half
% 0.32/0.65  thf(fact_8493_one__diff__power__eq_H,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.32/0.65        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 0.32/0.65          @ ( groups2073611262835488442omplex
% 0.32/0.65            @ ^ [I5: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq'
% 0.32/0.65  thf(fact_8494_one__diff__power__eq_H,axiom,
% 0.32/0.65      ! [X: rat,N: nat] :
% 0.32/0.65        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.32/0.65        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.32/0.65          @ ( groups2906978787729119204at_rat
% 0.32/0.65            @ ^ [I5: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq'
% 0.32/0.65  thf(fact_8495_one__diff__power__eq_H,axiom,
% 0.32/0.65      ! [X: int,N: nat] :
% 0.32/0.65        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.32/0.65        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.32/0.65          @ ( groups3539618377306564664at_int
% 0.32/0.65            @ ^ [I5: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq'
% 0.32/0.65  thf(fact_8496_one__diff__power__eq_H,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.32/0.65        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_diff_power_eq'
% 0.32/0.65  thf(fact_8497_sum__split__even__odd,axiom,
% 0.32/0.65      ! [F: nat > real,G: nat > real,N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.65        = ( plus_plus_real
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_split_even_odd
% 0.32/0.65  thf(fact_8498_exp__bound__lemma,axiom,
% 0.32/0.65      ! [Z: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_bound_lemma
% 0.32/0.65  thf(fact_8499_exp__bound__lemma,axiom,
% 0.32/0.65      ! [Z: complex] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % exp_bound_lemma
% 0.32/0.65  thf(fact_8500_arctan__series,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( arctan @ X )
% 0.32/0.65          = ( suminf_real
% 0.32/0.65            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_series
% 0.32/0.65  thf(fact_8501_norm__divide__numeral,axiom,
% 0.32/0.65      ! [A: real,W: num] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.65        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_divide_numeral
% 0.32/0.65  thf(fact_8502_norm__divide__numeral,axiom,
% 0.32/0.65      ! [A: complex,W: num] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.65        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_divide_numeral
% 0.32/0.65  thf(fact_8503_norm__mult__numeral2,axiom,
% 0.32/0.65      ! [A: real,W: num] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.65        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_numeral2
% 0.32/0.65  thf(fact_8504_norm__mult__numeral2,axiom,
% 0.32/0.65      ! [A: complex,W: num] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.65        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_numeral2
% 0.32/0.65  thf(fact_8505_norm__mult__numeral1,axiom,
% 0.32/0.65      ! [W: num,A: real] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 0.32/0.65        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_numeral1
% 0.32/0.65  thf(fact_8506_norm__mult__numeral1,axiom,
% 0.32/0.65      ! [W: num,A: complex] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 0.32/0.65        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_numeral1
% 0.32/0.65  thf(fact_8507_norm__neg__numeral,axiom,
% 0.32/0.65      ! [W: num] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_neg_numeral
% 0.32/0.65  thf(fact_8508_norm__neg__numeral,axiom,
% 0.32/0.65      ! [W: num] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_neg_numeral
% 0.32/0.65  thf(fact_8509_norm__le__zero__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 0.32/0.65        = ( X = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_le_zero_iff
% 0.32/0.65  thf(fact_8510_norm__le__zero__iff,axiom,
% 0.32/0.65      ! [X: complex] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 0.32/0.65        = ( X = zero_zero_complex ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_le_zero_iff
% 0.32/0.65  thf(fact_8511_norm__zero,axiom,
% 0.32/0.65      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_zero
% 0.32/0.65  thf(fact_8512_norm__zero,axiom,
% 0.32/0.65      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_zero
% 0.32/0.65  thf(fact_8513_norm__eq__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( real_V7735802525324610683m_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( X = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_eq_zero
% 0.32/0.65  thf(fact_8514_norm__eq__zero,axiom,
% 0.32/0.65      ! [X: complex] :
% 0.32/0.65        ( ( ( real_V1022390504157884413omplex @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( X = zero_zero_complex ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_eq_zero
% 0.32/0.65  thf(fact_8515_norm__one,axiom,
% 0.32/0.65      ( ( real_V7735802525324610683m_real @ one_one_real )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_one
% 0.32/0.65  thf(fact_8516_norm__one,axiom,
% 0.32/0.65      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_one
% 0.32/0.65  thf(fact_8517_norm__numeral,axiom,
% 0.32/0.65      ! [W: num] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 0.32/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_numeral
% 0.32/0.65  thf(fact_8518_norm__numeral,axiom,
% 0.32/0.65      ! [W: num] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.65        = ( numeral_numeral_real @ W ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_numeral
% 0.32/0.65  thf(fact_8519_zero__less__norm__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 0.32/0.65        = ( X != zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % zero_less_norm_iff
% 0.32/0.65  thf(fact_8520_zero__less__norm__iff,axiom,
% 0.32/0.65      ! [X: complex] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 0.32/0.65        = ( X != zero_zero_complex ) ) ).
% 0.32/0.65  
% 0.32/0.65  % zero_less_norm_iff
% 0.32/0.65  thf(fact_8521_norm__minus__commute,axiom,
% 0.32/0.65      ! [A: real,B: real] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 0.32/0.65        = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_minus_commute
% 0.32/0.65  thf(fact_8522_norm__minus__commute,axiom,
% 0.32/0.65      ! [A: complex,B: complex] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 0.32/0.65        = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_minus_commute
% 0.32/0.65  thf(fact_8523_norm__not__less__zero,axiom,
% 0.32/0.65      ! [X: complex] :
% 0.32/0.65        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_not_less_zero
% 0.32/0.65  thf(fact_8524_norm__ge__zero,axiom,
% 0.32/0.65      ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_ge_zero
% 0.32/0.65  thf(fact_8525_norm__mult,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 0.32/0.65        = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult
% 0.32/0.65  thf(fact_8526_norm__mult,axiom,
% 0.32/0.65      ! [X: complex,Y: complex] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 0.32/0.65        = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult
% 0.32/0.65  thf(fact_8527_norm__divide,axiom,
% 0.32/0.65      ! [A: real,B: real] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.65        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_divide
% 0.32/0.65  thf(fact_8528_norm__divide,axiom,
% 0.32/0.65      ! [A: complex,B: complex] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.65        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_divide
% 0.32/0.65  thf(fact_8529_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_real,F: real > complex,G: real > real] :
% 0.32/0.65        ( ! [X6: real] :
% 0.32/0.65            ( ( member_real @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8530_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 0.32/0.65        ( ! [X6: set_nat] :
% 0.32/0.65            ( ( member_set_nat @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8531_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_int,F: int > complex,G: int > real] :
% 0.32/0.65        ( ! [X6: int] :
% 0.32/0.65            ( ( member_int @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8532_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 0.32/0.65        ( ! [X6: nat] :
% 0.32/0.65            ( ( member_nat @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8533_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 0.32/0.65        ( ! [X6: complex] :
% 0.32/0.65            ( ( member_complex @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8534_sum__norm__le,axiom,
% 0.32/0.65      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 0.32/0.65        ( ! [X6: nat] :
% 0.32/0.65            ( ( member_nat @ X6 @ S2 )
% 0.32/0.65           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_norm_le
% 0.32/0.65  thf(fact_8535_norm__power,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 0.32/0.65        = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_power
% 0.32/0.65  thf(fact_8536_norm__power,axiom,
% 0.32/0.65      ! [X: complex,N: nat] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 0.32/0.65        = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_power
% 0.32/0.65  thf(fact_8537_norm__sum,axiom,
% 0.32/0.65      ! [F: nat > complex,A2: set_nat] :
% 0.32/0.65        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 0.32/0.65        @ ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 0.32/0.65          @ A2 ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_sum
% 0.32/0.65  thf(fact_8538_norm__sum,axiom,
% 0.32/0.65      ! [F: complex > complex,A2: set_complex] :
% 0.32/0.65        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 0.32/0.65        @ ( groups5808333547571424918x_real
% 0.32/0.65          @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 0.32/0.65          @ A2 ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_sum
% 0.32/0.65  thf(fact_8539_norm__sum,axiom,
% 0.32/0.65      ! [F: nat > real,A2: set_nat] :
% 0.32/0.65        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 0.32/0.65        @ ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( F @ I5 ) )
% 0.32/0.65          @ A2 ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_sum
% 0.32/0.65  thf(fact_8540_norm__uminus__minus,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 0.32/0.65        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_uminus_minus
% 0.32/0.65  thf(fact_8541_norm__uminus__minus,axiom,
% 0.32/0.65      ! [X: complex,Y: complex] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 0.32/0.65        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_uminus_minus
% 0.32/0.65  thf(fact_8542_nonzero__norm__divide,axiom,
% 0.32/0.65      ! [B: real,A: real] :
% 0.32/0.65        ( ( B != zero_zero_real )
% 0.32/0.65       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.32/0.65          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % nonzero_norm_divide
% 0.32/0.65  thf(fact_8543_nonzero__norm__divide,axiom,
% 0.32/0.65      ! [B: complex,A: complex] :
% 0.32/0.65        ( ( B != zero_zero_complex )
% 0.32/0.65       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.65          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % nonzero_norm_divide
% 0.32/0.65  thf(fact_8544_power__eq__imp__eq__norm,axiom,
% 0.32/0.65      ! [W: real,N: nat,Z: real] :
% 0.32/0.65        ( ( ( power_power_real @ W @ N )
% 0.32/0.65          = ( power_power_real @ Z @ N ) )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ( ( real_V7735802525324610683m_real @ W )
% 0.32/0.65            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_eq_imp_eq_norm
% 0.32/0.65  thf(fact_8545_power__eq__imp__eq__norm,axiom,
% 0.32/0.65      ! [W: complex,N: nat,Z: complex] :
% 0.32/0.65        ( ( ( power_power_complex @ W @ N )
% 0.32/0.65          = ( power_power_complex @ Z @ N ) )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ( ( real_V1022390504157884413omplex @ W )
% 0.32/0.65            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_eq_imp_eq_norm
% 0.32/0.65  thf(fact_8546_norm__mult__less,axiom,
% 0.32/0.65      ! [X: real,R: real,Y: real,S: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.32/0.65         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_less
% 0.32/0.65  thf(fact_8547_norm__mult__less,axiom,
% 0.32/0.65      ! [X: complex,R: real,Y: complex,S: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.32/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_less
% 0.32/0.65  thf(fact_8548_norm__mult__ineq,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_ineq
% 0.32/0.65  thf(fact_8549_norm__mult__ineq,axiom,
% 0.32/0.65      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_mult_ineq
% 0.32/0.65  thf(fact_8550_norm__triangle__lt,axiom,
% 0.32/0.65      ! [X: real,Y: real,E: real] :
% 0.32/0.65        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_lt
% 0.32/0.65  thf(fact_8551_norm__triangle__lt,axiom,
% 0.32/0.65      ! [X: complex,Y: complex,E: real] :
% 0.32/0.65        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_lt
% 0.32/0.65  thf(fact_8552_norm__add__less,axiom,
% 0.32/0.65      ! [X: real,R: real,Y: real,S: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 0.32/0.65         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_add_less
% 0.32/0.65  thf(fact_8553_norm__add__less,axiom,
% 0.32/0.65      ! [X: complex,R: real,Y: complex,S: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 0.32/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_add_less
% 0.32/0.65  thf(fact_8554_norm__power__ineq,axiom,
% 0.32/0.65      ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_power_ineq
% 0.32/0.65  thf(fact_8555_norm__power__ineq,axiom,
% 0.32/0.65      ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_power_ineq
% 0.32/0.65  thf(fact_8556_norm__triangle__mono,axiom,
% 0.32/0.65      ! [A: real,R: real,B: real,S: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 0.32/0.65         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_mono
% 0.32/0.65  thf(fact_8557_norm__triangle__mono,axiom,
% 0.32/0.65      ! [A: complex,R: real,B: complex,S: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 0.32/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_mono
% 0.32/0.65  thf(fact_8558_norm__triangle__ineq,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq
% 0.32/0.65  thf(fact_8559_norm__triangle__ineq,axiom,
% 0.32/0.65      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq
% 0.32/0.65  thf(fact_8560_norm__triangle__le,axiom,
% 0.32/0.65      ! [X: real,Y: real,E: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_le
% 0.32/0.65  thf(fact_8561_norm__triangle__le,axiom,
% 0.32/0.65      ! [X: complex,Y: complex,E: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_le
% 0.32/0.65  thf(fact_8562_norm__add__leD,axiom,
% 0.32/0.65      ! [A: real,B: real,C: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_add_leD
% 0.32/0.65  thf(fact_8563_norm__add__leD,axiom,
% 0.32/0.65      ! [A: complex,B: complex,C: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_add_leD
% 0.32/0.65  thf(fact_8564_norm__diff__triangle__less,axiom,
% 0.32/0.65      ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 0.32/0.65         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_less
% 0.32/0.65  thf(fact_8565_norm__diff__triangle__less,axiom,
% 0.32/0.65      ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 0.32/0.65        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 0.32/0.65       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 0.32/0.65         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_less
% 0.32/0.65  thf(fact_8566_norm__triangle__le__diff,axiom,
% 0.32/0.65      ! [X: real,Y: real,E: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_le_diff
% 0.32/0.65  thf(fact_8567_norm__triangle__le__diff,axiom,
% 0.32/0.65      ! [X: complex,Y: complex,E: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 0.32/0.65       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_le_diff
% 0.32/0.65  thf(fact_8568_norm__diff__triangle__le,axiom,
% 0.32/0.65      ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 0.32/0.65         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_le
% 0.32/0.65  thf(fact_8569_norm__diff__triangle__le,axiom,
% 0.32/0.65      ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 0.32/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_le
% 0.32/0.65  thf(fact_8570_norm__triangle__ineq4,axiom,
% 0.32/0.65      ! [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 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq4
% 0.32/0.65  thf(fact_8571_norm__triangle__ineq4,axiom,
% 0.32/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq4
% 0.32/0.65  thf(fact_8572_norm__triangle__sub,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_sub
% 0.32/0.65  thf(fact_8573_norm__triangle__sub,axiom,
% 0.32/0.65      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_sub
% 0.32/0.65  thf(fact_8574_norm__diff__ineq,axiom,
% 0.32/0.65      ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_ineq
% 0.32/0.65  thf(fact_8575_norm__diff__ineq,axiom,
% 0.32/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_ineq
% 0.32/0.65  thf(fact_8576_norm__triangle__ineq2,axiom,
% 0.32/0.65      ! [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 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq2
% 0.32/0.65  thf(fact_8577_norm__triangle__ineq2,axiom,
% 0.32/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq2
% 0.32/0.65  thf(fact_8578_power__eq__1__iff,axiom,
% 0.32/0.65      ! [W: real,N: nat] :
% 0.32/0.65        ( ( ( power_power_real @ W @ N )
% 0.32/0.65          = one_one_real )
% 0.32/0.65       => ( ( ( real_V7735802525324610683m_real @ W )
% 0.32/0.65            = one_one_real )
% 0.32/0.65          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_eq_1_iff
% 0.32/0.65  thf(fact_8579_power__eq__1__iff,axiom,
% 0.32/0.65      ! [W: complex,N: nat] :
% 0.32/0.65        ( ( ( power_power_complex @ W @ N )
% 0.32/0.65          = one_one_complex )
% 0.32/0.65       => ( ( ( real_V1022390504157884413omplex @ W )
% 0.32/0.65            = one_one_real )
% 0.32/0.65          | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % power_eq_1_iff
% 0.32/0.65  thf(fact_8580_norm__diff__triangle__ineq,axiom,
% 0.32/0.65      ! [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 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_ineq
% 0.32/0.65  thf(fact_8581_norm__diff__triangle__ineq,axiom,
% 0.32/0.65      ! [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 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_diff_triangle_ineq
% 0.32/0.65  thf(fact_8582_norm__triangle__ineq3,axiom,
% 0.32/0.65      ! [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 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq3
% 0.32/0.65  thf(fact_8583_norm__triangle__ineq3,axiom,
% 0.32/0.65      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_triangle_ineq3
% 0.32/0.65  thf(fact_8584_square__norm__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65          = one_one_real )
% 0.32/0.65       => ( ( real_V7735802525324610683m_real @ X )
% 0.32/0.65          = one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % square_norm_one
% 0.32/0.65  thf(fact_8585_square__norm__one,axiom,
% 0.32/0.65      ! [X: complex] :
% 0.32/0.65        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65          = one_one_complex )
% 0.32/0.65       => ( ( real_V1022390504157884413omplex @ X )
% 0.32/0.65          = one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % square_norm_one
% 0.32/0.65  thf(fact_8586_norm__power__diff,axiom,
% 0.32/0.65      ! [Z: complex,W: complex,M: nat] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 0.32/0.65         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_power_diff
% 0.32/0.65  thf(fact_8587_sumr__cos__zero__one,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( groups6591440286371151544t_real
% 0.32/0.65          @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 0.32/0.65          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.32/0.65        = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sumr_cos_zero_one
% 0.32/0.65  thf(fact_8588_cos__coeff__0,axiom,
% 0.32/0.65      ( ( cos_coeff @ zero_zero_nat )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_coeff_0
% 0.32/0.65  thf(fact_8589_pi__series,axiom,
% 0.32/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.65      = ( suminf_real
% 0.32/0.65        @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_series
% 0.32/0.65  thf(fact_8590_ceiling__log__nat__eq__powr__iff,axiom,
% 0.32/0.65      ! [B: nat,K: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.65         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.32/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 0.32/0.65            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.32/0.65              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_log_nat_eq_powr_iff
% 0.32/0.65  thf(fact_8591_summable__arctan__series,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( summable_real
% 0.32/0.65          @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % summable_arctan_series
% 0.32/0.65  thf(fact_8592_ceiling__log__nat__eq__if,axiom,
% 0.32/0.65      ! [B: nat,N: nat,K: nat] :
% 0.32/0.65        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.32/0.65       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.32/0.65         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.32/0.65           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.32/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_log_nat_eq_if
% 0.32/0.65  thf(fact_8593_ceiling__divide__eq__div__numeral,axiom,
% 0.32/0.65      ! [A: num,B: num] :
% 0.32/0.65        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.32/0.65        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_divide_eq_div_numeral
% 0.32/0.65  thf(fact_8594_ceiling__minus__divide__eq__div__numeral,axiom,
% 0.32/0.65      ! [A: num,B: num] :
% 0.32/0.65        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.32/0.65        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_minus_divide_eq_div_numeral
% 0.32/0.65  thf(fact_8595_pi__neq__zero,axiom,
% 0.32/0.65      pi != zero_zero_real ).
% 0.32/0.65  
% 0.32/0.65  % pi_neq_zero
% 0.32/0.65  thf(fact_8596_pi__gt__zero,axiom,
% 0.32/0.65      ord_less_real @ zero_zero_real @ pi ).
% 0.32/0.65  
% 0.32/0.65  % pi_gt_zero
% 0.32/0.65  thf(fact_8597_pi__not__less__zero,axiom,
% 0.32/0.65      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_not_less_zero
% 0.32/0.65  thf(fact_8598_pi__ge__zero,axiom,
% 0.32/0.65      ord_less_eq_real @ zero_zero_real @ pi ).
% 0.32/0.65  
% 0.32/0.65  % pi_ge_zero
% 0.32/0.65  thf(fact_8599_summable__rabs__comparison__test,axiom,
% 0.32/0.65      ! [F: nat > real,G: nat > real] :
% 0.32/0.65        ( ? [N8: nat] :
% 0.32/0.65          ! [N3: nat] :
% 0.32/0.65            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.32/0.65           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 0.32/0.65       => ( ( summable_real @ G )
% 0.32/0.65         => ( summable_real
% 0.32/0.65            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % summable_rabs_comparison_test
% 0.32/0.65  thf(fact_8600_summable__rabs,axiom,
% 0.32/0.65      ! [F: nat > real] :
% 0.32/0.65        ( ( summable_real
% 0.32/0.65          @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 0.32/0.65          @ ( suminf_real
% 0.32/0.65            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % summable_rabs
% 0.32/0.65  thf(fact_8601_pi__less__4,axiom,
% 0.32/0.65      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_less_4
% 0.32/0.65  thf(fact_8602_pi__ge__two,axiom,
% 0.32/0.65      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 0.32/0.65  
% 0.32/0.65  % pi_ge_two
% 0.32/0.65  thf(fact_8603_pi__half__neq__two,axiom,
% 0.32/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_neq_two
% 0.32/0.65  thf(fact_8604_pi__half__neq__zero,axiom,
% 0.32/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65     != zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_neq_zero
% 0.32/0.65  thf(fact_8605_pi__half__less__two,axiom,
% 0.32/0.65      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_less_two
% 0.32/0.65  thf(fact_8606_pi__half__le__two,axiom,
% 0.32/0.65      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_le_two
% 0.32/0.65  thf(fact_8607_summable__power__series,axiom,
% 0.32/0.65      ! [F: nat > real,Z: real] :
% 0.32/0.65        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 0.32/0.65       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 0.32/0.65           => ( ( ord_less_real @ Z @ one_one_real )
% 0.32/0.65             => ( summable_real
% 0.32/0.65                @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % summable_power_series
% 0.32/0.65  thf(fact_8608_pi__half__gt__zero,axiom,
% 0.32/0.65      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_gt_zero
% 0.32/0.65  thf(fact_8609_pi__half__ge__zero,axiom,
% 0.32/0.65      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % pi_half_ge_zero
% 0.32/0.65  thf(fact_8610_m2pi__less__pi,axiom,
% 0.32/0.65      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.32/0.65  
% 0.32/0.65  % m2pi_less_pi
% 0.32/0.65  thf(fact_8611_arctan__ubound,axiom,
% 0.32/0.65      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_ubound
% 0.32/0.65  thf(fact_8612_arctan__one,axiom,
% 0.32/0.65      ( ( arctan @ one_one_real )
% 0.32/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_one
% 0.32/0.65  thf(fact_8613_minus__pi__half__less__zero,axiom,
% 0.32/0.65      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.32/0.65  
% 0.32/0.65  % minus_pi_half_less_zero
% 0.32/0.65  thf(fact_8614_arctan__lbound,axiom,
% 0.32/0.65      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_lbound
% 0.32/0.65  thf(fact_8615_arctan__bounded,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.32/0.65        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_bounded
% 0.32/0.65  thf(fact_8616_machin__Euler,axiom,
% 0.32/0.65      ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % machin_Euler
% 0.32/0.65  thf(fact_8617_machin,axiom,
% 0.32/0.65      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.65      = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % machin
% 0.32/0.65  thf(fact_8618_sum__pos__lt__pair,axiom,
% 0.32/0.65      ! [F: nat > real,K: nat] :
% 0.32/0.65        ( ( summable_real @ F )
% 0.32/0.65       => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 0.32/0.65         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sum_pos_lt_pair
% 0.32/0.65  thf(fact_8619_ceiling__log2__div2,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.65       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.65          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_log2_div2
% 0.32/0.65  thf(fact_8620_sin__cos__npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_cos_npi
% 0.32/0.65  thf(fact_8621_cos__pi__eq__zero,axiom,
% 0.32/0.65      ! [M: nat] :
% 0.32/0.65        ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_pi_eq_zero
% 0.32/0.65  thf(fact_8622_and__int_Opsimps,axiom,
% 0.32/0.65      ! [K: int,L2: int] :
% 0.32/0.65        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 0.32/0.65       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.65              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.65           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 0.32/0.65              = ( uminus_uminus_int
% 0.32/0.65                @ ( zero_n2684676970156552555ol_int
% 0.32/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.32/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 0.32/0.65          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.65                & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.65           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 0.32/0.65              = ( plus_plus_int
% 0.32/0.65                @ ( zero_n2684676970156552555ol_int
% 0.32/0.65                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.32/0.65                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.32/0.65                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % and_int.psimps
% 0.32/0.65  thf(fact_8623_and__int_Opelims,axiom,
% 0.32/0.65      ! [X: int,Xa2: int,Y: int] :
% 0.32/0.65        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.32/0.65          = Y )
% 0.32/0.65       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 0.32/0.65         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.65                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.65                 => ( Y
% 0.32/0.65                    = ( uminus_uminus_int
% 0.32/0.65                      @ ( zero_n2684676970156552555ol_int
% 0.32/0.65                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.32/0.65                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.32/0.65                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.65                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.65                 => ( Y
% 0.32/0.65                    = ( plus_plus_int
% 0.32/0.65                      @ ( zero_n2684676970156552555ol_int
% 0.32/0.65                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.32/0.65                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.32/0.65                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.32/0.65             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % and_int.pelims
% 0.32/0.65  thf(fact_8624_Maclaurin__exp__lt,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( X != zero_zero_real )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ? [T6: real] :
% 0.32/0.65              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.32/0.65              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.65              & ( ( exp_real @ X )
% 0.32/0.65                = ( plus_plus_real
% 0.32/0.65                  @ ( groups6591440286371151544t_real
% 0.32/0.65                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 0.32/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_exp_lt
% 0.32/0.65  thf(fact_8625_sin__pi,axiom,
% 0.32/0.65      ( ( sin_real @ pi )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_pi
% 0.32/0.65  thf(fact_8626_sin__pi__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 0.32/0.65        = ( sin_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_pi_minus
% 0.32/0.65  thf(fact_8627_cos__pi,axiom,
% 0.32/0.65      ( ( cos_real @ pi )
% 0.32/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_pi
% 0.32/0.65  thf(fact_8628_cos__periodic__pi2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_periodic_pi2
% 0.32/0.65  thf(fact_8629_cos__periodic__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_periodic_pi
% 0.32/0.65  thf(fact_8630_sin__periodic__pi2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_periodic_pi2
% 0.32/0.65  thf(fact_8631_sin__periodic__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_periodic_pi
% 0.32/0.65  thf(fact_8632_cos__minus__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_minus_pi
% 0.32/0.65  thf(fact_8633_cos__pi__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_pi_minus
% 0.32/0.65  thf(fact_8634_sin__minus__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_minus_pi
% 0.32/0.65  thf(fact_8635_sin__npi2,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_npi2
% 0.32/0.65  thf(fact_8636_sin__npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_npi
% 0.32/0.65  thf(fact_8637_sin__npi__int,axiom,
% 0.32/0.65      ! [N: int] :
% 0.32/0.65        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_npi_int
% 0.32/0.65  thf(fact_8638_cos__pi__half,axiom,
% 0.32/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_pi_half
% 0.32/0.65  thf(fact_8639_sin__two__pi,axiom,
% 0.32/0.65      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_two_pi
% 0.32/0.65  thf(fact_8640_sin__pi__half,axiom,
% 0.32/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_pi_half
% 0.32/0.65  thf(fact_8641_cos__two__pi,axiom,
% 0.32/0.65      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_two_pi
% 0.32/0.65  thf(fact_8642_cos__periodic,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.65        = ( cos_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_periodic
% 0.32/0.65  thf(fact_8643_sin__periodic,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.65        = ( sin_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_periodic
% 0.32/0.65  thf(fact_8644_cos__2pi__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.32/0.65        = ( cos_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_2pi_minus
% 0.32/0.65  thf(fact_8645_cos__npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.32/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_npi
% 0.32/0.65  thf(fact_8646_cos__npi2,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.65        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_npi2
% 0.32/0.65  thf(fact_8647_sin__2npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_2npi
% 0.32/0.65  thf(fact_8648_cos__2npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.32/0.65        = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_2npi
% 0.32/0.65  thf(fact_8649_sin__2pi__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_2pi_minus
% 0.32/0.65  thf(fact_8650_sin__int__2pin,axiom,
% 0.32/0.65      ! [N: int] :
% 0.32/0.65        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_int_2pin
% 0.32/0.65  thf(fact_8651_cos__int__2pin,axiom,
% 0.32/0.65      ! [N: int] :
% 0.32/0.65        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.32/0.65        = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_int_2pin
% 0.32/0.65  thf(fact_8652_cos__3over2__pi,axiom,
% 0.32/0.65      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_3over2_pi
% 0.32/0.65  thf(fact_8653_sin__3over2__pi,axiom,
% 0.32/0.65      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.32/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_3over2_pi
% 0.32/0.65  thf(fact_8654_cos__npi__int,axiom,
% 0.32/0.65      ! [N: int] :
% 0.32/0.65        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.32/0.65         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.32/0.65            = one_one_real ) )
% 0.32/0.65        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.32/0.65         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.32/0.65            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_npi_int
% 0.32/0.65  thf(fact_8655_polar__Ex,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65      ? [R2: real,A5: real] :
% 0.32/0.65        ( ( X
% 0.32/0.65          = ( times_times_real @ R2 @ ( cos_real @ A5 ) ) )
% 0.32/0.65        & ( Y
% 0.32/0.65          = ( times_times_real @ R2 @ ( sin_real @ A5 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % polar_Ex
% 0.32/0.65  thf(fact_8656_sin__zero__abs__cos__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sin_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65       => ( ( abs_abs_real @ ( cos_real @ X ) )
% 0.32/0.65          = one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_abs_cos_one
% 0.32/0.65  thf(fact_8657_sincos__principal__value,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65      ? [Y5: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y5 )
% 0.32/0.65        & ( ord_less_eq_real @ Y5 @ pi )
% 0.32/0.65        & ( ( sin_real @ Y5 )
% 0.32/0.65          = ( sin_real @ X ) )
% 0.32/0.65        & ( ( cos_real @ Y5 )
% 0.32/0.65          = ( cos_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sincos_principal_value
% 0.32/0.65  thf(fact_8658_sin__x__le__x,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_x_le_x
% 0.32/0.65  thf(fact_8659_sin__le__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_le_one
% 0.32/0.65  thf(fact_8660_cos__le__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_le_one
% 0.32/0.65  thf(fact_8661_abs__sin__x__le__abs__x,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % abs_sin_x_le_abs_x
% 0.32/0.65  thf(fact_8662_cos__arctan__not__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( arctan @ X ) )
% 0.32/0.65       != zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arctan_not_zero
% 0.32/0.65  thf(fact_8663_sin__cos__le1,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_cos_le1
% 0.32/0.65  thf(fact_8664_sin__gt__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ pi )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_gt_zero
% 0.32/0.65  thf(fact_8665_sin__x__ge__neg__x,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_x_ge_neg_x
% 0.32/0.65  thf(fact_8666_sin__ge__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_ge_zero
% 0.32/0.65  thf(fact_8667_sin__ge__minus__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_ge_minus_one
% 0.32/0.65  thf(fact_8668_cos__inj__pi,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ pi )
% 0.32/0.65             => ( ( ( cos_real @ X )
% 0.32/0.65                  = ( cos_real @ Y ) )
% 0.32/0.65               => ( X = Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_inj_pi
% 0.32/0.65  thf(fact_8669_cos__mono__le__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ pi )
% 0.32/0.65             => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 0.32/0.65                = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_mono_le_eq
% 0.32/0.65  thf(fact_8670_cos__monotone__0__pi__le,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65           => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_monotone_0_pi_le
% 0.32/0.65  thf(fact_8671_cos__ge__minus__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_ge_minus_one
% 0.32/0.65  thf(fact_8672_abs__sin__le__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % abs_sin_le_one
% 0.32/0.65  thf(fact_8673_abs__cos__le__one,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % abs_cos_le_one
% 0.32/0.65  thf(fact_8674_cos__two__neq__zero,axiom,
% 0.32/0.65      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65     != zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_two_neq_zero
% 0.32/0.65  thf(fact_8675_cos__mono__less__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ pi )
% 0.32/0.65             => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 0.32/0.65                = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_mono_less_eq
% 0.32/0.65  thf(fact_8676_cos__monotone__0__pi,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65           => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_monotone_0_pi
% 0.32/0.65  thf(fact_8677_sin__eq__0__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ pi )
% 0.32/0.65         => ( ( ( sin_real @ X )
% 0.32/0.65              = zero_zero_real )
% 0.32/0.65           => ( X = zero_zero_real ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_eq_0_pi
% 0.32/0.65  thf(fact_8678_sin__zero__pi__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 0.32/0.65       => ( ( ( sin_real @ X )
% 0.32/0.65            = zero_zero_real )
% 0.32/0.65          = ( X = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_pi_iff
% 0.32/0.65  thf(fact_8679_cos__monotone__minus__pi__0_H,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.65           => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_monotone_minus_pi_0'
% 0.32/0.65  thf(fact_8680_sin__zero__iff__int2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sin_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( ? [I5: int] :
% 0.32/0.65              ( X
% 0.32/0.65              = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_iff_int2
% 0.32/0.65  thf(fact_8681_sincos__total__pi,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65       => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65            = one_one_real )
% 0.32/0.65         => ? [T6: real] :
% 0.32/0.65              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.65              & ( ord_less_eq_real @ T6 @ pi )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( cos_real @ T6 ) )
% 0.32/0.65              & ( Y
% 0.32/0.65                = ( sin_real @ T6 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sincos_total_pi
% 0.32/0.65  thf(fact_8682_sin__expansion__lemma,axiom,
% 0.32/0.65      ! [X: real,M: nat] :
% 0.32/0.65        ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_expansion_lemma
% 0.32/0.65  thf(fact_8683_cos__expansion__lemma,axiom,
% 0.32/0.65      ! [X: real,M: nat] :
% 0.32/0.65        ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_expansion_lemma
% 0.32/0.65  thf(fact_8684_sin__gt__zero__02,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_gt_zero_02
% 0.32/0.65  thf(fact_8685_cos__two__less__zero,axiom,
% 0.32/0.65      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.32/0.65  
% 0.32/0.65  % cos_two_less_zero
% 0.32/0.65  thf(fact_8686_cos__is__zero,axiom,
% 0.32/0.65      ? [X6: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 0.32/0.65        & ( ord_less_eq_real @ X6 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65        & ( ( cos_real @ X6 )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        & ! [Y2: real] :
% 0.32/0.65            ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.32/0.65              & ( ord_less_eq_real @ Y2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65              & ( ( cos_real @ Y2 )
% 0.32/0.65                = zero_zero_real ) )
% 0.32/0.65           => ( Y2 = X6 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_is_zero
% 0.32/0.65  thf(fact_8687_cos__two__le__zero,axiom,
% 0.32/0.65      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.32/0.65  
% 0.32/0.65  % cos_two_le_zero
% 0.32/0.65  thf(fact_8688_cos__monotone__minus__pi__0,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.65           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_monotone_minus_pi_0
% 0.32/0.65  thf(fact_8689_cos__total,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ? [X6: real] :
% 0.32/0.65              ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 0.32/0.65              & ( ord_less_eq_real @ X6 @ pi )
% 0.32/0.65              & ( ( cos_real @ X6 )
% 0.32/0.65                = Y )
% 0.32/0.65              & ! [Y2: real] :
% 0.32/0.65                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 0.32/0.65                    & ( ord_less_eq_real @ Y2 @ pi )
% 0.32/0.65                    & ( ( cos_real @ Y2 )
% 0.32/0.65                      = Y ) )
% 0.32/0.65                 => ( Y2 = X6 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_total
% 0.32/0.65  thf(fact_8690_sincos__total__pi__half,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65              = one_one_real )
% 0.32/0.65           => ? [T6: real] :
% 0.32/0.65                ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.65                & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65                & ( X
% 0.32/0.65                  = ( cos_real @ T6 ) )
% 0.32/0.65                & ( Y
% 0.32/0.65                  = ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sincos_total_pi_half
% 0.32/0.65  thf(fact_8691_sincos__total__2pi__le,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65          = one_one_real )
% 0.32/0.65       => ? [T6: real] :
% 0.32/0.65            ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.65            & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65            & ( X
% 0.32/0.65              = ( cos_real @ T6 ) )
% 0.32/0.65            & ( Y
% 0.32/0.65              = ( sin_real @ T6 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sincos_total_2pi_le
% 0.32/0.65  thf(fact_8692_square__fact__le__2__fact,axiom,
% 0.32/0.65      ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % square_fact_le_2_fact
% 0.32/0.65  thf(fact_8693_sincos__total__2pi,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65          = one_one_real )
% 0.32/0.65       => ~ ! [T6: real] :
% 0.32/0.65              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.65             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65               => ( ( X
% 0.32/0.65                    = ( cos_real @ T6 ) )
% 0.32/0.65                 => ( Y
% 0.32/0.65                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sincos_total_2pi
% 0.32/0.65  thf(fact_8694_sin__pi__divide__n__ge__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( N != zero_zero_nat )
% 0.32/0.65       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_pi_divide_n_ge_0
% 0.32/0.65  thf(fact_8695_sin__gt__zero2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_gt_zero2
% 0.32/0.65  thf(fact_8696_sin__lt__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ pi @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_lt_zero
% 0.32/0.65  thf(fact_8697_cos__double__less__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.65         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_double_less_one
% 0.32/0.65  thf(fact_8698_sin__30,axiom,
% 0.32/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_30
% 0.32/0.65  thf(fact_8699_cos__gt__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_gt_zero
% 0.32/0.65  thf(fact_8700_sin__monotone__2pi__le,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_monotone_2pi_le
% 0.32/0.65  thf(fact_8701_sin__mono__le__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 0.32/0.65                = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_mono_le_eq
% 0.32/0.65  thf(fact_8702_sin__inj__pi,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ( sin_real @ X )
% 0.32/0.65                  = ( sin_real @ Y ) )
% 0.32/0.65               => ( X = Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_inj_pi
% 0.32/0.65  thf(fact_8703_cos__60,axiom,
% 0.32/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_60
% 0.32/0.65  thf(fact_8704_cos__one__2pi__int,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( cos_real @ X )
% 0.32/0.65          = one_one_real )
% 0.32/0.65        = ( ? [X3: int] :
% 0.32/0.65              ( X
% 0.32/0.65              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_one_2pi_int
% 0.32/0.65  thf(fact_8705_Maclaurin__cos__expansion,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65      ? [T6: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.65        & ( ( cos_real @ X )
% 0.32/0.65          = ( plus_plus_real
% 0.32/0.65            @ ( groups6591440286371151544t_real
% 0.32/0.65              @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_cos_expansion
% 0.32/0.65  thf(fact_8706_sin__le__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ pi @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65         => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_le_zero
% 0.32/0.65  thf(fact_8707_sin__less__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.65         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_less_zero
% 0.32/0.65  thf(fact_8708_sin__monotone__2pi,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_monotone_2pi
% 0.32/0.65  thf(fact_8709_sin__mono__less__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 0.32/0.65                = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_mono_less_eq
% 0.32/0.65  thf(fact_8710_sin__total,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ? [X6: real] :
% 0.32/0.65              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 0.32/0.65              & ( ord_less_eq_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65              & ( ( sin_real @ X6 )
% 0.32/0.65                = Y )
% 0.32/0.65              & ! [Y2: real] :
% 0.32/0.65                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.32/0.65                    & ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65                    & ( ( sin_real @ Y2 )
% 0.32/0.65                      = Y ) )
% 0.32/0.65                 => ( Y2 = X6 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_total
% 0.32/0.65  thf(fact_8711_cos__gt__zero__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_gt_zero_pi
% 0.32/0.65  thf(fact_8712_cos__ge__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_ge_zero
% 0.32/0.65  thf(fact_8713_cos__one__2pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( cos_real @ X )
% 0.32/0.65          = one_one_real )
% 0.32/0.65        = ( ? [X3: nat] :
% 0.32/0.65              ( X
% 0.32/0.65              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.32/0.65          | ? [X3: nat] :
% 0.32/0.65              ( X
% 0.32/0.65              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_one_2pi
% 0.32/0.65  thf(fact_8714_and__int_Opinduct,axiom,
% 0.32/0.65      ! [A0: int,A12: int,P: int > int > $o] :
% 0.32/0.65        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.32/0.65       => ( ! [K3: int,L4: int] :
% 0.32/0.65              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 0.32/0.65             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.32/0.65                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.32/0.65                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65               => ( P @ K3 @ L4 ) ) )
% 0.32/0.65         => ( P @ A0 @ A12 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % and_int.pinduct
% 0.32/0.65  thf(fact_8715_Maclaurin__lemma,axiom,
% 0.32/0.65      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.32/0.65       => ? [B8: real] :
% 0.32/0.65            ( ( F @ H2 )
% 0.32/0.65            = ( plus_plus_real
% 0.32/0.65              @ ( groups6591440286371151544t_real
% 0.32/0.65                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.32/0.65                @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65              @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_lemma
% 0.32/0.65  thf(fact_8716_Maclaurin__minus__cos__expansion,axiom,
% 0.32/0.65      ! [N: nat,X: real] :
% 0.32/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.65         => ? [T6: real] :
% 0.32/0.65              ( ( ord_less_real @ X @ T6 )
% 0.32/0.65              & ( ord_less_real @ T6 @ zero_zero_real )
% 0.32/0.65              & ( ( cos_real @ X )
% 0.32/0.65                = ( plus_plus_real
% 0.32/0.65                  @ ( groups6591440286371151544t_real
% 0.32/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_minus_cos_expansion
% 0.32/0.65  thf(fact_8717_Maclaurin__cos__expansion2,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65         => ? [T6: real] :
% 0.32/0.65              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.32/0.65              & ( ord_less_real @ T6 @ X )
% 0.32/0.65              & ( ( cos_real @ X )
% 0.32/0.65                = ( plus_plus_real
% 0.32/0.65                  @ ( groups6591440286371151544t_real
% 0.32/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_cos_expansion2
% 0.32/0.65  thf(fact_8718_sin__pi__divide__n__gt__0,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.65       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_pi_divide_n_gt_0
% 0.32/0.65  thf(fact_8719_Maclaurin__exp__le,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65      ? [T6: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.65        & ( ( exp_real @ X )
% 0.32/0.65          = ( plus_plus_real
% 0.32/0.65            @ ( groups6591440286371151544t_real
% 0.32/0.65              @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_exp_le
% 0.32/0.65  thf(fact_8720_sin__zero__iff__int,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sin_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( ? [I5: int] :
% 0.32/0.65              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_iff_int
% 0.32/0.65  thf(fact_8721_cos__zero__iff__int,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( cos_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( ? [I5: int] :
% 0.32/0.65              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_zero_iff_int
% 0.32/0.65  thf(fact_8722_sin__zero__lemma,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ( sin_real @ X )
% 0.32/0.65            = zero_zero_real )
% 0.32/0.65         => ? [N3: nat] :
% 0.32/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_lemma
% 0.32/0.65  thf(fact_8723_sin__zero__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sin_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( ? [N2: nat] :
% 0.32/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.65          | ? [N2: nat] :
% 0.32/0.65              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_zero_iff
% 0.32/0.65  thf(fact_8724_cos__coeff__def,axiom,
% 0.32/0.65      ( cos_coeff
% 0.32/0.65      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_coeff_def
% 0.32/0.65  thf(fact_8725_cos__zero__lemma,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ( cos_real @ X )
% 0.32/0.65            = zero_zero_real )
% 0.32/0.65         => ? [N3: nat] :
% 0.32/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_zero_lemma
% 0.32/0.65  thf(fact_8726_cos__zero__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( cos_real @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( ? [N2: nat] :
% 0.32/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.65          | ? [N2: nat] :
% 0.32/0.65              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.32/0.65              & ( X
% 0.32/0.65                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_zero_iff
% 0.32/0.65  thf(fact_8727_Maclaurin__sin__expansion3,axiom,
% 0.32/0.65      ! [N: nat,X: real] :
% 0.32/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ? [T6: real] :
% 0.32/0.65              ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.32/0.65              & ( ord_less_real @ T6 @ X )
% 0.32/0.65              & ( ( sin_real @ X )
% 0.32/0.65                = ( plus_plus_real
% 0.32/0.65                  @ ( groups6591440286371151544t_real
% 0.32/0.65                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_sin_expansion3
% 0.32/0.65  thf(fact_8728_Maclaurin__sin__expansion4,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ? [T6: real] :
% 0.32/0.65            ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.32/0.65            & ( ord_less_eq_real @ T6 @ X )
% 0.32/0.65            & ( ( sin_real @ X )
% 0.32/0.65              = ( plus_plus_real
% 0.32/0.65                @ ( groups6591440286371151544t_real
% 0.32/0.65                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65                  @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_sin_expansion4
% 0.32/0.65  thf(fact_8729_Maclaurin__sin__expansion2,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65      ? [T6: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.65        & ( ( sin_real @ X )
% 0.32/0.65          = ( plus_plus_real
% 0.32/0.65            @ ( groups6591440286371151544t_real
% 0.32/0.65              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65              @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_sin_expansion2
% 0.32/0.65  thf(fact_8730_Maclaurin__sin__expansion,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65      ? [T6: real] :
% 0.32/0.65        ( ( sin_real @ X )
% 0.32/0.65        = ( plus_plus_real
% 0.32/0.65          @ ( groups6591440286371151544t_real
% 0.32/0.65            @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.65            @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.65          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Maclaurin_sin_expansion
% 0.32/0.65  thf(fact_8731_sin__coeff__def,axiom,
% 0.32/0.65      ( sin_coeff
% 0.32/0.65      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_coeff_def
% 0.32/0.65  thf(fact_8732_sin__coeff__0,axiom,
% 0.32/0.65      ( ( sin_coeff @ zero_zero_nat )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_coeff_0
% 0.32/0.65  thf(fact_8733_fact__ge__self,axiom,
% 0.32/0.65      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_ge_self
% 0.32/0.65  thf(fact_8734_fact__mono__nat,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.65       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_mono_nat
% 0.32/0.65  thf(fact_8735_fact__less__mono__nat,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.65       => ( ( ord_less_nat @ M @ N )
% 0.32/0.65         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_less_mono_nat
% 0.32/0.65  thf(fact_8736_fact__ge__Suc__0__nat,axiom,
% 0.32/0.65      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_ge_Suc_0_nat
% 0.32/0.65  thf(fact_8737_dvd__fact,axiom,
% 0.32/0.65      ! [M: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.32/0.65       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.65         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % dvd_fact
% 0.32/0.65  thf(fact_8738_fact__diff__Suc,axiom,
% 0.32/0.65      ! [N: nat,M: nat] :
% 0.32/0.65        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.32/0.65       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 0.32/0.65          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_diff_Suc
% 0.32/0.65  thf(fact_8739_fact__div__fact__le__pow,axiom,
% 0.32/0.65      ! [R: nat,N: nat] :
% 0.32/0.65        ( ( ord_less_eq_nat @ R @ N )
% 0.32/0.65       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % fact_div_fact_le_pow
% 0.32/0.65  thf(fact_8740_upto_Opinduct,axiom,
% 0.32/0.65      ! [A0: int,A12: int,P: int > int > $o] :
% 0.32/0.65        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.32/0.65       => ( ! [I4: int,J2: int] :
% 0.32/0.65              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 0.32/0.65             => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 0.32/0.65                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 0.32/0.65               => ( P @ I4 @ J2 ) ) )
% 0.32/0.65         => ( P @ A0 @ A12 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % upto.pinduct
% 0.32/0.65  thf(fact_8741_complex__unimodular__polar,axiom,
% 0.32/0.65      ! [Z: complex] :
% 0.32/0.65        ( ( ( real_V1022390504157884413omplex @ Z )
% 0.32/0.65          = one_one_real )
% 0.32/0.65       => ~ ! [T6: real] :
% 0.32/0.65              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.65             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.65               => ( Z
% 0.32/0.65                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_unimodular_polar
% 0.32/0.65  thf(fact_8742_sin__paired,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( sums_real
% 0.32/0.65        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.32/0.65        @ ( sin_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_paired
% 0.32/0.65  thf(fact_8743_tan__pi,axiom,
% 0.32/0.65      ( ( tan_real @ pi )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_pi
% 0.32/0.65  thf(fact_8744_tan__periodic__pi,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 0.32/0.65        = ( tan_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_periodic_pi
% 0.32/0.65  thf(fact_8745_tan__npi,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.32/0.65        = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_npi
% 0.32/0.65  thf(fact_8746_tan__periodic__n,axiom,
% 0.32/0.65      ! [X: real,N: num] :
% 0.32/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 0.32/0.65        = ( tan_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_periodic_n
% 0.32/0.65  thf(fact_8747_tan__periodic__nat,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 0.32/0.65        = ( tan_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_periodic_nat
% 0.32/0.65  thf(fact_8748_tan__periodic__int,axiom,
% 0.32/0.65      ! [X: real,I: int] :
% 0.32/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 0.32/0.65        = ( tan_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_periodic_int
% 0.32/0.65  thf(fact_8749_norm__cos__sin,axiom,
% 0.32/0.65      ! [T: real] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 0.32/0.65        = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % norm_cos_sin
% 0.32/0.65  thf(fact_8750_tan__periodic,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.65        = ( tan_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_periodic
% 0.32/0.65  thf(fact_8751_complex__diff,axiom,
% 0.32/0.65      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.65        ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 0.32/0.65        = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_diff
% 0.32/0.65  thf(fact_8752_Complex__eq__numeral,axiom,
% 0.32/0.65      ! [A: real,B: real,W: num] :
% 0.32/0.65        ( ( ( complex2 @ A @ B )
% 0.32/0.65          = ( numera6690914467698888265omplex @ W ) )
% 0.32/0.65        = ( ( A
% 0.32/0.65            = ( numeral_numeral_real @ W ) )
% 0.32/0.65          & ( B = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_eq_numeral
% 0.32/0.65  thf(fact_8753_Complex__eq__0,axiom,
% 0.32/0.65      ! [A: real,B: real] :
% 0.32/0.65        ( ( ( complex2 @ A @ B )
% 0.32/0.65          = zero_zero_complex )
% 0.32/0.65        = ( ( A = zero_zero_real )
% 0.32/0.65          & ( B = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_eq_0
% 0.32/0.65  thf(fact_8754_zero__complex_Ocode,axiom,
% 0.32/0.65      ( zero_zero_complex
% 0.32/0.65      = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % zero_complex.code
% 0.32/0.65  thf(fact_8755_complex__add,axiom,
% 0.32/0.65      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.65        ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 0.32/0.65        = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_add
% 0.32/0.65  thf(fact_8756_Complex__eq__neg__numeral,axiom,
% 0.32/0.65      ! [A: real,B: real,W: num] :
% 0.32/0.65        ( ( ( complex2 @ A @ B )
% 0.32/0.65          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.65        = ( ( A
% 0.32/0.65            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 0.32/0.65          & ( B = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_eq_neg_numeral
% 0.32/0.65  thf(fact_8757_complex__mult,axiom,
% 0.32/0.65      ! [A: real,B: real,C: real,D: real] :
% 0.32/0.65        ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 0.32/0.65        = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_mult
% 0.32/0.65  thf(fact_8758_Complex__eq__1,axiom,
% 0.32/0.65      ! [A: real,B: real] :
% 0.32/0.65        ( ( ( complex2 @ A @ B )
% 0.32/0.65          = one_one_complex )
% 0.32/0.65        = ( ( A = one_one_real )
% 0.32/0.65          & ( B = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_eq_1
% 0.32/0.65  thf(fact_8759_one__complex_Ocode,axiom,
% 0.32/0.65      ( one_one_complex
% 0.32/0.65      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % one_complex.code
% 0.32/0.65  thf(fact_8760_Complex__eq__neg__1,axiom,
% 0.32/0.65      ! [A: real,B: real] :
% 0.32/0.65        ( ( ( complex2 @ A @ B )
% 0.32/0.65          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.32/0.65        = ( ( A
% 0.32/0.65            = ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.65          & ( B = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_eq_neg_1
% 0.32/0.65  thf(fact_8761_tan__45,axiom,
% 0.32/0.65      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_45
% 0.32/0.65  thf(fact_8762_power__half__series,axiom,
% 0.32/0.65      ( sums_real
% 0.32/0.65      @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 0.32/0.65      @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % power_half_series
% 0.32/0.65  thf(fact_8763_lemma__tan__total,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.65       => ? [X6: real] :
% 0.32/0.65            ( ( ord_less_real @ zero_zero_real @ X6 )
% 0.32/0.65            & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65            & ( ord_less_real @ Y @ ( tan_real @ X6 ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_tan_total
% 0.32/0.65  thf(fact_8764_tan__gt__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_gt_zero
% 0.32/0.65  thf(fact_8765_lemma__tan__total1,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65      ? [X6: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 0.32/0.65        & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        & ( ( tan_real @ X6 )
% 0.32/0.65          = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_tan_total1
% 0.32/0.65  thf(fact_8766_tan__mono__lt__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 0.32/0.65                = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_mono_lt_eq
% 0.32/0.65  thf(fact_8767_tan__monotone_H,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65           => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ord_less_real @ Y @ X )
% 0.32/0.65                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_monotone'
% 0.32/0.65  thf(fact_8768_tan__monotone,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ X )
% 0.32/0.65         => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_monotone
% 0.32/0.65  thf(fact_8769_tan__total,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65      ? [X6: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 0.32/0.65        & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        & ( ( tan_real @ X6 )
% 0.32/0.65          = Y )
% 0.32/0.65        & ! [Y2: real] :
% 0.32/0.65            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 0.32/0.65              & ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65              & ( ( tan_real @ Y2 )
% 0.32/0.65                = Y ) )
% 0.32/0.65           => ( Y2 = X6 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_total
% 0.32/0.65  thf(fact_8770_tan__minus__45,axiom,
% 0.32/0.65      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.65      = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_minus_45
% 0.32/0.65  thf(fact_8771_tan__inverse,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 0.32/0.65        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_inverse
% 0.32/0.65  thf(fact_8772_sums__if_H,axiom,
% 0.32/0.65      ! [G: nat > real,X: real] :
% 0.32/0.65        ( ( sums_real @ G @ X )
% 0.32/0.65       => ( sums_real
% 0.32/0.65          @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65          @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sums_if'
% 0.32/0.65  thf(fact_8773_sums__if,axiom,
% 0.32/0.65      ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 0.32/0.65        ( ( sums_real @ G @ X )
% 0.32/0.65       => ( ( sums_real @ F @ Y )
% 0.32/0.65         => ( sums_real
% 0.32/0.65            @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65            @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sums_if
% 0.32/0.65  thf(fact_8774_tan__pos__pi2__le,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_pos_pi2_le
% 0.32/0.65  thf(fact_8775_tan__total__pos,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65       => ? [X6: real] :
% 0.32/0.65            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 0.32/0.65            & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65            & ( ( tan_real @ X6 )
% 0.32/0.65              = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_total_pos
% 0.32/0.65  thf(fact_8776_tan__less__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.65         => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_less_zero
% 0.32/0.65  thf(fact_8777_tan__mono__le__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.32/0.65           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65             => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 0.32/0.65                = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_mono_le_eq
% 0.32/0.65  thf(fact_8778_tan__mono__le,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_mono_le
% 0.32/0.65  thf(fact_8779_tan__bound__pi2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_bound_pi2
% 0.32/0.65  thf(fact_8780_arctan__unique,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ( tan_real @ X )
% 0.32/0.65              = Y )
% 0.32/0.65           => ( ( arctan @ Y )
% 0.32/0.65              = X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_unique
% 0.32/0.65  thf(fact_8781_arctan__tan,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( arctan @ ( tan_real @ X ) )
% 0.32/0.65            = X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_tan
% 0.32/0.65  thf(fact_8782_arctan,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.32/0.65        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        & ( ( tan_real @ ( arctan @ Y ) )
% 0.32/0.65          = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan
% 0.32/0.65  thf(fact_8783_tan__total__pi4,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ? [Z5: real] :
% 0.32/0.65            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z5 )
% 0.32/0.65            & ( ord_less_real @ Z5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65            & ( ( tan_real @ Z5 )
% 0.32/0.65              = X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_total_pi4
% 0.32/0.65  thf(fact_8784_cos__paired,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( sums_real
% 0.32/0.65        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.65        @ ( cos_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_paired
% 0.32/0.65  thf(fact_8785_ceiling__log__eq__powr__iff,axiom,
% 0.32/0.65      ! [X: real,B: real,K: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 0.32/0.65              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.32/0.65            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 0.32/0.65              & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ceiling_log_eq_powr_iff
% 0.32/0.65  thf(fact_8786_sin__tan,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ( sin_real @ X )
% 0.32/0.65          = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_tan
% 0.32/0.65  thf(fact_8787_real__sqrt__eq__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( sqrt @ X )
% 0.32/0.65          = ( sqrt @ Y ) )
% 0.32/0.65        = ( X = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_eq_iff
% 0.32/0.65  thf(fact_8788_real__sqrt__eq__zero__cancel__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sqrt @ X )
% 0.32/0.65          = zero_zero_real )
% 0.32/0.65        = ( X = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_eq_zero_cancel_iff
% 0.32/0.65  thf(fact_8789_real__sqrt__zero,axiom,
% 0.32/0.65      ( ( sqrt @ zero_zero_real )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_zero
% 0.32/0.65  thf(fact_8790_real__sqrt__less__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_real @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_less_iff
% 0.32/0.65  thf(fact_8791_real__sqrt__le__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_le_iff
% 0.32/0.65  thf(fact_8792_real__sqrt__eq__1__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( sqrt @ X )
% 0.32/0.65          = one_one_real )
% 0.32/0.65        = ( X = one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_eq_1_iff
% 0.32/0.65  thf(fact_8793_real__sqrt__one,axiom,
% 0.32/0.65      ( ( sqrt @ one_one_real )
% 0.32/0.65      = one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_one
% 0.32/0.65  thf(fact_8794_real__sqrt__lt__0__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.32/0.65        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_lt_0_iff
% 0.32/0.65  thf(fact_8795_real__sqrt__gt__0__iff,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_gt_0_iff
% 0.32/0.65  thf(fact_8796_real__sqrt__le__0__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.32/0.65        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_le_0_iff
% 0.32/0.65  thf(fact_8797_real__sqrt__ge__0__iff,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_0_iff
% 0.32/0.65  thf(fact_8798_powr__gt__zero,axiom,
% 0.32/0.65      ! [X: real,A: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 0.32/0.65        = ( X != zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_gt_zero
% 0.32/0.65  thf(fact_8799_powr__nonneg__iff,axiom,
% 0.32/0.65      ! [A: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 0.32/0.65        = ( A = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_nonneg_iff
% 0.32/0.65  thf(fact_8800_real__sqrt__gt__1__iff,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_gt_1_iff
% 0.32/0.65  thf(fact_8801_real__sqrt__lt__1__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 0.32/0.65        = ( ord_less_real @ X @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_lt_1_iff
% 0.32/0.65  thf(fact_8802_real__sqrt__le__1__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 0.32/0.65        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_le_1_iff
% 0.32/0.65  thf(fact_8803_real__sqrt__ge__1__iff,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 0.32/0.65        = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_1_iff
% 0.32/0.65  thf(fact_8804_powr__less__cancel__iff,axiom,
% 0.32/0.65      ! [X: real,A: real,B: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.32/0.65          = ( ord_less_real @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_cancel_iff
% 0.32/0.65  thf(fact_8805_real__sqrt__mult__self,axiom,
% 0.32/0.65      ! [A: real] :
% 0.32/0.65        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 0.32/0.65        = ( abs_abs_real @ A ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_mult_self
% 0.32/0.65  thf(fact_8806_real__sqrt__abs2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sqrt @ ( times_times_real @ X @ X ) )
% 0.32/0.65        = ( abs_abs_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_abs2
% 0.32/0.65  thf(fact_8807_real__sqrt__four,axiom,
% 0.32/0.65      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.32/0.65      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_four
% 0.32/0.65  thf(fact_8808_powr__eq__one__iff,axiom,
% 0.32/0.65      ! [A: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ A )
% 0.32/0.65       => ( ( ( powr_real @ A @ X )
% 0.32/0.65            = one_one_real )
% 0.32/0.65          = ( X = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_eq_one_iff
% 0.32/0.65  thf(fact_8809_powr__one__gt__zero__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( powr_real @ X @ one_one_real )
% 0.32/0.65          = X )
% 0.32/0.65        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_one_gt_zero_iff
% 0.32/0.65  thf(fact_8810_powr__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ one_one_real )
% 0.32/0.65          = X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_one
% 0.32/0.65  thf(fact_8811_powr__le__cancel__iff,axiom,
% 0.32/0.65      ! [X: real,A: real,B: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.32/0.65          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_le_cancel_iff
% 0.32/0.65  thf(fact_8812_numeral__powr__numeral__real,axiom,
% 0.32/0.65      ! [M: num,N: num] :
% 0.32/0.65        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.32/0.65        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % numeral_powr_numeral_real
% 0.32/0.65  thf(fact_8813_powr__log__cancel,axiom,
% 0.32/0.65      ! [A: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( A != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( powr_real @ A @ ( log @ A @ X ) )
% 0.32/0.65              = X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_log_cancel
% 0.32/0.65  thf(fact_8814_log__powr__cancel,axiom,
% 0.32/0.65      ! [A: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( A != one_one_real )
% 0.32/0.65         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 0.32/0.65            = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_powr_cancel
% 0.32/0.65  thf(fact_8815_real__sqrt__abs,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65        = ( abs_abs_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_abs
% 0.32/0.65  thf(fact_8816_powr__numeral,axiom,
% 0.32/0.65      ! [X: real,N: num] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 0.32/0.65          = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_numeral
% 0.32/0.65  thf(fact_8817_real__sqrt__pow2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65          = X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_pow2
% 0.32/0.65  thf(fact_8818_real__sqrt__pow2__iff,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65          = X )
% 0.32/0.65        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_pow2_iff
% 0.32/0.65  thf(fact_8819_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 0.32/0.65      ! [X: real,Y: real,Xa2: real,Ya: real] :
% 0.32/0.65        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_mult_squared_eq
% 0.32/0.65  thf(fact_8820_square__powr__half,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65        = ( abs_abs_real @ X ) ) ).
% 0.32/0.65  
% 0.32/0.65  % square_powr_half
% 0.32/0.65  thf(fact_8821_real__sqrt__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 0.32/0.65        = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_minus
% 0.32/0.65  thf(fact_8822_real__sqrt__le__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65       => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_le_mono
% 0.32/0.65  thf(fact_8823_real__sqrt__power,axiom,
% 0.32/0.65      ! [X: real,K: nat] :
% 0.32/0.65        ( ( sqrt @ ( power_power_real @ X @ K ) )
% 0.32/0.65        = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_power
% 0.32/0.65  thf(fact_8824_real__sqrt__mult,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 0.32/0.65        = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_mult
% 0.32/0.65  thf(fact_8825_real__sqrt__divide,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 0.32/0.65        = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_divide
% 0.32/0.65  thf(fact_8826_powr__powr,axiom,
% 0.32/0.65      ! [X: real,A: real,B: real] :
% 0.32/0.65        ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 0.32/0.65        = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_powr
% 0.32/0.65  thf(fact_8827_real__sqrt__less__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ X @ Y )
% 0.32/0.65       => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_less_mono
% 0.32/0.65  thf(fact_8828_powr__non__neg,axiom,
% 0.32/0.65      ! [A: real,X: real] :
% 0.32/0.65        ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_non_neg
% 0.32/0.65  thf(fact_8829_powr__less__mono2__neg,axiom,
% 0.32/0.65      ! [A: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ A @ zero_zero_real )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ X @ Y )
% 0.32/0.65           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_mono2_neg
% 0.32/0.65  thf(fact_8830_powr__ge__pzero,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_ge_pzero
% 0.32/0.65  thf(fact_8831_powr__mono2,axiom,
% 0.32/0.65      ! [A: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mono2
% 0.32/0.65  thf(fact_8832_real__sqrt__gt__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_gt_zero
% 0.32/0.65  thf(fact_8833_real__sqrt__eq__zero__cancel,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ( sqrt @ X )
% 0.32/0.65            = zero_zero_real )
% 0.32/0.65         => ( X = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_eq_zero_cancel
% 0.32/0.65  thf(fact_8834_real__sqrt__ge__zero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_zero
% 0.32/0.65  thf(fact_8835_powr__less__mono,axiom,
% 0.32/0.65      ! [A: real,B: real,X: real] :
% 0.32/0.65        ( ( ord_less_real @ A @ B )
% 0.32/0.65       => ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65         => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_mono
% 0.32/0.65  thf(fact_8836_powr__less__cancel,axiom,
% 0.32/0.65      ! [X: real,A: real,B: real] :
% 0.32/0.65        ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.32/0.65       => ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65         => ( ord_less_real @ A @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_cancel
% 0.32/0.65  thf(fact_8837_powr__mono,axiom,
% 0.32/0.65      ! [A: real,B: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.65       => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mono
% 0.32/0.65  thf(fact_8838_real__sqrt__ge__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_one
% 0.32/0.65  thf(fact_8839_powr__mono2_H,axiom,
% 0.32/0.65      ! [A: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mono2'
% 0.32/0.65  thf(fact_8840_powr__less__mono2,axiom,
% 0.32/0.65      ! [A: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ X @ Y )
% 0.32/0.65           => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_mono2
% 0.32/0.65  thf(fact_8841_powr__inj,axiom,
% 0.32/0.65      ! [A: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( A != one_one_real )
% 0.32/0.65         => ( ( ( powr_real @ A @ X )
% 0.32/0.65              = ( powr_real @ A @ Y ) )
% 0.32/0.65            = ( X = Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_inj
% 0.32/0.65  thf(fact_8842_gr__one__powr,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % gr_one_powr
% 0.32/0.65  thf(fact_8843_ge__one__powr__ge__zero,axiom,
% 0.32/0.65      ! [X: real,A: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.65         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ge_one_powr_ge_zero
% 0.32/0.65  thf(fact_8844_powr__mono__both,axiom,
% 0.32/0.65      ! [A: real,B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( ord_less_eq_real @ A @ B )
% 0.32/0.65         => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65           => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65             => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mono_both
% 0.32/0.65  thf(fact_8845_powr__le1,axiom,
% 0.32/0.65      ! [A: real,X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_le1
% 0.32/0.65  thf(fact_8846_powr__divide,axiom,
% 0.32/0.65      ! [X: real,Y: real,A: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 0.32/0.65            = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_divide
% 0.32/0.65  thf(fact_8847_powr__mult,axiom,
% 0.32/0.65      ! [X: real,Y: real,A: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 0.32/0.65            = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mult
% 0.32/0.65  thf(fact_8848_real__div__sqrt,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 0.32/0.65          = ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_div_sqrt
% 0.32/0.65  thf(fact_8849_sqrt__add__le__add__sqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_add_le_add_sqrt
% 0.32/0.65  thf(fact_8850_le__real__sqrt__sumsq,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % le_real_sqrt_sumsq
% 0.32/0.65  thf(fact_8851_divide__powr__uminus,axiom,
% 0.32/0.65      ! [A: real,B: real,C: real] :
% 0.32/0.65        ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 0.32/0.65        = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % divide_powr_uminus
% 0.32/0.65  thf(fact_8852_log__base__powr,axiom,
% 0.32/0.65      ! [A: real,B: real,X: real] :
% 0.32/0.65        ( ( A != zero_zero_real )
% 0.32/0.65       => ( ( log @ ( powr_real @ A @ B ) @ X )
% 0.32/0.65          = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_base_powr
% 0.32/0.65  thf(fact_8853_ln__powr,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( X != zero_zero_real )
% 0.32/0.65       => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 0.32/0.65          = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_powr
% 0.32/0.65  thf(fact_8854_log__powr,axiom,
% 0.32/0.65      ! [X: real,B: real,Y: real] :
% 0.32/0.65        ( ( X != zero_zero_real )
% 0.32/0.65       => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 0.32/0.65          = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_powr
% 0.32/0.65  thf(fact_8855_powr__half__sqrt,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65          = ( sqrt @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_half_sqrt
% 0.32/0.65  thf(fact_8856_sqrt2__less__2,axiom,
% 0.32/0.65      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt2_less_2
% 0.32/0.65  thf(fact_8857_powr__realpow,axiom,
% 0.32/0.65      ! [X: real,N: nat] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.32/0.65          = ( power_power_real @ X @ N ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_realpow
% 0.32/0.65  thf(fact_8858_powr__less__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 0.32/0.65            = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_less_iff
% 0.32/0.65  thf(fact_8859_less__powr__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 0.32/0.65            = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % less_powr_iff
% 0.32/0.65  thf(fact_8860_log__less__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 0.32/0.65            = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_less_iff
% 0.32/0.65  thf(fact_8861_less__log__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 0.32/0.65            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % less_log_iff
% 0.32/0.65  thf(fact_8862_real__less__rsqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.32/0.65       => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_less_rsqrt
% 0.32/0.65  thf(fact_8863_sqrt__le__D,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 0.32/0.65       => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_le_D
% 0.32/0.65  thf(fact_8864_real__le__rsqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.32/0.65       => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_le_rsqrt
% 0.32/0.65  thf(fact_8865_powr__neg__one,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.65          = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_neg_one
% 0.32/0.65  thf(fact_8866_powr__mult__base,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 0.32/0.65          = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_mult_base
% 0.32/0.65  thf(fact_8867_tan__60,axiom,
% 0.32/0.65      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.32/0.65      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_60
% 0.32/0.65  thf(fact_8868_le__log__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 0.32/0.65            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % le_log_iff
% 0.32/0.65  thf(fact_8869_log__le__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 0.32/0.65            = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_le_iff
% 0.32/0.65  thf(fact_8870_le__powr__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 0.32/0.65            = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % le_powr_iff
% 0.32/0.65  thf(fact_8871_powr__le__iff,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 0.32/0.65            = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_le_iff
% 0.32/0.65  thf(fact_8872_real__le__lsqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_le_lsqrt
% 0.32/0.65  thf(fact_8873_real__sqrt__unique,axiom,
% 0.32/0.65      ! [Y: real,X: real] :
% 0.32/0.65        ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.65          = X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( sqrt @ X )
% 0.32/0.65            = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_unique
% 0.32/0.65  thf(fact_8874_lemma__real__divide__sqrt__less,axiom,
% 0.32/0.65      ! [U: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ U )
% 0.32/0.65       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.32/0.65  
% 0.32/0.65  % lemma_real_divide_sqrt_less
% 0.32/0.65  thf(fact_8875_real__sqrt__sum__squares__eq__cancel,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65          = X )
% 0.32/0.65       => ( Y = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_eq_cancel
% 0.32/0.65  thf(fact_8876_real__sqrt__sum__squares__eq__cancel2,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65          = Y )
% 0.32/0.65       => ( X = zero_zero_real ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_eq_cancel2
% 0.32/0.65  thf(fact_8877_real__sqrt__sum__squares__ge1,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_ge1
% 0.32/0.65  thf(fact_8878_real__sqrt__sum__squares__ge2,axiom,
% 0.32/0.65      ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_ge2
% 0.32/0.65  thf(fact_8879_real__sqrt__sum__squares__triangle__ineq,axiom,
% 0.32/0.65      ! [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 ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_triangle_ineq
% 0.32/0.65  thf(fact_8880_sqrt__ge__absD,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 0.32/0.65       => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_ge_absD
% 0.32/0.65  thf(fact_8881_ln__powr__bound,axiom,
% 0.32/0.65      ! [X: real,A: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65         => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_powr_bound
% 0.32/0.65  thf(fact_8882_ln__powr__bound2,axiom,
% 0.32/0.65      ! [X: real,A: real] :
% 0.32/0.65        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.65       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.65         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_powr_bound2
% 0.32/0.65  thf(fact_8883_cos__45,axiom,
% 0.32/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_45
% 0.32/0.65  thf(fact_8884_sin__45,axiom,
% 0.32/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_45
% 0.32/0.65  thf(fact_8885_add__log__eq__powr,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.65       => ( ( B != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 0.32/0.65              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % add_log_eq_powr
% 0.32/0.65  thf(fact_8886_log__add__eq__powr,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.65       => ( ( B != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 0.32/0.65              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_add_eq_powr
% 0.32/0.65  thf(fact_8887_minus__log__eq__powr,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.65       => ( ( B != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 0.32/0.65              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % minus_log_eq_powr
% 0.32/0.65  thf(fact_8888_real__less__lsqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.65           => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_less_lsqrt
% 0.32/0.65  thf(fact_8889_sqrt__sum__squares__le__sum,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_sum_squares_le_sum
% 0.32/0.65  thf(fact_8890_sqrt__even__pow2,axiom,
% 0.32/0.65      ! [N: nat] :
% 0.32/0.65        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.65       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.65          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_even_pow2
% 0.32/0.65  thf(fact_8891_tan__30,axiom,
% 0.32/0.65      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % tan_30
% 0.32/0.65  thf(fact_8892_real__sqrt__ge__abs1,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_abs1
% 0.32/0.65  thf(fact_8893_real__sqrt__ge__abs2,axiom,
% 0.32/0.65      ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_ge_abs2
% 0.32/0.65  thf(fact_8894_sqrt__sum__squares__le__sum__abs,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_sum_squares_le_sum_abs
% 0.32/0.65  thf(fact_8895_ln__sqrt,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ln_ln_real @ ( sqrt @ X ) )
% 0.32/0.65          = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % ln_sqrt
% 0.32/0.65  thf(fact_8896_arsinh__real__def,axiom,
% 0.32/0.65      ( arsinh_real
% 0.32/0.65      = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arsinh_real_def
% 0.32/0.65  thf(fact_8897_cos__30,axiom,
% 0.32/0.65      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_30
% 0.32/0.65  thf(fact_8898_sin__60,axiom,
% 0.32/0.65      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 0.32/0.65      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_60
% 0.32/0.65  thf(fact_8899_log__minus__eq__powr,axiom,
% 0.32/0.65      ! [B: real,X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.65       => ( ( B != one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 0.32/0.65              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % log_minus_eq_powr
% 0.32/0.65  thf(fact_8900_complex__norm,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 0.32/0.65        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_norm
% 0.32/0.65  thf(fact_8901_arsinh__real__aux,axiom,
% 0.32/0.65      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arsinh_real_aux
% 0.32/0.65  thf(fact_8902_real__sqrt__power__even,axiom,
% 0.32/0.65      ! [N: nat,X: real] :
% 0.32/0.65        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65         => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 0.32/0.65            = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_power_even
% 0.32/0.65  thf(fact_8903_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.32/0.65      ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_mult_ge_zero
% 0.32/0.65  thf(fact_8904_arith__geo__mean__sqrt,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arith_geo_mean_sqrt
% 0.32/0.65  thf(fact_8905_powr__neg__numeral,axiom,
% 0.32/0.65      ! [X: real,N: num] :
% 0.32/0.65        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.32/0.65          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % powr_neg_numeral
% 0.32/0.65  thf(fact_8906_cos__x__y__le__one,axiom,
% 0.32/0.65      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_x_y_le_one
% 0.32/0.65  thf(fact_8907_real__sqrt__sum__squares__less,axiom,
% 0.32/0.65      ! [X: real,U: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.65         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % real_sqrt_sum_squares_less
% 0.32/0.65  thf(fact_8908_arcosh__real__def,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.65       => ( ( arcosh_real @ X )
% 0.32/0.65          = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcosh_real_def
% 0.32/0.65  thf(fact_8909_cos__arctan,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( cos_real @ ( arctan @ X ) )
% 0.32/0.65        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arctan
% 0.32/0.65  thf(fact_8910_sin__arctan,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( sin_real @ ( arctan @ X ) )
% 0.32/0.65        = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_arctan
% 0.32/0.65  thf(fact_8911_sqrt__sum__squares__half__less,axiom,
% 0.32/0.65      ! [X: real,U: real,Y: real] :
% 0.32/0.65        ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sqrt_sum_squares_half_less
% 0.32/0.65  thf(fact_8912_sin__cos__sqrt,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 0.32/0.65       => ( ( sin_real @ X )
% 0.32/0.65          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_cos_sqrt
% 0.32/0.65  thf(fact_8913_arctan__half,axiom,
% 0.32/0.65      ( arctan
% 0.32/0.65      = ( ^ [X3: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X3 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arctan_half
% 0.32/0.65  thf(fact_8914_cos__tan,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.65       => ( ( cos_real @ X )
% 0.32/0.65          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_tan
% 0.32/0.65  thf(fact_8915_vebt__mint_Opelims,axiom,
% 0.32/0.65      ! [X: vEBT_VEBT,Y: option_nat] :
% 0.32/0.65        ( ( ( vEBT_vebt_mint @ X )
% 0.32/0.65          = Y )
% 0.32/0.65       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 0.32/0.65         => ( ! [A5: $o,B5: $o] :
% 0.32/0.65                ( ( X
% 0.32/0.65                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.65               => ( ( ( A5
% 0.32/0.65                     => ( Y
% 0.32/0.65                        = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.65                    & ( ~ A5
% 0.32/0.65                     => ( ( B5
% 0.32/0.65                         => ( Y
% 0.32/0.65                            = ( some_nat @ one_one_nat ) ) )
% 0.32/0.65                        & ( ~ B5
% 0.32/0.65                         => ( Y = none_nat ) ) ) ) )
% 0.32/0.65                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 0.32/0.65           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.65                  ( ( X
% 0.32/0.65                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.65                 => ( ( Y = none_nat )
% 0.32/0.65                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.32/0.65             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.65                    ( ( X
% 0.32/0.65                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.65                   => ( ( Y
% 0.32/0.65                        = ( some_nat @ Mi2 ) )
% 0.32/0.65                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % vebt_mint.pelims
% 0.32/0.65  thf(fact_8916_vebt__maxt_Opelims,axiom,
% 0.32/0.65      ! [X: vEBT_VEBT,Y: option_nat] :
% 0.32/0.65        ( ( ( vEBT_vebt_maxt @ X )
% 0.32/0.65          = Y )
% 0.32/0.65       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 0.32/0.65         => ( ! [A5: $o,B5: $o] :
% 0.32/0.65                ( ( X
% 0.32/0.65                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 0.32/0.65               => ( ( ( B5
% 0.32/0.65                     => ( Y
% 0.32/0.65                        = ( some_nat @ one_one_nat ) ) )
% 0.32/0.65                    & ( ~ B5
% 0.32/0.65                     => ( ( A5
% 0.32/0.65                         => ( Y
% 0.32/0.65                            = ( some_nat @ zero_zero_nat ) ) )
% 0.32/0.65                        & ( ~ A5
% 0.32/0.65                         => ( Y = none_nat ) ) ) ) )
% 0.32/0.65                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 0.32/0.65           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.32/0.65                  ( ( X
% 0.32/0.65                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.32/0.65                 => ( ( Y = none_nat )
% 0.32/0.65                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 0.32/0.65             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.32/0.65                    ( ( X
% 0.32/0.65                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 0.32/0.65                   => ( ( Y
% 0.32/0.65                        = ( some_nat @ Ma2 ) )
% 0.32/0.65                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % vebt_maxt.pelims
% 0.32/0.65  thf(fact_8917_complex__exp__exists,axiom,
% 0.32/0.65      ! [Z: complex] :
% 0.32/0.65      ? [A5: complex,R2: real] :
% 0.32/0.65        ( Z
% 0.32/0.65        = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( exp_complex @ A5 ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_exp_exists
% 0.32/0.65  thf(fact_8918_complex__of__real__def,axiom,
% 0.32/0.65      ( real_V4546457046886955230omplex
% 0.32/0.65      = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_of_real_def
% 0.32/0.65  thf(fact_8919_complex__of__real__code,axiom,
% 0.32/0.65      ( real_V4546457046886955230omplex
% 0.32/0.65      = ( ^ [X3: real] : ( complex2 @ X3 @ zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_of_real_code
% 0.32/0.65  thf(fact_8920_complex__eq__cancel__iff2,axiom,
% 0.32/0.65      ! [X: real,Y: real,Xa2: real] :
% 0.32/0.65        ( ( ( complex2 @ X @ Y )
% 0.32/0.65          = ( real_V4546457046886955230omplex @ Xa2 ) )
% 0.32/0.65        = ( ( X = Xa2 )
% 0.32/0.65          & ( Y = zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_eq_cancel_iff2
% 0.32/0.65  thf(fact_8921_complex__of__real__mult__Complex,axiom,
% 0.32/0.65      ! [R: real,X: real,Y: real] :
% 0.32/0.65        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 0.32/0.65        = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_of_real_mult_Complex
% 0.32/0.65  thf(fact_8922_Complex__mult__complex__of__real,axiom,
% 0.32/0.65      ! [X: real,Y: real,R: real] :
% 0.32/0.65        ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 0.32/0.65        = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y @ R ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_mult_complex_of_real
% 0.32/0.65  thf(fact_8923_complex__of__real__add__Complex,axiom,
% 0.32/0.65      ! [R: real,X: real,Y: real] :
% 0.32/0.65        ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 0.32/0.65        = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % complex_of_real_add_Complex
% 0.32/0.65  thf(fact_8924_Complex__add__complex__of__real,axiom,
% 0.32/0.65      ! [X: real,Y: real,R: real] :
% 0.32/0.65        ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 0.32/0.65        = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % Complex_add_complex_of_real
% 0.32/0.65  thf(fact_8925_cos__arcsin,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65         => ( ( cos_real @ ( arcsin @ X ) )
% 0.32/0.65            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arcsin
% 0.32/0.65  thf(fact_8926_sin__arccos__abs,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65       => ( ( sin_real @ ( arccos @ Y ) )
% 0.32/0.65          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_arccos_abs
% 0.32/0.65  thf(fact_8927_sin__arccos,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65         => ( ( sin_real @ ( arccos @ X ) )
% 0.32/0.65            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_arccos
% 0.32/0.65  thf(fact_8928_arcsin__0,axiom,
% 0.32/0.65      ( ( arcsin @ zero_zero_real )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_0
% 0.32/0.65  thf(fact_8929_arccos__1,axiom,
% 0.32/0.65      ( ( arccos @ one_one_real )
% 0.32/0.65      = zero_zero_real ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_1
% 0.32/0.65  thf(fact_8930_arccos__minus__1,axiom,
% 0.32/0.65      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.65      = pi ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_minus_1
% 0.32/0.65  thf(fact_8931_cos__arccos,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( cos_real @ ( arccos @ Y ) )
% 0.32/0.65            = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arccos
% 0.32/0.65  thf(fact_8932_sin__arcsin,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( sin_real @ ( arcsin @ Y ) )
% 0.32/0.65            = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_arcsin
% 0.32/0.65  thf(fact_8933_arccos__0,axiom,
% 0.32/0.65      ( ( arccos @ zero_zero_real )
% 0.32/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_0
% 0.32/0.65  thf(fact_8934_arcsin__1,axiom,
% 0.32/0.65      ( ( arcsin @ one_one_real )
% 0.32/0.65      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_1
% 0.32/0.65  thf(fact_8935_arcsin__minus__1,axiom,
% 0.32/0.65      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 0.32/0.65      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_minus_1
% 0.32/0.65  thf(fact_8936_arccos__le__arccos,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65           => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_le_arccos
% 0.32/0.65  thf(fact_8937_arccos__eq__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65          & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 0.32/0.65       => ( ( ( arccos @ X )
% 0.32/0.65            = ( arccos @ Y ) )
% 0.32/0.65          = ( X = Y ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_eq_iff
% 0.32/0.65  thf(fact_8938_arccos__le__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 0.32/0.65            = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_le_mono
% 0.32/0.65  thf(fact_8939_arcsin__le__arcsin,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.65         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65           => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_le_arcsin
% 0.32/0.65  thf(fact_8940_arcsin__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65         => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 0.32/0.65            = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_minus
% 0.32/0.65  thf(fact_8941_arcsin__eq__iff,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65         => ( ( ( arcsin @ X )
% 0.32/0.65              = ( arcsin @ Y ) )
% 0.32/0.65            = ( X = Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_eq_iff
% 0.32/0.65  thf(fact_8942_arcsin__le__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 0.32/0.65            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_le_mono
% 0.32/0.65  thf(fact_8943_arccos__lbound,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_lbound
% 0.32/0.65  thf(fact_8944_arccos__less__arccos,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ Y )
% 0.32/0.65         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_less_arccos
% 0.32/0.65  thf(fact_8945_arccos__less__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 0.32/0.65            = ( ord_less_real @ Y @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_less_mono
% 0.32/0.65  thf(fact_8946_arccos__ubound,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_ubound
% 0.32/0.65  thf(fact_8947_arccos__cos,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.65         => ( ( arccos @ ( cos_real @ X ) )
% 0.32/0.65            = X ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_cos
% 0.32/0.65  thf(fact_8948_arcsin__less__arcsin,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ Y )
% 0.32/0.65         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65           => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_less_arcsin
% 0.32/0.65  thf(fact_8949_arcsin__less__mono,axiom,
% 0.32/0.65      ! [X: real,Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 0.32/0.65            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_less_mono
% 0.32/0.65  thf(fact_8950_cos__arccos__abs,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.32/0.65       => ( ( cos_real @ ( arccos @ Y ) )
% 0.32/0.65          = Y ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arccos_abs
% 0.32/0.65  thf(fact_8951_arccos__cos__eq__abs,axiom,
% 0.32/0.65      ! [Theta: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 0.32/0.65       => ( ( arccos @ ( cos_real @ Theta ) )
% 0.32/0.65          = ( abs_abs_real @ Theta ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_cos_eq_abs
% 0.32/0.65  thf(fact_8952_arccos__lt__bounded,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.32/0.65            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_lt_bounded
% 0.32/0.65  thf(fact_8953_arccos__bounded,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.32/0.65            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_bounded
% 0.32/0.65  thf(fact_8954_sin__arccos__nonzero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.65         => ( ( sin_real @ ( arccos @ X ) )
% 0.32/0.65           != zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % sin_arccos_nonzero
% 0.32/0.65  thf(fact_8955_arccos__cos2,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.65       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.32/0.65         => ( ( arccos @ ( cos_real @ X ) )
% 0.32/0.65            = ( uminus_uminus_real @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_cos2
% 0.32/0.65  thf(fact_8956_arccos__minus,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.65         => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.32/0.65            = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_minus
% 0.32/0.65  thf(fact_8957_cos__arcsin__nonzero,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.65       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.65         => ( ( cos_real @ ( arcsin @ X ) )
% 0.32/0.65           != zero_zero_real ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % cos_arcsin_nonzero
% 0.32/0.65  thf(fact_8958_arccos,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.32/0.65            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 0.32/0.65            & ( ( cos_real @ ( arccos @ Y ) )
% 0.32/0.65              = Y ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos
% 0.32/0.65  thf(fact_8959_arccos__minus__abs,axiom,
% 0.32/0.65      ! [X: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.65       => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.32/0.65          = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_minus_abs
% 0.32/0.65  thf(fact_8960_arccos__le__pi2,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arccos_le_pi2
% 0.32/0.65  thf(fact_8961_arcsin__lt__bounded,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.32/0.65            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_lt_bounded
% 0.32/0.65  thf(fact_8962_arcsin__bounded,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.65         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.32/0.65            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.65  
% 0.32/0.65  % arcsin_bounded
% 0.32/0.65  thf(fact_8963_arcsin__ubound,axiom,
% 0.32/0.65      ! [Y: real] :
% 0.32/0.65        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.65       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.66         => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_ubound
% 0.32/0.66  thf(fact_8964_arcsin__lbound,axiom,
% 0.32/0.66      ! [Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.66       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.66         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_lbound
% 0.32/0.66  thf(fact_8965_arcsin__sin,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.32/0.66       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66         => ( ( arcsin @ ( sin_real @ X ) )
% 0.32/0.66            = X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_sin
% 0.32/0.66  thf(fact_8966_le__arcsin__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.32/0.66           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66             => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 0.32/0.66                = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % le_arcsin_iff
% 0.32/0.66  thf(fact_8967_arcsin__le__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.66       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.32/0.66           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66             => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 0.32/0.66                = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_le_iff
% 0.32/0.66  thf(fact_8968_arcsin__pi,axiom,
% 0.32/0.66      ! [Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.66       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.32/0.66            & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 0.32/0.66            & ( ( sin_real @ ( arcsin @ Y ) )
% 0.32/0.66              = Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_pi
% 0.32/0.66  thf(fact_8969_arcsin,axiom,
% 0.32/0.66      ! [Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.32/0.66       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.32/0.66            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66            & ( ( sin_real @ ( arcsin @ Y ) )
% 0.32/0.66              = Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin
% 0.32/0.66  thf(fact_8970_arccos__cos__eq__abs__2pi,axiom,
% 0.32/0.66      ! [Theta: real] :
% 0.32/0.66        ~ ! [K3: int] :
% 0.32/0.66            ( ( arccos @ ( cos_real @ Theta ) )
% 0.32/0.66           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arccos_cos_eq_abs_2pi
% 0.32/0.66  thf(fact_8971_exp__two__pi__i_H,axiom,
% 0.32/0.66      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_two_pi_i'
% 0.32/0.66  thf(fact_8972_exp__two__pi__i,axiom,
% 0.32/0.66      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_two_pi_i
% 0.32/0.66  thf(fact_8973_binomial__code,axiom,
% 0.32/0.66      ( binomial
% 0.32/0.66      = ( ^ [N2: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K2 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_code
% 0.32/0.66  thf(fact_8974_binomial__n__n,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( binomial @ N @ N )
% 0.32/0.66        = one_one_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_n_n
% 0.32/0.66  thf(fact_8975_binomial__1,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = N ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_1
% 0.32/0.66  thf(fact_8976_binomial__0__Suc,axiom,
% 0.32/0.66      ! [K: nat] :
% 0.32/0.66        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.32/0.66        = zero_zero_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_0_Suc
% 0.32/0.66  thf(fact_8977_binomial__eq__0__iff,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( ( binomial @ N @ K )
% 0.32/0.66          = zero_zero_nat )
% 0.32/0.66        = ( ord_less_nat @ N @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_eq_0_iff
% 0.32/0.66  thf(fact_8978_binomial__Suc__Suc,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.32/0.66        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_Suc_Suc
% 0.32/0.66  thf(fact_8979_binomial__n__0,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( binomial @ N @ zero_zero_nat )
% 0.32/0.66        = one_one_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_n_0
% 0.32/0.66  thf(fact_8980_norm__ii,axiom,
% 0.32/0.66      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 0.32/0.66      = one_one_real ) ).
% 0.32/0.66  
% 0.32/0.66  % norm_ii
% 0.32/0.66  thf(fact_8981_complex__i__mult__minus,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 0.32/0.66        = ( uminus1482373934393186551omplex @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_i_mult_minus
% 0.32/0.66  thf(fact_8982_divide__i,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 0.32/0.66        = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_i
% 0.32/0.66  thf(fact_8983_zero__less__binomial__iff,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 0.32/0.66        = ( ord_less_eq_nat @ K @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_less_binomial_iff
% 0.32/0.66  thf(fact_8984_i__squared,axiom,
% 0.32/0.66      ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % i_squared
% 0.32/0.66  thf(fact_8985_divide__numeral__i,axiom,
% 0.32/0.66      ! [Z: complex,N: num] :
% 0.32/0.66        ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 0.32/0.66        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_numeral_i
% 0.32/0.66  thf(fact_8986_power2__i,axiom,
% 0.32/0.66      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % power2_i
% 0.32/0.66  thf(fact_8987_exp__pi__i,axiom,
% 0.32/0.66      ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_pi_i
% 0.32/0.66  thf(fact_8988_exp__pi__i_H,axiom,
% 0.32/0.66      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_pi_i'
% 0.32/0.66  thf(fact_8989_i__even__power,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % i_even_power
% 0.32/0.66  thf(fact_8990_choose__one,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( binomial @ N @ one_one_nat )
% 0.32/0.66        = N ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_one
% 0.32/0.66  thf(fact_8991_complex__i__not__zero,axiom,
% 0.32/0.66      imaginary_unit != zero_zero_complex ).
% 0.32/0.66  
% 0.32/0.66  % complex_i_not_zero
% 0.32/0.66  thf(fact_8992_complex__i__not__one,axiom,
% 0.32/0.66      imaginary_unit != one_one_complex ).
% 0.32/0.66  
% 0.32/0.66  % complex_i_not_one
% 0.32/0.66  thf(fact_8993_complex__i__not__numeral,axiom,
% 0.32/0.66      ! [W: num] :
% 0.32/0.66        ( imaginary_unit
% 0.32/0.66       != ( numera6690914467698888265omplex @ W ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_i_not_numeral
% 0.32/0.66  thf(fact_8994_binomial__eq__0,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( ord_less_nat @ N @ K )
% 0.32/0.66       => ( ( binomial @ N @ K )
% 0.32/0.66          = zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_eq_0
% 0.32/0.66  thf(fact_8995_Suc__times__binomial,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 0.32/0.66        = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_times_binomial
% 0.32/0.66  thf(fact_8996_Suc__times__binomial__eq,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 0.32/0.66        = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_times_binomial_eq
% 0.32/0.66  thf(fact_8997_binomial__symmetric,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.66       => ( ( binomial @ N @ K )
% 0.32/0.66          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_symmetric
% 0.32/0.66  thf(fact_8998_choose__mult__lemma,axiom,
% 0.32/0.66      ! [M: nat,R: nat,K: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 0.32/0.66        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_mult_lemma
% 0.32/0.66  thf(fact_8999_binomial__le__pow,axiom,
% 0.32/0.66      ! [R: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ R @ N )
% 0.32/0.66       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_le_pow
% 0.32/0.66  thf(fact_9000_i__times__eq__iff,axiom,
% 0.32/0.66      ! [W: complex,Z: complex] :
% 0.32/0.66        ( ( ( times_times_complex @ imaginary_unit @ W )
% 0.32/0.66          = Z )
% 0.32/0.66        = ( W
% 0.32/0.66          = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % i_times_eq_iff
% 0.32/0.66  thf(fact_9001_zero__less__binomial,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.66       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_less_binomial
% 0.32/0.66  thf(fact_9002_Suc__times__binomial__add,axiom,
% 0.32/0.66      ! [A: nat,B: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.32/0.66        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_times_binomial_add
% 0.32/0.66  thf(fact_9003_binomial__Suc__Suc__eq__times,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.32/0.66        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_Suc_Suc_eq_times
% 0.32/0.66  thf(fact_9004_choose__mult,axiom,
% 0.32/0.66      ! [K: nat,M: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.66       => ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 0.32/0.66            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_mult
% 0.32/0.66  thf(fact_9005_binomial__absorb__comp,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 0.32/0.66        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_absorb_comp
% 0.32/0.66  thf(fact_9006_complex__i__not__neg__numeral,axiom,
% 0.32/0.66      ! [W: num] :
% 0.32/0.66        ( imaginary_unit
% 0.32/0.66       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_i_not_neg_numeral
% 0.32/0.66  thf(fact_9007_imaginary__unit_Ocode,axiom,
% 0.32/0.66      ( imaginary_unit
% 0.32/0.66      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % imaginary_unit.code
% 0.32/0.66  thf(fact_9008_Complex__eq__i,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ( complex2 @ X @ Y )
% 0.32/0.66          = imaginary_unit )
% 0.32/0.66        = ( ( X = zero_zero_real )
% 0.32/0.66          & ( Y = one_one_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Complex_eq_i
% 0.32/0.66  thf(fact_9009_binomial__absorption,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 0.32/0.66        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_absorption
% 0.32/0.66  thf(fact_9010_i__mult__Complex,axiom,
% 0.32/0.66      ! [A: real,B: real] :
% 0.32/0.66        ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 0.32/0.66        = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.32/0.66  
% 0.32/0.66  % i_mult_Complex
% 0.32/0.66  thf(fact_9011_Complex__mult__i,axiom,
% 0.32/0.66      ! [A: real,B: real] :
% 0.32/0.66        ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 0.32/0.66        = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Complex_mult_i
% 0.32/0.66  thf(fact_9012_binomial__fact__lemma,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.66       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 0.32/0.66          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_fact_lemma
% 0.32/0.66  thf(fact_9013_binomial__mono,axiom,
% 0.32/0.66      ! [K: nat,K6: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ K6 )
% 0.32/0.66       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.32/0.66         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_mono
% 0.32/0.66  thf(fact_9014_binomial__maximum_H,axiom,
% 0.32/0.66      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_maximum'
% 0.32/0.66  thf(fact_9015_binomial__maximum,axiom,
% 0.32/0.66      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_maximum
% 0.32/0.66  thf(fact_9016_binomial__antimono,axiom,
% 0.32/0.66      ! [K: nat,K6: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ K6 )
% 0.32/0.66       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.32/0.66         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.32/0.66           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_antimono
% 0.32/0.66  thf(fact_9017_binomial__le__pow2,axiom,
% 0.32/0.66      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_le_pow2
% 0.32/0.66  thf(fact_9018_choose__reduce__nat,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.66         => ( ( binomial @ N @ K )
% 0.32/0.66            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_reduce_nat
% 0.32/0.66  thf(fact_9019_times__binomial__minus1__eq,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.66       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.32/0.66          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_binomial_minus1_eq
% 0.32/0.66  thf(fact_9020_binomial__altdef__nat,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.66       => ( ( binomial @ N @ K )
% 0.32/0.66          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_altdef_nat
% 0.32/0.66  thf(fact_9021_i__complex__of__real,axiom,
% 0.32/0.66      ! [R: real] :
% 0.32/0.66        ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R ) )
% 0.32/0.66        = ( complex2 @ zero_zero_real @ R ) ) ).
% 0.32/0.66  
% 0.32/0.66  % i_complex_of_real
% 0.32/0.66  thf(fact_9022_complex__of__real__i,axiom,
% 0.32/0.66      ! [R: real] :
% 0.32/0.66        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ imaginary_unit )
% 0.32/0.66        = ( complex2 @ zero_zero_real @ R ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_of_real_i
% 0.32/0.66  thf(fact_9023_Complex__eq,axiom,
% 0.32/0.66      ( complex2
% 0.32/0.66      = ( ^ [A3: real,B2: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Complex_eq
% 0.32/0.66  thf(fact_9024_binomial__less__binomial__Suc,axiom,
% 0.32/0.66      ! [K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_less_binomial_Suc
% 0.32/0.66  thf(fact_9025_binomial__strict__mono,axiom,
% 0.32/0.66      ! [K: nat,K6: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ K @ K6 )
% 0.32/0.66       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.32/0.66         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_strict_mono
% 0.32/0.66  thf(fact_9026_binomial__strict__antimono,axiom,
% 0.32/0.66      ! [K: nat,K6: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ K @ K6 )
% 0.32/0.66       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.32/0.66         => ( ( ord_less_eq_nat @ K6 @ N )
% 0.32/0.66           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_strict_antimono
% 0.32/0.66  thf(fact_9027_central__binomial__odd,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.66       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.66          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % central_binomial_odd
% 0.32/0.66  thf(fact_9028_binomial__addition__formula,axiom,
% 0.32/0.66      ! [N: nat,K: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( binomial @ N @ ( suc @ K ) )
% 0.32/0.66          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_addition_formula
% 0.32/0.66  thf(fact_9029_choose__two,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_two
% 0.32/0.66  thf(fact_9030_complex__split__polar,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66      ? [R2: real,A5: real] :
% 0.32/0.66        ( Z
% 0.32/0.66        = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_split_polar
% 0.32/0.66  thf(fact_9031_cmod__unit__one,axiom,
% 0.32/0.66      ! [A: real] :
% 0.32/0.66        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 0.32/0.66        = one_one_real ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_unit_one
% 0.32/0.66  thf(fact_9032_cmod__complex__polar,axiom,
% 0.32/0.66      ! [R: real,A: real] :
% 0.32/0.66        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 0.32/0.66        = ( abs_abs_real @ R ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_complex_polar
% 0.32/0.66  thf(fact_9033_central__binomial__lower__bound,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % central_binomial_lower_bound
% 0.32/0.66  thf(fact_9034_Arg__minus__ii,axiom,
% 0.32/0.66      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 0.32/0.66      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_minus_ii
% 0.32/0.66  thf(fact_9035_csqrt__ii,axiom,
% 0.32/0.66      ( ( csqrt @ imaginary_unit )
% 0.32/0.66      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_ii
% 0.32/0.66  thf(fact_9036_Arg__ii,axiom,
% 0.32/0.66      ( ( arg @ imaginary_unit )
% 0.32/0.66      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_ii
% 0.32/0.66  thf(fact_9037_finite__atMost,axiom,
% 0.32/0.66      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % finite_atMost
% 0.32/0.66  thf(fact_9038_csqrt__0,axiom,
% 0.32/0.66      ( ( csqrt @ zero_zero_complex )
% 0.32/0.66      = zero_zero_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_0
% 0.32/0.66  thf(fact_9039_csqrt__eq__0,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( csqrt @ Z )
% 0.32/0.66          = zero_zero_complex )
% 0.32/0.66        = ( Z = zero_zero_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_eq_0
% 0.32/0.66  thf(fact_9040_csqrt__eq__1,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( csqrt @ Z )
% 0.32/0.66          = one_one_complex )
% 0.32/0.66        = ( Z = one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_eq_1
% 0.32/0.66  thf(fact_9041_csqrt__1,axiom,
% 0.32/0.66      ( ( csqrt @ one_one_complex )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_1
% 0.32/0.66  thf(fact_9042_atMost__0,axiom,
% 0.32/0.66      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.32/0.66      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atMost_0
% 0.32/0.66  thf(fact_9043_power2__csqrt,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66        = Z ) ).
% 0.32/0.66  
% 0.32/0.66  % power2_csqrt
% 0.32/0.66  thf(fact_9044_atMost__atLeast0,axiom,
% 0.32/0.66      ( set_ord_atMost_nat
% 0.32/0.66      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atMost_atLeast0
% 0.32/0.66  thf(fact_9045_lessThan__Suc__atMost,axiom,
% 0.32/0.66      ! [K: nat] :
% 0.32/0.66        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.32/0.66        = ( set_ord_atMost_nat @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % lessThan_Suc_atMost
% 0.32/0.66  thf(fact_9046_atMost__Suc,axiom,
% 0.32/0.66      ! [K: nat] :
% 0.32/0.66        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.32/0.66        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atMost_Suc
% 0.32/0.66  thf(fact_9047_finite__nat__iff__bounded__le,axiom,
% 0.32/0.66      ( finite_finite_nat
% 0.32/0.66      = ( ^ [S6: set_nat] :
% 0.32/0.66          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % finite_nat_iff_bounded_le
% 0.32/0.66  thf(fact_9048_atMost__nat__numeral,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 0.32/0.66        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atMost_nat_numeral
% 0.32/0.66  thf(fact_9049_Arg__zero,axiom,
% 0.32/0.66      ( ( arg @ zero_zero_complex )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_zero
% 0.32/0.66  thf(fact_9050_sum__choose__lower,axiom,
% 0.32/0.66      ! [R: nat,N: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 0.32/0.66          @ ( set_ord_atMost_nat @ N ) )
% 0.32/0.66        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sum_choose_lower
% 0.32/0.66  thf(fact_9051_choose__rising__sum_I2_J,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.32/0.66          @ ( set_ord_atMost_nat @ M ) )
% 0.32/0.66        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_rising_sum(2)
% 0.32/0.66  thf(fact_9052_choose__rising__sum_I1_J,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.32/0.66          @ ( set_ord_atMost_nat @ M ) )
% 0.32/0.66        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_rising_sum(1)
% 0.32/0.66  thf(fact_9053_atLeast1__atMost__eq__remove0,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.66        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeast1_atMost_eq_remove0
% 0.32/0.66  thf(fact_9054_sum__choose__diagonal,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66       => ( ( groups3542108847815614940at_nat
% 0.32/0.66            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 0.32/0.66            @ ( set_ord_atMost_nat @ M ) )
% 0.32/0.66          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sum_choose_diagonal
% 0.32/0.66  thf(fact_9055_vandermonde,axiom,
% 0.32/0.66      ! [M: nat,N: nat,R: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 0.32/0.66          @ ( set_ord_atMost_nat @ R ) )
% 0.32/0.66        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 0.32/0.66  
% 0.32/0.66  % vandermonde
% 0.32/0.66  thf(fact_9056_of__real__sqrt,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 0.32/0.66          = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % of_real_sqrt
% 0.32/0.66  thf(fact_9057_choose__row__sum,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 0.32/0.66        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_row_sum
% 0.32/0.66  thf(fact_9058_Arg__bounded,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.32/0.66        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_bounded
% 0.32/0.66  thf(fact_9059_binomial,axiom,
% 0.32/0.66      ! [A: nat,B: nat,N: nat] :
% 0.32/0.66        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.32/0.66        = ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 0.32/0.66          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial
% 0.32/0.66  thf(fact_9060_polynomial__product__nat,axiom,
% 0.32/0.66      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 0.32/0.66        ( ! [I4: nat] :
% 0.32/0.66            ( ( ord_less_nat @ M @ I4 )
% 0.32/0.66           => ( ( A @ I4 )
% 0.32/0.66              = zero_zero_nat ) )
% 0.32/0.66       => ( ! [J2: nat] :
% 0.32/0.66              ( ( ord_less_nat @ N @ J2 )
% 0.32/0.66             => ( ( B @ J2 )
% 0.32/0.66                = zero_zero_nat ) )
% 0.32/0.66         => ( ( times_times_nat
% 0.32/0.66              @ ( groups3542108847815614940at_nat
% 0.32/0.66                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X @ I5 ) )
% 0.32/0.66                @ ( set_ord_atMost_nat @ M ) )
% 0.32/0.66              @ ( groups3542108847815614940at_nat
% 0.32/0.66                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 0.32/0.66                @ ( set_ord_atMost_nat @ N ) ) )
% 0.32/0.66            = ( groups3542108847815614940at_nat
% 0.32/0.66              @ ^ [R5: nat] :
% 0.32/0.66                  ( times_times_nat
% 0.32/0.66                  @ ( groups3542108847815614940at_nat
% 0.32/0.66                    @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 0.32/0.66                    @ ( set_ord_atMost_nat @ R5 ) )
% 0.32/0.66                  @ ( power_power_nat @ X @ R5 ) )
% 0.32/0.66              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % polynomial_product_nat
% 0.32/0.66  thf(fact_9061_choose__square__sum,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66          @ ( set_ord_atMost_nat @ N ) )
% 0.32/0.66        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_square_sum
% 0.32/0.66  thf(fact_9062_binomial__r__part__sum,axiom,
% 0.32/0.66      ! [M: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.32/0.66        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_r_part_sum
% 0.32/0.66  thf(fact_9063_choose__linear__sum,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N @ I5 ) )
% 0.32/0.66          @ ( set_ord_atMost_nat @ N ) )
% 0.32/0.66        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % choose_linear_sum
% 0.32/0.66  thf(fact_9064_of__nat__id,axiom,
% 0.32/0.66      ( semiri1316708129612266289at_nat
% 0.32/0.66      = ( ^ [N2: nat] : N2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % of_nat_id
% 0.32/0.66  thf(fact_9065_real__scaleR__def,axiom,
% 0.32/0.66      real_V1485227260804924795R_real = times_times_real ).
% 0.32/0.66  
% 0.32/0.66  % real_scaleR_def
% 0.32/0.66  thf(fact_9066_complex__scaleR,axiom,
% 0.32/0.66      ! [R: real,A: real,B: real] :
% 0.32/0.66        ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 0.32/0.66        = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_scaleR
% 0.32/0.66  thf(fact_9067_cis__minus__pi__half,axiom,
% 0.32/0.66      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_minus_pi_half
% 0.32/0.66  thf(fact_9068_floor__log__nat__eq__powr__iff,axiom,
% 0.32/0.66      ! [B: nat,K: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.32/0.66       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.66         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.32/0.66              = ( semiri1314217659103216013at_int @ N ) )
% 0.32/0.66            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.32/0.66              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_log_nat_eq_powr_iff
% 0.32/0.66  thf(fact_9069_norm__cis,axiom,
% 0.32/0.66      ! [A: real] :
% 0.32/0.66        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 0.32/0.66        = one_one_real ) ).
% 0.32/0.66  
% 0.32/0.66  % norm_cis
% 0.32/0.66  thf(fact_9070_cis__zero,axiom,
% 0.32/0.66      ( ( cis @ zero_zero_real )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_zero
% 0.32/0.66  thf(fact_9071_cis__pi,axiom,
% 0.32/0.66      ( ( cis @ pi )
% 0.32/0.66      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_pi
% 0.32/0.66  thf(fact_9072_floor__divide__eq__div__numeral,axiom,
% 0.32/0.66      ! [A: num,B: num] :
% 0.32/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 0.32/0.66        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_divide_eq_div_numeral
% 0.32/0.66  thf(fact_9073_cis__pi__half,axiom,
% 0.32/0.66      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66      = imaginary_unit ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_pi_half
% 0.32/0.66  thf(fact_9074_floor__one__divide__eq__div__numeral,axiom,
% 0.32/0.66      ! [B: num] :
% 0.32/0.66        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 0.32/0.66        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_one_divide_eq_div_numeral
% 0.32/0.66  thf(fact_9075_cis__2pi,axiom,
% 0.32/0.66      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_2pi
% 0.32/0.66  thf(fact_9076_floor__minus__divide__eq__div__numeral,axiom,
% 0.32/0.66      ! [A: num,B: num] :
% 0.32/0.66        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 0.32/0.66        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_minus_divide_eq_div_numeral
% 0.32/0.66  thf(fact_9077_floor__minus__one__divide__eq__div__numeral,axiom,
% 0.32/0.66      ! [B: num] :
% 0.32/0.66        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 0.32/0.66        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_minus_one_divide_eq_div_numeral
% 0.32/0.66  thf(fact_9078_real__sqrt__inverse,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 0.32/0.66        = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_sqrt_inverse
% 0.32/0.66  thf(fact_9079_cis__neq__zero,axiom,
% 0.32/0.66      ! [A: real] :
% 0.32/0.66        ( ( cis @ A )
% 0.32/0.66       != zero_zero_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_neq_zero
% 0.32/0.66  thf(fact_9080_divide__real__def,axiom,
% 0.32/0.66      ( divide_divide_real
% 0.32/0.66      = ( ^ [X3: real,Y3: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y3 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_real_def
% 0.32/0.66  thf(fact_9081_cis__mult,axiom,
% 0.32/0.66      ! [A: real,B: real] :
% 0.32/0.66        ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 0.32/0.66        = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_mult
% 0.32/0.66  thf(fact_9082_cis__divide,axiom,
% 0.32/0.66      ! [A: real,B: real] :
% 0.32/0.66        ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 0.32/0.66        = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_divide
% 0.32/0.66  thf(fact_9083_inverse__powr,axiom,
% 0.32/0.66      ! [Y: real,A: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.66       => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 0.32/0.66          = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % inverse_powr
% 0.32/0.66  thf(fact_9084_real__of__int__floor__add__one__gt,axiom,
% 0.32/0.66      ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_of_int_floor_add_one_gt
% 0.32/0.66  thf(fact_9085_floor__eq,axiom,
% 0.32/0.66      ! [N: int,X: real] :
% 0.32/0.66        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.32/0.66         => ( ( archim6058952711729229775r_real @ X )
% 0.32/0.66            = N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_eq
% 0.32/0.66  thf(fact_9086_real__of__int__floor__add__one__ge,axiom,
% 0.32/0.66      ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_of_int_floor_add_one_ge
% 0.32/0.66  thf(fact_9087_real__of__int__floor__gt__diff__one,axiom,
% 0.32/0.66      ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_of_int_floor_gt_diff_one
% 0.32/0.66  thf(fact_9088_real__of__int__floor__ge__diff__one,axiom,
% 0.32/0.66      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_of_int_floor_ge_diff_one
% 0.32/0.66  thf(fact_9089_forall__pos__mono__1,axiom,
% 0.32/0.66      ! [P: real > $o,E: real] :
% 0.32/0.66        ( ! [D3: real,E2: real] :
% 0.32/0.66            ( ( ord_less_real @ D3 @ E2 )
% 0.32/0.66           => ( ( P @ D3 )
% 0.32/0.66             => ( P @ E2 ) ) )
% 0.32/0.66       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.32/0.66         => ( ( ord_less_real @ zero_zero_real @ E )
% 0.32/0.66           => ( P @ E ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % forall_pos_mono_1
% 0.32/0.66  thf(fact_9090_DeMoivre,axiom,
% 0.32/0.66      ! [A: real,N: nat] :
% 0.32/0.66        ( ( power_power_complex @ ( cis @ A ) @ N )
% 0.32/0.66        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % DeMoivre
% 0.32/0.66  thf(fact_9091_forall__pos__mono,axiom,
% 0.32/0.66      ! [P: real > $o,E: real] :
% 0.32/0.66        ( ! [D3: real,E2: real] :
% 0.32/0.66            ( ( ord_less_real @ D3 @ E2 )
% 0.32/0.66           => ( ( P @ D3 )
% 0.32/0.66             => ( P @ E2 ) ) )
% 0.32/0.66       => ( ! [N3: nat] :
% 0.32/0.66              ( ( N3 != zero_zero_nat )
% 0.32/0.66             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 0.32/0.66         => ( ( ord_less_real @ zero_zero_real @ E )
% 0.32/0.66           => ( P @ E ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % forall_pos_mono
% 0.32/0.66  thf(fact_9092_real__arch__inverse,axiom,
% 0.32/0.66      ! [E: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ E )
% 0.32/0.66        = ( ? [N2: nat] :
% 0.32/0.66              ( ( N2 != zero_zero_nat )
% 0.32/0.66              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 0.32/0.66              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_arch_inverse
% 0.32/0.66  thf(fact_9093_sqrt__divide__self__eq,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 0.32/0.66          = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sqrt_divide_self_eq
% 0.32/0.66  thf(fact_9094_ln__inverse,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 0.32/0.66          = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % ln_inverse
% 0.32/0.66  thf(fact_9095_floor__eq2,axiom,
% 0.32/0.66      ! [N: int,X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.32/0.66         => ( ( archim6058952711729229775r_real @ X )
% 0.32/0.66            = N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_eq2
% 0.32/0.66  thf(fact_9096_floor__divide__real__eq__div,axiom,
% 0.32/0.66      ! [B: int,A: real] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.66       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 0.32/0.66          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_divide_real_eq_div
% 0.32/0.66  thf(fact_9097_log__inverse,axiom,
% 0.32/0.66      ! [A: real,X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.66       => ( ( A != one_one_real )
% 0.32/0.66         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66           => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 0.32/0.66              = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % log_inverse
% 0.32/0.66  thf(fact_9098_cis__conv__exp,axiom,
% 0.32/0.66      ( cis
% 0.32/0.66      = ( ^ [B2: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_conv_exp
% 0.32/0.66  thf(fact_9099_exp__plus__inverse__exp,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_plus_inverse_exp
% 0.32/0.66  thf(fact_9100_plus__inverse__ge__2,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_inverse_ge_2
% 0.32/0.66  thf(fact_9101_real__inv__sqrt__pow2,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66          = ( inverse_inverse_real @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_inv_sqrt_pow2
% 0.32/0.66  thf(fact_9102_tan__cot,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 0.32/0.66        = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % tan_cot
% 0.32/0.66  thf(fact_9103_real__le__x__sinh,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_le_x_sinh
% 0.32/0.66  thf(fact_9104_real__le__abs__sinh,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_le_abs_sinh
% 0.32/0.66  thf(fact_9105_floor__log__eq__powr__iff,axiom,
% 0.32/0.66      ! [X: real,B: real,K: int] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ord_less_real @ one_one_real @ B )
% 0.32/0.66         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 0.32/0.66              = K )
% 0.32/0.66            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 0.32/0.66              & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_log_eq_powr_iff
% 0.32/0.66  thf(fact_9106_floor__log2__div2,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.66       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.66          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_log2_div2
% 0.32/0.66  thf(fact_9107_floor__log__nat__eq__if,axiom,
% 0.32/0.66      ! [B: nat,N: nat,K: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.32/0.66       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.32/0.66         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.32/0.66           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.32/0.66              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_log_nat_eq_if
% 0.32/0.66  thf(fact_9108_Maclaurin__sin__bound,axiom,
% 0.32/0.66      ! [X: real,N: nat] :
% 0.32/0.66        ( ord_less_eq_real
% 0.32/0.66        @ ( abs_abs_real
% 0.32/0.66          @ ( minus_minus_real @ ( sin_real @ X )
% 0.32/0.66            @ ( groups6591440286371151544t_real
% 0.32/0.66              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.66              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.32/0.66        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Maclaurin_sin_bound
% 0.32/0.66  thf(fact_9109_bij__betw__roots__unity,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( bij_betw_nat_complex
% 0.32/0.66          @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.32/0.66          @ ( set_ord_lessThan_nat @ N )
% 0.32/0.66          @ ( collect_complex
% 0.32/0.66            @ ^ [Z3: complex] :
% 0.32/0.66                ( ( power_power_complex @ Z3 @ N )
% 0.32/0.66                = one_one_complex ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bij_betw_roots_unity
% 0.32/0.66  thf(fact_9110_sinh__real__zero__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ( sinh_real @ X )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66        = ( X = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_zero_iff
% 0.32/0.66  thf(fact_9111_sinh__real__le__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 0.32/0.66        = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_le_iff
% 0.32/0.66  thf(fact_9112_sinh__real__neg__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_neg_iff
% 0.32/0.66  thf(fact_9113_sinh__real__pos__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.32/0.66        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_pos_iff
% 0.32/0.66  thf(fact_9114_sinh__real__nonpos__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_nonpos_iff
% 0.32/0.66  thf(fact_9115_sinh__real__nonneg__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.32/0.66        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_real_nonneg_iff
% 0.32/0.66  thf(fact_9116_divide__complex__def,axiom,
% 0.32/0.66      ( divide1717551699836669952omplex
% 0.32/0.66      = ( ^ [X3: complex,Y3: complex] : ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ Y3 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_complex_def
% 0.32/0.66  thf(fact_9117_fact__eq__fact__times,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.66       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.32/0.66          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.32/0.66            @ ( groups708209901874060359at_nat
% 0.32/0.66              @ ^ [X3: nat] : X3
% 0.32/0.66              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % fact_eq_fact_times
% 0.32/0.66  thf(fact_9118_fact__div__fact,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.66       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.32/0.66          = ( groups708209901874060359at_nat
% 0.32/0.66            @ ^ [X3: nat] : X3
% 0.32/0.66            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % fact_div_fact
% 0.32/0.66  thf(fact_9119_complex__inverse,axiom,
% 0.32/0.66      ! [A: real,B: real] :
% 0.32/0.66        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 0.32/0.66        = ( 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 ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_inverse
% 0.32/0.66  thf(fact_9120_sinh__ln__real,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 0.32/0.66          = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_ln_real
% 0.32/0.66  thf(fact_9121_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 0.32/0.66      ! [X: vEBT_VEBT,Y: $o] :
% 0.32/0.66        ( ( ( vEBT_VEBT_minNull @ X )
% 0.32/0.66          = Y )
% 0.32/0.66       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.32/0.66         => ( ( ( X
% 0.32/0.66                = ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.66             => ( Y
% 0.32/0.66               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.32/0.66           => ( ! [Uv2: $o] :
% 0.32/0.66                  ( ( X
% 0.32/0.66                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.32/0.66                 => ( ~ Y
% 0.32/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 0.32/0.66             => ( ! [Uu2: $o] :
% 0.32/0.66                    ( ( X
% 0.32/0.66                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.32/0.66                   => ( ~ Y
% 0.32/0.66                     => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 0.32/0.66               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.66                      ( ( X
% 0.32/0.66                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.32/0.66                     => ( Y
% 0.32/0.66                       => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 0.32/0.66                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.66                        ( ( X
% 0.32/0.66                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.32/0.66                       => ( ~ Y
% 0.32/0.66                         => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT_internal.minNull.pelims(1)
% 0.32/0.66  thf(fact_9122_sinh__le__cosh__real,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sinh_le_cosh_real
% 0.32/0.66  thf(fact_9123_cosh__real__nonzero,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( cosh_real @ X )
% 0.32/0.66       != zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonzero
% 0.32/0.66  thf(fact_9124_cosh__real__pos,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_pos
% 0.32/0.66  thf(fact_9125_cosh__real__nonneg,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonneg
% 0.32/0.66  thf(fact_9126_cosh__real__nonneg__le__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.32/0.66            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonneg_le_iff
% 0.32/0.66  thf(fact_9127_cosh__real__nonpos__le__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.66       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.32/0.66         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.32/0.66            = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonpos_le_iff
% 0.32/0.66  thf(fact_9128_cosh__real__ge__1,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_ge_1
% 0.32/0.66  thf(fact_9129_cosh__real__nonpos__less__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.66       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.32/0.66         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.32/0.66            = ( ord_less_real @ Y @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonpos_less_iff
% 0.32/0.66  thf(fact_9130_cosh__real__nonneg__less__iff,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.66         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.32/0.66            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_nonneg_less_iff
% 0.32/0.66  thf(fact_9131_cosh__real__strict__mono,axiom,
% 0.32/0.66      ! [X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ Y )
% 0.32/0.66         => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_real_strict_mono
% 0.32/0.66  thf(fact_9132_prod__int__eq,axiom,
% 0.32/0.66      ! [I: nat,J: nat] :
% 0.32/0.66        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.32/0.66        = ( groups1705073143266064639nt_int
% 0.32/0.66          @ ^ [X3: int] : X3
% 0.32/0.66          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % prod_int_eq
% 0.32/0.66  thf(fact_9133_arcosh__cosh__real,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( arcosh_real @ ( cosh_real @ X ) )
% 0.32/0.66          = X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcosh_cosh_real
% 0.32/0.66  thf(fact_9134_prod__int__plus__eq,axiom,
% 0.32/0.66      ! [I: nat,J: nat] :
% 0.32/0.66        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.32/0.66        = ( groups1705073143266064639nt_int
% 0.32/0.66          @ ^ [X3: int] : X3
% 0.32/0.66          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % prod_int_plus_eq
% 0.32/0.66  thf(fact_9135_cosh__ln__real,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 0.32/0.66          = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cosh_ln_real
% 0.32/0.66  thf(fact_9136_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 0.32/0.66      ! [X: vEBT_VEBT] :
% 0.32/0.66        ( ~ ( vEBT_VEBT_minNull @ X )
% 0.32/0.66       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.32/0.66         => ( ! [Uv2: $o] :
% 0.32/0.66                ( ( X
% 0.32/0.66                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.32/0.66               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 0.32/0.66           => ( ! [Uu2: $o] :
% 0.32/0.66                  ( ( X
% 0.32/0.66                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.32/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 0.32/0.66             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.32/0.66                    ( ( X
% 0.32/0.66                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.32/0.66                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT_internal.minNull.pelims(3)
% 0.32/0.66  thf(fact_9137_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 0.32/0.66      ! [X: vEBT_VEBT] :
% 0.32/0.66        ( ( vEBT_VEBT_minNull @ X )
% 0.32/0.66       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.32/0.66         => ( ( ( X
% 0.32/0.66                = ( vEBT_Leaf @ $false @ $false ) )
% 0.32/0.66             => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 0.32/0.66           => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.32/0.66                  ( ( X
% 0.32/0.66                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.32/0.66                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT_internal.minNull.pelims(2)
% 0.32/0.66  thf(fact_9138_bij__betw__nth__root__unity,axiom,
% 0.32/0.66      ! [C: complex,N: nat] :
% 0.32/0.66        ( ( C != zero_zero_complex )
% 0.32/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.32/0.66            @ ( collect_complex
% 0.32/0.66              @ ^ [Z3: complex] :
% 0.32/0.66                  ( ( power_power_complex @ Z3 @ N )
% 0.32/0.66                  = one_one_complex ) )
% 0.32/0.66            @ ( collect_complex
% 0.32/0.66              @ ^ [Z3: complex] :
% 0.32/0.66                  ( ( power_power_complex @ Z3 @ N )
% 0.32/0.66                  = C ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bij_betw_nth_root_unity
% 0.32/0.66  thf(fact_9139_cot__less__zero,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.66         => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cot_less_zero
% 0.32/0.66  thf(fact_9140_int__ge__less__than__def,axiom,
% 0.32/0.66      ( int_ge_less_than
% 0.32/0.66      = ( ^ [D2: int] :
% 0.32/0.66            ( collec213857154873943460nt_int
% 0.32/0.66            @ ( produc4947309494688390418_int_o
% 0.32/0.66              @ ^ [Z6: int,Z3: int] :
% 0.32/0.66                  ( ( ord_less_eq_int @ D2 @ Z6 )
% 0.32/0.66                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_ge_less_than_def
% 0.32/0.66  thf(fact_9141_int__ge__less__than2__def,axiom,
% 0.32/0.66      ( int_ge_less_than2
% 0.32/0.66      = ( ^ [D2: int] :
% 0.32/0.66            ( collec213857154873943460nt_int
% 0.32/0.66            @ ( produc4947309494688390418_int_o
% 0.32/0.66              @ ^ [Z6: int,Z3: int] :
% 0.32/0.66                  ( ( ord_less_eq_int @ D2 @ Z3 )
% 0.32/0.66                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_ge_less_than2_def
% 0.32/0.66  thf(fact_9142_real__root__zero,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( root @ N @ zero_zero_real )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_zero
% 0.32/0.66  thf(fact_9143_real__root__Suc__0,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 0.32/0.66        = X ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_Suc_0
% 0.32/0.66  thf(fact_9144_real__root__eq__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ( root @ N @ X )
% 0.32/0.66            = ( root @ N @ Y ) )
% 0.32/0.66          = ( X = Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_eq_iff
% 0.32/0.66  thf(fact_9145_root__0,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( root @ zero_zero_nat @ X )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % root_0
% 0.32/0.66  thf(fact_9146_cot__pi,axiom,
% 0.32/0.66      ( ( cot_real @ pi )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % cot_pi
% 0.32/0.66  thf(fact_9147_real__root__eq__0__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ( root @ N @ X )
% 0.32/0.66            = zero_zero_real )
% 0.32/0.66          = ( X = zero_zero_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_eq_0_iff
% 0.32/0.66  thf(fact_9148_real__root__less__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_real @ X @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_less_iff
% 0.32/0.66  thf(fact_9149_real__root__le__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_le_iff
% 0.32/0.66  thf(fact_9150_real__root__eq__1__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ( root @ N @ X )
% 0.32/0.66            = one_one_real )
% 0.32/0.66          = ( X = one_one_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_eq_1_iff
% 0.32/0.66  thf(fact_9151_real__root__one,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( root @ N @ one_one_real )
% 0.32/0.66          = one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_one
% 0.32/0.66  thf(fact_9152_real__root__gt__0__iff,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_gt_0_iff
% 0.32/0.66  thf(fact_9153_real__root__lt__0__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.32/0.66          = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_lt_0_iff
% 0.32/0.66  thf(fact_9154_real__root__ge__0__iff,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_ge_0_iff
% 0.32/0.66  thf(fact_9155_real__root__le__0__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.32/0.66          = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_le_0_iff
% 0.32/0.66  thf(fact_9156_real__root__lt__1__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 0.32/0.66          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_lt_1_iff
% 0.32/0.66  thf(fact_9157_real__root__gt__1__iff,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_gt_1_iff
% 0.32/0.66  thf(fact_9158_real__root__le__1__iff,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 0.32/0.66          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_le_1_iff
% 0.32/0.66  thf(fact_9159_real__root__ge__1__iff,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 0.32/0.66          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_ge_1_iff
% 0.32/0.66  thf(fact_9160_cot__npi,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % cot_npi
% 0.32/0.66  thf(fact_9161_real__root__pow__pos2,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.32/0.66            = X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_pow_pos2
% 0.32/0.66  thf(fact_9162_cot__periodic,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.66        = ( cot_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cot_periodic
% 0.32/0.66  thf(fact_9163_real__root__inverse,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 0.32/0.66        = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_inverse
% 0.32/0.66  thf(fact_9164_real__root__divide,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( root @ N @ ( divide_divide_real @ X @ Y ) )
% 0.32/0.66        = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_divide
% 0.32/0.66  thf(fact_9165_real__root__commute,axiom,
% 0.32/0.66      ! [M: nat,N: nat,X: real] :
% 0.32/0.66        ( ( root @ M @ ( root @ N @ X ) )
% 0.32/0.66        = ( root @ N @ ( root @ M @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_commute
% 0.32/0.66  thf(fact_9166_real__root__mult__exp,axiom,
% 0.32/0.66      ! [M: nat,N: nat,X: real] :
% 0.32/0.66        ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 0.32/0.66        = ( root @ M @ ( root @ N @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_mult_exp
% 0.32/0.66  thf(fact_9167_real__root__mult,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 0.32/0.66        = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_mult
% 0.32/0.66  thf(fact_9168_real__root__minus,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 0.32/0.66        = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_minus
% 0.32/0.66  thf(fact_9169_real__root__pos__pos__le,axiom,
% 0.32/0.66      ! [X: real,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_pos_pos_le
% 0.32/0.66  thf(fact_9170_real__root__less__mono,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ X @ Y )
% 0.32/0.66         => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_less_mono
% 0.32/0.66  thf(fact_9171_real__root__le__mono,axiom,
% 0.32/0.66      ! [N: nat,X: real,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.66         => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_le_mono
% 0.32/0.66  thf(fact_9172_real__root__power,axiom,
% 0.32/0.66      ! [N: nat,X: real,K: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 0.32/0.66          = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_power
% 0.32/0.66  thf(fact_9173_real__root__abs,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( root @ N @ ( abs_abs_real @ X ) )
% 0.32/0.66          = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_abs
% 0.32/0.66  thf(fact_9174_real__root__gt__zero,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_gt_zero
% 0.32/0.66  thf(fact_9175_real__root__strict__decreasing,axiom,
% 0.32/0.66      ! [N: nat,N4: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_nat @ N @ N4 )
% 0.32/0.66         => ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.66           => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_strict_decreasing
% 0.32/0.66  thf(fact_9176_sqrt__def,axiom,
% 0.32/0.66      ( sqrt
% 0.32/0.66      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sqrt_def
% 0.32/0.66  thf(fact_9177_root__abs__power,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 0.32/0.66          = ( abs_abs_real @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % root_abs_power
% 0.32/0.66  thf(fact_9178_real__root__pos__pos,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_pos_pos
% 0.32/0.66  thf(fact_9179_real__root__strict__increasing,axiom,
% 0.32/0.66      ! [N: nat,N4: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_nat @ N @ N4 )
% 0.32/0.66         => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66           => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.66             => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_strict_increasing
% 0.32/0.66  thf(fact_9180_real__root__decreasing,axiom,
% 0.32/0.66      ! [N: nat,N4: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.32/0.66         => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.32/0.66           => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_decreasing
% 0.32/0.66  thf(fact_9181_real__root__pow__pos,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.32/0.66            = X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_pow_pos
% 0.32/0.66  thf(fact_9182_real__root__pos__unique,axiom,
% 0.32/0.66      ! [N: nat,Y: real,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.32/0.66         => ( ( ( power_power_real @ Y @ N )
% 0.32/0.66              = X )
% 0.32/0.66           => ( ( root @ N @ X )
% 0.32/0.66              = Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_pos_unique
% 0.32/0.66  thf(fact_9183_real__root__power__cancel,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.32/0.66            = X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_power_cancel
% 0.32/0.66  thf(fact_9184_odd__real__root__pow,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.66       => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.32/0.66          = X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % odd_real_root_pow
% 0.32/0.66  thf(fact_9185_odd__real__root__unique,axiom,
% 0.32/0.66      ! [N: nat,Y: real,X: real] :
% 0.32/0.66        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.66       => ( ( ( power_power_real @ Y @ N )
% 0.32/0.66            = X )
% 0.32/0.66         => ( ( root @ N @ X )
% 0.32/0.66            = Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % odd_real_root_unique
% 0.32/0.66  thf(fact_9186_odd__real__root__power__cancel,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.66       => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.32/0.66          = X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % odd_real_root_power_cancel
% 0.32/0.66  thf(fact_9187_real__root__increasing,axiom,
% 0.32/0.66      ! [N: nat,N4: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_eq_nat @ N @ N4 )
% 0.32/0.66         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.66           => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.66             => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_root_increasing
% 0.32/0.66  thf(fact_9188_ln__root,axiom,
% 0.32/0.66      ! [N: nat,B: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.66         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 0.32/0.66            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % ln_root
% 0.32/0.66  thf(fact_9189_log__root,axiom,
% 0.32/0.66      ! [N: nat,A: real,B: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.66         => ( ( log @ B @ ( root @ N @ A ) )
% 0.32/0.66            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % log_root
% 0.32/0.66  thf(fact_9190_log__base__root,axiom,
% 0.32/0.66      ! [N: nat,B: real,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ B )
% 0.32/0.66         => ( ( log @ ( root @ N @ B ) @ X )
% 0.32/0.66            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % log_base_root
% 0.32/0.66  thf(fact_9191_root__powr__inverse,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66         => ( ( root @ N @ X )
% 0.32/0.66            = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % root_powr_inverse
% 0.32/0.66  thf(fact_9192_cot__gt__zero,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cot_gt_zero
% 0.32/0.66  thf(fact_9193_tan__cot_H,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 0.32/0.66        = ( cot_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % tan_cot'
% 0.32/0.66  thf(fact_9194_arctan__def,axiom,
% 0.32/0.66      ( arctan
% 0.32/0.66      = ( ^ [Y3: real] :
% 0.32/0.66            ( the_real
% 0.32/0.66            @ ^ [X3: real] :
% 0.32/0.66                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.32/0.66                & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66                & ( ( tan_real @ X3 )
% 0.32/0.66                  = Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arctan_def
% 0.32/0.66  thf(fact_9195_arcsin__def,axiom,
% 0.32/0.66      ( arcsin
% 0.32/0.66      = ( ^ [Y3: real] :
% 0.32/0.66            ( the_real
% 0.32/0.66            @ ^ [X3: real] :
% 0.32/0.66                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.32/0.66                & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66                & ( ( sin_real @ X3 )
% 0.32/0.66                  = Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arcsin_def
% 0.32/0.66  thf(fact_9196_signed__take__bit__eq__take__bit__minus,axiom,
% 0.32/0.66      ( bit_ri631733984087533419it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % signed_take_bit_eq_take_bit_minus
% 0.32/0.66  thf(fact_9197_modulo__int__unfold,axiom,
% 0.32/0.66      ! [L2: int,K: int,N: nat,M: nat] :
% 0.32/0.66        ( ( ( ( ( sgn_sgn_int @ L2 )
% 0.32/0.66              = zero_zero_int )
% 0.32/0.66            | ( ( sgn_sgn_int @ K )
% 0.32/0.66              = zero_zero_int )
% 0.32/0.66            | ( N = zero_zero_nat ) )
% 0.32/0.66         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.32/0.66        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 0.32/0.66                = zero_zero_int )
% 0.32/0.66              | ( ( sgn_sgn_int @ K )
% 0.32/0.66                = zero_zero_int )
% 0.32/0.66              | ( N = zero_zero_nat ) )
% 0.32/0.66         => ( ( ( ( sgn_sgn_int @ K )
% 0.32/0.66                = ( sgn_sgn_int @ L2 ) )
% 0.32/0.66             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66                = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 0.32/0.66            & ( ( ( sgn_sgn_int @ K )
% 0.32/0.66               != ( sgn_sgn_int @ L2 ) )
% 0.32/0.66             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66                = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.32/0.66                  @ ( minus_minus_int
% 0.32/0.66                    @ ( semiri1314217659103216013at_int
% 0.32/0.66                      @ ( times_times_nat @ N
% 0.32/0.66                        @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 0.32/0.66                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % modulo_int_unfold
% 0.32/0.66  thf(fact_9198_dvd__mult__sgn__iff,axiom,
% 0.32/0.66      ! [L2: int,K: int,R: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 0.32/0.66        = ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66          | ( R = zero_zero_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % dvd_mult_sgn_iff
% 0.32/0.66  thf(fact_9199_dvd__sgn__mult__iff,axiom,
% 0.32/0.66      ! [L2: int,R: int,K: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 0.32/0.66        = ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66          | ( R = zero_zero_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % dvd_sgn_mult_iff
% 0.32/0.66  thf(fact_9200_mult__sgn__dvd__iff,axiom,
% 0.32/0.66      ! [L2: int,R: int,K: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R ) ) @ K )
% 0.32/0.66        = ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66          & ( ( R = zero_zero_int )
% 0.32/0.66           => ( K = zero_zero_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % mult_sgn_dvd_iff
% 0.32/0.66  thf(fact_9201_sgn__mult__dvd__iff,axiom,
% 0.32/0.66      ! [R: int,L2: int,K: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L2 ) @ K )
% 0.32/0.66        = ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66          & ( ( R = zero_zero_int )
% 0.32/0.66           => ( K = zero_zero_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_mult_dvd_iff
% 0.32/0.66  thf(fact_9202_signed__take__bit__nonnegative__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.32/0.66        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % signed_take_bit_nonnegative_iff
% 0.32/0.66  thf(fact_9203_signed__take__bit__negative__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 0.32/0.66        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % signed_take_bit_negative_iff
% 0.32/0.66  thf(fact_9204_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.32/0.66      ! [W: num,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 0.32/0.66        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_minus_numeral_Bit0_Suc_iff
% 0.32/0.66  thf(fact_9205_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.32/0.66      ! [W: num,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 0.32/0.66        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_minus_numeral_Bit1_Suc_iff
% 0.32/0.66  thf(fact_9206_bit__minus__numeral__int_I1_J,axiom,
% 0.32/0.66      ! [W: num,N: num] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.66        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_minus_numeral_int(1)
% 0.32/0.66  thf(fact_9207_bit__minus__numeral__int_I2_J,axiom,
% 0.32/0.66      ! [W: num,N: num] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.66        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_minus_numeral_int(2)
% 0.32/0.66  thf(fact_9208_bit__and__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 0.32/0.66        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.32/0.66          & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_and_int_iff
% 0.32/0.66  thf(fact_9209_int__sgnE,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ~ ! [N3: nat,L4: int] :
% 0.32/0.66            ( K
% 0.32/0.66           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_sgnE
% 0.32/0.66  thf(fact_9210_div__eq__sgn__abs,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( ( sgn_sgn_int @ K )
% 0.32/0.66          = ( sgn_sgn_int @ L2 ) )
% 0.32/0.66       => ( ( divide_divide_int @ K @ L2 )
% 0.32/0.66          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % div_eq_sgn_abs
% 0.32/0.66  thf(fact_9211_bit__not__int__iff_H,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 0.32/0.66        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_not_int_iff'
% 0.32/0.66  thf(fact_9212_sgn__mod,axiom,
% 0.32/0.66      ! [L2: int,K: int] :
% 0.32/0.66        ( ( L2 != zero_zero_int )
% 0.32/0.66       => ( ~ ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 0.32/0.66            = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_mod
% 0.32/0.66  thf(fact_9213_ln__neg__is__const,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.66       => ( ( ln_ln_real @ X )
% 0.32/0.66          = ( the_real
% 0.32/0.66            @ ^ [X3: real] : $false ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % ln_neg_is_const
% 0.32/0.66  thf(fact_9214_zsgn__def,axiom,
% 0.32/0.66      ( sgn_sgn_int
% 0.32/0.66      = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zsgn_def
% 0.32/0.66  thf(fact_9215_div__sgn__abs__cancel,axiom,
% 0.32/0.66      ! [V: int,K: int,L2: int] :
% 0.32/0.66        ( ( V != zero_zero_int )
% 0.32/0.66       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 0.32/0.66          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % div_sgn_abs_cancel
% 0.32/0.66  thf(fact_9216_bit__imp__take__bit__positive,axiom,
% 0.32/0.66      ! [N: nat,M: nat,K: int] :
% 0.32/0.66        ( ( ord_less_nat @ N @ M )
% 0.32/0.66       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.32/0.66         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_imp_take_bit_positive
% 0.32/0.66  thf(fact_9217_div__dvd__sgn__abs,axiom,
% 0.32/0.66      ! [L2: int,K: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ L2 @ K )
% 0.32/0.66       => ( ( divide_divide_int @ K @ L2 )
% 0.32/0.66          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % div_dvd_sgn_abs
% 0.32/0.66  thf(fact_9218_bit__concat__bit__iff,axiom,
% 0.32/0.66      ! [M: nat,K: int,L2: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 0.32/0.66        = ( ( ( ord_less_nat @ N @ M )
% 0.32/0.66            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 0.32/0.66          | ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66            & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_concat_bit_iff
% 0.32/0.66  thf(fact_9219_signed__take__bit__eq__concat__bit,axiom,
% 0.32/0.66      ( bit_ri631733984087533419it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( bit_concat_bit @ N2 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % signed_take_bit_eq_concat_bit
% 0.32/0.66  thf(fact_9220_int__bit__bound,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ~ ! [N3: nat] :
% 0.32/0.66            ( ! [M2: nat] :
% 0.32/0.66                ( ( ord_less_eq_nat @ N3 @ M2 )
% 0.32/0.66               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 0.32/0.66                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 0.32/0.66           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.32/0.66               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.32/0.66                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_bit_bound
% 0.32/0.66  thf(fact_9221_bit__int__def,axiom,
% 0.32/0.66      ( bit_se1146084159140164899it_int
% 0.32/0.66      = ( ^ [K2: int,N2: nat] :
% 0.32/0.66            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_int_def
% 0.32/0.66  thf(fact_9222_arccos__def,axiom,
% 0.32/0.66      ( arccos
% 0.32/0.66      = ( ^ [Y3: real] :
% 0.32/0.66            ( the_real
% 0.32/0.66            @ ^ [X3: real] :
% 0.32/0.66                ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.32/0.66                & ( ord_less_eq_real @ X3 @ pi )
% 0.32/0.66                & ( ( cos_real @ X3 )
% 0.32/0.66                  = Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arccos_def
% 0.32/0.66  thf(fact_9223_eucl__rel__int__remainderI,axiom,
% 0.32/0.66      ! [R: int,L2: int,K: int,Q2: int] :
% 0.32/0.66        ( ( ( sgn_sgn_int @ R )
% 0.32/0.66          = ( sgn_sgn_int @ L2 ) )
% 0.32/0.66       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 0.32/0.66         => ( ( K
% 0.32/0.66              = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 0.32/0.66           => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % eucl_rel_int_remainderI
% 0.32/0.66  thf(fact_9224_eucl__rel__int_Ocases,axiom,
% 0.32/0.66      ! [A12: int,A23: int,A32: product_prod_int_int] :
% 0.32/0.66        ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 0.32/0.66       => ( ( ( A23 = zero_zero_int )
% 0.32/0.66           => ( A32
% 0.32/0.66             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.32/0.66         => ( ! [Q3: int] :
% 0.32/0.66                ( ( A32
% 0.32/0.66                  = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 0.32/0.66               => ( ( A23 != zero_zero_int )
% 0.32/0.66                 => ( A12
% 0.32/0.66                   != ( times_times_int @ Q3 @ A23 ) ) ) )
% 0.32/0.66           => ~ ! [R2: int,Q3: int] :
% 0.32/0.66                  ( ( A32
% 0.32/0.66                    = ( product_Pair_int_int @ Q3 @ R2 ) )
% 0.32/0.66                 => ( ( ( sgn_sgn_int @ R2 )
% 0.32/0.66                      = ( sgn_sgn_int @ A23 ) )
% 0.32/0.66                   => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 0.32/0.66                     => ( A12
% 0.32/0.66                       != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % eucl_rel_int.cases
% 0.32/0.66  thf(fact_9225_eucl__rel__int_Osimps,axiom,
% 0.32/0.66      ( eucl_rel_int
% 0.32/0.66      = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 0.32/0.66            ( ? [K2: int] :
% 0.32/0.66                ( ( A1 = K2 )
% 0.32/0.66                & ( A22 = zero_zero_int )
% 0.32/0.66                & ( A33
% 0.32/0.66                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 0.32/0.66            | ? [L: int,K2: int,Q5: int] :
% 0.32/0.66                ( ( A1 = K2 )
% 0.32/0.66                & ( A22 = L )
% 0.32/0.66                & ( A33
% 0.32/0.66                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.32/0.66                & ( L != zero_zero_int )
% 0.32/0.66                & ( K2
% 0.32/0.66                  = ( times_times_int @ Q5 @ L ) ) )
% 0.32/0.66            | ? [R5: int,L: int,K2: int,Q5: int] :
% 0.32/0.66                ( ( A1 = K2 )
% 0.32/0.66                & ( A22 = L )
% 0.32/0.66                & ( A33
% 0.32/0.66                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 0.32/0.66                & ( ( sgn_sgn_int @ R5 )
% 0.32/0.66                  = ( sgn_sgn_int @ L ) )
% 0.32/0.66                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 0.32/0.66                & ( K2
% 0.32/0.66                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L ) @ R5 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % eucl_rel_int.simps
% 0.32/0.66  thf(fact_9226_div__noneq__sgn__abs,axiom,
% 0.32/0.66      ! [L2: int,K: int] :
% 0.32/0.66        ( ( L2 != zero_zero_int )
% 0.32/0.66       => ( ( ( sgn_sgn_int @ K )
% 0.32/0.66           != ( sgn_sgn_int @ L2 ) )
% 0.32/0.66         => ( ( divide_divide_int @ K @ L2 )
% 0.32/0.66            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 0.32/0.66              @ ( zero_n2684676970156552555ol_int
% 0.32/0.66                @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % div_noneq_sgn_abs
% 0.32/0.66  thf(fact_9227_set__bit__eq,axiom,
% 0.32/0.66      ( bit_se7879613467334960850it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] :
% 0.32/0.66            ( plus_plus_int @ K2
% 0.32/0.66            @ ( times_times_int
% 0.32/0.66              @ ( zero_n2684676970156552555ol_int
% 0.32/0.66                @ ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 0.32/0.66              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % set_bit_eq
% 0.32/0.66  thf(fact_9228_unset__bit__eq,axiom,
% 0.32/0.66      ( bit_se4203085406695923979it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % unset_bit_eq
% 0.32/0.66  thf(fact_9229_pi__half,axiom,
% 0.32/0.66      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.66      = ( the_real
% 0.32/0.66        @ ^ [X3: real] :
% 0.32/0.66            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.32/0.66            & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.66            & ( ( cos_real @ X3 )
% 0.32/0.66              = zero_zero_real ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % pi_half
% 0.32/0.66  thf(fact_9230_pi__def,axiom,
% 0.32/0.66      ( pi
% 0.32/0.66      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.32/0.66        @ ( the_real
% 0.32/0.66          @ ^ [X3: real] :
% 0.32/0.66              ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.32/0.66              & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.32/0.66              & ( ( cos_real @ X3 )
% 0.32/0.66                = zero_zero_real ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % pi_def
% 0.32/0.66  thf(fact_9231_take__bit__Suc__from__most,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 0.32/0.66        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % take_bit_Suc_from_most
% 0.32/0.66  thf(fact_9232_divide__int__unfold,axiom,
% 0.32/0.66      ! [L2: int,K: int,N: nat,M: nat] :
% 0.32/0.66        ( ( ( ( ( sgn_sgn_int @ L2 )
% 0.32/0.66              = zero_zero_int )
% 0.32/0.66            | ( ( sgn_sgn_int @ K )
% 0.32/0.66              = zero_zero_int )
% 0.32/0.66            | ( N = zero_zero_nat ) )
% 0.32/0.66         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66            = zero_zero_int ) )
% 0.32/0.66        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 0.32/0.66                = zero_zero_int )
% 0.32/0.66              | ( ( sgn_sgn_int @ K )
% 0.32/0.66                = zero_zero_int )
% 0.32/0.66              | ( N = zero_zero_nat ) )
% 0.32/0.66         => ( ( ( ( sgn_sgn_int @ K )
% 0.32/0.66                = ( sgn_sgn_int @ L2 ) )
% 0.32/0.66             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.32/0.66            & ( ( ( sgn_sgn_int @ K )
% 0.32/0.66               != ( sgn_sgn_int @ L2 ) )
% 0.32/0.66             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66                = ( uminus_uminus_int
% 0.32/0.66                  @ ( semiri1314217659103216013at_int
% 0.32/0.66                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.32/0.66                      @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_int_unfold
% 0.32/0.66  thf(fact_9233_modulo__int__def,axiom,
% 0.32/0.66      ( modulo_modulo_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( if_int @ ( L = zero_zero_int ) @ K2
% 0.32/0.66            @ ( if_int
% 0.32/0.66              @ ( ( sgn_sgn_int @ K2 )
% 0.32/0.66                = ( sgn_sgn_int @ L ) )
% 0.32/0.66              @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 0.32/0.66              @ ( times_times_int @ ( sgn_sgn_int @ L )
% 0.32/0.66                @ ( minus_minus_int
% 0.32/0.66                  @ ( times_times_int @ ( abs_abs_int @ L )
% 0.32/0.66                    @ ( zero_n2684676970156552555ol_int
% 0.32/0.66                      @ ~ ( dvd_dvd_int @ L @ K2 ) ) )
% 0.32/0.66                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % modulo_int_def
% 0.32/0.66  thf(fact_9234_divide__int__def,axiom,
% 0.32/0.66      ( divide_divide_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 0.32/0.66            @ ( if_int
% 0.32/0.66              @ ( ( sgn_sgn_int @ K2 )
% 0.32/0.66                = ( sgn_sgn_int @ L ) )
% 0.32/0.66              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 0.32/0.66              @ ( uminus_uminus_int
% 0.32/0.66                @ ( semiri1314217659103216013at_int
% 0.32/0.66                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 0.32/0.66                    @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66                      @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divide_int_def
% 0.32/0.66  thf(fact_9235_powr__int,axiom,
% 0.32/0.66      ! [X: real,I: int] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.32/0.66           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 0.32/0.66              = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 0.32/0.66          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 0.32/0.66           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 0.32/0.66              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % powr_int
% 0.32/0.66  thf(fact_9236_zero__le__sgn__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 0.32/0.66        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_le_sgn_iff
% 0.32/0.66  thf(fact_9237_sgn__le__0__iff,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_le_0_iff
% 0.32/0.66  thf(fact_9238_nat__numeral,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 0.32/0.66        = ( numeral_numeral_nat @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_numeral
% 0.32/0.66  thf(fact_9239_nat__1,axiom,
% 0.32/0.66      ( ( nat2 @ one_one_int )
% 0.32/0.66      = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_1
% 0.32/0.66  thf(fact_9240_nat__le__0,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.32/0.66       => ( ( nat2 @ Z )
% 0.32/0.66          = zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_le_0
% 0.32/0.66  thf(fact_9241_nat__0__iff,axiom,
% 0.32/0.66      ! [I: int] :
% 0.32/0.66        ( ( ( nat2 @ I )
% 0.32/0.66          = zero_zero_nat )
% 0.32/0.66        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_0_iff
% 0.32/0.66  thf(fact_9242_zless__nat__conj,axiom,
% 0.32/0.66      ! [W: int,Z: int] :
% 0.32/0.66        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.32/0.66        = ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.66          & ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zless_nat_conj
% 0.32/0.66  thf(fact_9243_nat__neg__numeral,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.66        = zero_zero_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_neg_numeral
% 0.32/0.66  thf(fact_9244_nat__zminus__int,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.32/0.66        = zero_zero_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_zminus_int
% 0.32/0.66  thf(fact_9245_int__nat__eq,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.32/0.66            = Z ) )
% 0.32/0.66        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.32/0.66            = zero_zero_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_nat_eq
% 0.32/0.66  thf(fact_9246_zero__less__nat__eq,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 0.32/0.66        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_less_nat_eq
% 0.32/0.66  thf(fact_9247_diff__nat__numeral,axiom,
% 0.32/0.66      ! [V: num,V3: num] :
% 0.32/0.66        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 0.32/0.66        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % diff_nat_numeral
% 0.32/0.66  thf(fact_9248_nat__eq__numeral__power__cancel__iff,axiom,
% 0.32/0.66      ! [Y: int,X: num,N: nat] :
% 0.32/0.66        ( ( ( nat2 @ Y )
% 0.32/0.66          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.32/0.66        = ( Y
% 0.32/0.66          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_eq_numeral_power_cancel_iff
% 0.32/0.66  thf(fact_9249_numeral__power__eq__nat__cancel__iff,axiom,
% 0.32/0.66      ! [X: num,N: nat,Y: int] :
% 0.32/0.66        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 0.32/0.66          = ( nat2 @ Y ) )
% 0.32/0.66        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 0.32/0.66          = Y ) ) ).
% 0.32/0.66  
% 0.32/0.66  % numeral_power_eq_nat_cancel_iff
% 0.32/0.66  thf(fact_9250_nat__ceiling__le__eq,axiom,
% 0.32/0.66      ! [X: real,A: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 0.32/0.66        = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_ceiling_le_eq
% 0.32/0.66  thf(fact_9251_one__less__nat__eq,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.32/0.66        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.32/0.66  
% 0.32/0.66  % one_less_nat_eq
% 0.32/0.66  thf(fact_9252_nat__numeral__diff__1,axiom,
% 0.32/0.66      ! [V: num] :
% 0.32/0.66        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.32/0.66        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_numeral_diff_1
% 0.32/0.66  thf(fact_9253_nat__less__numeral__power__cancel__iff,axiom,
% 0.32/0.66      ! [A: int,X: num,N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.32/0.66        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_less_numeral_power_cancel_iff
% 0.32/0.66  thf(fact_9254_numeral__power__less__nat__cancel__iff,axiom,
% 0.32/0.66      ! [X: num,N: nat,A: int] :
% 0.32/0.66        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.32/0.66        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.66  
% 0.32/0.66  % numeral_power_less_nat_cancel_iff
% 0.32/0.66  thf(fact_9255_numeral__power__le__nat__cancel__iff,axiom,
% 0.32/0.66      ! [X: num,N: nat,A: int] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.32/0.66        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.32/0.66  
% 0.32/0.66  % numeral_power_le_nat_cancel_iff
% 0.32/0.66  thf(fact_9256_nat__le__numeral__power__cancel__iff,axiom,
% 0.32/0.66      ! [A: int,X: num,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.32/0.66        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_le_numeral_power_cancel_iff
% 0.32/0.66  thf(fact_9257_bit__nat__iff,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 0.32/0.66        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_nat_iff
% 0.32/0.66  thf(fact_9258_not__bit__Suc__0__Suc,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_bit_Suc_0_Suc
% 0.32/0.66  thf(fact_9259_bit__Suc__0__iff,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.66        = ( N = zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_Suc_0_iff
% 0.32/0.66  thf(fact_9260_nat__zero__as__int,axiom,
% 0.32/0.66      ( zero_zero_nat
% 0.32/0.66      = ( nat2 @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_zero_as_int
% 0.32/0.66  thf(fact_9261_nat__numeral__as__int,axiom,
% 0.32/0.66      ( numeral_numeral_nat
% 0.32/0.66      = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_numeral_as_int
% 0.32/0.66  thf(fact_9262_nat__mono,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ X @ Y )
% 0.32/0.66       => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mono
% 0.32/0.66  thf(fact_9263_ex__nat,axiom,
% 0.32/0.66      ( ( ^ [P3: nat > $o] :
% 0.32/0.66          ? [X7: nat] : ( P3 @ X7 ) )
% 0.32/0.66      = ( ^ [P4: nat > $o] :
% 0.32/0.66          ? [X3: int] :
% 0.32/0.66            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.32/0.66            & ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % ex_nat
% 0.32/0.66  thf(fact_9264_all__nat,axiom,
% 0.32/0.66      ( ( ^ [P3: nat > $o] :
% 0.32/0.66          ! [X7: nat] : ( P3 @ X7 ) )
% 0.32/0.66      = ( ^ [P4: nat > $o] :
% 0.32/0.66          ! [X3: int] :
% 0.32/0.66            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.32/0.66           => ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % all_nat
% 0.32/0.66  thf(fact_9265_eq__nat__nat__iff,axiom,
% 0.32/0.66      ! [Z: int,Z7: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.32/0.66         => ( ( ( nat2 @ Z )
% 0.32/0.66              = ( nat2 @ Z7 ) )
% 0.32/0.66            = ( Z = Z7 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % eq_nat_nat_iff
% 0.32/0.66  thf(fact_9266_nat__one__as__int,axiom,
% 0.32/0.66      ( one_one_nat
% 0.32/0.66      = ( nat2 @ one_one_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_one_as_int
% 0.32/0.66  thf(fact_9267_unset__bit__nat__def,axiom,
% 0.32/0.66      ( bit_se4205575877204974255it_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % unset_bit_nat_def
% 0.32/0.66  thf(fact_9268_nat__mask__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 0.32/0.66        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mask_eq
% 0.32/0.66  thf(fact_9269_not__bit__Suc__0__numeral,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_bit_Suc_0_numeral
% 0.32/0.66  thf(fact_9270_sgn__root,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 0.32/0.66          = ( sgn_sgn_real @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_root
% 0.32/0.66  thf(fact_9271_nat__mono__iff,axiom,
% 0.32/0.66      ! [Z: int,W: int] :
% 0.32/0.66        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.32/0.66          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mono_iff
% 0.32/0.66  thf(fact_9272_zless__nat__eq__int__zless,axiom,
% 0.32/0.66      ! [M: nat,Z: int] :
% 0.32/0.66        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 0.32/0.66        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zless_nat_eq_int_zless
% 0.32/0.66  thf(fact_9273_nat__le__iff,axiom,
% 0.32/0.66      ! [X: int,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 0.32/0.66        = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_le_iff
% 0.32/0.66  thf(fact_9274_int__eq__iff,axiom,
% 0.32/0.66      ! [M: nat,Z: int] :
% 0.32/0.66        ( ( ( semiri1314217659103216013at_int @ M )
% 0.32/0.66          = Z )
% 0.32/0.66        = ( ( M
% 0.32/0.66            = ( nat2 @ Z ) )
% 0.32/0.66          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_eq_iff
% 0.32/0.66  thf(fact_9275_nat__0__le,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.32/0.66          = Z ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_0_le
% 0.32/0.66  thf(fact_9276_nat__int__add,axiom,
% 0.32/0.66      ! [A: nat,B: nat] :
% 0.32/0.66        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 0.32/0.66        = ( plus_plus_nat @ A @ B ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_int_add
% 0.32/0.66  thf(fact_9277_int__minus,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.66        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_minus
% 0.32/0.66  thf(fact_9278_nat__abs__mult__distrib,axiom,
% 0.32/0.66      ! [W: int,Z: int] :
% 0.32/0.66        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 0.32/0.66        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_abs_mult_distrib
% 0.32/0.66  thf(fact_9279_and__nat__def,axiom,
% 0.32/0.66      ( bit_se727722235901077358nd_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_nat_def
% 0.32/0.66  thf(fact_9280_nat__plus__as__int,axiom,
% 0.32/0.66      ( plus_plus_nat
% 0.32/0.66      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_plus_as_int
% 0.32/0.66  thf(fact_9281_nat__times__as__int,axiom,
% 0.32/0.66      ( times_times_nat
% 0.32/0.66      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_times_as_int
% 0.32/0.66  thf(fact_9282_real__nat__ceiling__ge,axiom,
% 0.32/0.66      ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_nat_ceiling_ge
% 0.32/0.66  thf(fact_9283_nat__minus__as__int,axiom,
% 0.32/0.66      ( minus_minus_nat
% 0.32/0.66      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_minus_as_int
% 0.32/0.66  thf(fact_9284_nat__div__as__int,axiom,
% 0.32/0.66      ( divide_divide_nat
% 0.32/0.66      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_div_as_int
% 0.32/0.66  thf(fact_9285_nat__mod__as__int,axiom,
% 0.32/0.66      ( modulo_modulo_nat
% 0.32/0.66      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mod_as_int
% 0.32/0.66  thf(fact_9286_cis__Arg,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( Z != zero_zero_complex )
% 0.32/0.66       => ( ( cis @ ( arg @ Z ) )
% 0.32/0.66          = ( sgn_sgn_complex @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_Arg
% 0.32/0.66  thf(fact_9287_sgn__real__def,axiom,
% 0.32/0.66      ( sgn_sgn_real
% 0.32/0.66      = ( ^ [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 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_real_def
% 0.32/0.66  thf(fact_9288_nat__less__eq__zless,axiom,
% 0.32/0.66      ! [W: int,Z: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.32/0.66          = ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_less_eq_zless
% 0.32/0.66  thf(fact_9289_nat__le__eq__zle,axiom,
% 0.32/0.66      ! [W: int,Z: int] :
% 0.32/0.66        ( ( ( ord_less_int @ zero_zero_int @ W )
% 0.32/0.66          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.32/0.66       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 0.32/0.66          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_le_eq_zle
% 0.32/0.66  thf(fact_9290_nat__eq__iff,axiom,
% 0.32/0.66      ! [W: int,M: nat] :
% 0.32/0.66        ( ( ( nat2 @ W )
% 0.32/0.66          = M )
% 0.32/0.66        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66           => ( W
% 0.32/0.66              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.66          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66           => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_eq_iff
% 0.32/0.66  thf(fact_9291_nat__eq__iff2,axiom,
% 0.32/0.66      ! [M: nat,W: int] :
% 0.32/0.66        ( ( M
% 0.32/0.66          = ( nat2 @ W ) )
% 0.32/0.66        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66           => ( W
% 0.32/0.66              = ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.66          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66           => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_eq_iff2
% 0.32/0.66  thf(fact_9292_split__nat,axiom,
% 0.32/0.66      ! [P: nat > $o,I: int] :
% 0.32/0.66        ( ( P @ ( nat2 @ I ) )
% 0.32/0.66        = ( ! [N2: nat] :
% 0.32/0.66              ( ( I
% 0.32/0.66                = ( semiri1314217659103216013at_int @ N2 ) )
% 0.32/0.66             => ( P @ N2 ) )
% 0.32/0.66          & ( ( ord_less_int @ I @ zero_zero_int )
% 0.32/0.66           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % split_nat
% 0.32/0.66  thf(fact_9293_le__nat__iff,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 0.32/0.66          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % le_nat_iff
% 0.32/0.66  thf(fact_9294_nat__add__distrib,axiom,
% 0.32/0.66      ! [Z: int,Z7: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.32/0.66         => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 0.32/0.66            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_add_distrib
% 0.32/0.66  thf(fact_9295_nat__mult__distrib,axiom,
% 0.32/0.66      ! [Z: int,Z7: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 0.32/0.66          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mult_distrib
% 0.32/0.66  thf(fact_9296_Suc__as__int,axiom,
% 0.32/0.66      ( suc
% 0.32/0.66      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_as_int
% 0.32/0.66  thf(fact_9297_nat__diff__distrib,axiom,
% 0.32/0.66      ! [Z7: int,Z: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.32/0.66       => ( ( ord_less_eq_int @ Z7 @ Z )
% 0.32/0.66         => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 0.32/0.66            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_diff_distrib
% 0.32/0.66  thf(fact_9298_nat__diff__distrib_H,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.66         => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 0.32/0.66            = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_diff_distrib'
% 0.32/0.66  thf(fact_9299_nat__abs__triangle__ineq,axiom,
% 0.32/0.66      ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_abs_triangle_ineq
% 0.32/0.66  thf(fact_9300_nat__div__distrib,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 0.32/0.66          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_div_distrib
% 0.32/0.66  thf(fact_9301_nat__div__distrib_H,axiom,
% 0.32/0.66      ! [Y: int,X: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.66       => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 0.32/0.66          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_div_distrib'
% 0.32/0.66  thf(fact_9302_nat__power__eq,axiom,
% 0.32/0.66      ! [Z: int,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 0.32/0.66          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_power_eq
% 0.32/0.66  thf(fact_9303_nat__floor__neg,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.32/0.66       => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.32/0.66          = zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_floor_neg
% 0.32/0.66  thf(fact_9304_nat__mod__distrib,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.66         => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 0.32/0.66            = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mod_distrib
% 0.32/0.66  thf(fact_9305_div__abs__eq__div__nat,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 0.32/0.66        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % div_abs_eq_div_nat
% 0.32/0.66  thf(fact_9306_floor__eq3,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.32/0.66         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.32/0.66            = N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_eq3
% 0.32/0.66  thf(fact_9307_le__nat__floor,axiom,
% 0.32/0.66      ! [X: nat,A: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 0.32/0.66       => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % le_nat_floor
% 0.32/0.66  thf(fact_9308_mod__abs__eq__div__nat,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 0.32/0.66        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % mod_abs_eq_div_nat
% 0.32/0.66  thf(fact_9309_nat__take__bit__eq,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.32/0.66          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_take_bit_eq
% 0.32/0.66  thf(fact_9310_take__bit__nat__eq,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 0.32/0.66          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % take_bit_nat_eq
% 0.32/0.66  thf(fact_9311_nat__2,axiom,
% 0.32/0.66      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.66      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_2
% 0.32/0.66  thf(fact_9312_sgn__power__injE,axiom,
% 0.32/0.66      ! [A: real,N: nat,X: real,B: real] :
% 0.32/0.66        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.32/0.66          = X )
% 0.32/0.66       => ( ( X
% 0.32/0.66            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 0.32/0.66         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66           => ( A = B ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_power_injE
% 0.32/0.66  thf(fact_9313_Suc__nat__eq__nat__zadd1,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66       => ( ( suc @ ( nat2 @ Z ) )
% 0.32/0.66          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_nat_eq_nat_zadd1
% 0.32/0.66  thf(fact_9314_nat__less__iff,axiom,
% 0.32/0.66      ! [W: int,M: nat] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.66       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.32/0.66          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_less_iff
% 0.32/0.66  thf(fact_9315_nat__mult__distrib__neg,axiom,
% 0.32/0.66      ! [Z: int,Z7: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.32/0.66       => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 0.32/0.66          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_mult_distrib_neg
% 0.32/0.66  thf(fact_9316_nat__abs__int__diff,axiom,
% 0.32/0.66      ! [A: nat,B: nat] :
% 0.32/0.66        ( ( ( ord_less_eq_nat @ A @ B )
% 0.32/0.66         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.32/0.66            = ( minus_minus_nat @ B @ A ) ) )
% 0.32/0.66        & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.32/0.66         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.32/0.66            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_abs_int_diff
% 0.32/0.66  thf(fact_9317_floor__eq4,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.32/0.66       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.32/0.66         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.32/0.66            = N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_eq4
% 0.32/0.66  thf(fact_9318_diff__nat__eq__if,axiom,
% 0.32/0.66      ! [Z7: int,Z: int] :
% 0.32/0.66        ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 0.32/0.66         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 0.32/0.66            = ( nat2 @ Z ) ) )
% 0.32/0.66        & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 0.32/0.66         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 0.32/0.66            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % diff_nat_eq_if
% 0.32/0.66  thf(fact_9319_bit__nat__def,axiom,
% 0.32/0.66      ( bit_se1148574629649215175it_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.66            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_nat_def
% 0.32/0.66  thf(fact_9320_root__sgn__power,axiom,
% 0.32/0.66      ! [N: nat,Y: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 0.32/0.66          = Y ) ) ).
% 0.32/0.66  
% 0.32/0.66  % root_sgn_power
% 0.32/0.66  thf(fact_9321_sgn__power__root,axiom,
% 0.32/0.66      ! [N: nat,X: real] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 0.32/0.66          = X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_power_root
% 0.32/0.66  thf(fact_9322_nat__dvd__iff,axiom,
% 0.32/0.66      ! [Z: int,M: nat] :
% 0.32/0.66        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 0.32/0.66        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.32/0.66          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.66           => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_dvd_iff
% 0.32/0.66  thf(fact_9323_cis__Arg__unique,axiom,
% 0.32/0.66      ! [Z: complex,X: real] :
% 0.32/0.66        ( ( ( sgn_sgn_complex @ Z )
% 0.32/0.66          = ( cis @ X ) )
% 0.32/0.66       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.32/0.66         => ( ( ord_less_eq_real @ X @ pi )
% 0.32/0.66           => ( ( arg @ Z )
% 0.32/0.66              = X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_Arg_unique
% 0.32/0.66  thf(fact_9324_split__root,axiom,
% 0.32/0.66      ! [P: real > $o,N: nat,X: real] :
% 0.32/0.66        ( ( P @ ( root @ N @ X ) )
% 0.32/0.66        = ( ( ( N = zero_zero_nat )
% 0.32/0.66           => ( P @ zero_zero_real ) )
% 0.32/0.66          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66           => ! [Y3: real] :
% 0.32/0.66                ( ( ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) )
% 0.32/0.66                  = X )
% 0.32/0.66               => ( P @ Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % split_root
% 0.32/0.66  thf(fact_9325_Arg__correct,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( Z != zero_zero_complex )
% 0.32/0.66       => ( ( ( sgn_sgn_complex @ Z )
% 0.32/0.66            = ( cis @ ( arg @ Z ) ) )
% 0.32/0.66          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 0.32/0.66          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_correct
% 0.32/0.66  thf(fact_9326_even__nat__iff,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.32/0.66          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % even_nat_iff
% 0.32/0.66  thf(fact_9327_powr__real__of__int,axiom,
% 0.32/0.66      ! [X: real,N: int] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.66       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.66           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.32/0.66              = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 0.32/0.66          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.66           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.32/0.66              = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % powr_real_of_int
% 0.32/0.66  thf(fact_9328_arctan__inverse,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( X != zero_zero_real )
% 0.32/0.66       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 0.32/0.66          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % arctan_inverse
% 0.32/0.66  thf(fact_9329_Arg__def,axiom,
% 0.32/0.66      ( arg
% 0.32/0.66      = ( ^ [Z3: complex] :
% 0.32/0.66            ( if_real @ ( Z3 = zero_zero_complex ) @ zero_zero_real
% 0.32/0.66            @ ( fChoice_real
% 0.32/0.66              @ ^ [A3: real] :
% 0.32/0.66                  ( ( ( sgn_sgn_complex @ Z3 )
% 0.32/0.66                    = ( cis @ A3 ) )
% 0.32/0.66                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 0.32/0.66                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Arg_def
% 0.32/0.66  thf(fact_9330_or__int__unfold,axiom,
% 0.32/0.66      ( bit_se1409905431419307370or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( if_int
% 0.32/0.66            @ ( ( K2
% 0.32/0.66                = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.66              | ( L
% 0.32/0.66                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.32/0.66            @ ( uminus_uminus_int @ one_one_int )
% 0.32/0.66            @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_int_unfold
% 0.32/0.66  thf(fact_9331_or__nonnegative__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 0.32/0.66        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66          & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nonnegative_int_iff
% 0.32/0.66  thf(fact_9332_or__negative__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 0.32/0.66        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.66          | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_negative_int_iff
% 0.32/0.66  thf(fact_9333_or__minus__numerals_I6_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(6)
% 0.32/0.66  thf(fact_9334_or__minus__numerals_I2_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(2)
% 0.32/0.66  thf(fact_9335_bit__or__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 0.32/0.66        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.32/0.66          | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_or_int_iff
% 0.32/0.66  thf(fact_9336_or__greater__eq,axiom,
% 0.32/0.66      ! [L2: int,K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 0.32/0.66       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_greater_eq
% 0.32/0.66  thf(fact_9337_OR__lower,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.66         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % OR_lower
% 0.32/0.66  thf(fact_9338_plus__and__or,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 0.32/0.66        = ( plus_plus_int @ X @ Y ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_and_or
% 0.32/0.66  thf(fact_9339_OR__upper,axiom,
% 0.32/0.66      ! [X: int,N: nat,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.66         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.66           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % OR_upper
% 0.32/0.66  thf(fact_9340_or__int__rec,axiom,
% 0.32/0.66      ( bit_se1409905431419307370or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( plus_plus_int
% 0.32/0.66            @ ( zero_n2684676970156552555ol_int
% 0.32/0.66              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.32/0.66                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.32/0.66            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_int_rec
% 0.32/0.66  thf(fact_9341_or__minus__numerals_I5_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(5)
% 0.32/0.66  thf(fact_9342_or__minus__numerals_I1_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(1)
% 0.32/0.66  thf(fact_9343_cis__multiple__2pi,axiom,
% 0.32/0.66      ! [N: real] :
% 0.32/0.66        ( ( member_real @ N @ ring_1_Ints_real )
% 0.32/0.66       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.32/0.66          = one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cis_multiple_2pi
% 0.32/0.66  thf(fact_9344_or__nat__numerals_I2_J,axiom,
% 0.32/0.66      ! [Y: num] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_numerals(2)
% 0.32/0.66  thf(fact_9345_or__nat__numerals_I4_J,axiom,
% 0.32/0.66      ! [X: num] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_numerals(4)
% 0.32/0.66  thf(fact_9346_or__nat__numerals_I3_J,axiom,
% 0.32/0.66      ! [X: num] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_numerals(3)
% 0.32/0.66  thf(fact_9347_or__nat__numerals_I1_J,axiom,
% 0.32/0.66      ! [Y: num] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_numerals(1)
% 0.32/0.66  thf(fact_9348_or__minus__numerals_I8_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(8)
% 0.32/0.66  thf(fact_9349_or__minus__numerals_I4_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(4)
% 0.32/0.66  thf(fact_9350_or__minus__numerals_I7_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(7)
% 0.32/0.66  thf(fact_9351_or__minus__numerals_I3_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_numerals(3)
% 0.32/0.66  thf(fact_9352_or__not__num__neg_Osimps_I1_J,axiom,
% 0.32/0.66      ( ( bit_or_not_num_neg @ one @ one )
% 0.32/0.66      = one ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(1)
% 0.32/0.66  thf(fact_9353_or__not__num__neg_Osimps_I4_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 0.32/0.66        = ( bit0 @ one ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(4)
% 0.32/0.66  thf(fact_9354_or__not__num__neg_Osimps_I6_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 0.32/0.66        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(6)
% 0.32/0.66  thf(fact_9355_or__not__num__neg_Osimps_I7_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 0.32/0.66        = one ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(7)
% 0.32/0.66  thf(fact_9356_or__not__num__neg_Osimps_I3_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 0.32/0.66        = ( bit1 @ M ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(3)
% 0.32/0.66  thf(fact_9357_or__not__num__neg_Osimps_I5_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 0.32/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(5)
% 0.32/0.66  thf(fact_9358_or__not__num__neg_Osimps_I9_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 0.32/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(9)
% 0.32/0.66  thf(fact_9359_or__nat__def,axiom,
% 0.32/0.66      ( bit_se1412395901928357646or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_def
% 0.32/0.66  thf(fact_9360_or__not__num__neg_Osimps_I2_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 0.32/0.66        = ( bit1 @ M ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(2)
% 0.32/0.66  thf(fact_9361_or__not__num__neg_Osimps_I8_J,axiom,
% 0.32/0.66      ! [N: num,M: num] :
% 0.32/0.66        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 0.32/0.66        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.simps(8)
% 0.32/0.66  thf(fact_9362_sin__times__pi__eq__0,axiom,
% 0.32/0.66      ! [X: real] :
% 0.32/0.66        ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66        = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sin_times_pi_eq_0
% 0.32/0.66  thf(fact_9363_or__not__num__neg_Oelims,axiom,
% 0.32/0.66      ! [X: num,Xa2: num,Y: num] :
% 0.32/0.66        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 0.32/0.66          = Y )
% 0.32/0.66       => ( ( ( X = one )
% 0.32/0.66           => ( ( Xa2 = one )
% 0.32/0.66             => ( Y != one ) ) )
% 0.32/0.66         => ( ( ( X = one )
% 0.32/0.66             => ! [M4: num] :
% 0.32/0.66                  ( ( Xa2
% 0.32/0.66                    = ( bit0 @ M4 ) )
% 0.32/0.66                 => ( Y
% 0.32/0.66                   != ( bit1 @ M4 ) ) ) )
% 0.32/0.66           => ( ( ( X = one )
% 0.32/0.66               => ! [M4: num] :
% 0.32/0.66                    ( ( Xa2
% 0.32/0.66                      = ( bit1 @ M4 ) )
% 0.32/0.66                   => ( Y
% 0.32/0.66                     != ( bit1 @ M4 ) ) ) )
% 0.32/0.66             => ( ( ? [N3: num] :
% 0.32/0.66                      ( X
% 0.32/0.66                      = ( bit0 @ N3 ) )
% 0.32/0.66                 => ( ( Xa2 = one )
% 0.32/0.66                   => ( Y
% 0.32/0.66                     != ( bit0 @ one ) ) ) )
% 0.32/0.66               => ( ! [N3: num] :
% 0.32/0.66                      ( ( X
% 0.32/0.66                        = ( bit0 @ N3 ) )
% 0.32/0.66                     => ! [M4: num] :
% 0.32/0.66                          ( ( Xa2
% 0.32/0.66                            = ( bit0 @ M4 ) )
% 0.32/0.66                         => ( Y
% 0.32/0.66                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.32/0.66                 => ( ! [N3: num] :
% 0.32/0.66                        ( ( X
% 0.32/0.66                          = ( bit0 @ N3 ) )
% 0.32/0.66                       => ! [M4: num] :
% 0.32/0.66                            ( ( Xa2
% 0.32/0.66                              = ( bit1 @ M4 ) )
% 0.32/0.66                           => ( Y
% 0.32/0.66                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.32/0.66                   => ( ( ? [N3: num] :
% 0.32/0.66                            ( X
% 0.32/0.66                            = ( bit1 @ N3 ) )
% 0.32/0.66                       => ( ( Xa2 = one )
% 0.32/0.66                         => ( Y != one ) ) )
% 0.32/0.66                     => ( ! [N3: num] :
% 0.32/0.66                            ( ( X
% 0.32/0.66                              = ( bit1 @ N3 ) )
% 0.32/0.66                           => ! [M4: num] :
% 0.32/0.66                                ( ( Xa2
% 0.32/0.66                                  = ( bit0 @ M4 ) )
% 0.32/0.66                               => ( Y
% 0.32/0.66                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 0.32/0.66                       => ~ ! [N3: num] :
% 0.32/0.66                              ( ( X
% 0.32/0.66                                = ( bit1 @ N3 ) )
% 0.32/0.66                             => ! [M4: num] :
% 0.32/0.66                                  ( ( Xa2
% 0.32/0.66                                    = ( bit1 @ M4 ) )
% 0.32/0.66                                 => ( Y
% 0.32/0.66                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.elims
% 0.32/0.66  thf(fact_9364_sin__integer__2pi,axiom,
% 0.32/0.66      ! [N: real] :
% 0.32/0.66        ( ( member_real @ N @ ring_1_Ints_real )
% 0.32/0.66       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sin_integer_2pi
% 0.32/0.66  thf(fact_9365_cos__integer__2pi,axiom,
% 0.32/0.66      ! [N: real] :
% 0.32/0.66        ( ( member_real @ N @ ring_1_Ints_real )
% 0.32/0.66       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.32/0.66          = one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cos_integer_2pi
% 0.32/0.66  thf(fact_9366_or__Suc__0__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_Suc_0_eq
% 0.32/0.66  thf(fact_9367_Suc__0__or__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.66        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_0_or_eq
% 0.32/0.66  thf(fact_9368_or__nat__rec,axiom,
% 0.32/0.66      ( bit_se1412395901928357646or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.66            ( plus_plus_nat
% 0.32/0.66            @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 0.32/0.66                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.66            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_rec
% 0.32/0.66  thf(fact_9369_or__nat__unfold,axiom,
% 0.32/0.66      ( bit_se1412395901928357646or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_nat_unfold
% 0.32/0.66  thf(fact_9370_or__not__num__neg_Opelims,axiom,
% 0.32/0.66      ! [X: num,Xa2: num,Y: num] :
% 0.32/0.66        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 0.32/0.66          = Y )
% 0.32/0.66       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 0.32/0.66         => ( ( ( X = one )
% 0.32/0.66             => ( ( Xa2 = one )
% 0.32/0.66               => ( ( Y = one )
% 0.32/0.66                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.32/0.66           => ( ( ( X = one )
% 0.32/0.66               => ! [M4: num] :
% 0.32/0.66                    ( ( Xa2
% 0.32/0.66                      = ( bit0 @ M4 ) )
% 0.32/0.66                   => ( ( Y
% 0.32/0.66                        = ( bit1 @ M4 ) )
% 0.32/0.66                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 0.32/0.66             => ( ( ( X = one )
% 0.32/0.66                 => ! [M4: num] :
% 0.32/0.66                      ( ( Xa2
% 0.32/0.66                        = ( bit1 @ M4 ) )
% 0.32/0.66                     => ( ( Y
% 0.32/0.66                          = ( bit1 @ M4 ) )
% 0.32/0.66                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 0.32/0.66               => ( ! [N3: num] :
% 0.32/0.66                      ( ( X
% 0.32/0.66                        = ( bit0 @ N3 ) )
% 0.32/0.66                     => ( ( Xa2 = one )
% 0.32/0.66                       => ( ( Y
% 0.32/0.66                            = ( bit0 @ one ) )
% 0.32/0.66                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 0.32/0.66                 => ( ! [N3: num] :
% 0.32/0.66                        ( ( X
% 0.32/0.66                          = ( bit0 @ N3 ) )
% 0.32/0.66                       => ! [M4: num] :
% 0.32/0.66                            ( ( Xa2
% 0.32/0.66                              = ( bit0 @ M4 ) )
% 0.32/0.66                           => ( ( Y
% 0.32/0.66                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.32/0.66                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.32/0.66                   => ( ! [N3: num] :
% 0.32/0.66                          ( ( X
% 0.32/0.66                            = ( bit0 @ N3 ) )
% 0.32/0.66                         => ! [M4: num] :
% 0.32/0.66                              ( ( Xa2
% 0.32/0.66                                = ( bit1 @ M4 ) )
% 0.32/0.66                             => ( ( Y
% 0.32/0.66                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.32/0.66                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 0.32/0.66                     => ( ! [N3: num] :
% 0.32/0.66                            ( ( X
% 0.32/0.66                              = ( bit1 @ N3 ) )
% 0.32/0.66                           => ( ( Xa2 = one )
% 0.32/0.66                             => ( ( Y = one )
% 0.32/0.66                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 0.32/0.66                       => ( ! [N3: num] :
% 0.32/0.66                              ( ( X
% 0.32/0.66                                = ( bit1 @ N3 ) )
% 0.32/0.66                             => ! [M4: num] :
% 0.32/0.66                                  ( ( Xa2
% 0.32/0.66                                    = ( bit0 @ M4 ) )
% 0.32/0.66                                 => ( ( Y
% 0.32/0.66                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.32/0.66                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 0.32/0.66                         => ~ ! [N3: num] :
% 0.32/0.66                                ( ( X
% 0.32/0.66                                  = ( bit1 @ N3 ) )
% 0.32/0.66                               => ! [M4: num] :
% 0.32/0.66                                    ( ( Xa2
% 0.32/0.66                                      = ( bit1 @ M4 ) )
% 0.32/0.66                                   => ( ( Y
% 0.32/0.66                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 0.32/0.66                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_num_neg.pelims
% 0.32/0.66  thf(fact_9371_xor__Suc__0__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.66          @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_Suc_0_eq
% 0.32/0.66  thf(fact_9372_Suc__0__xor__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.66        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.66          @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_0_xor_eq
% 0.32/0.66  thf(fact_9373_xor__nat__numerals_I1_J,axiom,
% 0.32/0.66      ! [Y: num] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_numerals(1)
% 0.32/0.66  thf(fact_9374_xor__nat__numerals_I2_J,axiom,
% 0.32/0.66      ! [Y: num] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_numerals(2)
% 0.32/0.66  thf(fact_9375_xor__nat__numerals_I3_J,axiom,
% 0.32/0.66      ! [X: num] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_numerals(3)
% 0.32/0.66  thf(fact_9376_xor__nat__numerals_I4_J,axiom,
% 0.32/0.66      ! [X: num] :
% 0.32/0.66        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_numerals(4)
% 0.32/0.66  thf(fact_9377_xor__nat__unfold,axiom,
% 0.32/0.66      ( bit_se6528837805403552850or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_unfold
% 0.32/0.66  thf(fact_9378_xor__nat__rec,axiom,
% 0.32/0.66      ( bit_se6528837805403552850or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.66            ( plus_plus_nat
% 0.32/0.66            @ ( zero_n2687167440665602831ol_nat
% 0.32/0.66              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.32/0.66               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.32/0.66            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_rec
% 0.32/0.66  thf(fact_9379_horner__sum__of__bool__2__less,axiom,
% 0.32/0.66      ! [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 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % horner_sum_of_bool_2_less
% 0.32/0.66  thf(fact_9380_push__bit__nonnegative__int__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.32/0.66        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_nonnegative_int_iff
% 0.32/0.66  thf(fact_9381_push__bit__negative__int__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 0.32/0.66        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_negative_int_iff
% 0.32/0.66  thf(fact_9382_concat__bit__of__zero__1,axiom,
% 0.32/0.66      ! [N: nat,L2: int] :
% 0.32/0.66        ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 0.32/0.66        = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % concat_bit_of_zero_1
% 0.32/0.66  thf(fact_9383_xor__nonnegative__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 0.32/0.66        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.66          = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nonnegative_int_iff
% 0.32/0.66  thf(fact_9384_xor__negative__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 0.32/0.66        = ( ( ord_less_int @ K @ zero_zero_int )
% 0.32/0.66         != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_negative_int_iff
% 0.32/0.66  thf(fact_9385_push__bit__of__Suc__0,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.66        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_of_Suc_0
% 0.32/0.66  thf(fact_9386_bit__xor__int__iff,axiom,
% 0.32/0.66      ! [K: int,L2: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 0.32/0.66        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.32/0.66         != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_xor_int_iff
% 0.32/0.66  thf(fact_9387_flip__bit__int__def,axiom,
% 0.32/0.66      ( bit_se2159334234014336723it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % flip_bit_int_def
% 0.32/0.66  thf(fact_9388_push__bit__nat__eq,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 0.32/0.66        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_nat_eq
% 0.32/0.66  thf(fact_9389_XOR__lower,axiom,
% 0.32/0.66      ! [X: int,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.66         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % XOR_lower
% 0.32/0.66  thf(fact_9390_set__bit__nat__def,axiom,
% 0.32/0.66      ( bit_se7882103937844011126it_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % set_bit_nat_def
% 0.32/0.66  thf(fact_9391_flip__bit__nat__def,axiom,
% 0.32/0.66      ( bit_se2161824704523386999it_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % flip_bit_nat_def
% 0.32/0.66  thf(fact_9392_bit__push__bit__iff__int,axiom,
% 0.32/0.66      ! [M: nat,K: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 0.32/0.66        = ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_push_bit_iff_int
% 0.32/0.66  thf(fact_9393_xor__nat__def,axiom,
% 0.32/0.66      ( bit_se6528837805403552850or_nat
% 0.32/0.66      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_nat_def
% 0.32/0.66  thf(fact_9394_bit__push__bit__iff__nat,axiom,
% 0.32/0.66      ! [M: nat,Q2: nat,N: nat] :
% 0.32/0.66        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 0.32/0.66        = ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_push_bit_iff_nat
% 0.32/0.66  thf(fact_9395_concat__bit__eq,axiom,
% 0.32/0.66      ( bit_concat_bit
% 0.32/0.66      = ( ^ [N2: nat,K2: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % concat_bit_eq
% 0.32/0.66  thf(fact_9396_concat__bit__def,axiom,
% 0.32/0.66      ( bit_concat_bit
% 0.32/0.66      = ( ^ [N2: nat,K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % concat_bit_def
% 0.32/0.66  thf(fact_9397_set__bit__int__def,axiom,
% 0.32/0.66      ( bit_se7879613467334960850it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % set_bit_int_def
% 0.32/0.66  thf(fact_9398_push__bit__nat__def,axiom,
% 0.32/0.66      ( bit_se547839408752420682it_nat
% 0.32/0.66      = ( ^ [N2: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_nat_def
% 0.32/0.66  thf(fact_9399_push__bit__int__def,axiom,
% 0.32/0.66      ( bit_se545348938243370406it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_int_def
% 0.32/0.66  thf(fact_9400_push__bit__minus__one,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % push_bit_minus_one
% 0.32/0.66  thf(fact_9401_XOR__upper,axiom,
% 0.32/0.66      ! [X: int,N: nat,Y: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.66       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.66         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.32/0.66           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % XOR_upper
% 0.32/0.66  thf(fact_9402_xor__int__rec,axiom,
% 0.32/0.66      ( bit_se6526347334894502574or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( plus_plus_int
% 0.32/0.66            @ ( zero_n2684676970156552555ol_int
% 0.32/0.66              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 0.32/0.66               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 0.32/0.66            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_int_rec
% 0.32/0.66  thf(fact_9403_xor__int__unfold,axiom,
% 0.32/0.66      ( bit_se6526347334894502574or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] :
% 0.32/0.66            ( if_int
% 0.32/0.66            @ ( K2
% 0.32/0.66              = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.66            @ ( bit_ri7919022796975470100ot_int @ L )
% 0.32/0.66            @ ( if_int
% 0.32/0.66              @ ( L
% 0.32/0.66                = ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.66              @ ( bit_ri7919022796975470100ot_int @ K2 )
% 0.32/0.66              @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_int_unfold
% 0.32/0.66  thf(fact_9404_Sum__Ico__nat,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [X3: nat] : X3
% 0.32/0.66          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.32/0.66        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Sum_Ico_nat
% 0.32/0.66  thf(fact_9405_finite__atLeastLessThan,axiom,
% 0.32/0.66      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % finite_atLeastLessThan
% 0.32/0.66  thf(fact_9406_not__negative__int__iff,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.32/0.66        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_negative_int_iff
% 0.32/0.66  thf(fact_9407_not__nonnegative__int__iff,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.32/0.66        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_nonnegative_int_iff
% 0.32/0.66  thf(fact_9408_atLeastLessThan__singleton,axiom,
% 0.32/0.66      ! [M: nat] :
% 0.32/0.66        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.32/0.66        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThan_singleton
% 0.32/0.66  thf(fact_9409_or__minus__minus__numerals,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_minus_minus_numerals
% 0.32/0.66  thf(fact_9410_and__minus__minus__numerals,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_minus_minus_numerals
% 0.32/0.66  thf(fact_9411_bit__not__int__iff,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 0.32/0.66        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_not_int_iff
% 0.32/0.66  thf(fact_9412_all__nat__less__eq,axiom,
% 0.32/0.66      ! [N: nat,P: nat > $o] :
% 0.32/0.66        ( ( ! [M3: nat] :
% 0.32/0.66              ( ( ord_less_nat @ M3 @ N )
% 0.32/0.66             => ( P @ M3 ) ) )
% 0.32/0.66        = ( ! [X3: nat] :
% 0.32/0.66              ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.32/0.66             => ( P @ X3 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % all_nat_less_eq
% 0.32/0.66  thf(fact_9413_ex__nat__less__eq,axiom,
% 0.32/0.66      ! [N: nat,P: nat > $o] :
% 0.32/0.66        ( ( ? [M3: nat] :
% 0.32/0.66              ( ( ord_less_nat @ M3 @ N )
% 0.32/0.66              & ( P @ M3 ) ) )
% 0.32/0.66        = ( ? [X3: nat] :
% 0.32/0.66              ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.32/0.66              & ( P @ X3 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % ex_nat_less_eq
% 0.32/0.66  thf(fact_9414_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.32/0.66      ! [L2: nat,U: nat] :
% 0.32/0.66        ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 0.32/0.66        = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThanSuc_atLeastAtMost
% 0.32/0.66  thf(fact_9415_lessThan__atLeast0,axiom,
% 0.32/0.66      ( set_ord_lessThan_nat
% 0.32/0.66      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % lessThan_atLeast0
% 0.32/0.66  thf(fact_9416_atLeastLessThan0,axiom,
% 0.32/0.66      ! [M: nat] :
% 0.32/0.66        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.32/0.66        = bot_bot_set_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThan0
% 0.32/0.66  thf(fact_9417_or__int__def,axiom,
% 0.32/0.66      ( bit_se1409905431419307370or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_int_def
% 0.32/0.66  thf(fact_9418_not__int__def,axiom,
% 0.32/0.66      ( bit_ri7919022796975470100ot_int
% 0.32/0.66      = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_int_def
% 0.32/0.66  thf(fact_9419_and__not__numerals_I1_J,axiom,
% 0.32/0.66      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66      = zero_zero_int ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(1)
% 0.32/0.66  thf(fact_9420_or__not__numerals_I1_J,axiom,
% 0.32/0.66      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(1)
% 0.32/0.66  thf(fact_9421_atLeast0__lessThan__Suc,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.32/0.66        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeast0_lessThan_Suc
% 0.32/0.66  thf(fact_9422_unset__bit__int__def,axiom,
% 0.32/0.66      ( bit_se4203085406695923979it_int
% 0.32/0.66      = ( ^ [N2: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % unset_bit_int_def
% 0.32/0.66  thf(fact_9423_xor__int__def,axiom,
% 0.32/0.66      ( bit_se6526347334894502574or_int
% 0.32/0.66      = ( ^ [K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % xor_int_def
% 0.32/0.66  thf(fact_9424_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.32/0.66      ! [N4: set_nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.32/0.66       => ( finite_finite_nat @ N4 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % subset_eq_atLeast0_lessThan_finite
% 0.32/0.66  thf(fact_9425_not__int__div__2,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_int_div_2
% 0.32/0.66  thf(fact_9426_even__not__iff__int,axiom,
% 0.32/0.66      ! [K: int] :
% 0.32/0.66        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.32/0.66        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % even_not_iff_int
% 0.32/0.66  thf(fact_9427_and__not__numerals_I4_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(4)
% 0.32/0.66  thf(fact_9428_and__not__numerals_I2_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = one_one_int ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(2)
% 0.32/0.66  thf(fact_9429_or__not__numerals_I2_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(2)
% 0.32/0.66  thf(fact_9430_or__not__numerals_I4_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(4)
% 0.32/0.66  thf(fact_9431_bit__minus__int__iff,axiom,
% 0.32/0.66      ! [K: int,N: nat] :
% 0.32/0.66        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 0.32/0.66        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_minus_int_iff
% 0.32/0.66  thf(fact_9432_int__numeral__or__not__num__neg,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_numeral_or_not_num_neg
% 0.32/0.66  thf(fact_9433_int__numeral__not__or__num__neg,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_numeral_not_or_num_neg
% 0.32/0.66  thf(fact_9434_numeral__or__not__num__eq,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 0.32/0.66        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % numeral_or_not_num_eq
% 0.32/0.66  thf(fact_9435_atLeastLessThanSuc,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.66         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.32/0.66            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.32/0.66        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.32/0.66         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.32/0.66            = bot_bot_set_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThanSuc
% 0.32/0.66  thf(fact_9436_prod__Suc__Suc__fact,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.32/0.66        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % prod_Suc_Suc_fact
% 0.32/0.66  thf(fact_9437_prod__Suc__fact,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.32/0.66        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % prod_Suc_fact
% 0.32/0.66  thf(fact_9438_and__not__numerals_I5_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(5)
% 0.32/0.66  thf(fact_9439_and__not__numerals_I7_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(7)
% 0.32/0.66  thf(fact_9440_or__not__numerals_I3_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(3)
% 0.32/0.66  thf(fact_9441_and__not__numerals_I3_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = zero_zero_int ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(3)
% 0.32/0.66  thf(fact_9442_or__not__numerals_I7_J,axiom,
% 0.32/0.66      ! [M: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.32/0.66        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(7)
% 0.32/0.66  thf(fact_9443_atLeastLessThan__nat__numeral,axiom,
% 0.32/0.66      ! [M: nat,K: num] :
% 0.32/0.66        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.32/0.66         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.32/0.66            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.32/0.66        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.32/0.66         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.32/0.66            = bot_bot_set_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThan_nat_numeral
% 0.32/0.66  thf(fact_9444_and__not__numerals_I9_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(9)
% 0.32/0.66  thf(fact_9445_and__not__numerals_I6_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(6)
% 0.32/0.66  thf(fact_9446_or__not__numerals_I6_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(6)
% 0.32/0.66  thf(fact_9447_or__not__numerals_I5_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(5)
% 0.32/0.66  thf(fact_9448_atLeast1__lessThan__eq__remove0,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.32/0.66        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeast1_lessThan_eq_remove0
% 0.32/0.66  thf(fact_9449_and__not__numerals_I8_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % and_not_numerals(8)
% 0.32/0.66  thf(fact_9450_or__not__numerals_I9_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.66        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(9)
% 0.32/0.66  thf(fact_9451_or__not__numerals_I8_J,axiom,
% 0.32/0.66      ! [M: num,N: num] :
% 0.32/0.66        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.66        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % or_not_numerals(8)
% 0.32/0.66  thf(fact_9452_not__int__rec,axiom,
% 0.32/0.66      ( bit_ri7919022796975470100ot_int
% 0.32/0.66      = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % not_int_rec
% 0.32/0.66  thf(fact_9453_sum__power2,axiom,
% 0.32/0.66      ! [K: nat] :
% 0.32/0.66        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.32/0.66        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sum_power2
% 0.32/0.66  thf(fact_9454_Chebyshev__sum__upper__nat,axiom,
% 0.32/0.66      ! [N: nat,A: nat > nat,B: nat > nat] :
% 0.32/0.66        ( ! [I4: nat,J2: nat] :
% 0.32/0.66            ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.32/0.66           => ( ( ord_less_nat @ J2 @ N )
% 0.32/0.66             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 0.32/0.66       => ( ! [I4: nat,J2: nat] :
% 0.32/0.66              ( ( ord_less_eq_nat @ I4 @ J2 )
% 0.32/0.66             => ( ( ord_less_nat @ J2 @ N )
% 0.32/0.66               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 0.32/0.66         => ( ord_less_eq_nat
% 0.32/0.66            @ ( times_times_nat @ N
% 0.32/0.66              @ ( groups3542108847815614940at_nat
% 0.32/0.66                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 0.32/0.66                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.32/0.66            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Chebyshev_sum_upper_nat
% 0.32/0.66  thf(fact_9455_finite__atLeastLessThan__int,axiom,
% 0.32/0.66      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % finite_atLeastLessThan_int
% 0.32/0.66  thf(fact_9456_finite__atLeastZeroLessThan__int,axiom,
% 0.32/0.66      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % finite_atLeastZeroLessThan_int
% 0.32/0.66  thf(fact_9457_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.32/0.66      ! [L2: int,U: int] :
% 0.32/0.66        ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 0.32/0.66        = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.32/0.66  thf(fact_9458_Cauchy__iff2,axiom,
% 0.32/0.66      ( topolo4055970368930404560y_real
% 0.32/0.66      = ( ^ [X2: nat > real] :
% 0.32/0.66          ! [J3: nat] :
% 0.32/0.66          ? [M8: nat] :
% 0.32/0.66          ! [M3: nat] :
% 0.32/0.66            ( ( ord_less_eq_nat @ M8 @ M3 )
% 0.32/0.66           => ! [N2: nat] :
% 0.32/0.66                ( ( ord_less_eq_nat @ M8 @ N2 )
% 0.32/0.66               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X2 @ M3 ) @ ( X2 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Cauchy_iff2
% 0.32/0.66  thf(fact_9459_VEBT_Osize_I3_J,axiom,
% 0.32/0.66      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.32/0.66        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.32/0.66        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT.size(3)
% 0.32/0.66  thf(fact_9460_VEBT_Osize__gen_I1_J,axiom,
% 0.32/0.66      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.32/0.66        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.32/0.66        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT.size_gen(1)
% 0.32/0.66  thf(fact_9461_valid__eq,axiom,
% 0.32/0.66      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.32/0.66  
% 0.32/0.66  % valid_eq
% 0.32/0.66  thf(fact_9462_valid__eq1,axiom,
% 0.32/0.66      ! [T: vEBT_VEBT,D: nat] :
% 0.32/0.66        ( ( vEBT_invar_vebt @ T @ D )
% 0.32/0.66       => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 0.32/0.66  
% 0.32/0.66  % valid_eq1
% 0.32/0.66  thf(fact_9463_valid__eq2,axiom,
% 0.32/0.66      ! [T: vEBT_VEBT,D: nat] :
% 0.32/0.66        ( ( vEBT_VEBT_valid @ T @ D )
% 0.32/0.66       => ( vEBT_invar_vebt @ T @ D ) ) ).
% 0.32/0.66  
% 0.32/0.66  % valid_eq2
% 0.32/0.66  thf(fact_9464_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.32/0.66      ! [Uu: $o,Uv: $o,D: nat] :
% 0.32/0.66        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 0.32/0.66        = ( D = one_one_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT_internal.valid'.simps(1)
% 0.32/0.66  thf(fact_9465_VEBT_Osize__gen_I2_J,axiom,
% 0.32/0.66      ! [X21: $o,X222: $o] :
% 0.32/0.66        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 0.32/0.66        = zero_zero_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % VEBT.size_gen(2)
% 0.32/0.66  thf(fact_9466_Code__Target__Int_Opositive__def,axiom,
% 0.32/0.66      code_Target_positive = numeral_numeral_int ).
% 0.32/0.66  
% 0.32/0.66  % Code_Target_Int.positive_def
% 0.32/0.66  thf(fact_9467_csqrt_Osimps_I1_J,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( re @ ( csqrt @ Z ) )
% 0.32/0.66        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt.simps(1)
% 0.32/0.66  thf(fact_9468_complex__Re__numeral,axiom,
% 0.32/0.66      ! [V: num] :
% 0.32/0.66        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 0.32/0.66        = ( numeral_numeral_real @ V ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Re_numeral
% 0.32/0.66  thf(fact_9469_Re__divide__numeral,axiom,
% 0.32/0.66      ! [Z: complex,W: num] :
% 0.32/0.66        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.66        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_divide_numeral
% 0.32/0.66  thf(fact_9470_cos__Arg__i__mult__zero,axiom,
% 0.32/0.66      ! [Y: complex] :
% 0.32/0.66        ( ( Y != zero_zero_complex )
% 0.32/0.66       => ( ( ( re @ Y )
% 0.32/0.66            = zero_zero_real )
% 0.32/0.66         => ( ( cos_real @ ( arg @ Y ) )
% 0.32/0.66            = zero_zero_real ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cos_Arg_i_mult_zero
% 0.32/0.66  thf(fact_9471_imaginary__unit_Osimps_I1_J,axiom,
% 0.32/0.66      ( ( re @ imaginary_unit )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % imaginary_unit.simps(1)
% 0.32/0.66  thf(fact_9472_complex__Re__le__cmod,axiom,
% 0.32/0.66      ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Re_le_cmod
% 0.32/0.66  thf(fact_9473_zero__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ( ( re @ zero_zero_complex )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_complex.simps(1)
% 0.32/0.66  thf(fact_9474_one__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ( ( re @ one_one_complex )
% 0.32/0.66      = one_one_real ) ).
% 0.32/0.66  
% 0.32/0.66  % one_complex.simps(1)
% 0.32/0.66  thf(fact_9475_plus__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 0.32/0.66        = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_complex.simps(1)
% 0.32/0.66  thf(fact_9476_scaleR__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ! [R: real,X: complex] :
% 0.32/0.66        ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 0.32/0.66        = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % scaleR_complex.simps(1)
% 0.32/0.66  thf(fact_9477_minus__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 0.32/0.66        = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_complex.simps(1)
% 0.32/0.66  thf(fact_9478_abs__Re__le__cmod,axiom,
% 0.32/0.66      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % abs_Re_le_cmod
% 0.32/0.66  thf(fact_9479_Re__csqrt,axiom,
% 0.32/0.66      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_csqrt
% 0.32/0.66  thf(fact_9480_cmod__plus__Re__le__0__iff,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 0.32/0.66        = ( ( re @ Z )
% 0.32/0.66          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_plus_Re_le_0_iff
% 0.32/0.66  thf(fact_9481_cos__n__Re__cis__pow__n,axiom,
% 0.32/0.66      ! [N: nat,A: real] :
% 0.32/0.66        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.32/0.66        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cos_n_Re_cis_pow_n
% 0.32/0.66  thf(fact_9482_csqrt_Ocode,axiom,
% 0.32/0.66      ( csqrt
% 0.32/0.66      = ( ^ [Z3: complex] :
% 0.32/0.66            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.66            @ ( times_times_real
% 0.32/0.66              @ ( if_real
% 0.32/0.66                @ ( ( im @ Z3 )
% 0.32/0.66                  = zero_zero_real )
% 0.32/0.66                @ one_one_real
% 0.32/0.66                @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 0.32/0.66              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt.code
% 0.32/0.66  thf(fact_9483_csqrt_Osimps_I2_J,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( im @ ( csqrt @ Z ) )
% 0.32/0.66        = ( times_times_real
% 0.32/0.66          @ ( if_real
% 0.32/0.66            @ ( ( im @ Z )
% 0.32/0.66              = zero_zero_real )
% 0.32/0.66            @ one_one_real
% 0.32/0.66            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 0.32/0.66          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt.simps(2)
% 0.32/0.66  thf(fact_9484_csqrt__of__real__nonpos,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( ( im @ X )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 0.32/0.66         => ( ( csqrt @ X )
% 0.32/0.66            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_of_real_nonpos
% 0.32/0.66  thf(fact_9485_complex__Im__fact,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Im_fact
% 0.32/0.66  thf(fact_9486_complex__Im__of__int,axiom,
% 0.32/0.66      ! [Z: int] :
% 0.32/0.66        ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Im_of_int
% 0.32/0.66  thf(fact_9487_complex__Im__of__nat,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Im_of_nat
% 0.32/0.66  thf(fact_9488_Im__complex__of__real,axiom,
% 0.32/0.66      ! [Z: real] :
% 0.32/0.66        ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_of_real
% 0.32/0.66  thf(fact_9489_Im__power__real,axiom,
% 0.32/0.66      ! [X: complex,N: nat] :
% 0.32/0.66        ( ( ( im @ X )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( im @ ( power_power_complex @ X @ N ) )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_power_real
% 0.32/0.66  thf(fact_9490_complex__Im__numeral,axiom,
% 0.32/0.66      ! [V: num] :
% 0.32/0.66        ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_Im_numeral
% 0.32/0.66  thf(fact_9491_Im__i__times,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 0.32/0.66        = ( re @ Z ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_i_times
% 0.32/0.66  thf(fact_9492_Re__power__real,axiom,
% 0.32/0.66      ! [X: complex,N: nat] :
% 0.32/0.66        ( ( ( im @ X )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( re @ ( power_power_complex @ X @ N ) )
% 0.32/0.66          = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_power_real
% 0.32/0.66  thf(fact_9493_Re__i__times,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 0.32/0.66        = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_i_times
% 0.32/0.66  thf(fact_9494_Im__divide__numeral,axiom,
% 0.32/0.66      ! [Z: complex,W: num] :
% 0.32/0.66        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.66        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_divide_numeral
% 0.32/0.66  thf(fact_9495_csqrt__of__real__nonneg,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( ( im @ X )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 0.32/0.66         => ( ( csqrt @ X )
% 0.32/0.66            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_of_real_nonneg
% 0.32/0.66  thf(fact_9496_csqrt__minus,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 0.32/0.66          | ( ( ( im @ X )
% 0.32/0.66              = zero_zero_real )
% 0.32/0.66            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 0.32/0.66       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 0.32/0.66          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_minus
% 0.32/0.66  thf(fact_9497_imaginary__unit_Osimps_I2_J,axiom,
% 0.32/0.66      ( ( im @ imaginary_unit )
% 0.32/0.66      = one_one_real ) ).
% 0.32/0.66  
% 0.32/0.66  % imaginary_unit.simps(2)
% 0.32/0.66  thf(fact_9498_zero__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ( ( im @ zero_zero_complex )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_complex.simps(2)
% 0.32/0.66  thf(fact_9499_one__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ( ( im @ one_one_complex )
% 0.32/0.66      = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % one_complex.simps(2)
% 0.32/0.66  thf(fact_9500_plus__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 0.32/0.66        = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_complex.simps(2)
% 0.32/0.66  thf(fact_9501_scaleR__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ! [R: real,X: complex] :
% 0.32/0.66        ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 0.32/0.66        = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % scaleR_complex.simps(2)
% 0.32/0.66  thf(fact_9502_minus__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 0.32/0.66        = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_complex.simps(2)
% 0.32/0.66  thf(fact_9503_complex__is__Int__iff,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( member_complex @ Z @ ring_1_Ints_complex )
% 0.32/0.66        = ( ( ( im @ Z )
% 0.32/0.66            = zero_zero_real )
% 0.32/0.66          & ? [I5: int] :
% 0.32/0.66              ( ( re @ Z )
% 0.32/0.66              = ( ring_1_of_int_real @ I5 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_is_Int_iff
% 0.32/0.66  thf(fact_9504_abs__Im__le__cmod,axiom,
% 0.32/0.66      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % abs_Im_le_cmod
% 0.32/0.66  thf(fact_9505_times__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( im @ ( times_times_complex @ X @ Y ) )
% 0.32/0.66        = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_complex.simps(2)
% 0.32/0.66  thf(fact_9506_cmod__eq__Re,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( im @ Z )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( real_V1022390504157884413omplex @ Z )
% 0.32/0.66          = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_eq_Re
% 0.32/0.66  thf(fact_9507_cmod__eq__Im,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( re @ Z )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66       => ( ( real_V1022390504157884413omplex @ Z )
% 0.32/0.66          = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_eq_Im
% 0.32/0.66  thf(fact_9508_Im__eq__0,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( abs_abs_real @ ( re @ Z ) )
% 0.32/0.66          = ( real_V1022390504157884413omplex @ Z ) )
% 0.32/0.66       => ( ( im @ Z )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_eq_0
% 0.32/0.66  thf(fact_9509_cmod__Re__le__iff,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( ( im @ X )
% 0.32/0.66          = ( im @ Y ) )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 0.32/0.66          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_Re_le_iff
% 0.32/0.66  thf(fact_9510_cmod__Im__le__iff,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( ( re @ X )
% 0.32/0.66          = ( re @ Y ) )
% 0.32/0.66       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 0.32/0.66          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_Im_le_iff
% 0.32/0.66  thf(fact_9511_times__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( re @ ( times_times_complex @ X @ Y ) )
% 0.32/0.66        = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_complex.simps(1)
% 0.32/0.66  thf(fact_9512_plus__complex_Ocode,axiom,
% 0.32/0.66      ( plus_plus_complex
% 0.32/0.66      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( plus_plus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_complex.code
% 0.32/0.66  thf(fact_9513_scaleR__complex_Ocode,axiom,
% 0.32/0.66      ( real_V2046097035970521341omplex
% 0.32/0.66      = ( ^ [R5: real,X3: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X3 ) ) @ ( times_times_real @ R5 @ ( im @ X3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % scaleR_complex.code
% 0.32/0.66  thf(fact_9514_minus__complex_Ocode,axiom,
% 0.32/0.66      ( minus_minus_complex
% 0.32/0.66      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( minus_minus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_complex.code
% 0.32/0.66  thf(fact_9515_csqrt__principal,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 0.32/0.66        | ( ( ( re @ ( csqrt @ Z ) )
% 0.32/0.66            = zero_zero_real )
% 0.32/0.66          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_principal
% 0.32/0.66  thf(fact_9516_cmod__le,axiom,
% 0.32/0.66      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_le
% 0.32/0.66  thf(fact_9517_sin__n__Im__cis__pow__n,axiom,
% 0.32/0.66      ! [N: nat,A: real] :
% 0.32/0.66        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.32/0.66        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sin_n_Im_cis_pow_n
% 0.32/0.66  thf(fact_9518_Re__exp,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( re @ ( exp_complex @ Z ) )
% 0.32/0.66        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_exp
% 0.32/0.66  thf(fact_9519_Im__exp,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( im @ ( exp_complex @ Z ) )
% 0.32/0.66        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_exp
% 0.32/0.66  thf(fact_9520_complex__eq,axiom,
% 0.32/0.66      ! [A: complex] :
% 0.32/0.66        ( A
% 0.32/0.66        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_eq
% 0.32/0.66  thf(fact_9521_times__complex_Ocode,axiom,
% 0.32/0.66      ( times_times_complex
% 0.32/0.66      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_complex.code
% 0.32/0.66  thf(fact_9522_exp__eq__polar,axiom,
% 0.32/0.66      ( exp_complex
% 0.32/0.66      = ( ^ [Z3: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z3 ) ) ) @ ( cis @ ( im @ Z3 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % exp_eq_polar
% 0.32/0.66  thf(fact_9523_cmod__power2,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cmod_power2
% 0.32/0.66  thf(fact_9524_Im__power2,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_power2
% 0.32/0.66  thf(fact_9525_Re__power2,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66        = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_power2
% 0.32/0.66  thf(fact_9526_complex__eq__0,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( Z = zero_zero_complex )
% 0.32/0.66        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_eq_0
% 0.32/0.66  thf(fact_9527_norm__complex__def,axiom,
% 0.32/0.66      ( real_V1022390504157884413omplex
% 0.32/0.66      = ( ^ [Z3: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % norm_complex_def
% 0.32/0.66  thf(fact_9528_inverse__complex_Osimps_I1_J,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 0.32/0.66        = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % inverse_complex.simps(1)
% 0.32/0.66  thf(fact_9529_complex__neq__0,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( Z != zero_zero_complex )
% 0.32/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_neq_0
% 0.32/0.66  thf(fact_9530_Re__divide,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.32/0.66        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( 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 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_divide
% 0.32/0.66  thf(fact_9531_csqrt__unique,axiom,
% 0.32/0.66      ! [W: complex,Z: complex] :
% 0.32/0.66        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.32/0.66          = Z )
% 0.32/0.66       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 0.32/0.66            | ( ( ( re @ W )
% 0.32/0.66                = zero_zero_real )
% 0.32/0.66              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 0.32/0.66         => ( ( csqrt @ Z )
% 0.32/0.66            = W ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_unique
% 0.32/0.66  thf(fact_9532_csqrt__square,axiom,
% 0.32/0.66      ! [B: complex] :
% 0.32/0.66        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 0.32/0.66          | ( ( ( re @ B )
% 0.32/0.66              = zero_zero_real )
% 0.32/0.66            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 0.32/0.66       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66          = B ) ) ).
% 0.32/0.66  
% 0.32/0.66  % csqrt_square
% 0.32/0.66  thf(fact_9533_inverse__complex_Osimps_I2_J,axiom,
% 0.32/0.66      ! [X: complex] :
% 0.32/0.66        ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 0.32/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % inverse_complex.simps(2)
% 0.32/0.66  thf(fact_9534_Im__divide,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.32/0.66        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( 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 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_divide
% 0.32/0.66  thf(fact_9535_complex__abs__le__norm,axiom,
% 0.32/0.66      ! [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 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_abs_le_norm
% 0.32/0.66  thf(fact_9536_complex__unit__circle,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( Z != zero_zero_complex )
% 0.32/0.66       => ( ( 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 ) ) ) )
% 0.32/0.66          = one_one_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_unit_circle
% 0.32/0.66  thf(fact_9537_inverse__complex_Ocode,axiom,
% 0.32/0.66      ( invers8013647133539491842omplex
% 0.32/0.66      = ( ^ [X3: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X3 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X3 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % inverse_complex.code
% 0.32/0.66  thf(fact_9538_Complex__divide,axiom,
% 0.32/0.66      ( divide1717551699836669952omplex
% 0.32/0.66      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Complex_divide
% 0.32/0.66  thf(fact_9539_Im__Reals__divide,axiom,
% 0.32/0.66      ! [R: complex,Z: complex] :
% 0.32/0.66        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.32/0.66       => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 0.32/0.66          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_Reals_divide
% 0.32/0.66  thf(fact_9540_Re__Reals__divide,axiom,
% 0.32/0.66      ! [R: complex,Z: complex] :
% 0.32/0.66        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 0.32/0.66       => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 0.32/0.66          = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_Reals_divide
% 0.32/0.66  thf(fact_9541_imaginary__eq__real__iff,axiom,
% 0.32/0.66      ! [Y: complex,X: complex] :
% 0.32/0.66        ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 0.32/0.66       => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 0.32/0.66         => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 0.32/0.66              = X )
% 0.32/0.66            = ( ( X = zero_zero_complex )
% 0.32/0.66              & ( Y = zero_zero_complex ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % imaginary_eq_real_iff
% 0.32/0.66  thf(fact_9542_real__eq__imaginary__iff,axiom,
% 0.32/0.66      ! [Y: complex,X: complex] :
% 0.32/0.66        ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 0.32/0.66       => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 0.32/0.66         => ( ( X
% 0.32/0.66              = ( times_times_complex @ imaginary_unit @ Y ) )
% 0.32/0.66            = ( ( X = zero_zero_complex )
% 0.32/0.66              & ( Y = zero_zero_complex ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % real_eq_imaginary_iff
% 0.32/0.66  thf(fact_9543_complex__is__Real__iff,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 0.32/0.66        = ( ( im @ Z )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_is_Real_iff
% 0.32/0.66  thf(fact_9544_Complex__in__Reals,axiom,
% 0.32/0.66      ! [X: real] : ( member_complex @ ( complex2 @ X @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 0.32/0.66  
% 0.32/0.66  % Complex_in_Reals
% 0.32/0.66  thf(fact_9545_complex__diff__cnj,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 0.32/0.66        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_diff_cnj
% 0.32/0.66  thf(fact_9546_complex__mult__cnj,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 0.32/0.66        = ( 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 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_mult_cnj
% 0.32/0.66  thf(fact_9547_complex__cnj__mult,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 0.32/0.66        = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_mult
% 0.32/0.66  thf(fact_9548_complex__cnj__zero,axiom,
% 0.32/0.66      ( ( cnj @ zero_zero_complex )
% 0.32/0.66      = zero_zero_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_zero
% 0.32/0.66  thf(fact_9549_complex__cnj__zero__iff,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( cnj @ Z )
% 0.32/0.66          = zero_zero_complex )
% 0.32/0.66        = ( Z = zero_zero_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_zero_iff
% 0.32/0.66  thf(fact_9550_complex__cnj__one__iff,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( ( cnj @ Z )
% 0.32/0.66          = one_one_complex )
% 0.32/0.66        = ( Z = one_one_complex ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_one_iff
% 0.32/0.66  thf(fact_9551_complex__cnj__one,axiom,
% 0.32/0.66      ( ( cnj @ one_one_complex )
% 0.32/0.66      = one_one_complex ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_one
% 0.32/0.66  thf(fact_9552_complex__cnj__power,axiom,
% 0.32/0.66      ! [X: complex,N: nat] :
% 0.32/0.66        ( ( cnj @ ( power_power_complex @ X @ N ) )
% 0.32/0.66        = ( power_power_complex @ ( cnj @ X ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_power
% 0.32/0.66  thf(fact_9553_complex__cnj__add,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( cnj @ ( plus_plus_complex @ X @ Y ) )
% 0.32/0.66        = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_add
% 0.32/0.66  thf(fact_9554_complex__cnj__numeral,axiom,
% 0.32/0.66      ! [W: num] :
% 0.32/0.66        ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 0.32/0.66        = ( numera6690914467698888265omplex @ W ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_numeral
% 0.32/0.66  thf(fact_9555_complex__cnj__diff,axiom,
% 0.32/0.66      ! [X: complex,Y: complex] :
% 0.32/0.66        ( ( cnj @ ( minus_minus_complex @ X @ Y ) )
% 0.32/0.66        = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_diff
% 0.32/0.66  thf(fact_9556_complex__cnj__neg__numeral,axiom,
% 0.32/0.66      ! [W: num] :
% 0.32/0.66        ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 0.32/0.66        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_cnj_neg_numeral
% 0.32/0.66  thf(fact_9557_complex__In__mult__cnj__zero,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.32/0.66        = zero_zero_real ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_In_mult_cnj_zero
% 0.32/0.66  thf(fact_9558_Re__complex__div__eq__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66        = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_complex_div_eq_0
% 0.32/0.66  thf(fact_9559_Im__complex__div__eq__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.32/0.66          = zero_zero_real )
% 0.32/0.66        = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.32/0.66          = zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_div_eq_0
% 0.32/0.66  thf(fact_9560_complex__mod__sqrt__Re__mult__cnj,axiom,
% 0.32/0.66      ( real_V1022390504157884413omplex
% 0.32/0.66      = ( ^ [Z3: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_mod_sqrt_Re_mult_cnj
% 0.32/0.66  thf(fact_9561_Re__complex__div__gt__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_complex_div_gt_0
% 0.32/0.66  thf(fact_9562_Re__complex__div__lt__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_complex_div_lt_0
% 0.32/0.66  thf(fact_9563_Re__complex__div__ge__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_complex_div_ge_0
% 0.32/0.66  thf(fact_9564_Re__complex__div__le__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Re_complex_div_le_0
% 0.32/0.66  thf(fact_9565_Im__complex__div__gt__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_div_gt_0
% 0.32/0.66  thf(fact_9566_Im__complex__div__lt__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_div_lt_0
% 0.32/0.66  thf(fact_9567_Im__complex__div__ge__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_div_ge_0
% 0.32/0.66  thf(fact_9568_Im__complex__div__le__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.32/0.66        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Im_complex_div_le_0
% 0.32/0.66  thf(fact_9569_complex__mod__mult__cnj,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 0.32/0.66        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_mod_mult_cnj
% 0.32/0.66  thf(fact_9570_complex__div__gt__0,axiom,
% 0.32/0.66      ! [A: complex,B: complex] :
% 0.32/0.66        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 0.32/0.66        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.32/0.66          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_div_gt_0
% 0.32/0.66  thf(fact_9571_complex__norm__square,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.32/0.66        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_norm_square
% 0.32/0.66  thf(fact_9572_complex__add__cnj,axiom,
% 0.32/0.66      ! [Z: complex] :
% 0.32/0.66        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 0.32/0.66        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_add_cnj
% 0.32/0.66  thf(fact_9573_complex__div__cnj,axiom,
% 0.32/0.66      ( divide1717551699836669952omplex
% 0.32/0.66      = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % complex_div_cnj
% 0.32/0.66  thf(fact_9574_cnj__add__mult__eq__Re,axiom,
% 0.32/0.66      ! [Z: complex,W: complex] :
% 0.32/0.66        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 0.32/0.66        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % cnj_add_mult_eq_Re
% 0.32/0.66  thf(fact_9575_divmod__step__integer__def,axiom,
% 0.32/0.66      ( unique4921790084139445826nteger
% 0.32/0.66      = ( ^ [L: num] :
% 0.32/0.66            ( produc6916734918728496179nteger
% 0.32/0.66            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_step_integer_def
% 0.32/0.66  thf(fact_9576_card__lessThan,axiom,
% 0.32/0.66      ! [U: nat] :
% 0.32/0.66        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.32/0.66        = U ) ).
% 0.32/0.66  
% 0.32/0.66  % card_lessThan
% 0.32/0.66  thf(fact_9577_card__Collect__less__nat,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( finite_card_nat
% 0.32/0.66          @ ( collect_nat
% 0.32/0.66            @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N ) ) )
% 0.32/0.66        = N ) ).
% 0.32/0.66  
% 0.32/0.66  % card_Collect_less_nat
% 0.32/0.66  thf(fact_9578_card__atMost,axiom,
% 0.32/0.66      ! [U: nat] :
% 0.32/0.66        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.32/0.66        = ( suc @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atMost
% 0.32/0.66  thf(fact_9579_card__atLeastLessThan,axiom,
% 0.32/0.66      ! [L2: nat,U: nat] :
% 0.32/0.66        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 0.32/0.66        = ( minus_minus_nat @ U @ L2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atLeastLessThan
% 0.32/0.66  thf(fact_9580_card__Collect__le__nat,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( finite_card_nat
% 0.32/0.66          @ ( collect_nat
% 0.32/0.66            @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N ) ) )
% 0.32/0.66        = ( suc @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_Collect_le_nat
% 0.32/0.66  thf(fact_9581_card__atLeastAtMost,axiom,
% 0.32/0.66      ! [L2: nat,U: nat] :
% 0.32/0.66        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 0.32/0.66        = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atLeastAtMost
% 0.32/0.66  thf(fact_9582_card__atLeastLessThan__int,axiom,
% 0.32/0.66      ! [L2: int,U: int] :
% 0.32/0.66        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 0.32/0.66        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atLeastLessThan_int
% 0.32/0.66  thf(fact_9583_card__atLeastAtMost__int,axiom,
% 0.32/0.66      ! [L2: int,U: int] :
% 0.32/0.66        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 0.32/0.66        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atLeastAtMost_int
% 0.32/0.66  thf(fact_9584_minus__integer__code_I1_J,axiom,
% 0.32/0.66      ! [K: code_integer] :
% 0.32/0.66        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.32/0.66        = K ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_integer_code(1)
% 0.32/0.66  thf(fact_9585_minus__integer__code_I2_J,axiom,
% 0.32/0.66      ! [L2: code_integer] :
% 0.32/0.66        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.32/0.66        = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_integer_code(2)
% 0.32/0.66  thf(fact_9586_times__integer__code_I1_J,axiom,
% 0.32/0.66      ! [K: code_integer] :
% 0.32/0.66        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 0.32/0.66        = zero_z3403309356797280102nteger ) ).
% 0.32/0.66  
% 0.32/0.66  % times_integer_code(1)
% 0.32/0.66  thf(fact_9587_times__integer__code_I2_J,axiom,
% 0.32/0.66      ! [L2: code_integer] :
% 0.32/0.66        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.32/0.66        = zero_z3403309356797280102nteger ) ).
% 0.32/0.66  
% 0.32/0.66  % times_integer_code(2)
% 0.32/0.66  thf(fact_9588_plus__integer__code_I2_J,axiom,
% 0.32/0.66      ! [L2: code_integer] :
% 0.32/0.66        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.32/0.66        = L2 ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_integer_code(2)
% 0.32/0.66  thf(fact_9589_plus__integer__code_I1_J,axiom,
% 0.32/0.66      ! [K: code_integer] :
% 0.32/0.66        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 0.32/0.66        = K ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_integer_code(1)
% 0.32/0.66  thf(fact_9590_less__eq__integer__code_I1_J,axiom,
% 0.32/0.66      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.32/0.66  
% 0.32/0.66  % less_eq_integer_code(1)
% 0.32/0.66  thf(fact_9591_exhaustive__integer_H_Ocases,axiom,
% 0.32/0.66      ! [X: produc8763457246119570046nteger] :
% 0.32/0.66        ~ ! [F2: code_integer > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 0.32/0.66            ( X
% 0.32/0.66           != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % exhaustive_integer'.cases
% 0.32/0.66  thf(fact_9592_full__exhaustive__integer_H_Ocases,axiom,
% 0.32/0.66      ! [X: produc1908205239877642774nteger] :
% 0.32/0.66        ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 0.32/0.66            ( X
% 0.32/0.66           != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % full_exhaustive_integer'.cases
% 0.32/0.66  thf(fact_9593_divmod__integer_H__def,axiom,
% 0.32/0.66      ( unique3479559517661332726nteger
% 0.32/0.66      = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_integer'_def
% 0.32/0.66  thf(fact_9594_sgn__integer__code,axiom,
% 0.32/0.66      ( sgn_sgn_Code_integer
% 0.32/0.66      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % sgn_integer_code
% 0.32/0.66  thf(fact_9595_nat_Odisc__eq__case_I2_J,axiom,
% 0.32/0.66      ! [Nat: nat] :
% 0.32/0.66        ( ( Nat != zero_zero_nat )
% 0.32/0.66        = ( case_nat_o @ $false
% 0.32/0.66          @ ^ [Uu3: nat] : $true
% 0.32/0.66          @ Nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat.disc_eq_case(2)
% 0.32/0.66  thf(fact_9596_nat_Odisc__eq__case_I1_J,axiom,
% 0.32/0.66      ! [Nat: nat] :
% 0.32/0.66        ( ( Nat = zero_zero_nat )
% 0.32/0.66        = ( case_nat_o @ $true
% 0.32/0.66          @ ^ [Uu3: nat] : $false
% 0.32/0.66          @ Nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat.disc_eq_case(1)
% 0.32/0.66  thf(fact_9597_zero__natural_Orsp,axiom,
% 0.32/0.66      zero_zero_nat = zero_zero_nat ).
% 0.32/0.66  
% 0.32/0.66  % zero_natural.rsp
% 0.32/0.66  thf(fact_9598_card__less,axiom,
% 0.32/0.66      ! [M5: set_nat,I: nat] :
% 0.32/0.66        ( ( member_nat @ zero_zero_nat @ M5 )
% 0.32/0.66       => ( ( finite_card_nat
% 0.32/0.66            @ ( collect_nat
% 0.32/0.66              @ ^ [K2: nat] :
% 0.32/0.66                  ( ( member_nat @ K2 @ M5 )
% 0.32/0.66                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 0.32/0.66         != zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_less
% 0.32/0.66  thf(fact_9599_card__less__Suc,axiom,
% 0.32/0.66      ! [M5: set_nat,I: nat] :
% 0.32/0.66        ( ( member_nat @ zero_zero_nat @ M5 )
% 0.32/0.66       => ( ( suc
% 0.32/0.66            @ ( finite_card_nat
% 0.32/0.66              @ ( collect_nat
% 0.32/0.66                @ ^ [K2: nat] :
% 0.32/0.66                    ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 0.32/0.66                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 0.32/0.66          = ( finite_card_nat
% 0.32/0.66            @ ( collect_nat
% 0.32/0.66              @ ^ [K2: nat] :
% 0.32/0.66                  ( ( member_nat @ K2 @ M5 )
% 0.32/0.66                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_less_Suc
% 0.32/0.66  thf(fact_9600_card__less__Suc2,axiom,
% 0.32/0.66      ! [M5: set_nat,I: nat] :
% 0.32/0.66        ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.32/0.66       => ( ( finite_card_nat
% 0.32/0.66            @ ( collect_nat
% 0.32/0.66              @ ^ [K2: nat] :
% 0.32/0.66                  ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 0.32/0.66                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 0.32/0.66          = ( finite_card_nat
% 0.32/0.66            @ ( collect_nat
% 0.32/0.66              @ ^ [K2: nat] :
% 0.32/0.66                  ( ( member_nat @ K2 @ M5 )
% 0.32/0.66                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_less_Suc2
% 0.32/0.66  thf(fact_9601_card__atLeastZeroLessThan__int,axiom,
% 0.32/0.66      ! [U: int] :
% 0.32/0.66        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.32/0.66        = ( nat2 @ U ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_atLeastZeroLessThan_int
% 0.32/0.66  thf(fact_9602_zero__integer_Orsp,axiom,
% 0.32/0.66      zero_zero_int = zero_zero_int ).
% 0.32/0.66  
% 0.32/0.66  % zero_integer.rsp
% 0.32/0.66  thf(fact_9603_one__integer_Orsp,axiom,
% 0.32/0.66      one_one_int = one_one_int ).
% 0.32/0.66  
% 0.32/0.66  % one_integer.rsp
% 0.32/0.66  thf(fact_9604_subset__card__intvl__is__intvl,axiom,
% 0.32/0.66      ! [A2: set_nat,K: nat] :
% 0.32/0.66        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 0.32/0.66       => ( A2
% 0.32/0.66          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % subset_card_intvl_is_intvl
% 0.32/0.66  thf(fact_9605_one__natural_Orsp,axiom,
% 0.32/0.66      one_one_nat = one_one_nat ).
% 0.32/0.66  
% 0.32/0.66  % one_natural.rsp
% 0.32/0.66  thf(fact_9606_less__eq__nat_Osimps_I2_J,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.32/0.66        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % less_eq_nat.simps(2)
% 0.32/0.66  thf(fact_9607_max__Suc2,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 0.32/0.66        = ( case_nat_nat @ ( suc @ N )
% 0.32/0.66          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 0.32/0.66          @ M ) ) ).
% 0.32/0.66  
% 0.32/0.66  % max_Suc2
% 0.32/0.66  thf(fact_9608_max__Suc1,axiom,
% 0.32/0.66      ! [N: nat,M: nat] :
% 0.32/0.66        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 0.32/0.66        = ( case_nat_nat @ ( suc @ N )
% 0.32/0.66          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 0.32/0.66          @ M ) ) ).
% 0.32/0.66  
% 0.32/0.66  % max_Suc1
% 0.32/0.66  thf(fact_9609_subset__eq__atLeast0__lessThan__card,axiom,
% 0.32/0.66      ! [N4: set_nat,N: nat] :
% 0.32/0.66        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.32/0.66       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % subset_eq_atLeast0_lessThan_card
% 0.32/0.66  thf(fact_9610_card__sum__le__nat__sum,axiom,
% 0.32/0.66      ! [S2: set_nat] :
% 0.32/0.66        ( ord_less_eq_nat
% 0.32/0.66        @ ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [X3: nat] : X3
% 0.32/0.66          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 0.32/0.66        @ ( groups3542108847815614940at_nat
% 0.32/0.66          @ ^ [X3: nat] : X3
% 0.32/0.66          @ S2 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_sum_le_nat_sum
% 0.32/0.66  thf(fact_9611_card__nth__roots,axiom,
% 0.32/0.66      ! [C: complex,N: nat] :
% 0.32/0.66        ( ( C != zero_zero_complex )
% 0.32/0.66       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66         => ( ( finite_card_complex
% 0.32/0.66              @ ( collect_complex
% 0.32/0.66                @ ^ [Z3: complex] :
% 0.32/0.66                    ( ( power_power_complex @ Z3 @ N )
% 0.32/0.66                    = C ) ) )
% 0.32/0.66            = N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_nth_roots
% 0.32/0.66  thf(fact_9612_card__roots__unity__eq,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.66       => ( ( finite_card_complex
% 0.32/0.66            @ ( collect_complex
% 0.32/0.66              @ ^ [Z3: complex] :
% 0.32/0.66                  ( ( power_power_complex @ Z3 @ N )
% 0.32/0.66                  = one_one_complex ) ) )
% 0.32/0.66          = N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % card_roots_unity_eq
% 0.32/0.66  thf(fact_9613_diff__Suc,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.32/0.66        = ( case_nat_nat @ zero_zero_nat
% 0.32/0.66          @ ^ [K2: nat] : K2
% 0.32/0.66          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % diff_Suc
% 0.32/0.66  thf(fact_9614_integer__of__int__code,axiom,
% 0.32/0.66      ( code_integer_of_int
% 0.32/0.66      = ( ^ [K2: int] :
% 0.32/0.66            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 0.32/0.66            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.32/0.66              @ ( if_Code_integer
% 0.32/0.66                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.32/0.66                  = zero_zero_int )
% 0.32/0.66                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.32/0.66                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_int_code
% 0.32/0.66  thf(fact_9615_abs__integer__code,axiom,
% 0.32/0.66      ( abs_abs_Code_integer
% 0.32/0.66      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % abs_integer_code
% 0.32/0.66  thf(fact_9616_uminus__integer__code_I1_J,axiom,
% 0.32/0.66      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.32/0.66      = zero_z3403309356797280102nteger ) ).
% 0.32/0.66  
% 0.32/0.66  % uminus_integer_code(1)
% 0.32/0.66  thf(fact_9617_zero__integer__def,axiom,
% 0.32/0.66      ( zero_z3403309356797280102nteger
% 0.32/0.66      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_integer_def
% 0.32/0.66  thf(fact_9618_less__integer__code_I1_J,axiom,
% 0.32/0.66      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.32/0.66  
% 0.32/0.66  % less_integer_code(1)
% 0.32/0.66  thf(fact_9619_modulo__integer_Oabs__eq,axiom,
% 0.32/0.66      ! [Xa2: int,X: int] :
% 0.32/0.66        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.32/0.66        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % modulo_integer.abs_eq
% 0.32/0.66  thf(fact_9620_plus__integer_Oabs__eq,axiom,
% 0.32/0.66      ! [Xa2: int,X: int] :
% 0.32/0.66        ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.32/0.66        = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_integer.abs_eq
% 0.32/0.66  thf(fact_9621_times__integer_Oabs__eq,axiom,
% 0.32/0.66      ! [Xa2: int,X: int] :
% 0.32/0.66        ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.32/0.66        = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_integer.abs_eq
% 0.32/0.66  thf(fact_9622_one__integer__def,axiom,
% 0.32/0.66      ( one_one_Code_integer
% 0.32/0.66      = ( code_integer_of_int @ one_one_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % one_integer_def
% 0.32/0.66  thf(fact_9623_less__eq__integer_Oabs__eq,axiom,
% 0.32/0.66      ! [Xa2: int,X: int] :
% 0.32/0.66        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.32/0.66        = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 0.32/0.66  
% 0.32/0.66  % less_eq_integer.abs_eq
% 0.32/0.66  thf(fact_9624_minus__integer_Oabs__eq,axiom,
% 0.32/0.66      ! [Xa2: int,X: int] :
% 0.32/0.66        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.32/0.66        = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_integer.abs_eq
% 0.32/0.66  thf(fact_9625_Code__Numeral_Opositive__def,axiom,
% 0.32/0.66      code_positive = numera6620942414471956472nteger ).
% 0.32/0.66  
% 0.32/0.66  % Code_Numeral.positive_def
% 0.32/0.66  thf(fact_9626_integer__of__num_I3_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 0.32/0.66        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_num(3)
% 0.32/0.66  thf(fact_9627_integer__of__num__def,axiom,
% 0.32/0.66      code_integer_of_num = numera6620942414471956472nteger ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_num_def
% 0.32/0.66  thf(fact_9628_integer__of__num__triv_I1_J,axiom,
% 0.32/0.66      ( ( code_integer_of_num @ one )
% 0.32/0.66      = one_one_Code_integer ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_num_triv(1)
% 0.32/0.66  thf(fact_9629_integer__of__num_I2_J,axiom,
% 0.32/0.66      ! [N: num] :
% 0.32/0.66        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.32/0.66        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_num(2)
% 0.32/0.66  thf(fact_9630_integer__of__num__triv_I2_J,axiom,
% 0.32/0.66      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.32/0.66      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_of_num_triv(2)
% 0.32/0.66  thf(fact_9631_int__of__integer__code,axiom,
% 0.32/0.66      ( code_int_of_integer
% 0.32/0.66      = ( ^ [K2: code_integer] :
% 0.32/0.66            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 0.32/0.66            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.32/0.66              @ ( produc1553301316500091796er_int
% 0.32/0.66                @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 0.32/0.66                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_of_integer_code
% 0.32/0.66  thf(fact_9632_bit__cut__integer__def,axiom,
% 0.32/0.66      ( code_bit_cut_integer
% 0.32/0.66      = ( ^ [K2: code_integer] :
% 0.32/0.66            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.32/0.66            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_cut_integer_def
% 0.32/0.66  thf(fact_9633_num__of__integer__code,axiom,
% 0.32/0.66      ( code_num_of_integer
% 0.32/0.66      = ( ^ [K2: code_integer] :
% 0.32/0.66            ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 0.32/0.66            @ ( produc7336495610019696514er_num
% 0.32/0.66              @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 0.32/0.66              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % num_of_integer_code
% 0.32/0.66  thf(fact_9634_zero__integer_Orep__eq,axiom,
% 0.32/0.66      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 0.32/0.66      = zero_zero_int ) ).
% 0.32/0.66  
% 0.32/0.66  % zero_integer.rep_eq
% 0.32/0.66  thf(fact_9635_int__of__integer__numeral,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.32/0.66        = ( numeral_numeral_int @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % int_of_integer_numeral
% 0.32/0.66  thf(fact_9636_plus__integer_Orep__eq,axiom,
% 0.32/0.66      ! [X: code_integer,Xa2: code_integer] :
% 0.32/0.66        ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 0.32/0.66        = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % plus_integer.rep_eq
% 0.32/0.66  thf(fact_9637_times__integer_Orep__eq,axiom,
% 0.32/0.66      ! [X: code_integer,Xa2: code_integer] :
% 0.32/0.66        ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 0.32/0.66        = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % times_integer.rep_eq
% 0.32/0.66  thf(fact_9638_one__integer_Orep__eq,axiom,
% 0.32/0.66      ( ( code_int_of_integer @ one_one_Code_integer )
% 0.32/0.66      = one_one_int ) ).
% 0.32/0.66  
% 0.32/0.66  % one_integer.rep_eq
% 0.32/0.66  thf(fact_9639_minus__integer_Orep__eq,axiom,
% 0.32/0.66      ! [X: code_integer,Xa2: code_integer] :
% 0.32/0.66        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 0.32/0.66        = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % minus_integer.rep_eq
% 0.32/0.66  thf(fact_9640_modulo__integer_Orep__eq,axiom,
% 0.32/0.66      ! [X: code_integer,Xa2: code_integer] :
% 0.32/0.66        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa2 ) )
% 0.32/0.66        = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % modulo_integer.rep_eq
% 0.32/0.66  thf(fact_9641_integer__less__eq__iff,axiom,
% 0.32/0.66      ( ord_le3102999989581377725nteger
% 0.32/0.66      = ( ^ [K2: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % integer_less_eq_iff
% 0.32/0.66  thf(fact_9642_less__eq__integer_Orep__eq,axiom,
% 0.32/0.66      ( ord_le3102999989581377725nteger
% 0.32/0.66      = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % less_eq_integer.rep_eq
% 0.32/0.66  thf(fact_9643_divmod__integer__def,axiom,
% 0.32/0.66      ( code_divmod_integer
% 0.32/0.66      = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L ) @ ( modulo364778990260209775nteger @ K2 @ L ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_integer_def
% 0.32/0.66  thf(fact_9644_bit__cut__integer__code,axiom,
% 0.32/0.66      ( code_bit_cut_integer
% 0.32/0.66      = ( ^ [K2: code_integer] :
% 0.32/0.66            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.32/0.66            @ ( produc9125791028180074456eger_o
% 0.32/0.66              @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 0.32/0.66              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bit_cut_integer_code
% 0.32/0.66  thf(fact_9645_nat__of__integer__code,axiom,
% 0.32/0.66      ( code_nat_of_integer
% 0.32/0.66      = ( ^ [K2: code_integer] :
% 0.32/0.66            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.32/0.66            @ ( produc1555791787009142072er_nat
% 0.32/0.66              @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 0.32/0.66              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_of_integer_code
% 0.32/0.66  thf(fact_9646_of__nat__of__integer,axiom,
% 0.32/0.66      ! [K: code_integer] :
% 0.32/0.66        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 0.32/0.66        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % of_nat_of_integer
% 0.32/0.66  thf(fact_9647_nat__of__integer__non__positive,axiom,
% 0.32/0.66      ! [K: code_integer] :
% 0.32/0.66        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.32/0.66       => ( ( code_nat_of_integer @ K )
% 0.32/0.66          = zero_zero_nat ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_of_integer_non_positive
% 0.32/0.66  thf(fact_9648_nat__of__integer__code__post_I1_J,axiom,
% 0.32/0.66      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 0.32/0.66      = zero_zero_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_of_integer_code_post(1)
% 0.32/0.66  thf(fact_9649_nat__of__integer__code__post_I3_J,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.32/0.66        = ( numeral_numeral_nat @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_of_integer_code_post(3)
% 0.32/0.66  thf(fact_9650_divmod__abs__code_I6_J,axiom,
% 0.32/0.66      ! [J: code_integer] :
% 0.32/0.66        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.32/0.66        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_abs_code(6)
% 0.32/0.66  thf(fact_9651_nat__of__integer__code__post_I2_J,axiom,
% 0.32/0.66      ( ( code_nat_of_integer @ one_one_Code_integer )
% 0.32/0.66      = one_one_nat ) ).
% 0.32/0.66  
% 0.32/0.66  % nat_of_integer_code_post(2)
% 0.32/0.66  thf(fact_9652_divmod__abs__code_I5_J,axiom,
% 0.32/0.66      ! [J: code_integer] :
% 0.32/0.66        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.32/0.66        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_abs_code(5)
% 0.32/0.66  thf(fact_9653_pred__def,axiom,
% 0.32/0.66      ( pred
% 0.32/0.66      = ( case_nat_nat @ zero_zero_nat
% 0.32/0.66        @ ^ [X24: nat] : X24 ) ) ).
% 0.32/0.66  
% 0.32/0.66  % pred_def
% 0.32/0.66  thf(fact_9654_divmod__abs__def,axiom,
% 0.32/0.66      ( code_divmod_abs
% 0.32/0.66      = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_abs_def
% 0.32/0.66  thf(fact_9655_divmod__integer__code,axiom,
% 0.32/0.66      ( code_divmod_integer
% 0.32/0.66      = ( ^ [K2: code_integer,L: code_integer] :
% 0.32/0.66            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.32/0.66            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 0.32/0.66              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L )
% 0.32/0.66                @ ( produc6916734918728496179nteger
% 0.32/0.66                  @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S7 ) ) )
% 0.32/0.66                  @ ( code_divmod_abs @ K2 @ L ) ) )
% 0.32/0.66              @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 0.32/0.66                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.32/0.66                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L )
% 0.32/0.66                    @ ( produc6916734918728496179nteger
% 0.32/0.66                      @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S7 ) ) )
% 0.32/0.66                      @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % divmod_integer_code
% 0.32/0.66  thf(fact_9656_binomial__def,axiom,
% 0.32/0.66      ( binomial
% 0.32/0.66      = ( ^ [N2: nat,K2: nat] :
% 0.32/0.66            ( finite_card_set_nat
% 0.32/0.66            @ ( collect_set_nat
% 0.32/0.66              @ ^ [K7: set_nat] :
% 0.32/0.66                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 0.32/0.66                  & ( ( finite_card_nat @ K7 )
% 0.32/0.66                    = K2 ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % binomial_def
% 0.32/0.66  thf(fact_9657_bezw__0,axiom,
% 0.32/0.66      ! [X: nat] :
% 0.32/0.66        ( ( bezw @ X @ zero_zero_nat )
% 0.32/0.66        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % bezw_0
% 0.32/0.66  thf(fact_9658_floor__real__def,axiom,
% 0.32/0.66      ( archim6058952711729229775r_real
% 0.32/0.66      = ( ^ [X3: real] :
% 0.32/0.66            ( the_int
% 0.32/0.66            @ ^ [Z3: int] :
% 0.32/0.66                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 0.32/0.66                & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_real_def
% 0.32/0.66  thf(fact_9659_floor__rat__def,axiom,
% 0.32/0.66      ( archim3151403230148437115or_rat
% 0.32/0.66      = ( ^ [X3: rat] :
% 0.32/0.66            ( the_int
% 0.32/0.66            @ ^ [Z3: int] :
% 0.32/0.66                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 0.32/0.66                & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % floor_rat_def
% 0.32/0.66  thf(fact_9660_drop__bit__numeral__minus__bit1,axiom,
% 0.32/0.66      ! [L2: num,K: num] :
% 0.32/0.66        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.66        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_numeral_minus_bit1
% 0.32/0.66  thf(fact_9661_Suc__0__mod__numeral,axiom,
% 0.32/0.66      ! [K: num] :
% 0.32/0.66        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.66        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % Suc_0_mod_numeral
% 0.32/0.66  thf(fact_9662_drop__bit__nonnegative__int__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 0.32/0.66        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_nonnegative_int_iff
% 0.32/0.66  thf(fact_9663_drop__bit__negative__int__iff,axiom,
% 0.32/0.66      ! [N: nat,K: int] :
% 0.32/0.66        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 0.32/0.66        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_negative_int_iff
% 0.32/0.66  thf(fact_9664_drop__bit__minus__one,axiom,
% 0.32/0.66      ! [N: nat] :
% 0.32/0.66        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.32/0.66        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_minus_one
% 0.32/0.66  thf(fact_9665_snd__divmod__nat,axiom,
% 0.32/0.66      ! [M: nat,N: nat] :
% 0.32/0.66        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.32/0.66        = ( modulo_modulo_nat @ M @ N ) ) ).
% 0.32/0.66  
% 0.32/0.66  % snd_divmod_nat
% 0.32/0.66  thf(fact_9666_drop__bit__Suc__minus__bit0,axiom,
% 0.32/0.66      ! [N: nat,K: num] :
% 0.32/0.66        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.66        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_Suc_minus_bit0
% 0.32/0.66  thf(fact_9667_drop__bit__numeral__minus__bit0,axiom,
% 0.32/0.66      ! [L2: num,K: num] :
% 0.32/0.66        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.32/0.66        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.32/0.66  
% 0.32/0.66  % drop_bit_numeral_minus_bit0
% 0.32/0.66  thf(fact_9668_drop__bit__Suc__minus__bit1,axiom,
% 0.32/0.66      ! [N: nat,K: num] :
% 0.32/0.66        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.32/0.67        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_Suc_minus_bit1
% 0.32/0.67  thf(fact_9669_less__eq__rat__def,axiom,
% 0.32/0.67      ( ord_less_eq_rat
% 0.32/0.67      = ( ^ [X3: rat,Y3: rat] :
% 0.32/0.67            ( ( ord_less_rat @ X3 @ Y3 )
% 0.32/0.67            | ( X3 = Y3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_eq_rat_def
% 0.32/0.67  thf(fact_9670_abs__rat__def,axiom,
% 0.32/0.67      ( abs_abs_rat
% 0.32/0.67      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % abs_rat_def
% 0.32/0.67  thf(fact_9671_sgn__rat__def,axiom,
% 0.32/0.67      ( sgn_sgn_rat
% 0.32/0.67      = ( ^ [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 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sgn_rat_def
% 0.32/0.67  thf(fact_9672_obtain__pos__sum,axiom,
% 0.32/0.67      ! [R: rat] :
% 0.32/0.67        ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.32/0.67       => ~ ! [S3: rat] :
% 0.32/0.67              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 0.32/0.67             => ! [T6: rat] :
% 0.32/0.67                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 0.32/0.67                 => ( R
% 0.32/0.67                   != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % obtain_pos_sum
% 0.32/0.67  thf(fact_9673_drop__bit__push__bit__int,axiom,
% 0.32/0.67      ! [M: nat,N: nat,K: int] :
% 0.32/0.67        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.32/0.67        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_push_bit_int
% 0.32/0.67  thf(fact_9674_drop__bit__int__def,axiom,
% 0.32/0.67      ( bit_se8568078237143864401it_int
% 0.32/0.67      = ( ^ [N2: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_int_def
% 0.32/0.67  thf(fact_9675_rat__inverse__code,axiom,
% 0.32/0.67      ! [P5: rat] :
% 0.32/0.67        ( ( quotient_of @ ( inverse_inverse_rat @ P5 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_inverse_code
% 0.32/0.67  thf(fact_9676_normalize__negative,axiom,
% 0.32/0.67      ! [Q2: int,P5: int] :
% 0.32/0.67        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 0.32/0.67       => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_negative
% 0.32/0.67  thf(fact_9677_prod__decode__aux_Osimps,axiom,
% 0.32/0.67      ( nat_prod_decode_aux
% 0.32/0.67      = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % prod_decode_aux.simps
% 0.32/0.67  thf(fact_9678_snd__divmod__integer,axiom,
% 0.32/0.67      ! [K: code_integer,L2: code_integer] :
% 0.32/0.67        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 0.32/0.67        = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % snd_divmod_integer
% 0.32/0.67  thf(fact_9679_snd__divmod__abs,axiom,
% 0.32/0.67      ! [K: code_integer,L2: code_integer] :
% 0.32/0.67        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 0.32/0.67        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % snd_divmod_abs
% 0.32/0.67  thf(fact_9680_quotient__of__number_I3_J,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.32/0.67        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_number(3)
% 0.32/0.67  thf(fact_9681_normalize__denom__zero,axiom,
% 0.32/0.67      ! [P5: int] :
% 0.32/0.67        ( ( normalize @ ( product_Pair_int_int @ P5 @ zero_zero_int ) )
% 0.32/0.67        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_denom_zero
% 0.32/0.67  thf(fact_9682_rat__one__code,axiom,
% 0.32/0.67      ( ( quotient_of @ one_one_rat )
% 0.32/0.67      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_one_code
% 0.32/0.67  thf(fact_9683_drop__bit__of__Suc__0,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.32/0.67        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_of_Suc_0
% 0.32/0.67  thf(fact_9684_rat__zero__code,axiom,
% 0.32/0.67      ( ( quotient_of @ zero_zero_rat )
% 0.32/0.67      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_zero_code
% 0.32/0.67  thf(fact_9685_quotient__of__number_I5_J,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.32/0.67        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_number(5)
% 0.32/0.67  thf(fact_9686_quotient__of__number_I4_J,axiom,
% 0.32/0.67      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.32/0.67      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_number(4)
% 0.32/0.67  thf(fact_9687_quotient__of__denom__pos_H,axiom,
% 0.32/0.67      ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_denom_pos'
% 0.32/0.67  thf(fact_9688_divide__rat__def,axiom,
% 0.32/0.67      ( divide_divide_rat
% 0.32/0.67      = ( ^ [Q5: rat,R5: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % divide_rat_def
% 0.32/0.67  thf(fact_9689_diff__rat__def,axiom,
% 0.32/0.67      ( minus_minus_rat
% 0.32/0.67      = ( ^ [Q5: rat,R5: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % diff_rat_def
% 0.32/0.67  thf(fact_9690_rat__divide__code,axiom,
% 0.32/0.67      ! [P5: rat,Q2: rat] :
% 0.32/0.67        ( ( quotient_of @ ( divide_divide_rat @ P5 @ Q2 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int,C3: int] :
% 0.32/0.67              ( produc4245557441103728435nt_int
% 0.32/0.67              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) ) )
% 0.32/0.67              @ ( quotient_of @ Q2 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_divide_code
% 0.32/0.67  thf(fact_9691_rat__times__code,axiom,
% 0.32/0.67      ! [P5: rat,Q2: rat] :
% 0.32/0.67        ( ( quotient_of @ ( times_times_rat @ P5 @ Q2 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int,C3: int] :
% 0.32/0.67              ( produc4245557441103728435nt_int
% 0.32/0.67              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.32/0.67              @ ( quotient_of @ Q2 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_times_code
% 0.32/0.67  thf(fact_9692_drop__bit__nat__eq,axiom,
% 0.32/0.67      ! [N: nat,K: int] :
% 0.32/0.67        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 0.32/0.67        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_nat_eq
% 0.32/0.67  thf(fact_9693_quotient__of__div,axiom,
% 0.32/0.67      ! [R: rat,N: int,D: int] :
% 0.32/0.67        ( ( ( quotient_of @ R )
% 0.32/0.67          = ( product_Pair_int_int @ N @ D ) )
% 0.32/0.67       => ( R
% 0.32/0.67          = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_div
% 0.32/0.67  thf(fact_9694_rat__plus__code,axiom,
% 0.32/0.67      ! [P5: rat,Q2: rat] :
% 0.32/0.67        ( ( quotient_of @ ( plus_plus_rat @ P5 @ Q2 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int,C3: int] :
% 0.32/0.67              ( produc4245557441103728435nt_int
% 0.32/0.67              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.32/0.67              @ ( quotient_of @ Q2 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_plus_code
% 0.32/0.67  thf(fact_9695_rat__minus__code,axiom,
% 0.32/0.67      ! [P5: rat,Q2: rat] :
% 0.32/0.67        ( ( quotient_of @ ( minus_minus_rat @ P5 @ Q2 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int,C3: int] :
% 0.32/0.67              ( produc4245557441103728435nt_int
% 0.32/0.67              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.32/0.67              @ ( quotient_of @ Q2 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_minus_code
% 0.32/0.67  thf(fact_9696_quotient__of__denom__pos,axiom,
% 0.32/0.67      ! [R: rat,P5: int,Q2: int] :
% 0.32/0.67        ( ( ( quotient_of @ R )
% 0.32/0.67          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_denom_pos
% 0.32/0.67  thf(fact_9697_rat__uminus__code,axiom,
% 0.32/0.67      ! [P5: rat] :
% 0.32/0.67        ( ( quotient_of @ ( uminus_uminus_rat @ P5 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_uminus_code
% 0.32/0.67  thf(fact_9698_rat__abs__code,axiom,
% 0.32/0.67      ! [P5: rat] :
% 0.32/0.67        ( ( quotient_of @ ( abs_abs_rat @ P5 ) )
% 0.32/0.67        = ( produc4245557441103728435nt_int
% 0.32/0.67          @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 0.32/0.67          @ ( quotient_of @ P5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_abs_code
% 0.32/0.67  thf(fact_9699_normalize__denom__pos,axiom,
% 0.32/0.67      ! [R: product_prod_int_int,P5: int,Q2: int] :
% 0.32/0.67        ( ( ( normalize @ R )
% 0.32/0.67          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_denom_pos
% 0.32/0.67  thf(fact_9700_normalize__crossproduct,axiom,
% 0.32/0.67      ! [Q2: int,S: int,P5: int,R: int] :
% 0.32/0.67        ( ( Q2 != zero_zero_int )
% 0.32/0.67       => ( ( S != zero_zero_int )
% 0.32/0.67         => ( ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67              = ( normalize @ ( product_Pair_int_int @ R @ S ) ) )
% 0.32/0.67           => ( ( times_times_int @ P5 @ S )
% 0.32/0.67              = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_crossproduct
% 0.32/0.67  thf(fact_9701_drop__bit__nat__def,axiom,
% 0.32/0.67      ( bit_se8570568707652914677it_nat
% 0.32/0.67      = ( ^ [N2: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % drop_bit_nat_def
% 0.32/0.67  thf(fact_9702_rat__less__code,axiom,
% 0.32/0.67      ( ord_less_rat
% 0.32/0.67      = ( ^ [P2: rat,Q5: rat] :
% 0.32/0.67            ( produc4947309494688390418_int_o
% 0.32/0.67            @ ^ [A3: int,C3: int] :
% 0.32/0.67                ( produc4947309494688390418_int_o
% 0.32/0.67                @ ^ [B2: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 0.32/0.67                @ ( quotient_of @ Q5 ) )
% 0.32/0.67            @ ( quotient_of @ P2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_less_code
% 0.32/0.67  thf(fact_9703_rat__less__eq__code,axiom,
% 0.32/0.67      ( ord_less_eq_rat
% 0.32/0.67      = ( ^ [P2: rat,Q5: rat] :
% 0.32/0.67            ( produc4947309494688390418_int_o
% 0.32/0.67            @ ^ [A3: int,C3: int] :
% 0.32/0.67                ( produc4947309494688390418_int_o
% 0.32/0.67                @ ^ [B2: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 0.32/0.67                @ ( quotient_of @ Q5 ) )
% 0.32/0.67            @ ( quotient_of @ P2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_less_eq_code
% 0.32/0.67  thf(fact_9704_prod__decode__aux_Oelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.32/0.67        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.32/0.67          & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % prod_decode_aux.elims
% 0.32/0.67  thf(fact_9705_minus__one__mod__numeral,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % minus_one_mod_numeral
% 0.32/0.67  thf(fact_9706_one__mod__minus__numeral,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % one_mod_minus_numeral
% 0.32/0.67  thf(fact_9707_prod__decode__aux_Opelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.32/0.67        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.32/0.67         => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.32/0.67                & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 0.32/0.67             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % prod_decode_aux.pelims
% 0.32/0.67  thf(fact_9708_numeral__mod__minus__numeral,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % numeral_mod_minus_numeral
% 0.32/0.67  thf(fact_9709_minus__numeral__mod__numeral,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % minus_numeral_mod_numeral
% 0.32/0.67  thf(fact_9710_Divides_Oadjust__mod__def,axiom,
% 0.32/0.67      ( adjust_mod
% 0.32/0.67      = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Divides.adjust_mod_def
% 0.32/0.67  thf(fact_9711_quotient__of__int,axiom,
% 0.32/0.67      ! [A: int] :
% 0.32/0.67        ( ( quotient_of @ ( of_int @ A ) )
% 0.32/0.67        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_int
% 0.32/0.67  thf(fact_9712_Frct__code__post_I5_J,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.32/0.67        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(5)
% 0.32/0.67  thf(fact_9713_bezw_Osimps,axiom,
% 0.32/0.67      ( bezw
% 0.32/0.67      = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezw.simps
% 0.32/0.67  thf(fact_9714_Frct__code__post_I2_J,axiom,
% 0.32/0.67      ! [A: int] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 0.32/0.67        = zero_zero_rat ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(2)
% 0.32/0.67  thf(fact_9715_Frct__code__post_I1_J,axiom,
% 0.32/0.67      ! [A: int] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 0.32/0.67        = zero_zero_rat ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(1)
% 0.32/0.67  thf(fact_9716_Frct__code__post_I7_J,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.32/0.67        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(7)
% 0.32/0.67  thf(fact_9717_Frct__code__post_I8_J,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 0.32/0.67        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(8)
% 0.32/0.67  thf(fact_9718_Frct__code__post_I3_J,axiom,
% 0.32/0.67      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 0.32/0.67      = one_one_rat ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(3)
% 0.32/0.67  thf(fact_9719_rat__sgn__code,axiom,
% 0.32/0.67      ! [P5: rat] :
% 0.32/0.67        ( ( quotient_of @ ( sgn_sgn_rat @ P5 ) )
% 0.32/0.67        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P5 ) ) ) @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_sgn_code
% 0.32/0.67  thf(fact_9720_Frct__code__post_I4_J,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.32/0.67        = ( numeral_numeral_rat @ K ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(4)
% 0.32/0.67  thf(fact_9721_Frct__code__post_I6_J,axiom,
% 0.32/0.67      ! [K: num,L2: num] :
% 0.32/0.67        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 0.32/0.67        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Frct_code_post(6)
% 0.32/0.67  thf(fact_9722_bezw__non__0,axiom,
% 0.32/0.67      ! [Y: nat,X: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.32/0.67       => ( ( bezw @ X @ Y )
% 0.32/0.67          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezw_non_0
% 0.32/0.67  thf(fact_9723_bezw_Oelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.32/0.67        ( ( ( bezw @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.32/0.67          & ( ( Xa2 != zero_zero_nat )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezw.elims
% 0.32/0.67  thf(fact_9724_bezw_Opelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.32/0.67        ( ( ( bezw @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.32/0.67         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.32/0.67                & ( ( Xa2 != zero_zero_nat )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 0.32/0.67             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezw.pelims
% 0.32/0.67  thf(fact_9725_fst__divmod__nat,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.32/0.67        = ( divide_divide_nat @ M @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % fst_divmod_nat
% 0.32/0.67  thf(fact_9726_Suc__0__div__numeral,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.32/0.67        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Suc_0_div_numeral
% 0.32/0.67  thf(fact_9727_normalize__def,axiom,
% 0.32/0.67      ( normalize
% 0.32/0.67      = ( ^ [P2: product_prod_int_int] :
% 0.32/0.67            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P2 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) )
% 0.32/0.67            @ ( if_Pro3027730157355071871nt_int
% 0.32/0.67              @ ( ( product_snd_int_int @ P2 )
% 0.32/0.67                = zero_zero_int )
% 0.32/0.67              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.32/0.67              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_def
% 0.32/0.67  thf(fact_9728_gcd__1__int,axiom,
% 0.32/0.67      ! [M: int] :
% 0.32/0.67        ( ( gcd_gcd_int @ M @ one_one_int )
% 0.32/0.67        = one_one_int ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_1_int
% 0.32/0.67  thf(fact_9729_gcd__pos__int,axiom,
% 0.32/0.67      ! [M: int,N: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 0.32/0.67        = ( ( M != zero_zero_int )
% 0.32/0.67          | ( N != zero_zero_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_pos_int
% 0.32/0.67  thf(fact_9730_gcd__neg__numeral__1__int,axiom,
% 0.32/0.67      ! [N: num,X: int] :
% 0.32/0.67        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 0.32/0.67        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_neg_numeral_1_int
% 0.32/0.67  thf(fact_9731_gcd__neg__numeral__2__int,axiom,
% 0.32/0.67      ! [X: int,N: num] :
% 0.32/0.67        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_neg_numeral_2_int
% 0.32/0.67  thf(fact_9732_gcd__0__left__int,axiom,
% 0.32/0.67      ! [X: int] :
% 0.32/0.67        ( ( gcd_gcd_int @ zero_zero_int @ X )
% 0.32/0.67        = ( abs_abs_int @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_0_left_int
% 0.32/0.67  thf(fact_9733_gcd__0__int,axiom,
% 0.32/0.67      ! [X: int] :
% 0.32/0.67        ( ( gcd_gcd_int @ X @ zero_zero_int )
% 0.32/0.67        = ( abs_abs_int @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_0_int
% 0.32/0.67  thf(fact_9734_gcd__mult__distrib__int,axiom,
% 0.32/0.67      ! [K: int,M: int,N: int] :
% 0.32/0.67        ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 0.32/0.67        = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_mult_distrib_int
% 0.32/0.67  thf(fact_9735_bezout__int,axiom,
% 0.32/0.67      ! [X: int,Y: int] :
% 0.32/0.67      ? [U3: int,V2: int] :
% 0.32/0.67        ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y ) )
% 0.32/0.67        = ( gcd_gcd_int @ X @ Y ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezout_int
% 0.32/0.67  thf(fact_9736_gcd__red__int,axiom,
% 0.32/0.67      ( gcd_gcd_int
% 0.32/0.67      = ( ^ [X3: int,Y3: int] : ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X3 @ Y3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_red_int
% 0.32/0.67  thf(fact_9737_gcd__ge__0__int,axiom,
% 0.32/0.67      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_ge_0_int
% 0.32/0.67  thf(fact_9738_gcd__le1__int,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.67       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_le1_int
% 0.32/0.67  thf(fact_9739_gcd__le2__int,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_le2_int
% 0.32/0.67  thf(fact_9740_gcd__cases__int,axiom,
% 0.32/0.67      ! [X: int,Y: int,P: int > $o] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.67         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.67           => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 0.32/0.67       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.67           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.32/0.67             => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.32/0.67         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.32/0.67             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.67               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 0.32/0.67           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.32/0.67               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.32/0.67                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.32/0.67             => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_cases_int
% 0.32/0.67  thf(fact_9741_gcd__unique__int,axiom,
% 0.32/0.67      ! [D: int,A: int,B: int] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.32/0.67          & ( dvd_dvd_int @ D @ A )
% 0.32/0.67          & ( dvd_dvd_int @ D @ B )
% 0.32/0.67          & ! [E3: int] :
% 0.32/0.67              ( ( ( dvd_dvd_int @ E3 @ A )
% 0.32/0.67                & ( dvd_dvd_int @ E3 @ B ) )
% 0.32/0.67             => ( dvd_dvd_int @ E3 @ D ) ) )
% 0.32/0.67        = ( D
% 0.32/0.67          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_unique_int
% 0.32/0.67  thf(fact_9742_gcd__non__0__int,axiom,
% 0.32/0.67      ! [Y: int,X: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ Y )
% 0.32/0.67       => ( ( gcd_gcd_int @ X @ Y )
% 0.32/0.67          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_non_0_int
% 0.32/0.67  thf(fact_9743_gcd__code__int,axiom,
% 0.32/0.67      ( gcd_gcd_int
% 0.32/0.67      = ( ^ [K2: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_code_int
% 0.32/0.67  thf(fact_9744_nat__descend__induct,axiom,
% 0.32/0.67      ! [N: nat,P: nat > $o,M: nat] :
% 0.32/0.67        ( ! [K3: nat] :
% 0.32/0.67            ( ( ord_less_nat @ N @ K3 )
% 0.32/0.67           => ( P @ K3 ) )
% 0.32/0.67       => ( ! [K3: nat] :
% 0.32/0.67              ( ( ord_less_eq_nat @ K3 @ N )
% 0.32/0.67             => ( ! [I2: nat] :
% 0.32/0.67                    ( ( ord_less_nat @ K3 @ I2 )
% 0.32/0.67                   => ( P @ I2 ) )
% 0.32/0.67               => ( P @ K3 ) ) )
% 0.32/0.67         => ( P @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nat_descend_induct
% 0.32/0.67  thf(fact_9745_finite__enumerate,axiom,
% 0.32/0.67      ! [S2: set_nat] :
% 0.32/0.67        ( ( finite_finite_nat @ S2 )
% 0.32/0.67       => ? [R2: nat > nat] :
% 0.32/0.67            ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 0.32/0.67            & ! [N7: nat] :
% 0.32/0.67                ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S2 ) )
% 0.32/0.67               => ( member_nat @ ( R2 @ N7 ) @ S2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_enumerate
% 0.32/0.67  thf(fact_9746_divmod__integer__eq__cases,axiom,
% 0.32/0.67      ( code_divmod_integer
% 0.32/0.67      = ( ^ [K2: code_integer,L: code_integer] :
% 0.32/0.67            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.32/0.67            @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 0.32/0.67              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 0.32/0.67                @ ( if_Pro6119634080678213985nteger
% 0.32/0.67                  @ ( ( sgn_sgn_Code_integer @ K2 )
% 0.32/0.67                    = ( sgn_sgn_Code_integer @ L ) )
% 0.32/0.67                  @ ( code_divmod_abs @ K2 @ L )
% 0.32/0.67                  @ ( produc6916734918728496179nteger
% 0.32/0.67                    @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S7 ) ) )
% 0.32/0.67                    @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % divmod_integer_eq_cases
% 0.32/0.67  thf(fact_9747_gcd__nat_Oeq__neutr__iff,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( ( gcd_gcd_nat @ A @ B )
% 0.32/0.67          = zero_zero_nat )
% 0.32/0.67        = ( ( A = zero_zero_nat )
% 0.32/0.67          & ( B = zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.eq_neutr_iff
% 0.32/0.67  thf(fact_9748_gcd__nat_Oleft__neutral,axiom,
% 0.32/0.67      ! [A: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 0.32/0.67        = A ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.left_neutral
% 0.32/0.67  thf(fact_9749_gcd__nat_Oneutr__eq__iff,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( zero_zero_nat
% 0.32/0.67          = ( gcd_gcd_nat @ A @ B ) )
% 0.32/0.67        = ( ( A = zero_zero_nat )
% 0.32/0.67          & ( B = zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.neutr_eq_iff
% 0.32/0.67  thf(fact_9750_gcd__nat_Oright__neutral,axiom,
% 0.32/0.67      ! [A: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 0.32/0.67        = A ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.right_neutral
% 0.32/0.67  thf(fact_9751_gcd__0__nat,axiom,
% 0.32/0.67      ! [X: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_0_nat
% 0.32/0.67  thf(fact_9752_gcd__0__left__nat,axiom,
% 0.32/0.67      ! [X: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_0_left_nat
% 0.32/0.67  thf(fact_9753_gcd__1__nat,axiom,
% 0.32/0.67      ! [M: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 0.32/0.67        = one_one_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_1_nat
% 0.32/0.67  thf(fact_9754_gcd__Suc__0,axiom,
% 0.32/0.67      ! [M: nat] :
% 0.32/0.67        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.32/0.67        = ( suc @ zero_zero_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_Suc_0
% 0.32/0.67  thf(fact_9755_gcd__pos__nat,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 0.32/0.67        = ( ( M != zero_zero_nat )
% 0.32/0.67          | ( N != zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_pos_nat
% 0.32/0.67  thf(fact_9756_gcd__mult__distrib__nat,axiom,
% 0.32/0.67      ! [K: nat,M: nat,N: nat] :
% 0.32/0.67        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 0.32/0.67        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_mult_distrib_nat
% 0.32/0.67  thf(fact_9757_gcd__diff1__nat,axiom,
% 0.32/0.67      ! [N: nat,M: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.67       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.32/0.67          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_diff1_nat
% 0.32/0.67  thf(fact_9758_gcd__diff2__nat,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.67       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 0.32/0.67          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_diff2_nat
% 0.32/0.67  thf(fact_9759_gcd__red__nat,axiom,
% 0.32/0.67      ( gcd_gcd_nat
% 0.32/0.67      = ( ^ [X3: nat,Y3: nat] : ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_red_nat
% 0.32/0.67  thf(fact_9760_gcd__nat_Oelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: nat] :
% 0.32/0.67        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.67           => ( Y = X ) )
% 0.32/0.67          & ( ( Xa2 != zero_zero_nat )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.elims
% 0.32/0.67  thf(fact_9761_gcd__nat_Osimps,axiom,
% 0.32/0.67      ( gcd_gcd_nat
% 0.32/0.67      = ( ^ [X3: nat,Y3: nat] : ( if_nat @ ( Y3 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.simps
% 0.32/0.67  thf(fact_9762_gcd__non__0__nat,axiom,
% 0.32/0.67      ! [Y: nat,X: nat] :
% 0.32/0.67        ( ( Y != zero_zero_nat )
% 0.32/0.67       => ( ( gcd_gcd_nat @ X @ Y )
% 0.32/0.67          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_non_0_nat
% 0.32/0.67  thf(fact_9763_gcd__le1__nat,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( A != zero_zero_nat )
% 0.32/0.67       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_le1_nat
% 0.32/0.67  thf(fact_9764_gcd__le2__nat,axiom,
% 0.32/0.67      ! [B: nat,A: nat] :
% 0.32/0.67        ( ( B != zero_zero_nat )
% 0.32/0.67       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_le2_nat
% 0.32/0.67  thf(fact_9765_bezout__nat,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( A != zero_zero_nat )
% 0.32/0.67       => ? [X6: nat,Y5: nat] :
% 0.32/0.67            ( ( times_times_nat @ A @ X6 )
% 0.32/0.67            = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezout_nat
% 0.32/0.67  thf(fact_9766_bezout__gcd__nat_H,axiom,
% 0.32/0.67      ! [B: nat,A: nat] :
% 0.32/0.67      ? [X6: nat,Y5: nat] :
% 0.32/0.67        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y5 ) @ ( times_times_nat @ A @ X6 ) )
% 0.32/0.67          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 0.32/0.67            = ( gcd_gcd_nat @ A @ B ) ) )
% 0.32/0.67        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y5 ) @ ( times_times_nat @ B @ X6 ) )
% 0.32/0.67          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 0.32/0.67            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezout_gcd_nat'
% 0.32/0.67  thf(fact_9767_gcd__code__integer,axiom,
% 0.32/0.67      ( gcd_gcd_Code_integer
% 0.32/0.67      = ( ^ [K2: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_code_integer
% 0.32/0.67  thf(fact_9768_bezw__aux,axiom,
% 0.32/0.67      ! [X: nat,Y: nat] :
% 0.32/0.67        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 0.32/0.67        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bezw_aux
% 0.32/0.67  thf(fact_9769_gcd__nat_Opelims,axiom,
% 0.32/0.67      ! [X: nat,Xa2: nat,Y: nat] :
% 0.32/0.67        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.32/0.67         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.32/0.67                 => ( Y = X ) )
% 0.32/0.67                & ( ( Xa2 != zero_zero_nat )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 0.32/0.67             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.pelims
% 0.32/0.67  thf(fact_9770_Code__Numeral_Onegative__def,axiom,
% 0.32/0.67      ( code_negative
% 0.32/0.67      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Code_Numeral.negative_def
% 0.32/0.67  thf(fact_9771_Code__Target__Int_Onegative__def,axiom,
% 0.32/0.67      ( code_Target_negative
% 0.32/0.67      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Code_Target_Int.negative_def
% 0.32/0.67  thf(fact_9772_card__greaterThanLessThan__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] :
% 0.32/0.67        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 0.32/0.67        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_greaterThanLessThan_int
% 0.32/0.67  thf(fact_9773_finite__greaterThanLessThan__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_greaterThanLessThan_int
% 0.32/0.67  thf(fact_9774_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] :
% 0.32/0.67        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 0.32/0.67        = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.32/0.67  thf(fact_9775_xor__minus__numerals_I1_J,axiom,
% 0.32/0.67      ! [N: num,K: int] :
% 0.32/0.67        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 0.32/0.67        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % xor_minus_numerals(1)
% 0.32/0.67  thf(fact_9776_xor__minus__numerals_I2_J,axiom,
% 0.32/0.67      ! [K: int,N: num] :
% 0.32/0.67        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % xor_minus_numerals(2)
% 0.32/0.67  thf(fact_9777_finite__greaterThanLessThan,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_greaterThanLessThan
% 0.32/0.67  thf(fact_9778_card__greaterThanLessThan,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] :
% 0.32/0.67        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 0.32/0.67        = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_greaterThanLessThan
% 0.32/0.67  thf(fact_9779_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] :
% 0.32/0.67        ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 0.32/0.67        = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastSucLessThan_greaterThanLessThan
% 0.32/0.67  thf(fact_9780_tanh__real__bounds,axiom,
% 0.32/0.67      ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % tanh_real_bounds
% 0.32/0.67  thf(fact_9781_sub__BitM__One__eq,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 0.32/0.67        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sub_BitM_One_eq
% 0.32/0.67  thf(fact_9782_Suc__funpow,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( compow_nat_nat @ N @ suc )
% 0.32/0.67        = ( plus_plus_nat @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Suc_funpow
% 0.32/0.67  thf(fact_9783_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.32/0.67      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.32/0.67      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 0.32/0.67      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % max_nat.semilattice_neutr_order_axioms
% 0.32/0.67  thf(fact_9784_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.32/0.67      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.32/0.67      @ ^ [M3: nat,N2: nat] :
% 0.32/0.67          ( ( dvd_dvd_nat @ M3 @ N2 )
% 0.32/0.67          & ( M3 != N2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_nat.semilattice_neutr_order_axioms
% 0.32/0.67  thf(fact_9785_Sup__nat__empty,axiom,
% 0.32/0.67      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.32/0.67      = zero_zero_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % Sup_nat_empty
% 0.32/0.67  thf(fact_9786_Gcd__remove0__nat,axiom,
% 0.32/0.67      ! [M5: set_nat] :
% 0.32/0.67        ( ( finite_finite_nat @ M5 )
% 0.32/0.67       => ( ( gcd_Gcd_nat @ M5 )
% 0.32/0.67          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Gcd_remove0_nat
% 0.32/0.67  thf(fact_9787_times__int_Oabs__eq,axiom,
% 0.32/0.67      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.32/0.67        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( abs_Integ
% 0.32/0.67          @ ( produc27273713700761075at_nat
% 0.32/0.67            @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67                ( produc2626176000494625587at_nat
% 0.32/0.67                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 0.32/0.67            @ Xa2
% 0.32/0.67            @ X ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % times_int.abs_eq
% 0.32/0.67  thf(fact_9788_eq__Abs__Integ,axiom,
% 0.32/0.67      ! [Z: int] :
% 0.32/0.67        ~ ! [X6: nat,Y5: nat] :
% 0.32/0.67            ( Z
% 0.32/0.67           != ( abs_Integ @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eq_Abs_Integ
% 0.32/0.67  thf(fact_9789_Gcd__nat__eq__one,axiom,
% 0.32/0.67      ! [N4: set_nat] :
% 0.32/0.67        ( ( member_nat @ one_one_nat @ N4 )
% 0.32/0.67       => ( ( gcd_Gcd_nat @ N4 )
% 0.32/0.67          = one_one_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Gcd_nat_eq_one
% 0.32/0.67  thf(fact_9790_nat_Oabs__eq,axiom,
% 0.32/0.67      ! [X: product_prod_nat_nat] :
% 0.32/0.67        ( ( nat2 @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nat.abs_eq
% 0.32/0.67  thf(fact_9791_zero__int__def,axiom,
% 0.32/0.67      ( zero_zero_int
% 0.32/0.67      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % zero_int_def
% 0.32/0.67  thf(fact_9792_int__def,axiom,
% 0.32/0.67      ( semiri1314217659103216013at_int
% 0.32/0.67      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % int_def
% 0.32/0.67  thf(fact_9793_uminus__int_Oabs__eq,axiom,
% 0.32/0.67      ! [X: product_prod_nat_nat] :
% 0.32/0.67        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( abs_Integ
% 0.32/0.67          @ ( produc2626176000494625587at_nat
% 0.32/0.67            @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 0.32/0.67            @ X ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % uminus_int.abs_eq
% 0.32/0.67  thf(fact_9794_one__int__def,axiom,
% 0.32/0.67      ( one_one_int
% 0.32/0.67      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % one_int_def
% 0.32/0.67  thf(fact_9795_less__int_Oabs__eq,axiom,
% 0.32/0.67      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.32/0.67        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( produc8739625826339149834_nat_o
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc6081775807080527818_nat_o
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.32/0.67          @ Xa2
% 0.32/0.67          @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_int.abs_eq
% 0.32/0.67  thf(fact_9796_less__eq__int_Oabs__eq,axiom,
% 0.32/0.67      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.32/0.67        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( produc8739625826339149834_nat_o
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc6081775807080527818_nat_o
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.32/0.67          @ Xa2
% 0.32/0.67          @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_eq_int.abs_eq
% 0.32/0.67  thf(fact_9797_plus__int_Oabs__eq,axiom,
% 0.32/0.67      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.32/0.67        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( abs_Integ
% 0.32/0.67          @ ( produc27273713700761075at_nat
% 0.32/0.67            @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67                ( produc2626176000494625587at_nat
% 0.32/0.67                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) )
% 0.32/0.67            @ Xa2
% 0.32/0.67            @ X ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % plus_int.abs_eq
% 0.32/0.67  thf(fact_9798_minus__int_Oabs__eq,axiom,
% 0.32/0.67      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.32/0.67        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.32/0.67        = ( abs_Integ
% 0.32/0.67          @ ( produc27273713700761075at_nat
% 0.32/0.67            @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67                ( produc2626176000494625587at_nat
% 0.32/0.67                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 0.32/0.67            @ Xa2
% 0.32/0.67            @ X ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % minus_int.abs_eq
% 0.32/0.67  thf(fact_9799_Gcd__int__greater__eq__0,axiom,
% 0.32/0.67      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Gcd_int_greater_eq_0
% 0.32/0.67  thf(fact_9800_less__eq__int_Orep__eq,axiom,
% 0.32/0.67      ( ord_less_eq_int
% 0.32/0.67      = ( ^ [X3: int,Xa4: int] :
% 0.32/0.67            ( produc8739625826339149834_nat_o
% 0.32/0.67            @ ^ [Y3: nat,Z3: nat] :
% 0.32/0.67                ( produc6081775807080527818_nat_o
% 0.32/0.67                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.32/0.67            @ ( rep_Integ @ X3 )
% 0.32/0.67            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_eq_int.rep_eq
% 0.32/0.67  thf(fact_9801_less__int_Orep__eq,axiom,
% 0.32/0.67      ( ord_less_int
% 0.32/0.67      = ( ^ [X3: int,Xa4: int] :
% 0.32/0.67            ( produc8739625826339149834_nat_o
% 0.32/0.67            @ ^ [Y3: nat,Z3: nat] :
% 0.32/0.67                ( produc6081775807080527818_nat_o
% 0.32/0.67                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.32/0.67            @ ( rep_Integ @ X3 )
% 0.32/0.67            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_int.rep_eq
% 0.32/0.67  thf(fact_9802_nat_Orep__eq,axiom,
% 0.32/0.67      ( nat2
% 0.32/0.67      = ( ^ [X3: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nat.rep_eq
% 0.32/0.67  thf(fact_9803_prod__encode__def,axiom,
% 0.32/0.67      ( nat_prod_encode
% 0.32/0.67      = ( produc6842872674320459806at_nat
% 0.32/0.67        @ ^ [M3: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N2 ) ) @ M3 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % prod_encode_def
% 0.32/0.67  thf(fact_9804_le__prod__encode__1,axiom,
% 0.32/0.67      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % le_prod_encode_1
% 0.32/0.67  thf(fact_9805_le__prod__encode__2,axiom,
% 0.32/0.67      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % le_prod_encode_2
% 0.32/0.67  thf(fact_9806_prod__encode__prod__decode__aux,axiom,
% 0.32/0.67      ! [K: nat,M: nat] :
% 0.32/0.67        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 0.32/0.67        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 0.32/0.67  
% 0.32/0.67  % prod_encode_prod_decode_aux
% 0.32/0.67  thf(fact_9807_uminus__int__def,axiom,
% 0.32/0.67      ( uminus_uminus_int
% 0.32/0.67      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.32/0.67        @ ( produc2626176000494625587at_nat
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % uminus_int_def
% 0.32/0.67  thf(fact_9808_times__int__def,axiom,
% 0.32/0.67      ( times_times_int
% 0.32/0.67      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.32/0.67        @ ( produc27273713700761075at_nat
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc2626176000494625587at_nat
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % times_int_def
% 0.32/0.67  thf(fact_9809_minus__int__def,axiom,
% 0.32/0.67      ( minus_minus_int
% 0.32/0.67      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.32/0.67        @ ( produc27273713700761075at_nat
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc2626176000494625587at_nat
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % minus_int_def
% 0.32/0.67  thf(fact_9810_plus__int__def,axiom,
% 0.32/0.67      ( plus_plus_int
% 0.32/0.67      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.32/0.67        @ ( produc27273713700761075at_nat
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc2626176000494625587at_nat
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % plus_int_def
% 0.32/0.67  thf(fact_9811_num__of__nat_Osimps_I2_J,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( num_of_nat @ ( suc @ N ) )
% 0.32/0.67            = ( inc @ ( num_of_nat @ N ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( num_of_nat @ ( suc @ N ) )
% 0.32/0.67            = one ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat.simps(2)
% 0.32/0.67  thf(fact_9812_num__of__nat__numeral__eq,axiom,
% 0.32/0.67      ! [Q2: num] :
% 0.32/0.67        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 0.32/0.67        = Q2 ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat_numeral_eq
% 0.32/0.67  thf(fact_9813_num__of__nat_Osimps_I1_J,axiom,
% 0.32/0.67      ( ( num_of_nat @ zero_zero_nat )
% 0.32/0.67      = one ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat.simps(1)
% 0.32/0.67  thf(fact_9814_numeral__num__of__nat,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 0.32/0.67          = N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % numeral_num_of_nat
% 0.32/0.67  thf(fact_9815_num__of__nat__One,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.32/0.67       => ( ( num_of_nat @ N )
% 0.32/0.67          = one ) ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat_One
% 0.32/0.67  thf(fact_9816_num__of__nat__double,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 0.32/0.67          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat_double
% 0.32/0.67  thf(fact_9817_num__of__nat__plus__distrib,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.67       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.67            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % num_of_nat_plus_distrib
% 0.32/0.67  thf(fact_9818_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.32/0.67      ! [N: nat,J: nat,I: nat] :
% 0.32/0.67        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.32/0.67       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 0.32/0.67          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nth_sorted_list_of_set_greaterThanLessThan
% 0.32/0.67  thf(fact_9819_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.32/0.67      ! [N: nat,J: nat,I: nat] :
% 0.32/0.67        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 0.32/0.67       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 0.32/0.67          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nth_sorted_list_of_set_greaterThanAtMost
% 0.32/0.67  thf(fact_9820_pow_Osimps_I3_J,axiom,
% 0.32/0.67      ! [X: num,Y: num] :
% 0.32/0.67        ( ( pow @ X @ ( bit1 @ Y ) )
% 0.32/0.67        = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 0.32/0.67  
% 0.32/0.67  % pow.simps(3)
% 0.32/0.67  thf(fact_9821_finite__greaterThanAtMost,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_greaterThanAtMost
% 0.32/0.67  thf(fact_9822_card__greaterThanAtMost,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] :
% 0.32/0.67        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 0.32/0.67        = ( minus_minus_nat @ U @ L2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_greaterThanAtMost
% 0.32/0.67  thf(fact_9823_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.32/0.67      ! [L2: nat,U: nat] :
% 0.32/0.67        ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 0.32/0.67        = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastSucAtMost_greaterThanAtMost
% 0.32/0.67  thf(fact_9824_sqr_Osimps_I2_J,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( sqr @ ( bit0 @ N ) )
% 0.32/0.67        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sqr.simps(2)
% 0.32/0.67  thf(fact_9825_sqr_Osimps_I1_J,axiom,
% 0.32/0.67      ( ( sqr @ one )
% 0.32/0.67      = one ) ).
% 0.32/0.67  
% 0.32/0.67  % sqr.simps(1)
% 0.32/0.67  thf(fact_9826_sqr__conv__mult,axiom,
% 0.32/0.67      ( sqr
% 0.32/0.67      = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sqr_conv_mult
% 0.32/0.67  thf(fact_9827_pow_Osimps_I2_J,axiom,
% 0.32/0.67      ! [X: num,Y: num] :
% 0.32/0.67        ( ( pow @ X @ ( bit0 @ Y ) )
% 0.32/0.67        = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % pow.simps(2)
% 0.32/0.67  thf(fact_9828_sqr_Osimps_I3_J,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( sqr @ ( bit1 @ N ) )
% 0.32/0.67        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sqr.simps(3)
% 0.32/0.67  thf(fact_9829_rat__floor__lemma,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.32/0.67        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_floor_lemma
% 0.32/0.67  thf(fact_9830_finite__greaterThanAtMost__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_greaterThanAtMost_int
% 0.32/0.67  thf(fact_9831_mult__rat,axiom,
% 0.32/0.67      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.67        ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67        = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mult_rat
% 0.32/0.67  thf(fact_9832_divide__rat,axiom,
% 0.32/0.67      ! [A: int,B: int,C: int,D: int] :
% 0.32/0.67        ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67        = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % divide_rat
% 0.32/0.67  thf(fact_9833_card__greaterThanAtMost__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] :
% 0.32/0.67        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 0.32/0.67        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_greaterThanAtMost_int
% 0.32/0.67  thf(fact_9834_less__rat,axiom,
% 0.32/0.67      ! [B: int,D: int,A: int,C: int] :
% 0.32/0.67        ( ( B != zero_zero_int )
% 0.32/0.67       => ( ( D != zero_zero_int )
% 0.32/0.67         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67            = ( 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 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_rat
% 0.32/0.67  thf(fact_9835_add__rat,axiom,
% 0.32/0.67      ! [B: int,D: int,A: int,C: int] :
% 0.32/0.67        ( ( B != zero_zero_int )
% 0.32/0.67       => ( ( D != zero_zero_int )
% 0.32/0.67         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % add_rat
% 0.32/0.67  thf(fact_9836_le__rat,axiom,
% 0.32/0.67      ! [B: int,D: int,A: int,C: int] :
% 0.32/0.67        ( ( B != zero_zero_int )
% 0.32/0.67       => ( ( D != zero_zero_int )
% 0.32/0.67         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67            = ( 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 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % le_rat
% 0.32/0.67  thf(fact_9837_diff__rat,axiom,
% 0.32/0.67      ! [B: int,D: int,A: int,C: int] :
% 0.32/0.67        ( ( B != zero_zero_int )
% 0.32/0.67       => ( ( D != zero_zero_int )
% 0.32/0.67         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 0.32/0.67            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % diff_rat
% 0.32/0.67  thf(fact_9838_sgn__rat,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 0.32/0.67        = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sgn_rat
% 0.32/0.67  thf(fact_9839_Fract__of__int__eq,axiom,
% 0.32/0.67      ! [K: int] :
% 0.32/0.67        ( ( fract @ K @ one_one_int )
% 0.32/0.67        = ( ring_1_of_int_rat @ K ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_of_int_eq
% 0.32/0.67  thf(fact_9840_quotient__of__eq,axiom,
% 0.32/0.67      ! [A: int,B: int,P5: int,Q2: int] :
% 0.32/0.67        ( ( ( quotient_of @ ( fract @ A @ B ) )
% 0.32/0.67          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67       => ( ( fract @ P5 @ Q2 )
% 0.32/0.67          = ( fract @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_eq
% 0.32/0.67  thf(fact_9841_One__rat__def,axiom,
% 0.32/0.67      ( one_one_rat
% 0.32/0.67      = ( fract @ one_one_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % One_rat_def
% 0.32/0.67  thf(fact_9842_rat__number__collapse_I1_J,axiom,
% 0.32/0.67      ! [K: int] :
% 0.32/0.67        ( ( fract @ zero_zero_int @ K )
% 0.32/0.67        = zero_zero_rat ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_collapse(1)
% 0.32/0.67  thf(fact_9843_rat__number__collapse_I6_J,axiom,
% 0.32/0.67      ! [K: int] :
% 0.32/0.67        ( ( fract @ K @ zero_zero_int )
% 0.32/0.67        = zero_zero_rat ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_collapse(6)
% 0.32/0.67  thf(fact_9844_mult__rat__cancel,axiom,
% 0.32/0.67      ! [C: int,A: int,B: int] :
% 0.32/0.67        ( ( C != zero_zero_int )
% 0.32/0.67       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.32/0.67          = ( fract @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mult_rat_cancel
% 0.32/0.67  thf(fact_9845_eq__rat_I1_J,axiom,
% 0.32/0.67      ! [B: int,D: int,A: int,C: int] :
% 0.32/0.67        ( ( B != zero_zero_int )
% 0.32/0.67       => ( ( D != zero_zero_int )
% 0.32/0.67         => ( ( ( fract @ A @ B )
% 0.32/0.67              = ( fract @ C @ D ) )
% 0.32/0.67            = ( ( times_times_int @ A @ D )
% 0.32/0.67              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eq_rat(1)
% 0.32/0.67  thf(fact_9846_Fract__of__nat__eq,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 0.32/0.67        = ( semiri681578069525770553at_rat @ K ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_of_nat_eq
% 0.32/0.67  thf(fact_9847_eq__rat_I2_J,axiom,
% 0.32/0.67      ! [A: int] :
% 0.32/0.67        ( ( fract @ A @ zero_zero_int )
% 0.32/0.67        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eq_rat(2)
% 0.32/0.67  thf(fact_9848_eq__rat_I3_J,axiom,
% 0.32/0.67      ! [A: int,C: int] :
% 0.32/0.67        ( ( fract @ zero_zero_int @ A )
% 0.32/0.67        = ( fract @ zero_zero_int @ C ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eq_rat(3)
% 0.32/0.67  thf(fact_9849_Rat__induct__pos,axiom,
% 0.32/0.67      ! [P: rat > $o,Q2: rat] :
% 0.32/0.67        ( ! [A5: int,B5: int] :
% 0.32/0.67            ( ( ord_less_int @ zero_zero_int @ B5 )
% 0.32/0.67           => ( P @ ( fract @ A5 @ B5 ) ) )
% 0.32/0.67       => ( P @ Q2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Rat_induct_pos
% 0.32/0.67  thf(fact_9850_normalize__eq,axiom,
% 0.32/0.67      ! [A: int,B: int,P5: int,Q2: int] :
% 0.32/0.67        ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 0.32/0.67          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 0.32/0.67       => ( ( fract @ P5 @ Q2 )
% 0.32/0.67          = ( fract @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % normalize_eq
% 0.32/0.67  thf(fact_9851_Zero__rat__def,axiom,
% 0.32/0.67      ( zero_zero_rat
% 0.32/0.67      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Zero_rat_def
% 0.32/0.67  thf(fact_9852_rat__number__collapse_I3_J,axiom,
% 0.32/0.67      ! [W: num] :
% 0.32/0.67        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 0.32/0.67        = ( numeral_numeral_rat @ W ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_collapse(3)
% 0.32/0.67  thf(fact_9853_rat__number__expand_I3_J,axiom,
% 0.32/0.67      ( numeral_numeral_rat
% 0.32/0.67      = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_expand(3)
% 0.32/0.67  thf(fact_9854_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.32/0.67      ! [L2: int,U: int] :
% 0.32/0.67        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 0.32/0.67        = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.32/0.67  thf(fact_9855_quotient__of__Fract,axiom,
% 0.32/0.67      ! [A: int,B: int] :
% 0.32/0.67        ( ( quotient_of @ ( fract @ A @ B ) )
% 0.32/0.67        = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % quotient_of_Fract
% 0.32/0.67  thf(fact_9856_zero__less__Fract__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.32/0.67          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % zero_less_Fract_iff
% 0.32/0.67  thf(fact_9857_Fract__less__zero__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.32/0.67          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_less_zero_iff
% 0.32/0.67  thf(fact_9858_one__less__Fract__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.32/0.67          = ( ord_less_int @ B @ A ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % one_less_Fract_iff
% 0.32/0.67  thf(fact_9859_Fract__less__one__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.32/0.67          = ( ord_less_int @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_less_one_iff
% 0.32/0.67  thf(fact_9860_rat__number__collapse_I5_J,axiom,
% 0.32/0.67      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.32/0.67      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_collapse(5)
% 0.32/0.67  thf(fact_9861_Fract__add__one,axiom,
% 0.32/0.67      ! [N: int,M: int] :
% 0.32/0.67        ( ( N != zero_zero_int )
% 0.32/0.67       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 0.32/0.67          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_add_one
% 0.32/0.67  thf(fact_9862_Fract__le__zero__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 0.32/0.67          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_le_zero_iff
% 0.32/0.67  thf(fact_9863_zero__le__Fract__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 0.32/0.67          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % zero_le_Fract_iff
% 0.32/0.67  thf(fact_9864_Fract__le__one__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.32/0.67          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Fract_le_one_iff
% 0.32/0.67  thf(fact_9865_one__le__Fract__iff,axiom,
% 0.32/0.67      ! [B: int,A: int] :
% 0.32/0.67        ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.67       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.32/0.67          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % one_le_Fract_iff
% 0.32/0.67  thf(fact_9866_rat__number__collapse_I4_J,axiom,
% 0.32/0.67      ! [W: num] :
% 0.32/0.67        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 0.32/0.67        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_collapse(4)
% 0.32/0.67  thf(fact_9867_rat__number__expand_I5_J,axiom,
% 0.32/0.67      ! [K: num] :
% 0.32/0.67        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 0.32/0.67        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % rat_number_expand(5)
% 0.32/0.67  thf(fact_9868_image__minus__const__atLeastLessThan__nat,axiom,
% 0.32/0.67      ! [C: nat,Y: nat,X: nat] :
% 0.32/0.67        ( ( ( ord_less_nat @ C @ Y )
% 0.32/0.67         => ( ( image_nat_nat
% 0.32/0.67              @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.32/0.67              @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.32/0.67            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_nat @ C @ Y )
% 0.32/0.67         => ( ( ( ord_less_nat @ X @ Y )
% 0.32/0.67             => ( ( image_nat_nat
% 0.32/0.67                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.32/0.67                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.32/0.67                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.32/0.67            & ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.67             => ( ( image_nat_nat
% 0.32/0.67                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 0.32/0.67                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.32/0.67                = bot_bot_set_nat ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_minus_const_atLeastLessThan_nat
% 0.32/0.67  thf(fact_9869_of__nat__eq__id,axiom,
% 0.32/0.67      semiri1316708129612266289at_nat = id_nat ).
% 0.32/0.67  
% 0.32/0.67  % of_nat_eq_id
% 0.32/0.67  thf(fact_9870_bij__betw__Suc,axiom,
% 0.32/0.67      ! [M5: set_nat,N4: set_nat] :
% 0.32/0.67        ( ( bij_betw_nat_nat @ suc @ M5 @ N4 )
% 0.32/0.67        = ( ( image_nat_nat @ suc @ M5 )
% 0.32/0.67          = N4 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % bij_betw_Suc
% 0.32/0.67  thf(fact_9871_image__Suc__atLeastAtMost,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.32/0.67        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_Suc_atLeastAtMost
% 0.32/0.67  thf(fact_9872_image__Suc__atLeastLessThan,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.32/0.67        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_Suc_atLeastLessThan
% 0.32/0.67  thf(fact_9873_less__eq__int__def,axiom,
% 0.32/0.67      ( ord_less_eq_int
% 0.32/0.67      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.32/0.67        @ ( produc8739625826339149834_nat_o
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc6081775807080527818_nat_o
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_eq_int_def
% 0.32/0.67  thf(fact_9874_zero__notin__Suc__image,axiom,
% 0.32/0.67      ! [A2: set_nat] :
% 0.32/0.67        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % zero_notin_Suc_image
% 0.32/0.67  thf(fact_9875_less__int__def,axiom,
% 0.32/0.67      ( ord_less_int
% 0.32/0.67      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.32/0.67        @ ( produc8739625826339149834_nat_o
% 0.32/0.67          @ ^ [X3: nat,Y3: nat] :
% 0.32/0.67              ( produc6081775807080527818_nat_o
% 0.32/0.67              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % less_int_def
% 0.32/0.67  thf(fact_9876_nat__def,axiom,
% 0.32/0.67      ( nat2
% 0.32/0.67      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nat_def
% 0.32/0.67  thf(fact_9877_image__Suc__lessThan,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_Suc_lessThan
% 0.32/0.67  thf(fact_9878_image__Suc__atMost,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.32/0.67        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_Suc_atMost
% 0.32/0.67  thf(fact_9879_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.32/0.67        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast0_atMost_Suc_eq_insert_0
% 0.32/0.67  thf(fact_9880_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.32/0.67        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast0_lessThan_Suc_eq_insert_0
% 0.32/0.67  thf(fact_9881_lessThan__Suc__eq__insert__0,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.32/0.67        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lessThan_Suc_eq_insert_0
% 0.32/0.67  thf(fact_9882_atMost__Suc__eq__insert__0,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.32/0.67        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atMost_Suc_eq_insert_0
% 0.32/0.67  thf(fact_9883_UN__lessThan__UNIV,axiom,
% 0.32/0.67      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.32/0.67      = top_top_set_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % UN_lessThan_UNIV
% 0.32/0.67  thf(fact_9884_UN__atMost__UNIV,axiom,
% 0.32/0.67      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.32/0.67      = top_top_set_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % UN_atMost_UNIV
% 0.32/0.67  thf(fact_9885_Inf__real__def,axiom,
% 0.32/0.67      ( comple4887499456419720421f_real
% 0.32/0.67      = ( ^ [X2: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Inf_real_def
% 0.32/0.67  thf(fact_9886_finite__int__iff__bounded__le,axiom,
% 0.32/0.67      ( finite_finite_int
% 0.32/0.67      = ( ^ [S6: set_int] :
% 0.32/0.67          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_int_iff_bounded_le
% 0.32/0.67  thf(fact_9887_finite__int__iff__bounded,axiom,
% 0.32/0.67      ( finite_finite_int
% 0.32/0.67      = ( ^ [S6: set_int] :
% 0.32/0.67          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % finite_int_iff_bounded
% 0.32/0.67  thf(fact_9888_image__int__atLeastAtMost,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.32/0.67        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_int_atLeastAtMost
% 0.32/0.67  thf(fact_9889_image__int__atLeastLessThan,axiom,
% 0.32/0.67      ! [A: nat,B: nat] :
% 0.32/0.67        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.32/0.67        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_int_atLeastLessThan
% 0.32/0.67  thf(fact_9890_suminf__eq__SUP__real,axiom,
% 0.32/0.67      ! [X8: nat > real] :
% 0.32/0.67        ( ( summable_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 0.32/0.67         => ( ( suminf_real @ X8 )
% 0.32/0.67            = ( comple1385675409528146559p_real
% 0.32/0.67              @ ( image_nat_real
% 0.32/0.67                @ ^ [I5: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I5 ) )
% 0.32/0.67                @ top_top_set_nat ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % suminf_eq_SUP_real
% 0.32/0.67  thf(fact_9891_image__add__int__atLeastLessThan,axiom,
% 0.32/0.67      ! [L2: int,U: int] :
% 0.32/0.67        ( ( image_int_int
% 0.32/0.67          @ ^ [X3: int] : ( plus_plus_int @ X3 @ L2 )
% 0.32/0.67          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 0.32/0.67        = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_add_int_atLeastLessThan
% 0.32/0.67  thf(fact_9892_range__mod,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( image_nat_nat
% 0.32/0.67            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 0.32/0.67            @ top_top_set_nat )
% 0.32/0.67          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % range_mod
% 0.32/0.67  thf(fact_9893_image__atLeastZeroLessThan__int,axiom,
% 0.32/0.67      ! [U: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.32/0.67       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.32/0.67          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % image_atLeastZeroLessThan_int
% 0.32/0.67  thf(fact_9894_UNIV__nat__eq,axiom,
% 0.32/0.67      ( top_top_set_nat
% 0.32/0.67      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % UNIV_nat_eq
% 0.32/0.67  thf(fact_9895_card__UNIV__unit,axiom,
% 0.32/0.67      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.32/0.67      = one_one_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % card_UNIV_unit
% 0.32/0.67  thf(fact_9896_card__UNIV__bool,axiom,
% 0.32/0.67      ( ( finite_card_o @ top_top_set_o )
% 0.32/0.67      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_UNIV_bool
% 0.32/0.67  thf(fact_9897_range__mult,axiom,
% 0.32/0.67      ! [A: real] :
% 0.32/0.67        ( ( ( A = zero_zero_real )
% 0.32/0.67         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.32/0.67            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 0.32/0.67        & ( ( A != zero_zero_real )
% 0.32/0.67         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.32/0.67            = top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % range_mult
% 0.32/0.67  thf(fact_9898_root__def,axiom,
% 0.32/0.67      ( root
% 0.32/0.67      = ( ^ [N2: nat,X3: real] :
% 0.32/0.67            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 0.32/0.67            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.32/0.67              @ ^ [Y3: real] : ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N2 ) )
% 0.32/0.67              @ X3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % root_def
% 0.32/0.67  thf(fact_9899_card__UNIV__char,axiom,
% 0.32/0.67      ( ( finite_card_char @ top_top_set_char )
% 0.32/0.67      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_UNIV_char
% 0.32/0.67  thf(fact_9900_UNIV__char__of__nat,axiom,
% 0.32/0.67      ( top_top_set_char
% 0.32/0.67      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % UNIV_char_of_nat
% 0.32/0.67  thf(fact_9901_char_Osize_I2_J,axiom,
% 0.32/0.67      ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.32/0.67        ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.32/0.67        = zero_zero_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % char.size(2)
% 0.32/0.67  thf(fact_9902_nat__of__char__less__256,axiom,
% 0.32/0.67      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nat_of_char_less_256
% 0.32/0.67  thf(fact_9903_range__nat__of__char,axiom,
% 0.32/0.67      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.32/0.67      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % range_nat_of_char
% 0.32/0.67  thf(fact_9904_integer__of__char__code,axiom,
% 0.32/0.67      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 0.32/0.67        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 0.32/0.67        = ( 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 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % integer_of_char_code
% 0.32/0.67  thf(fact_9905_char_Osize__gen,axiom,
% 0.32/0.67      ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.32/0.67        ( ( size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.32/0.67        = zero_zero_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % char.size_gen
% 0.32/0.67  thf(fact_9906_String_Ochar__of__ascii__of,axiom,
% 0.32/0.67      ! [C: char] :
% 0.32/0.67        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 0.32/0.67        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % String.char_of_ascii_of
% 0.32/0.67  thf(fact_9907_sorted__list__of__set__lessThan__Suc,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 0.32/0.67        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sorted_list_of_set_lessThan_Suc
% 0.32/0.67  thf(fact_9908_sorted__list__of__set__atMost__Suc,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 0.32/0.67        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sorted_list_of_set_atMost_Suc
% 0.32/0.67  thf(fact_9909_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 0.32/0.67       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 0.32/0.67          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sorted_list_of_set_greaterThanAtMost
% 0.32/0.67  thf(fact_9910_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 0.32/0.67       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 0.32/0.67          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sorted_list_of_set_greaterThanLessThan
% 0.32/0.67  thf(fact_9911_list__encode_Oelims,axiom,
% 0.32/0.67      ! [X: list_nat,Y: nat] :
% 0.32/0.67        ( ( ( nat_list_encode @ X )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ( X = nil_nat )
% 0.32/0.67           => ( Y != zero_zero_nat ) )
% 0.32/0.67         => ~ ! [X6: nat,Xs3: list_nat] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( cons_nat @ X6 @ Xs3 ) )
% 0.32/0.67               => ( Y
% 0.32/0.67                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % list_encode.elims
% 0.32/0.67  thf(fact_9912_upto__aux__rec,axiom,
% 0.32/0.67      ( upto_aux
% 0.32/0.67      = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_aux_rec
% 0.32/0.67  thf(fact_9913_sup__enat__def,axiom,
% 0.32/0.67      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 0.32/0.67  
% 0.32/0.67  % sup_enat_def
% 0.32/0.67  thf(fact_9914_sup__nat__def,axiom,
% 0.32/0.67      sup_sup_nat = ord_max_nat ).
% 0.32/0.67  
% 0.32/0.67  % sup_nat_def
% 0.32/0.67  thf(fact_9915_atLeastLessThan__add__Un,axiom,
% 0.32/0.67      ! [I: nat,J: nat,K: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.67       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.32/0.67          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastLessThan_add_Un
% 0.32/0.67  thf(fact_9916_list__encode_Osimps_I1_J,axiom,
% 0.32/0.67      ( ( nat_list_encode @ nil_nat )
% 0.32/0.67      = zero_zero_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % list_encode.simps(1)
% 0.32/0.67  thf(fact_9917_list__encode_Osimps_I2_J,axiom,
% 0.32/0.67      ! [X: nat,Xs: list_nat] :
% 0.32/0.67        ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 0.32/0.67        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % list_encode.simps(2)
% 0.32/0.67  thf(fact_9918_list__encode_Opelims,axiom,
% 0.32/0.67      ! [X: list_nat,Y: nat] :
% 0.32/0.67        ( ( ( nat_list_encode @ X )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 0.32/0.67         => ( ( ( X = nil_nat )
% 0.32/0.67             => ( ( Y = zero_zero_nat )
% 0.32/0.67               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.32/0.67           => ~ ! [X6: nat,Xs3: list_nat] :
% 0.32/0.67                  ( ( X
% 0.32/0.67                    = ( cons_nat @ X6 @ Xs3 ) )
% 0.32/0.67                 => ( ( Y
% 0.32/0.67                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 0.32/0.67                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X6 @ Xs3 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % list_encode.pelims
% 0.32/0.67  thf(fact_9919_upto_Opelims,axiom,
% 0.32/0.67      ! [X: int,Xa2: int,Y: list_int] :
% 0.32/0.67        ( ( ( upto @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 0.32/0.67         => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 0.32/0.67                 => ( Y
% 0.32/0.67                    = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 0.32/0.67                & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 0.32/0.67                 => ( Y = nil_int ) ) )
% 0.32/0.67             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto.pelims
% 0.32/0.67  thf(fact_9920_upto__Nil,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( ( upto @ I @ J )
% 0.32/0.67          = nil_int )
% 0.32/0.67        = ( ord_less_int @ J @ I ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_Nil
% 0.32/0.67  thf(fact_9921_upto__Nil2,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( nil_int
% 0.32/0.67          = ( upto @ I @ J ) )
% 0.32/0.67        = ( ord_less_int @ J @ I ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_Nil2
% 0.32/0.67  thf(fact_9922_upto__empty,axiom,
% 0.32/0.67      ! [J: int,I: int] :
% 0.32/0.67        ( ( ord_less_int @ J @ I )
% 0.32/0.67       => ( ( upto @ I @ J )
% 0.32/0.67          = nil_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_empty
% 0.32/0.67  thf(fact_9923_upto__single,axiom,
% 0.32/0.67      ! [I: int] :
% 0.32/0.67        ( ( upto @ I @ I )
% 0.32/0.67        = ( cons_int @ I @ nil_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_single
% 0.32/0.67  thf(fact_9924_nth__upto,axiom,
% 0.32/0.67      ! [I: int,K: nat,J: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.32/0.67       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.32/0.67          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nth_upto
% 0.32/0.67  thf(fact_9925_length__upto,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.32/0.67        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % length_upto
% 0.32/0.67  thf(fact_9926_upto__rec__numeral_I1_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67            = nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec_numeral(1)
% 0.32/0.67  thf(fact_9927_upto__rec__numeral_I2_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67            = nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec_numeral(2)
% 0.32/0.67  thf(fact_9928_upto__rec__numeral_I3_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67            = nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec_numeral(3)
% 0.32/0.67  thf(fact_9929_upto__rec__numeral_I4_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67            = nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec_numeral(4)
% 0.32/0.67  thf(fact_9930_upto__aux__def,axiom,
% 0.32/0.67      ( upto_aux
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_aux_def
% 0.32/0.67  thf(fact_9931_upto__code,axiom,
% 0.32/0.67      ( upto
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_code
% 0.32/0.67  thf(fact_9932_distinct__upto,axiom,
% 0.32/0.67      ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 0.32/0.67  
% 0.32/0.67  % distinct_upto
% 0.32/0.67  thf(fact_9933_atLeastAtMost__upto,axiom,
% 0.32/0.67      ( set_or1266510415728281911st_int
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastAtMost_upto
% 0.32/0.67  thf(fact_9934_upto__split2,axiom,
% 0.32/0.67      ! [I: int,J: int,K: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.32/0.67         => ( ( upto @ I @ K )
% 0.32/0.67            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_split2
% 0.32/0.67  thf(fact_9935_upto__split1,axiom,
% 0.32/0.67      ! [I: int,J: int,K: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.32/0.67         => ( ( upto @ I @ K )
% 0.32/0.67            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_split1
% 0.32/0.67  thf(fact_9936_atLeastLessThan__upto,axiom,
% 0.32/0.67      ( set_or4662586982721622107an_int
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastLessThan_upto
% 0.32/0.67  thf(fact_9937_greaterThanAtMost__upto,axiom,
% 0.32/0.67      ( set_or6656581121297822940st_int
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThanAtMost_upto
% 0.32/0.67  thf(fact_9938_upto_Oelims,axiom,
% 0.32/0.67      ! [X: int,Xa2: int,Y: list_int] :
% 0.32/0.67        ( ( ( upto @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 0.32/0.67          & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 0.32/0.67           => ( Y = nil_int ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto.elims
% 0.32/0.67  thf(fact_9939_upto_Osimps,axiom,
% 0.32/0.67      ( upto
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto.simps
% 0.32/0.67  thf(fact_9940_upto__rec1,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67       => ( ( upto @ I @ J )
% 0.32/0.67          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec1
% 0.32/0.67  thf(fact_9941_upto__rec2,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67       => ( ( upto @ I @ J )
% 0.32/0.67          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_rec2
% 0.32/0.67  thf(fact_9942_greaterThanLessThan__upto,axiom,
% 0.32/0.67      ( set_or5832277885323065728an_int
% 0.32/0.67      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThanLessThan_upto
% 0.32/0.67  thf(fact_9943_upto__split3,axiom,
% 0.32/0.67      ! [I: int,J: int,K: int] :
% 0.32/0.67        ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67       => ( ( ord_less_eq_int @ J @ K )
% 0.32/0.67         => ( ( upto @ I @ K )
% 0.32/0.67            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto_split3
% 0.32/0.67  thf(fact_9944_upto_Opsimps,axiom,
% 0.32/0.67      ! [I: int,J: int] :
% 0.32/0.67        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.32/0.67       => ( ( ( ord_less_eq_int @ I @ J )
% 0.32/0.67           => ( ( upto @ I @ J )
% 0.32/0.67              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.32/0.67          & ( ~ ( ord_less_eq_int @ I @ J )
% 0.32/0.67           => ( ( upto @ I @ J )
% 0.32/0.67              = nil_int ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upto.psimps
% 0.32/0.67  thf(fact_9945_DERIV__real__root__generic,axiom,
% 0.32/0.67      ! [N: nat,X: real,D4: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( X != zero_zero_real )
% 0.32/0.67         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67             => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67               => ( D4
% 0.32/0.67                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.32/0.67           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67               => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.67                 => ( D4
% 0.32/0.67                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.32/0.67             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67                 => ( D4
% 0.32/0.67                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_real_root_generic
% 0.32/0.67  thf(fact_9946_DERIV__local__const,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,D: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.32/0.67         => ( ! [Y5: real] :
% 0.32/0.67                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 0.32/0.67               => ( ( F @ X )
% 0.32/0.67                  = ( F @ Y5 ) ) )
% 0.32/0.67           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_local_const
% 0.32/0.67  thf(fact_9947_DERIV__pos__inc__left,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pos_inc_left
% 0.32/0.67  thf(fact_9948_DERIV__neg__dec__left,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_neg_dec_left
% 0.32/0.67  thf(fact_9949_DERIV__const__ratio__const,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,K: real] :
% 0.32/0.67        ( ( A != B )
% 0.32/0.67       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67         => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.32/0.67            = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_const_ratio_const
% 0.32/0.67  thf(fact_9950_DERIV__const__ratio__const2,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,K: real] :
% 0.32/0.67        ( ( A != B )
% 0.32/0.67       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67         => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 0.32/0.67            = K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_const_ratio_const2
% 0.32/0.67  thf(fact_9951_DERIV__isconst__all,axiom,
% 0.32/0.67      ! [F: real > real,X: real,Y: real] :
% 0.32/0.67        ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67       => ( ( F @ X )
% 0.32/0.67          = ( F @ Y ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_isconst_all
% 0.32/0.67  thf(fact_9952_DERIV__neg__dec__right,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_neg_dec_right
% 0.32/0.67  thf(fact_9953_DERIV__pos__inc__right,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pos_inc_right
% 0.32/0.67  thf(fact_9954_DERIV__ln,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_ln
% 0.32/0.67  thf(fact_9955_DERIV__isconst3,axiom,
% 0.32/0.67      ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67           => ( ! [X6: real] :
% 0.32/0.67                  ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 0.32/0.67             => ( ( F @ X )
% 0.32/0.67                = ( F @ Y ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_isconst3
% 0.32/0.67  thf(fact_9956_has__real__derivative__pos__inc__right,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 0.32/0.67                   => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % has_real_derivative_pos_inc_right
% 0.32/0.67  thf(fact_9957_has__real__derivative__neg__dec__right,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.32/0.67       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 0.32/0.67                   => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % has_real_derivative_neg_dec_right
% 0.32/0.67  thf(fact_9958_has__real__derivative__pos__inc__left,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 0.32/0.67                   => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % has_real_derivative_pos_inc_left
% 0.32/0.67  thf(fact_9959_has__real__derivative__neg__dec__left,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 0.32/0.67       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.32/0.67         => ? [D3: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.32/0.67              & ! [H4: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 0.32/0.67                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 0.32/0.67                   => ( ( ord_less_real @ H4 @ D3 )
% 0.32/0.67                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % has_real_derivative_neg_dec_left
% 0.32/0.67  thf(fact_9960_MVT2,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,F5: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67         => ? [Z5: real] :
% 0.32/0.67              ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67              & ( ord_less_real @ Z5 @ B )
% 0.32/0.67              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.32/0.67                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z5 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % MVT2
% 0.32/0.67  thf(fact_9961_DERIV__neg__imp__decreasing,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 0.32/0.67         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_neg_imp_decreasing
% 0.32/0.67  thf(fact_9962_DERIV__pos__imp__increasing,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 0.32/0.67         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pos_imp_increasing
% 0.32/0.67  thf(fact_9963_deriv__nonneg__imp__mono,axiom,
% 0.32/0.67      ! [A: real,B: real,G: real > real,G2: real > real] :
% 0.32/0.67        ( ! [X6: real] :
% 0.32/0.67            ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.32/0.67           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.32/0.67             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X6 ) ) )
% 0.32/0.67         => ( ( ord_less_eq_real @ A @ B )
% 0.32/0.67           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % deriv_nonneg_imp_mono
% 0.32/0.67  thf(fact_9964_DERIV__nonpos__imp__nonincreasing,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_eq_real @ Y2 @ zero_zero_real ) ) ) )
% 0.32/0.67         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_nonpos_imp_nonincreasing
% 0.32/0.67  thf(fact_9965_DERIV__nonneg__imp__nondecreasing,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) )
% 0.32/0.67         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_nonneg_imp_nondecreasing
% 0.32/0.67  thf(fact_9966_DERIV__const__average,axiom,
% 0.32/0.67      ! [A: real,B: real,V: real > real,K: real] :
% 0.32/0.67        ( ( A != B )
% 0.32/0.67       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.32/0.67            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_const_average
% 0.32/0.67  thf(fact_9967_DERIV__local__min,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,D: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.32/0.67         => ( ! [Y5: real] :
% 0.32/0.67                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 0.32/0.67               => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y5 ) ) )
% 0.32/0.67           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_local_min
% 0.32/0.67  thf(fact_9968_DERIV__local__max,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,X: real,D: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ D )
% 0.32/0.67         => ( ! [Y5: real] :
% 0.32/0.67                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 0.32/0.67               => ( ord_less_eq_real @ ( F @ Y5 ) @ ( F @ X ) ) )
% 0.32/0.67           => ( L2 = zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_local_max
% 0.32/0.67  thf(fact_9969_DERIV__ln__divide,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_ln_divide
% 0.32/0.67  thf(fact_9970_DERIV__pow,axiom,
% 0.32/0.67      ! [N: nat,X: real,S: set_real] :
% 0.32/0.67        ( has_fi5821293074295781190e_real
% 0.32/0.67        @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 0.32/0.67        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.32/0.67        @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pow
% 0.32/0.67  thf(fact_9971_DERIV__fun__pow,axiom,
% 0.32/0.67      ! [G: real > real,M: real,X: real,N: nat] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( has_fi5821293074295781190e_real
% 0.32/0.67          @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 0.32/0.67          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_fun_pow
% 0.32/0.67  thf(fact_9972_has__real__derivative__powr,axiom,
% 0.32/0.67      ! [Z: real,R: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.67       => ( has_fi5821293074295781190e_real
% 0.32/0.67          @ ^ [Z3: real] : ( powr_real @ Z3 @ R )
% 0.32/0.67          @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % has_real_derivative_powr
% 0.32/0.67  thf(fact_9973_DERIV__log,axiom,
% 0.32/0.67      ! [X: real,B: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_log
% 0.32/0.67  thf(fact_9974_DERIV__fun__powr,axiom,
% 0.32/0.67      ! [G: real > real,M: real,X: real,R: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.32/0.67         => ( has_fi5821293074295781190e_real
% 0.32/0.67            @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R )
% 0.32/0.67            @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_fun_powr
% 0.32/0.67  thf(fact_9975_DERIV__powr,axiom,
% 0.32/0.67      ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.32/0.67         => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67           => ( has_fi5821293074295781190e_real
% 0.32/0.67              @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 0.32/0.67              @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_powr
% 0.32/0.67  thf(fact_9976_DERIV__real__sqrt,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_real_sqrt
% 0.32/0.67  thf(fact_9977_DERIV__series_H,axiom,
% 0.32/0.67      ! [F: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.32/0.67        ( ! [N3: nat] :
% 0.32/0.67            ( has_fi5821293074295781190e_real
% 0.32/0.67            @ ^ [X3: real] : ( F @ X3 @ N3 )
% 0.32/0.67            @ ( F5 @ X0 @ N3 )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67             => ( summable_real @ ( F @ X6 ) ) )
% 0.32/0.67         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67           => ( ( summable_real @ ( F5 @ X0 ) )
% 0.32/0.67             => ( ( summable_real @ L5 )
% 0.32/0.67               => ( ! [N3: nat,X6: real,Y5: real] :
% 0.32/0.67                      ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67                     => ( ( member_real @ Y5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.32/0.67                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X6 @ N3 ) @ ( F @ Y5 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X6 @ Y5 ) ) ) ) ) )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real
% 0.32/0.67                    @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 0.32/0.67                    @ ( suminf_real @ ( F5 @ X0 ) )
% 0.32/0.67                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_series'
% 0.32/0.67  thf(fact_9978_DERIV__arctan,axiom,
% 0.32/0.67      ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_arctan
% 0.32/0.67  thf(fact_9979_arsinh__real__has__field__derivative,axiom,
% 0.32/0.67      ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 0.32/0.67  
% 0.32/0.67  % arsinh_real_has_field_derivative
% 0.32/0.67  thf(fact_9980_DERIV__real__sqrt__generic,axiom,
% 0.32/0.67      ! [X: real,D4: real] :
% 0.32/0.67        ( ( X != zero_zero_real )
% 0.32/0.67       => ( ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67           => ( D4
% 0.32/0.67              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67         => ( ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.67             => ( D4
% 0.32/0.67                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_real_sqrt_generic
% 0.32/0.67  thf(fact_9981_arcosh__real__has__field__derivative,axiom,
% 0.32/0.67      ! [X: real,A2: set_real] :
% 0.32/0.67        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % arcosh_real_has_field_derivative
% 0.32/0.67  thf(fact_9982_artanh__real__has__field__derivative,axiom,
% 0.32/0.67      ! [X: real,A2: set_real] :
% 0.32/0.67        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.67       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % artanh_real_has_field_derivative
% 0.32/0.67  thf(fact_9983_DERIV__power__series_H,axiom,
% 0.32/0.67      ! [R4: real,F: nat > real,X0: real] :
% 0.32/0.67        ( ! [X6: real] :
% 0.32/0.67            ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 0.32/0.67           => ( summable_real
% 0.32/0.67              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X6 @ N2 ) ) ) )
% 0.32/0.67       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 0.32/0.67         => ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.32/0.67           => ( has_fi5821293074295781190e_real
% 0.32/0.67              @ ^ [X3: real] :
% 0.32/0.67                  ( suminf_real
% 0.32/0.67                  @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) )
% 0.32/0.67              @ ( suminf_real
% 0.32/0.67                @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_power_series'
% 0.32/0.67  thf(fact_9984_DERIV__real__root,axiom,
% 0.32/0.67      ! [N: nat,X: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.67         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_real_root
% 0.32/0.67  thf(fact_9985_DERIV__arccos,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_arccos
% 0.32/0.67  thf(fact_9986_DERIV__arcsin,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_arcsin
% 0.32/0.67  thf(fact_9987_Maclaurin__all__le__objl,axiom,
% 0.32/0.67      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.32/0.67        ( ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67            = F )
% 0.32/0.67          & ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 0.32/0.67       => ? [T6: real] :
% 0.32/0.67            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.67            & ( ( F @ X )
% 0.32/0.67              = ( plus_plus_real
% 0.32/0.67                @ ( groups6591440286371151544t_real
% 0.32/0.67                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.67                  @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_all_le_objl
% 0.32/0.67  thf(fact_9988_Maclaurin__all__le,axiom,
% 0.32/0.67      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.32/0.67        ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67          = F )
% 0.32/0.67       => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67         => ? [T6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.67              & ( ( F @ X )
% 0.32/0.67                = ( plus_plus_real
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_all_le
% 0.32/0.67  thf(fact_9989_DERIV__odd__real__root,axiom,
% 0.32/0.67      ! [N: nat,X: real] :
% 0.32/0.67        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67       => ( ( X != zero_zero_real )
% 0.32/0.67         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_odd_real_root
% 0.32/0.67  thf(fact_9990_Maclaurin__minus,axiom,
% 0.32/0.67      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ H2 @ zero_zero_real )
% 0.32/0.67       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67              = F )
% 0.32/0.67           => ( ! [M4: nat,T6: real] :
% 0.32/0.67                  ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                    & ( ord_less_eq_real @ H2 @ T6 )
% 0.32/0.67                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67             => ? [T6: real] :
% 0.32/0.67                  ( ( ord_less_real @ H2 @ T6 )
% 0.32/0.67                  & ( ord_less_real @ T6 @ zero_zero_real )
% 0.32/0.67                  & ( ( F @ H2 )
% 0.32/0.67                    = ( plus_plus_real
% 0.32/0.67                      @ ( groups6591440286371151544t_real
% 0.32/0.67                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.32/0.67                        @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_minus
% 0.32/0.67  thf(fact_9991_Maclaurin2,axiom,
% 0.32/0.67      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.32/0.67       => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67            = F )
% 0.32/0.67         => ( ! [M4: nat,T6: real] :
% 0.32/0.67                ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.67                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67           => ? [T6: real] :
% 0.32/0.67                ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.32/0.67                & ( ord_less_eq_real @ T6 @ H2 )
% 0.32/0.67                & ( ( F @ H2 )
% 0.32/0.67                  = ( plus_plus_real
% 0.32/0.67                    @ ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin2
% 0.32/0.67  thf(fact_9992_Maclaurin,axiom,
% 0.32/0.67      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.32/0.67       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67              = F )
% 0.32/0.67           => ( ! [M4: nat,T6: real] :
% 0.32/0.67                  ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.67                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67             => ? [T6: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.32/0.67                  & ( ord_less_real @ T6 @ H2 )
% 0.32/0.67                  & ( ( F @ H2 )
% 0.32/0.67                    = ( plus_plus_real
% 0.32/0.67                      @ ( groups6591440286371151544t_real
% 0.32/0.67                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 0.32/0.67                        @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin
% 0.32/0.67  thf(fact_9993_Maclaurin__all__lt,axiom,
% 0.32/0.67      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.32/0.67        ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67          = F )
% 0.32/0.67       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67         => ( ( X != zero_zero_real )
% 0.32/0.67           => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67             => ? [T6: real] :
% 0.32/0.67                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.32/0.67                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.67                  & ( ( F @ X )
% 0.32/0.67                    = ( plus_plus_real
% 0.32/0.67                      @ ( groups6591440286371151544t_real
% 0.32/0.67                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.67                        @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_all_lt
% 0.32/0.67  thf(fact_9994_Maclaurin__bi__le,axiom,
% 0.32/0.67      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.32/0.67        ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67          = F )
% 0.32/0.67       => ( ! [M4: nat,T6: real] :
% 0.32/0.67              ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 0.32/0.67             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67         => ? [T6: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.32/0.67              & ( ( F @ X )
% 0.32/0.67                = ( plus_plus_real
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_bi_le
% 0.32/0.67  thf(fact_9995_Taylor__down,axiom,
% 0.32/0.67      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67            = F )
% 0.32/0.67         => ( ! [M4: nat,T6: real] :
% 0.32/0.67                ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                  & ( ord_less_eq_real @ A @ T6 )
% 0.32/0.67                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67           => ( ( ord_less_real @ A @ C )
% 0.32/0.67             => ( ( ord_less_eq_real @ C @ B )
% 0.32/0.67               => ? [T6: real] :
% 0.32/0.67                    ( ( ord_less_real @ A @ T6 )
% 0.32/0.67                    & ( ord_less_real @ T6 @ C )
% 0.32/0.67                    & ( ( F @ A )
% 0.32/0.67                      = ( plus_plus_real
% 0.32/0.67                        @ ( groups6591440286371151544t_real
% 0.32/0.67                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 0.32/0.67                          @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Taylor_down
% 0.32/0.67  thf(fact_9996_Taylor__up,axiom,
% 0.32/0.67      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67            = F )
% 0.32/0.67         => ( ! [M4: nat,T6: real] :
% 0.32/0.67                ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                  & ( ord_less_eq_real @ A @ T6 )
% 0.32/0.67                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67           => ( ( ord_less_eq_real @ A @ C )
% 0.32/0.67             => ( ( ord_less_real @ C @ B )
% 0.32/0.67               => ? [T6: real] :
% 0.32/0.67                    ( ( ord_less_real @ C @ T6 )
% 0.32/0.67                    & ( ord_less_real @ T6 @ B )
% 0.32/0.67                    & ( ( F @ B )
% 0.32/0.67                      = ( plus_plus_real
% 0.32/0.67                        @ ( groups6591440286371151544t_real
% 0.32/0.67                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 0.32/0.67                          @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Taylor_up
% 0.32/0.67  thf(fact_9997_Taylor,axiom,
% 0.32/0.67      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( ( Diff @ zero_zero_nat )
% 0.32/0.67            = F )
% 0.32/0.67         => ( ! [M4: nat,T6: real] :
% 0.32/0.67                ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67                  & ( ord_less_eq_real @ A @ T6 )
% 0.32/0.67                  & ( ord_less_eq_real @ T6 @ B ) )
% 0.32/0.67               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67           => ( ( ord_less_eq_real @ A @ C )
% 0.32/0.67             => ( ( ord_less_eq_real @ C @ B )
% 0.32/0.67               => ( ( ord_less_eq_real @ A @ X )
% 0.32/0.67                 => ( ( ord_less_eq_real @ X @ B )
% 0.32/0.67                   => ( ( X != C )
% 0.32/0.67                     => ? [T6: real] :
% 0.32/0.67                          ( ( ( ord_less_real @ X @ C )
% 0.32/0.67                           => ( ( ord_less_real @ X @ T6 )
% 0.32/0.67                              & ( ord_less_real @ T6 @ C ) ) )
% 0.32/0.67                          & ( ~ ( ord_less_real @ X @ C )
% 0.32/0.67                           => ( ( ord_less_real @ C @ T6 )
% 0.32/0.67                              & ( ord_less_real @ T6 @ X ) ) )
% 0.32/0.67                          & ( ( F @ X )
% 0.32/0.67                            = ( plus_plus_real
% 0.32/0.67                              @ ( groups6591440286371151544t_real
% 0.32/0.67                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M3 ) )
% 0.32/0.67                                @ ( set_ord_lessThan_nat @ N ) )
% 0.32/0.67                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Taylor
% 0.32/0.67  thf(fact_9998_Maclaurin__lemma2,axiom,
% 0.32/0.67      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 0.32/0.67        ( ! [M4: nat,T6: real] :
% 0.32/0.67            ( ( ( ord_less_nat @ M4 @ N )
% 0.32/0.67              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.32/0.67              & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.32/0.67           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.32/0.67       => ( ( N
% 0.32/0.67            = ( suc @ K ) )
% 0.32/0.67         => ! [M2: nat,T7: real] :
% 0.32/0.67              ( ( ( ord_less_nat @ M2 @ N )
% 0.32/0.67                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 0.32/0.67                & ( ord_less_eq_real @ T7 @ H2 ) )
% 0.32/0.67             => ( has_fi5821293074295781190e_real
% 0.32/0.67                @ ^ [U2: real] :
% 0.32/0.67                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 0.32/0.67                    @ ( plus_plus_real
% 0.32/0.67                      @ ( groups6591440286371151544t_real
% 0.32/0.67                        @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ U2 @ P2 ) )
% 0.32/0.67                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 0.32/0.67                      @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 0.32/0.67                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 0.32/0.67                  @ ( plus_plus_real
% 0.32/0.67                    @ ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ T7 @ P2 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 0.32/0.67                    @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Maclaurin_lemma2
% 0.32/0.67  thf(fact_9999_DERIV__arctan__series,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.67       => ( has_fi5821293074295781190e_real
% 0.32/0.67          @ ^ [X9: real] :
% 0.32/0.67              ( suminf_real
% 0.32/0.67              @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.32/0.67          @ ( suminf_real
% 0.32/0.67            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_arctan_series
% 0.32/0.67  thf(fact_10000_DERIV__even__real__root,axiom,
% 0.32/0.67      ! [N: nat,X: real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67         => ( ( ord_less_real @ X @ zero_zero_real )
% 0.32/0.67           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_even_real_root
% 0.32/0.67  thf(fact_10001_take__bit__numeral__minus__numeral__int,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int
% 0.32/0.67          @ ^ [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 ) ) )
% 0.32/0.67          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_numeral_minus_numeral_int
% 0.32/0.67  thf(fact_10002_take__bit__num__simps_I1_J,axiom,
% 0.32/0.67      ! [M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 0.32/0.67        = none_num ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(1)
% 0.32/0.67  thf(fact_10003_take__bit__num__simps_I2_J,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 0.32/0.67        = ( some_num @ one ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(2)
% 0.32/0.67  thf(fact_10004_take__bit__num__simps_I5_J,axiom,
% 0.32/0.67      ! [R: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 0.32/0.67        = ( some_num @ one ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(5)
% 0.32/0.67  thf(fact_10005_take__bit__num__simps_I3_J,axiom,
% 0.32/0.67      ! [N: nat,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 0.32/0.67        = ( case_o6005452278849405969um_num @ none_num
% 0.32/0.67          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.32/0.67          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(3)
% 0.32/0.67  thf(fact_10006_take__bit__num__simps_I4_J,axiom,
% 0.32/0.67      ! [N: nat,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 0.32/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(4)
% 0.32/0.67  thf(fact_10007_take__bit__num__simps_I6_J,axiom,
% 0.32/0.67      ! [R: num,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 0.32/0.67        = ( case_o6005452278849405969um_num @ none_num
% 0.32/0.67          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.32/0.67          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(6)
% 0.32/0.67  thf(fact_10008_take__bit__num__simps_I7_J,axiom,
% 0.32/0.67      ! [R: num,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 0.32/0.67        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_simps(7)
% 0.32/0.67  thf(fact_10009_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 0.32/0.67      ! [N: nat,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 0.32/0.67        = ( case_nat_option_num @ none_num
% 0.32/0.67          @ ^ [N2: nat] :
% 0.32/0.67              ( case_o6005452278849405969um_num @ none_num
% 0.32/0.67              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.32/0.67              @ ( bit_take_bit_num @ N2 @ M ) )
% 0.32/0.67          @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Code_Abstract_Nat.take_bit_num_code(2)
% 0.32/0.67  thf(fact_10010_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( bit_take_bit_num @ N @ one )
% 0.32/0.67        = ( case_nat_option_num @ none_num
% 0.32/0.67          @ ^ [N2: nat] : ( some_num @ one )
% 0.32/0.67          @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Code_Abstract_Nat.take_bit_num_code(1)
% 0.32/0.67  thf(fact_10011_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 0.32/0.67      ! [N: nat,M: num] :
% 0.32/0.67        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 0.32/0.67        = ( case_nat_option_num @ none_num
% 0.32/0.67          @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 0.32/0.67          @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Code_Abstract_Nat.take_bit_num_code(3)
% 0.32/0.67  thf(fact_10012_take__bit__num__def,axiom,
% 0.32/0.67      ( bit_take_bit_num
% 0.32/0.67      = ( ^ [N2: nat,M3: num] :
% 0.32/0.67            ( if_option_num
% 0.32/0.67            @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) )
% 0.32/0.67              = zero_zero_nat )
% 0.32/0.67            @ none_num
% 0.32/0.67            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % take_bit_num_def
% 0.32/0.67  thf(fact_10013_and__minus__numerals_I7_J,axiom,
% 0.32/0.67      ! [N: num,M: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_minus_numerals(7)
% 0.32/0.67  thf(fact_10014_and__minus__numerals_I3_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_minus_numerals(3)
% 0.32/0.67  thf(fact_10015_and__minus__numerals_I4_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_minus_numerals(4)
% 0.32/0.67  thf(fact_10016_and__minus__numerals_I8_J,axiom,
% 0.32/0.67      ! [N: num,M: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_minus_numerals(8)
% 0.32/0.67  thf(fact_10017_and__not__num_Osimps_I3_J,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 0.32/0.67        = none_num ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(3)
% 0.32/0.67  thf(fact_10018_and__not__num_Osimps_I1_J,axiom,
% 0.32/0.67      ( ( bit_and_not_num @ one @ one )
% 0.32/0.67      = none_num ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(1)
% 0.32/0.67  thf(fact_10019_and__not__num_Osimps_I4_J,axiom,
% 0.32/0.67      ! [M: num] :
% 0.32/0.67        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 0.32/0.67        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(4)
% 0.32/0.67  thf(fact_10020_and__not__num_Osimps_I2_J,axiom,
% 0.32/0.67      ! [N: num] :
% 0.32/0.67        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 0.32/0.67        = ( some_num @ one ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(2)
% 0.32/0.67  thf(fact_10021_and__not__num_Osimps_I7_J,axiom,
% 0.32/0.67      ! [M: num] :
% 0.32/0.67        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 0.32/0.67        = ( some_num @ ( bit0 @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(7)
% 0.32/0.67  thf(fact_10022_and__not__num__eq__Some__iff,axiom,
% 0.32/0.67      ! [M: num,N: num,Q2: num] :
% 0.32/0.67        ( ( ( bit_and_not_num @ M @ N )
% 0.32/0.67          = ( some_num @ Q2 ) )
% 0.32/0.67        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67          = ( numeral_numeral_int @ Q2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num_eq_Some_iff
% 0.32/0.67  thf(fact_10023_and__not__num_Osimps_I8_J,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/0.67        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.32/0.67          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 0.32/0.67          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num.simps(8)
% 0.32/0.67  thf(fact_10024_and__not__num__eq__None__iff,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( bit_and_not_num @ M @ N )
% 0.32/0.67          = none_num )
% 0.32/0.67        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67          = zero_zero_int ) ) ).
% 0.32/0.67  
% 0.32/0.67  % and_not_num_eq_None_iff
% 0.32/0.67  thf(fact_10025_int__numeral__not__and__num,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % int_numeral_not_and_num
% 0.32/0.67  thf(fact_10026_int__numeral__and__not__num,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.32/0.67        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % int_numeral_and_not_num
% 0.32/0.67  thf(fact_10027_Bit__Operations_Otake__bit__num__code,axiom,
% 0.32/0.67      ( bit_take_bit_num
% 0.32/0.67      = ( ^ [N2: nat,M3: num] :
% 0.32/0.67            ( produc478579273971653890on_num
% 0.32/0.67            @ ^ [A3: nat,X3: num] :
% 0.32/0.67                ( case_nat_option_num @ none_num
% 0.32/0.67                @ ^ [O: nat] :
% 0.32/0.67                    ( case_num_option_num @ ( some_num @ one )
% 0.32/0.67                    @ ^ [P2: num] :
% 0.32/0.67                        ( case_o6005452278849405969um_num @ none_num
% 0.32/0.67                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.32/0.67                        @ ( bit_take_bit_num @ O @ P2 ) )
% 0.32/0.67                    @ ^ [P2: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P2 ) ) )
% 0.32/0.67                    @ X3 )
% 0.32/0.67                @ A3 )
% 0.32/0.67            @ ( product_Pair_nat_num @ N2 @ M3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Bit_Operations.take_bit_num_code
% 0.32/0.67  thf(fact_10028_isCont__Lb__Ub,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67                & ( ord_less_eq_real @ X6 @ B ) )
% 0.32/0.67             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 0.32/0.67         => ? [L6: real,M9: real] :
% 0.32/0.67              ( ! [X4: real] :
% 0.32/0.67                  ( ( ( ord_less_eq_real @ A @ X4 )
% 0.32/0.67                    & ( ord_less_eq_real @ X4 @ B ) )
% 0.32/0.67                 => ( ( ord_less_eq_real @ L6 @ ( F @ X4 ) )
% 0.32/0.67                    & ( ord_less_eq_real @ ( F @ X4 ) @ M9 ) ) )
% 0.32/0.67              & ! [Y2: real] :
% 0.32/0.67                  ( ( ( ord_less_eq_real @ L6 @ Y2 )
% 0.32/0.67                    & ( ord_less_eq_real @ Y2 @ M9 ) )
% 0.32/0.67                 => ? [X6: real] :
% 0.32/0.67                      ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67                      & ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67                      & ( ( F @ X6 )
% 0.32/0.67                        = Y2 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_Lb_Ub
% 0.32/0.67  thf(fact_10029_isCont__real__sqrt,axiom,
% 0.32/0.67      ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_real_sqrt
% 0.32/0.67  thf(fact_10030_isCont__real__root,axiom,
% 0.32/0.67      ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_real_root
% 0.32/0.67  thf(fact_10031_isCont__inverse__function2,axiom,
% 0.32/0.67      ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ B )
% 0.32/0.67         => ( ! [Z5: real] :
% 0.32/0.67                ( ( ord_less_eq_real @ A @ Z5 )
% 0.32/0.67               => ( ( ord_less_eq_real @ Z5 @ B )
% 0.32/0.67                 => ( ( G @ ( F @ Z5 ) )
% 0.32/0.67                    = Z5 ) ) )
% 0.32/0.67           => ( ! [Z5: real] :
% 0.32/0.67                  ( ( ord_less_eq_real @ A @ Z5 )
% 0.32/0.67                 => ( ( ord_less_eq_real @ Z5 @ B )
% 0.32/0.67                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 0.32/0.67             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_inverse_function2
% 0.32/0.67  thf(fact_10032_isCont__ln,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( X != zero_zero_real )
% 0.32/0.67       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_ln
% 0.32/0.67  thf(fact_10033_isCont__arcosh,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.67       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_arcosh
% 0.32/0.67  thf(fact_10034_DERIV__inverse__function,axiom,
% 0.32/0.67      ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 0.32/0.67        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 0.32/0.67       => ( ( D4 != zero_zero_real )
% 0.32/0.67         => ( ( ord_less_real @ A @ X )
% 0.32/0.67           => ( ( ord_less_real @ X @ B )
% 0.32/0.67             => ( ! [Y5: real] :
% 0.32/0.67                    ( ( ord_less_real @ A @ Y5 )
% 0.32/0.67                   => ( ( ord_less_real @ Y5 @ B )
% 0.32/0.67                     => ( ( F @ ( G @ Y5 ) )
% 0.32/0.67                        = Y5 ) ) )
% 0.32/0.67               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_inverse_function
% 0.32/0.67  thf(fact_10035_isCont__arccos,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_arccos
% 0.32/0.67  thf(fact_10036_isCont__arcsin,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_arcsin
% 0.32/0.67  thf(fact_10037_LIM__less__bound,axiom,
% 0.32/0.67      ! [B: real,X: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ B @ X )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 0.32/0.67             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 0.32/0.67         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 0.32/0.67           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIM_less_bound
% 0.32/0.67  thf(fact_10038_isCont__artanh,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_artanh
% 0.32/0.67  thf(fact_10039_isCont__inverse__function,axiom,
% 0.32/0.67      ! [D: real,X: real,G: real > real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ D )
% 0.32/0.67       => ( ! [Z5: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 0.32/0.67             => ( ( G @ ( F @ Z5 ) )
% 0.32/0.67                = Z5 ) )
% 0.32/0.67         => ( ! [Z5: real] :
% 0.32/0.67                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 0.32/0.67               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) )
% 0.32/0.67           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % isCont_inverse_function
% 0.32/0.67  thf(fact_10040_GMVT_H,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [Z5: real] :
% 0.32/0.67              ( ( ord_less_eq_real @ A @ Z5 )
% 0.32/0.67             => ( ( ord_less_eq_real @ Z5 @ B )
% 0.32/0.67               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 0.32/0.67         => ( ! [Z5: real] :
% 0.32/0.67                ( ( ord_less_eq_real @ A @ Z5 )
% 0.32/0.67               => ( ( ord_less_eq_real @ Z5 @ B )
% 0.32/0.67                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ G ) ) )
% 0.32/0.67           => ( ! [Z5: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67                 => ( ( ord_less_real @ Z5 @ B )
% 0.32/0.67                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 0.32/0.67             => ( ! [Z5: real] :
% 0.32/0.67                    ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67                   => ( ( ord_less_real @ Z5 @ B )
% 0.32/0.67                     => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 0.32/0.67               => ? [C2: real] :
% 0.32/0.67                    ( ( ord_less_real @ A @ C2 )
% 0.32/0.67                    & ( ord_less_real @ C2 @ B )
% 0.32/0.67                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 0.32/0.67                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F5 @ C2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % GMVT'
% 0.32/0.67  thf(fact_10041_Gcd__eq__Max,axiom,
% 0.32/0.67      ! [M5: set_nat] :
% 0.32/0.67        ( ( finite_finite_nat @ M5 )
% 0.32/0.67       => ( ( M5 != bot_bot_set_nat )
% 0.32/0.67         => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.32/0.67           => ( ( gcd_Gcd_nat @ M5 )
% 0.32/0.67              = ( lattic8265883725875713057ax_nat
% 0.32/0.67                @ ( comple7806235888213564991et_nat
% 0.32/0.67                  @ ( image_nat_set_nat
% 0.32/0.67                    @ ^ [M3: nat] :
% 0.32/0.67                        ( collect_nat
% 0.32/0.67                        @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M3 ) )
% 0.32/0.67                    @ M5 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Gcd_eq_Max
% 0.32/0.67  thf(fact_10042_Max__divisors__self__nat,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( N != zero_zero_nat )
% 0.32/0.67       => ( ( lattic8265883725875713057ax_nat
% 0.32/0.67            @ ( collect_nat
% 0.32/0.67              @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 0.32/0.67          = N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Max_divisors_self_nat
% 0.32/0.67  thf(fact_10043_LIM__fun__less__zero,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,C: real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 0.32/0.67         => ? [R2: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.32/0.67              & ! [X4: real] :
% 0.32/0.67                  ( ( ( X4 != C )
% 0.32/0.67                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 0.32/0.67                 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIM_fun_less_zero
% 0.32/0.67  thf(fact_10044_LIM__fun__not__zero,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,C: real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.32/0.67       => ( ( L2 != zero_zero_real )
% 0.32/0.67         => ? [R2: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.32/0.67              & ! [X4: real] :
% 0.32/0.67                  ( ( ( X4 != C )
% 0.32/0.67                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 0.32/0.67                 => ( ( F @ X4 )
% 0.32/0.67                   != zero_zero_real ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIM_fun_not_zero
% 0.32/0.67  thf(fact_10045_LIM__fun__gt__zero,axiom,
% 0.32/0.67      ! [F: real > real,L2: real,C: real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.32/0.67       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 0.32/0.67         => ? [R2: real] :
% 0.32/0.67              ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.32/0.67              & ! [X4: real] :
% 0.32/0.67                  ( ( ( X4 != C )
% 0.32/0.67                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 0.32/0.67                 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIM_fun_gt_zero
% 0.32/0.67  thf(fact_10046_card__le__Suc__Max,axiom,
% 0.32/0.67      ! [S2: set_nat] :
% 0.32/0.67        ( ( finite_finite_nat @ S2 )
% 0.32/0.67       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % card_le_Suc_Max
% 0.32/0.67  thf(fact_10047_Sup__nat__def,axiom,
% 0.32/0.67      ( complete_Sup_Sup_nat
% 0.32/0.67      = ( ^ [X2: set_nat] : ( if_nat @ ( X2 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Sup_nat_def
% 0.32/0.67  thf(fact_10048_divide__nat__def,axiom,
% 0.32/0.67      ( divide_divide_nat
% 0.32/0.67      = ( ^ [M3: nat,N2: nat] :
% 0.32/0.67            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 0.32/0.67            @ ( lattic8265883725875713057ax_nat
% 0.32/0.67              @ ( collect_nat
% 0.32/0.67                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N2 ) @ M3 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % divide_nat_def
% 0.32/0.67  thf(fact_10049_gcd__is__Max__divisors__nat,axiom,
% 0.32/0.67      ! [N: nat,M: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( gcd_gcd_nat @ M @ N )
% 0.32/0.67          = ( lattic8265883725875713057ax_nat
% 0.32/0.67            @ ( collect_nat
% 0.32/0.67              @ ^ [D2: nat] :
% 0.32/0.67                  ( ( dvd_dvd_nat @ D2 @ M )
% 0.32/0.67                  & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_is_Max_divisors_nat
% 0.32/0.67  thf(fact_10050_LIM__cos__div__sin,axiom,
% 0.32/0.67      ( filterlim_real_real
% 0.32/0.67      @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 0.32/0.67      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIM_cos_div_sin
% 0.32/0.67  thf(fact_10051_summable__Leibniz_I3_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ( topolo6980174941875973593q_real @ A )
% 0.32/0.67         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.32/0.67           => ! [N7: nat] :
% 0.32/0.67                ( member_real
% 0.32/0.67                @ ( suminf_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.32/0.67                @ ( set_or1222579329274155063t_real
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz(3)
% 0.32/0.67  thf(fact_10052_summable__Leibniz_I2_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ( topolo6980174941875973593q_real @ A )
% 0.32/0.67         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.32/0.67           => ! [N7: nat] :
% 0.32/0.67                ( member_real
% 0.32/0.67                @ ( suminf_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.32/0.67                @ ( set_or1222579329274155063t_real
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 0.32/0.67                  @ ( groups6591440286371151544t_real
% 0.32/0.67                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz(2)
% 0.32/0.67  thf(fact_10053_Max__divisors__self__int,axiom,
% 0.32/0.67      ! [N: int] :
% 0.32/0.67        ( ( N != zero_zero_int )
% 0.32/0.67       => ( ( lattic8263393255366662781ax_int
% 0.32/0.67            @ ( collect_int
% 0.32/0.67              @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ N ) ) )
% 0.32/0.67          = ( abs_abs_int @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Max_divisors_self_int
% 0.32/0.67  thf(fact_10054_mult__nat__right__at__top,axiom,
% 0.32/0.67      ! [C: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.67       => ( filterlim_nat_nat
% 0.32/0.67          @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 0.32/0.67          @ at_top_nat
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mult_nat_right_at_top
% 0.32/0.67  thf(fact_10055_mult__nat__left__at__top,axiom,
% 0.32/0.67      ! [C: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.32/0.67       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mult_nat_left_at_top
% 0.32/0.67  thf(fact_10056_monoseq__convergent,axiom,
% 0.32/0.67      ! [X8: nat > real,B3: real] :
% 0.32/0.67        ( ( topolo6980174941875973593q_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 0.32/0.67         => ~ ! [L6: real] :
% 0.32/0.67                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % monoseq_convergent
% 0.32/0.67  thf(fact_10057_LIMSEQ__root,axiom,
% 0.32/0.67      ( filterlim_nat_real
% 0.32/0.67      @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.32/0.67      @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.32/0.67      @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_root
% 0.32/0.67  thf(fact_10058_gcd__is__Max__divisors__int,axiom,
% 0.32/0.67      ! [N: int,M: int] :
% 0.32/0.67        ( ( N != zero_zero_int )
% 0.32/0.67       => ( ( gcd_gcd_int @ M @ N )
% 0.32/0.67          = ( lattic8263393255366662781ax_int
% 0.32/0.67            @ ( collect_int
% 0.32/0.67              @ ^ [D2: int] :
% 0.32/0.67                  ( ( dvd_dvd_int @ D2 @ M )
% 0.32/0.67                  & ( dvd_dvd_int @ D2 @ N ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % gcd_is_Max_divisors_int
% 0.32/0.67  thf(fact_10059_nested__sequence__unique,axiom,
% 0.32/0.67      ! [F: nat > real,G: nat > real] :
% 0.32/0.67        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 0.32/0.67           => ( ( filterlim_nat_real
% 0.32/0.67                @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.32/0.67                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67                @ at_top_nat )
% 0.32/0.67             => ? [L4: real] :
% 0.32/0.67                  ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 0.32/0.67                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 0.32/0.67                  & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 0.32/0.67                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nested_sequence_unique
% 0.32/0.67  thf(fact_10060_LIMSEQ__inverse__zero,axiom,
% 0.32/0.67      ! [X8: nat > real] :
% 0.32/0.67        ( ! [R2: real] :
% 0.32/0.67          ? [N8: nat] :
% 0.32/0.67          ! [N3: nat] :
% 0.32/0.67            ( ( ord_less_eq_nat @ N8 @ N3 )
% 0.32/0.67           => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 0.32/0.67       => ( filterlim_nat_real
% 0.32/0.67          @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_zero
% 0.32/0.67  thf(fact_10061_lim__inverse__n_H,axiom,
% 0.32/0.67      ( filterlim_nat_real
% 0.32/0.67      @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 0.32/0.67      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67      @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % lim_inverse_n'
% 0.32/0.67  thf(fact_10062_LIMSEQ__root__const,axiom,
% 0.32/0.67      ! [C: real] :
% 0.32/0.67        ( ( ord_less_real @ zero_zero_real @ C )
% 0.32/0.67       => ( filterlim_nat_real
% 0.32/0.67          @ ^ [N2: nat] : ( root @ N2 @ C )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_root_const
% 0.32/0.67  thf(fact_10063_LIMSEQ__inverse__real__of__nat,axiom,
% 0.32/0.67      ( filterlim_nat_real
% 0.32/0.67      @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 0.32/0.67      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67      @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_real_of_nat
% 0.32/0.67  thf(fact_10064_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.32/0.67      ! [R: real] :
% 0.32/0.67        ( filterlim_nat_real
% 0.32/0.67        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ R )
% 0.32/0.67        @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_real_of_nat_add
% 0.32/0.67  thf(fact_10065_increasing__LIMSEQ,axiom,
% 0.32/0.67      ! [F: nat > real,L2: real] :
% 0.32/0.67        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 0.32/0.67         => ( ! [E2: real] :
% 0.32/0.67                ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.32/0.67               => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 0.32/0.67           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % increasing_LIMSEQ
% 0.32/0.67  thf(fact_10066_LIMSEQ__realpow__zero,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.67       => ( ( ord_less_real @ X @ one_one_real )
% 0.32/0.67         => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_realpow_zero
% 0.32/0.67  thf(fact_10067_LIMSEQ__divide__realpow__zero,axiom,
% 0.32/0.67      ! [X: real,A: real] :
% 0.32/0.67        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.67       => ( filterlim_nat_real
% 0.32/0.67          @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_divide_realpow_zero
% 0.32/0.67  thf(fact_10068_LIMSEQ__abs__realpow__zero,axiom,
% 0.32/0.67      ! [C: real] :
% 0.32/0.67        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.32/0.67       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_abs_realpow_zero
% 0.32/0.67  thf(fact_10069_LIMSEQ__abs__realpow__zero2,axiom,
% 0.32/0.67      ! [C: real] :
% 0.32/0.67        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 0.32/0.67       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_abs_realpow_zero2
% 0.32/0.67  thf(fact_10070_LIMSEQ__inverse__realpow__zero,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_real @ one_one_real @ X )
% 0.32/0.67       => ( filterlim_nat_real
% 0.32/0.67          @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_realpow_zero
% 0.32/0.67  thf(fact_10071_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.32/0.67      ! [R: real] :
% 0.32/0.67        ( filterlim_nat_real
% 0.32/0.67        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ R )
% 0.32/0.67        @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_real_of_nat_add_minus
% 0.32/0.67  thf(fact_10072_tendsto__exp__limit__sequentially,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( filterlim_nat_real
% 0.32/0.67        @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.32/0.67        @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_exp_limit_sequentially
% 0.32/0.67  thf(fact_10073_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.32/0.67      ! [R: real] :
% 0.32/0.67        ( filterlim_nat_real
% 0.32/0.67        @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ R )
% 0.32/0.67        @ at_top_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.32/0.67  thf(fact_10074_summable__Leibniz_I1_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ( topolo6980174941875973593q_real @ A )
% 0.32/0.67         => ( summable_real
% 0.32/0.67            @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz(1)
% 0.32/0.67  thf(fact_10075_summable,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67           => ( summable_real
% 0.32/0.67              @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable
% 0.32/0.67  thf(fact_10076_cos__diff__limit__1,axiom,
% 0.32/0.67      ! [Theta: nat > real,Theta2: real] :
% 0.32/0.67        ( ( filterlim_nat_real
% 0.32/0.67          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.32/0.67          @ at_top_nat )
% 0.32/0.67       => ~ ! [K3: nat > int] :
% 0.32/0.67              ~ ( filterlim_nat_real
% 0.32/0.67                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.67                @ ( topolo2815343760600316023s_real @ Theta2 )
% 0.32/0.67                @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % cos_diff_limit_1
% 0.32/0.67  thf(fact_10077_cos__limit__1,axiom,
% 0.32/0.67      ! [Theta: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real
% 0.32/0.67          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.32/0.67          @ at_top_nat )
% 0.32/0.67       => ? [K3: nat > int] :
% 0.32/0.67            ( filterlim_nat_real
% 0.32/0.67            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.32/0.67            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67            @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % cos_limit_1
% 0.32/0.67  thf(fact_10078_summable__Leibniz_I4_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ( topolo6980174941875973593q_real @ A )
% 0.32/0.67         => ( filterlim_nat_real
% 0.32/0.67            @ ^ [N2: nat] :
% 0.32/0.67                ( groups6591440286371151544t_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.67            @ ( topolo2815343760600316023s_real
% 0.32/0.67              @ ( suminf_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.32/0.67            @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz(4)
% 0.32/0.67  thf(fact_10079_zeroseq__arctan__series,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.67       => ( filterlim_nat_real
% 0.32/0.67          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.32/0.67          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % zeroseq_arctan_series
% 0.32/0.67  thf(fact_10080_summable__Leibniz_H_I2_J,axiom,
% 0.32/0.67      ! [A: nat > real,N: nat] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67           => ( ord_less_eq_real
% 0.32/0.67              @ ( groups6591440286371151544t_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.32/0.67              @ ( suminf_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz'(2)
% 0.32/0.67  thf(fact_10081_summable__Leibniz_H_I3_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67           => ( filterlim_nat_real
% 0.32/0.67              @ ^ [N2: nat] :
% 0.32/0.67                  ( groups6591440286371151544t_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.67              @ ( topolo2815343760600316023s_real
% 0.32/0.67                @ ( suminf_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.32/0.67              @ at_top_nat ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz'(3)
% 0.32/0.67  thf(fact_10082_sums__alternating__upper__lower,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67           => ? [L4: real] :
% 0.32/0.67                ( ! [N7: nat] :
% 0.32/0.67                    ( ord_less_eq_real
% 0.32/0.67                    @ ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 0.32/0.67                    @ L4 )
% 0.32/0.67                & ( filterlim_nat_real
% 0.32/0.67                  @ ^ [N2: nat] :
% 0.32/0.67                      ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.32/0.67                  @ at_top_nat )
% 0.32/0.67                & ! [N7: nat] :
% 0.32/0.67                    ( ord_less_eq_real @ L4
% 0.32/0.67                    @ ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 0.32/0.67                & ( filterlim_nat_real
% 0.32/0.67                  @ ^ [N2: nat] :
% 0.32/0.67                      ( groups6591440286371151544t_real
% 0.32/0.67                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ L4 )
% 0.32/0.67                  @ at_top_nat ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sums_alternating_upper_lower
% 0.32/0.67  thf(fact_10083_summable__Leibniz_I5_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ( topolo6980174941875973593q_real @ A )
% 0.32/0.67         => ( filterlim_nat_real
% 0.32/0.67            @ ^ [N2: nat] :
% 0.32/0.67                ( groups6591440286371151544t_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.32/0.67            @ ( topolo2815343760600316023s_real
% 0.32/0.67              @ ( suminf_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.32/0.67            @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz(5)
% 0.32/0.67  thf(fact_10084_summable__Leibniz_H_I4_J,axiom,
% 0.32/0.67      ! [A: nat > real,N: nat] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67           => ( ord_less_eq_real
% 0.32/0.67              @ ( suminf_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 0.32/0.67              @ ( groups6591440286371151544t_real
% 0.32/0.67                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz'(4)
% 0.32/0.67  thf(fact_10085_summable__Leibniz_H_I5_J,axiom,
% 0.32/0.67      ! [A: nat > real] :
% 0.32/0.67        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.32/0.67       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.32/0.67         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.32/0.67           => ( filterlim_nat_real
% 0.32/0.67              @ ^ [N2: nat] :
% 0.32/0.67                  ( groups6591440286371151544t_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 0.32/0.67                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 0.32/0.67              @ ( topolo2815343760600316023s_real
% 0.32/0.67                @ ( suminf_real
% 0.32/0.67                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 0.32/0.67              @ at_top_nat ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % summable_Leibniz'(5)
% 0.32/0.67  thf(fact_10086_real__bounded__linear,axiom,
% 0.32/0.67      ( real_V5970128139526366754l_real
% 0.32/0.67      = ( ^ [F6: real > real] :
% 0.32/0.67          ? [C3: real] :
% 0.32/0.67            ( F6
% 0.32/0.67            = ( ^ [X3: real] : ( times_times_real @ X3 @ C3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % real_bounded_linear
% 0.32/0.67  thf(fact_10087_tendsto__exp__limit__at__right,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( filterlim_real_real
% 0.32/0.67        @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y3 ) ) @ ( divide_divide_real @ one_one_real @ Y3 ) )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.32/0.67        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_exp_limit_at_right
% 0.32/0.67  thf(fact_10088_dist__real__def,axiom,
% 0.32/0.67      ( real_V975177566351809787t_real
% 0.32/0.67      = ( ^ [X3: real,Y3: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % dist_real_def
% 0.32/0.67  thf(fact_10089_dist__complex__def,axiom,
% 0.32/0.67      ( real_V3694042436643373181omplex
% 0.32/0.67      = ( ^ [X3: complex,Y3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % dist_complex_def
% 0.32/0.67  thf(fact_10090_tendsto__arcosh__at__left__1,axiom,
% 0.32/0.67      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_arcosh_at_left_1
% 0.32/0.67  thf(fact_10091_greaterThan__0,axiom,
% 0.32/0.67      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.32/0.67      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThan_0
% 0.32/0.67  thf(fact_10092_greaterThan__Suc,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.32/0.67        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThan_Suc
% 0.32/0.67  thf(fact_10093_INT__greaterThan__UNIV,axiom,
% 0.32/0.67      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.32/0.67      = bot_bot_set_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % INT_greaterThan_UNIV
% 0.32/0.67  thf(fact_10094_filterlim__tan__at__right,axiom,
% 0.32/0.67      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 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_tan_at_right
% 0.32/0.67  thf(fact_10095_atLeast__0,axiom,
% 0.32/0.67      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.32/0.67      = top_top_set_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast_0
% 0.32/0.67  thf(fact_10096_atLeast__Suc__greaterThan,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.32/0.67        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast_Suc_greaterThan
% 0.32/0.67  thf(fact_10097_exp__at__bot,axiom,
% 0.32/0.67      filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 0.32/0.67  
% 0.32/0.67  % exp_at_bot
% 0.32/0.67  thf(fact_10098_filterlim__inverse__at__bot__neg,axiom,
% 0.32/0.67      filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_inverse_at_bot_neg
% 0.32/0.67  thf(fact_10099_UN__atLeast__UNIV,axiom,
% 0.32/0.67      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.32/0.67      = top_top_set_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % UN_atLeast_UNIV
% 0.32/0.67  thf(fact_10100_atLeast__Suc,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.32/0.67        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast_Suc
% 0.32/0.67  thf(fact_10101_tanh__real__at__bot,axiom,
% 0.32/0.67      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 0.32/0.67  
% 0.32/0.67  % tanh_real_at_bot
% 0.32/0.67  thf(fact_10102_ln__at__0,axiom,
% 0.32/0.67      filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % ln_at_0
% 0.32/0.67  thf(fact_10103_artanh__real__at__right__1,axiom,
% 0.32/0.67      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 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % artanh_real_at_right_1
% 0.32/0.67  thf(fact_10104_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.32/0.67      ! [B: real,F: real > real,Flim: real] :
% 0.32/0.67        ( ! [X6: real] :
% 0.32/0.67            ( ( ord_less_eq_real @ X6 @ B )
% 0.32/0.67           => ? [Y2: real] :
% 0.32/0.67                ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                & ( ord_less_real @ zero_zero_real @ Y2 ) ) )
% 0.32/0.67       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.32/0.67         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pos_imp_increasing_at_bot
% 0.32/0.67  thf(fact_10105_filterlim__pow__at__bot__odd,axiom,
% 0.32/0.67      ! [N: nat,F: real > real,F3: filter_real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 0.32/0.67         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67           => ( filterlim_real_real
% 0.32/0.67              @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 0.32/0.67              @ at_bot_real
% 0.32/0.67              @ F3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_pow_at_bot_odd
% 0.32/0.67  thf(fact_10106_tendsto__arctan__at__bot,axiom,
% 0.32/0.67      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_arctan_at_bot
% 0.32/0.67  thf(fact_10107_filterlim__pow__at__bot__even,axiom,
% 0.32/0.67      ! [N: nat,F: real > real,F3: filter_real] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 0.32/0.67         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.32/0.67           => ( filterlim_real_real
% 0.32/0.67              @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 0.32/0.67              @ at_top_real
% 0.32/0.67              @ F3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_pow_at_bot_even
% 0.32/0.67  thf(fact_10108_at__bot__le__at__infinity,axiom,
% 0.32/0.67      ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 0.32/0.67  
% 0.32/0.67  % at_bot_le_at_infinity
% 0.32/0.67  thf(fact_10109_at__top__le__at__infinity,axiom,
% 0.32/0.67      ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 0.32/0.67  
% 0.32/0.67  % at_top_le_at_infinity
% 0.32/0.67  thf(fact_10110_sqrt__at__top,axiom,
% 0.32/0.67      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 0.32/0.67  
% 0.32/0.67  % sqrt_at_top
% 0.32/0.67  thf(fact_10111_tanh__real__at__top,axiom,
% 0.32/0.67      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 0.32/0.67  
% 0.32/0.67  % tanh_real_at_top
% 0.32/0.67  thf(fact_10112_artanh__real__at__left__1,axiom,
% 0.32/0.67      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % artanh_real_at_left_1
% 0.32/0.67  thf(fact_10113_ln__x__over__x__tendsto__0,axiom,
% 0.32/0.67      ( filterlim_real_real
% 0.32/0.67      @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 0.32/0.67      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67      @ at_top_real ) ).
% 0.32/0.67  
% 0.32/0.67  % ln_x_over_x_tendsto_0
% 0.32/0.67  thf(fact_10114_filterlim__inverse__at__top__right,axiom,
% 0.32/0.67      filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_inverse_at_top_right
% 0.32/0.67  thf(fact_10115_filterlim__inverse__at__right__top,axiom,
% 0.32/0.67      filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_inverse_at_right_top
% 0.32/0.67  thf(fact_10116_tendsto__power__div__exp__0,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( filterlim_real_real
% 0.32/0.67        @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.32/0.67        @ at_top_real ) ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_power_div_exp_0
% 0.32/0.67  thf(fact_10117_tendsto__exp__limit__at__top,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( filterlim_real_real
% 0.32/0.67        @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y3 ) ) @ Y3 )
% 0.32/0.67        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.32/0.67        @ at_top_real ) ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_exp_limit_at_top
% 0.32/0.67  thf(fact_10118_filterlim__tan__at__left,axiom,
% 0.32/0.67      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 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filterlim_tan_at_left
% 0.32/0.67  thf(fact_10119_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.32/0.67      ! [B: real,F: real > real,Flim: real] :
% 0.32/0.67        ( ! [X6: real] :
% 0.32/0.67            ( ( ord_less_eq_real @ B @ X6 )
% 0.32/0.67           => ? [Y2: real] :
% 0.32/0.67                ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                & ( ord_less_real @ Y2 @ zero_zero_real ) ) )
% 0.32/0.67       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.32/0.67         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_neg_imp_decreasing_at_top
% 0.32/0.67  thf(fact_10120_tendsto__arctan__at__top,axiom,
% 0.32/0.67      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 0.32/0.67  
% 0.32/0.67  % tendsto_arctan_at_top
% 0.32/0.67  thf(fact_10121_lhopital__left__at__top,axiom,
% 0.32/0.67      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 0.32/0.67        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67       => ( ( eventually_real
% 0.32/0.67            @ ^ [X3: real] :
% 0.32/0.67                ( ( G2 @ X3 )
% 0.32/0.67               != zero_zero_real )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67             => ( ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67               => ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_left_at_top
% 0.32/0.67  thf(fact_10122_eventually__sequentially__seg,axiom,
% 0.32/0.67      ! [P: nat > $o,K: nat] :
% 0.32/0.67        ( ( eventually_nat
% 0.32/0.67          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 0.32/0.67          @ at_top_nat )
% 0.32/0.67        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_sequentially_seg
% 0.32/0.67  thf(fact_10123_eventually__sequentiallyI,axiom,
% 0.32/0.67      ! [C: nat,P: nat > $o] :
% 0.32/0.67        ( ! [X6: nat] :
% 0.32/0.67            ( ( ord_less_eq_nat @ C @ X6 )
% 0.32/0.67           => ( P @ X6 ) )
% 0.32/0.67       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_sequentiallyI
% 0.32/0.67  thf(fact_10124_eventually__sequentially,axiom,
% 0.32/0.67      ! [P: nat > $o] :
% 0.32/0.67        ( ( eventually_nat @ P @ at_top_nat )
% 0.32/0.67        = ( ? [N6: nat] :
% 0.32/0.67            ! [N2: nat] :
% 0.32/0.67              ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.32/0.67             => ( P @ N2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_sequentially
% 0.32/0.67  thf(fact_10125_le__sequentially,axiom,
% 0.32/0.67      ! [F3: filter_nat] :
% 0.32/0.67        ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 0.32/0.67        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F3 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % le_sequentially
% 0.32/0.67  thf(fact_10126_sequentially__offset,axiom,
% 0.32/0.67      ! [P: nat > $o,K: nat] :
% 0.32/0.67        ( ( eventually_nat @ P @ at_top_nat )
% 0.32/0.67       => ( eventually_nat
% 0.32/0.67          @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 0.32/0.67          @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sequentially_offset
% 0.32/0.67  thf(fact_10127_eventually__at__right__to__0,axiom,
% 0.32/0.67      ! [P: real > $o,A: real] :
% 0.32/0.67        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.32/0.67        = ( eventually_real
% 0.32/0.67          @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A ) )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_at_right_to_0
% 0.32/0.67  thf(fact_10128_eventually__at__top__to__right,axiom,
% 0.32/0.67      ! [P: real > $o] :
% 0.32/0.67        ( ( eventually_real @ P @ at_top_real )
% 0.32/0.67        = ( eventually_real
% 0.32/0.67          @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_at_top_to_right
% 0.32/0.67  thf(fact_10129_eventually__at__right__to__top,axiom,
% 0.32/0.67      ! [P: real > $o] :
% 0.32/0.67        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67        = ( eventually_real
% 0.32/0.67          @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 0.32/0.67          @ at_top_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_at_right_to_top
% 0.32/0.67  thf(fact_10130_lhopital,axiom,
% 0.32/0.67      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] :
% 0.32/0.67                  ( ( G @ X3 )
% 0.32/0.67                 != zero_zero_real )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] :
% 0.32/0.67                    ( ( G2 @ X3 )
% 0.32/0.67                   != zero_zero_real )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67             => ( ( eventually_real
% 0.32/0.67                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67               => ( ( eventually_real
% 0.32/0.67                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                    @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67                 => ( ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67                   => ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital
% 0.32/0.67  thf(fact_10131_lhopital__at__top,axiom,
% 0.32/0.67      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 0.32/0.67        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67       => ( ( eventually_real
% 0.32/0.67            @ ^ [X3: real] :
% 0.32/0.67                ( ( G2 @ X3 )
% 0.32/0.67               != zero_zero_real )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67             => ( ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.32/0.67               => ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_at_top
% 0.32/0.67  thf(fact_10132_lhospital__at__top__at__top,axiom,
% 0.32/0.67      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 0.32/0.67        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 0.32/0.67       => ( ( eventually_real
% 0.32/0.67            @ ^ [X3: real] :
% 0.32/0.67                ( ( G2 @ X3 )
% 0.32/0.67               != zero_zero_real )
% 0.32/0.67            @ at_top_real )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67              @ at_top_real )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                @ at_top_real )
% 0.32/0.67             => ( ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ X )
% 0.32/0.67                  @ at_top_real )
% 0.32/0.67               => ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ X )
% 0.32/0.67                  @ at_top_real ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhospital_at_top_at_top
% 0.32/0.67  thf(fact_10133_lhopital__right,axiom,
% 0.32/0.67      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] :
% 0.32/0.67                  ( ( G @ X3 )
% 0.32/0.67                 != zero_zero_real )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] :
% 0.32/0.67                    ( ( G2 @ X3 )
% 0.32/0.67                   != zero_zero_real )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67             => ( ( eventually_real
% 0.32/0.67                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67               => ( ( eventually_real
% 0.32/0.67                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67                 => ( ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67                   => ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_right
% 0.32/0.67  thf(fact_10134_lhopital__right__0,axiom,
% 0.32/0.67      ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 0.32/0.67        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] :
% 0.32/0.67                  ( ( G0 @ X3 )
% 0.32/0.67                 != zero_zero_real )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] :
% 0.32/0.67                    ( ( G2 @ X3 )
% 0.32/0.67                   != zero_zero_real )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67             => ( ( eventually_real
% 0.32/0.67                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67               => ( ( eventually_real
% 0.32/0.67                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67                 => ( ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67                   => ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_right_0
% 0.32/0.67  thf(fact_10135_lhopital__left,axiom,
% 0.32/0.67      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 0.32/0.67        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] :
% 0.32/0.67                  ( ( G @ X3 )
% 0.32/0.67                 != zero_zero_real )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] :
% 0.32/0.67                    ( ( G2 @ X3 )
% 0.32/0.67                   != zero_zero_real )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67             => ( ( eventually_real
% 0.32/0.67                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67               => ( ( eventually_real
% 0.32/0.67                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67                 => ( ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 0.32/0.67                   => ( filterlim_real_real
% 0.32/0.67                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                      @ F3
% 0.32/0.67                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_left
% 0.32/0.67  thf(fact_10136_lhopital__right__at__top,axiom,
% 0.32/0.67      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 0.32/0.67        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67       => ( ( eventually_real
% 0.32/0.67            @ ^ [X3: real] :
% 0.32/0.67                ( ( G2 @ X3 )
% 0.32/0.67               != zero_zero_real )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67             => ( ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 0.32/0.67               => ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ Y )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_right_at_top
% 0.32/0.67  thf(fact_10137_lhopital__right__0__at__top,axiom,
% 0.32/0.67      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 0.32/0.67        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67       => ( ( eventually_real
% 0.32/0.67            @ ^ [X3: real] :
% 0.32/0.67                ( ( G2 @ X3 )
% 0.32/0.67               != zero_zero_real )
% 0.32/0.67            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67         => ( ( eventually_real
% 0.32/0.67              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67           => ( ( eventually_real
% 0.32/0.67                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.32/0.67                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67             => ( ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ X )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67               => ( filterlim_real_real
% 0.32/0.67                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/0.67                  @ ( topolo2815343760600316023s_real @ X )
% 0.32/0.67                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % lhopital_right_0_at_top
% 0.32/0.67  thf(fact_10138_GreatestI__nat,axiom,
% 0.32/0.67      ! [P: nat > $o,K: nat,B: nat] :
% 0.32/0.67        ( ( P @ K )
% 0.32/0.67       => ( ! [Y5: nat] :
% 0.32/0.67              ( ( P @ Y5 )
% 0.32/0.67             => ( ord_less_eq_nat @ Y5 @ B ) )
% 0.32/0.67         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % GreatestI_nat
% 0.32/0.67  thf(fact_10139_Greatest__le__nat,axiom,
% 0.32/0.67      ! [P: nat > $o,K: nat,B: nat] :
% 0.32/0.67        ( ( P @ K )
% 0.32/0.67       => ( ! [Y5: nat] :
% 0.32/0.67              ( ( P @ Y5 )
% 0.32/0.67             => ( ord_less_eq_nat @ Y5 @ B ) )
% 0.32/0.67         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Greatest_le_nat
% 0.32/0.67  thf(fact_10140_GreatestI__ex__nat,axiom,
% 0.32/0.67      ! [P: nat > $o,B: nat] :
% 0.32/0.67        ( ? [X_12: nat] : ( P @ X_12 )
% 0.32/0.67       => ( ! [Y5: nat] :
% 0.32/0.67              ( ( P @ Y5 )
% 0.32/0.67             => ( ord_less_eq_nat @ Y5 @ B ) )
% 0.32/0.67         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % GreatestI_ex_nat
% 0.32/0.67  thf(fact_10141_Bseq__eq__bounded,axiom,
% 0.32/0.67      ! [F: nat > real,A: real,B: real] :
% 0.32/0.67        ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.32/0.67       => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Bseq_eq_bounded
% 0.32/0.67  thf(fact_10142_Bseq__realpow,axiom,
% 0.32/0.67      ! [X: real] :
% 0.32/0.67        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.32/0.67       => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.32/0.67         => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Bseq_realpow
% 0.32/0.67  thf(fact_10143_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.67        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( X
% 0.32/0.67                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67           => ( Xa2 = one_one_nat ) )
% 0.32/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67               => ( ( Deg2 = Xa2 )
% 0.32/0.67                  & ! [X6: vEBT_VEBT] :
% 0.32/0.67                      ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                     => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                  & ( case_o184042715313410164at_nat
% 0.32/0.67                    @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                      & ! [X3: vEBT_VEBT] :
% 0.32/0.67                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                         => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                    @ ( produc6081775807080527818_nat_o
% 0.32/0.67                      @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                          & ! [I5: nat] :
% 0.32/0.67                              ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                             => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                          & ( ( Mi3 = Ma3 )
% 0.32/0.67                           => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                          & ( ( Mi3 != Ma3 )
% 0.32/0.67                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                              & ! [X3: nat] :
% 0.32/0.67                                  ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                   => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                      & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                    @ Mima ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.elims(3)
% 0.32/0.67  thf(fact_10144_decseq__bounded,axiom,
% 0.32/0.67      ! [X8: nat > real,B3: real] :
% 0.32/0.67        ( ( order_9091379641038594480t_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 0.32/0.67         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % decseq_bounded
% 0.32/0.67  thf(fact_10145_decseq__convergent,axiom,
% 0.32/0.67      ! [X8: nat > real,B3: real] :
% 0.32/0.67        ( ( order_9091379641038594480t_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 0.32/0.67         => ~ ! [L6: real] :
% 0.32/0.67                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.32/0.67               => ~ ! [I2: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % decseq_convergent
% 0.32/0.67  thf(fact_10146_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.32/0.67      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 0.32/0.67        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 0.32/0.67        = ( ( Deg = Deg4 )
% 0.32/0.67          & ! [X3: vEBT_VEBT] :
% 0.32/0.67              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.67             => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.32/0.67            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67          & ( case_o184042715313410164at_nat
% 0.32/0.67            @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X2 )
% 0.32/0.67              & ! [X3: vEBT_VEBT] :
% 0.32/0.67                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.67                 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67            @ ( produc6081775807080527818_nat_o
% 0.32/0.67              @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.32/0.67                  & ! [I5: nat] :
% 0.32/0.67                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X2 ) )
% 0.32/0.67                        = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 0.32/0.67                  & ( ( Mi3 = Ma3 )
% 0.32/0.67                   => ! [X3: vEBT_VEBT] :
% 0.32/0.67                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.32/0.67                       => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                  & ( ( Mi3 != Ma3 )
% 0.32/0.67                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.32/0.67                      & ! [X3: nat] :
% 0.32/0.67                          ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.32/0.67                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 0.32/0.67                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67            @ Mima2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.simps(2)
% 0.32/0.67  thf(fact_10147_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.67        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( X
% 0.32/0.67                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67           => ( Y
% 0.32/0.67              = ( Xa2 != one_one_nat ) ) )
% 0.32/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67               => ( Y
% 0.32/0.67                  = ( ~ ( ( Deg2 = Xa2 )
% 0.32/0.67                        & ! [X3: vEBT_VEBT] :
% 0.32/0.67                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                           => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                        & ( case_o184042715313410164at_nat
% 0.32/0.67                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                            & ! [X3: vEBT_VEBT] :
% 0.32/0.67                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                          @ ( produc6081775807080527818_nat_o
% 0.32/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                & ! [I5: nat] :
% 0.32/0.67                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                                & ( ( Mi3 = Ma3 )
% 0.32/0.67                                 => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                                & ( ( Mi3 != Ma3 )
% 0.32/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                                    & ! [X3: nat] :
% 0.32/0.67                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                          @ Mima ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.elims(1)
% 0.32/0.67  thf(fact_10148_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.67        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67       => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( X
% 0.32/0.67                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67           => ( Xa2 != one_one_nat ) )
% 0.32/0.67         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67               => ~ ( ( Deg2 = Xa2 )
% 0.32/0.67                    & ! [X4: vEBT_VEBT] :
% 0.32/0.67                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                       => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                    & ( case_o184042715313410164at_nat
% 0.32/0.67                      @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                        & ! [X3: vEBT_VEBT] :
% 0.32/0.67                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                           => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                      @ ( produc6081775807080527818_nat_o
% 0.32/0.67                        @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                            & ! [I5: nat] :
% 0.32/0.67                                ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                               => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                            & ( ( Mi3 = Ma3 )
% 0.32/0.67                             => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                                 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                            & ( ( Mi3 != Ma3 )
% 0.32/0.67                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                                & ! [X3: nat] :
% 0.32/0.67                                    ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                     => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                        & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                      @ Mima ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.elims(2)
% 0.32/0.67  thf(fact_10149_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.67        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.67         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.32/0.67                 => ( Xa2 = one_one_nat ) ) )
% 0.32/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                  ( ( X
% 0.32/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.32/0.67                   => ( ( Deg2 = Xa2 )
% 0.32/0.67                      & ! [X6: vEBT_VEBT] :
% 0.32/0.67                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                         => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                      & ( case_o184042715313410164at_nat
% 0.32/0.67                        @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                          & ! [X3: vEBT_VEBT] :
% 0.32/0.67                              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                             => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                        @ ( produc6081775807080527818_nat_o
% 0.32/0.67                          @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                              & ! [I5: nat] :
% 0.32/0.67                                  ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                                 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                              & ( ( Mi3 = Ma3 )
% 0.32/0.67                               => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                              & ( ( Mi3 != Ma3 )
% 0.32/0.67                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                                  & ! [X3: nat] :
% 0.32/0.67                                      ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                       => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                          & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                        @ Mima ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.pelims(3)
% 0.32/0.67  thf(fact_10150_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat] :
% 0.32/0.67        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.67         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.32/0.67                 => ( Xa2 != one_one_nat ) ) )
% 0.32/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                  ( ( X
% 0.32/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 0.32/0.67                   => ~ ( ( Deg2 = Xa2 )
% 0.32/0.67                        & ! [X4: vEBT_VEBT] :
% 0.32/0.67                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                           => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                        & ( case_o184042715313410164at_nat
% 0.32/0.67                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                            & ! [X3: vEBT_VEBT] :
% 0.32/0.67                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                          @ ( produc6081775807080527818_nat_o
% 0.32/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                & ! [I5: nat] :
% 0.32/0.67                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                                & ( ( Mi3 = Ma3 )
% 0.32/0.67                                 => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                                & ( ( Mi3 != Ma3 )
% 0.32/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                                    & ! [X3: nat] :
% 0.32/0.67                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                          @ Mima ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.pelims(2)
% 0.32/0.67  thf(fact_10151_Sup__int__def,axiom,
% 0.32/0.67      ( complete_Sup_Sup_int
% 0.32/0.67      = ( ^ [X2: set_int] :
% 0.32/0.67            ( the_int
% 0.32/0.67            @ ^ [X3: int] :
% 0.32/0.67                ( ( member_int @ X3 @ X2 )
% 0.32/0.67                & ! [Y3: int] :
% 0.32/0.67                    ( ( member_int @ Y3 @ X2 )
% 0.32/0.67                   => ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Sup_int_def
% 0.32/0.67  thf(fact_10152_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.32/0.67        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.32/0.67          = Y )
% 0.32/0.67       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.32/0.67         => ( ! [Uu2: $o,Uv2: $o] :
% 0.32/0.67                ( ( X
% 0.32/0.67                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.32/0.67               => ( ( Y
% 0.32/0.67                    = ( Xa2 = one_one_nat ) )
% 0.32/0.67                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.32/0.67           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.32/0.67                  ( ( X
% 0.32/0.67                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 0.32/0.67                 => ( ( Y
% 0.32/0.67                      = ( ( Deg2 = Xa2 )
% 0.32/0.67                        & ! [X3: vEBT_VEBT] :
% 0.32/0.67                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                           => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.32/0.67                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.32/0.67                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                        & ( case_o184042715313410164at_nat
% 0.32/0.67                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 0.32/0.67                            & ! [X3: vEBT_VEBT] :
% 0.32/0.67                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                          @ ( produc6081775807080527818_nat_o
% 0.32/0.67                            @ ^ [Mi3: nat,Ma3: nat] :
% 0.32/0.67                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.32/0.67                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                & ! [I5: nat] :
% 0.32/0.67                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.32/0.67                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 0.32/0.67                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 0.32/0.67                                & ( ( Mi3 = Ma3 )
% 0.32/0.67                                 => ! [X3: vEBT_VEBT] :
% 0.32/0.67                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.32/0.67                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 0.32/0.67                                & ( ( Mi3 != Ma3 )
% 0.32/0.67                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 0.32/0.67                                    & ! [X3: nat] :
% 0.32/0.67                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.32/0.67                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 0.32/0.67                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 0.32/0.67                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 0.32/0.67                          @ Mima ) ) )
% 0.32/0.67                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % VEBT_internal.valid'.pelims(1)
% 0.32/0.67  thf(fact_10153_GMVT,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,G: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67                & ( ord_less_eq_real @ X6 @ B ) )
% 0.32/0.67             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 0.32/0.67         => ( ! [X6: real] :
% 0.32/0.67                ( ( ( ord_less_real @ A @ X6 )
% 0.32/0.67                  & ( ord_less_real @ X6 @ B ) )
% 0.32/0.67               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 0.32/0.67           => ( ! [X6: real] :
% 0.32/0.67                  ( ( ( ord_less_eq_real @ A @ X6 )
% 0.32/0.67                    & ( ord_less_eq_real @ X6 @ B ) )
% 0.32/0.67                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ G ) )
% 0.32/0.67             => ( ! [X6: real] :
% 0.32/0.67                    ( ( ( ord_less_real @ A @ X6 )
% 0.32/0.67                      & ( ord_less_real @ X6 @ B ) )
% 0.32/0.67                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 0.32/0.67               => ? [G_c: real,F_c: real,C2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.32/0.67                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_real @ A @ C2 )
% 0.32/0.67                    & ( ord_less_real @ C2 @ B )
% 0.32/0.67                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 0.32/0.67                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % GMVT
% 0.32/0.67  thf(fact_10154_MVT,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67         => ( ! [X6: real] :
% 0.32/0.67                ( ( ord_less_real @ A @ X6 )
% 0.32/0.67               => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67           => ? [L4: real,Z5: real] :
% 0.32/0.67                ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67                & ( ord_less_real @ Z5 @ B )
% 0.32/0.67                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) )
% 0.32/0.67                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.32/0.67                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % MVT
% 0.32/0.67  thf(fact_10155_continuous__on__arcosh_H,axiom,
% 0.32/0.67      ! [A2: set_real,F: real > real] :
% 0.32/0.67        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( member_real @ X6 @ A2 )
% 0.32/0.67             => ( ord_less_eq_real @ one_one_real @ ( F @ X6 ) ) )
% 0.32/0.67         => ( topolo5044208981011980120l_real @ A2
% 0.32/0.67            @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_arcosh'
% 0.32/0.67  thf(fact_10156_continuous__image__closed__interval,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_eq_real @ A @ B )
% 0.32/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67         => ? [C2: real,D3: real] :
% 0.32/0.67              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.32/0.67                = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 0.32/0.67              & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % continuous_image_closed_interval
% 0.32/0.67  thf(fact_10157_continuous__on__arcosh,axiom,
% 0.32/0.67      ! [A2: set_real] :
% 0.32/0.67        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 0.32/0.67       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_arcosh
% 0.32/0.67  thf(fact_10158_continuous__on__arccos_H,axiom,
% 0.32/0.67      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_arccos'
% 0.32/0.67  thf(fact_10159_continuous__on__arcsin_H,axiom,
% 0.32/0.67      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_arcsin'
% 0.32/0.67  thf(fact_10160_continuous__on__artanh_H,axiom,
% 0.32/0.67      ! [A2: set_real,F: real > real] :
% 0.32/0.67        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( member_real @ X6 @ A2 )
% 0.32/0.67             => ( member_real @ ( F @ X6 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 0.32/0.67         => ( topolo5044208981011980120l_real @ A2
% 0.32/0.67            @ ^ [X3: real] : ( artanh_real @ ( F @ X3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_artanh'
% 0.32/0.67  thf(fact_10161_Rolle__deriv,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( ( F @ A )
% 0.32/0.67            = ( F @ B ) )
% 0.32/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67           => ( ! [X6: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ X6 )
% 0.32/0.67                 => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                   => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67             => ? [Z5: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67                  & ( ord_less_real @ Z5 @ B )
% 0.32/0.67                  & ( ( F5 @ Z5 )
% 0.32/0.67                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Rolle_deriv
% 0.32/0.67  thf(fact_10162_mvt,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67         => ( ! [X6: real] :
% 0.32/0.67                ( ( ord_less_real @ A @ X6 )
% 0.32/0.67               => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67           => ~ ! [Xi: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ Xi )
% 0.32/0.67                 => ( ( ord_less_real @ Xi @ B )
% 0.32/0.67                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.32/0.67                     != ( F5 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mvt
% 0.32/0.67  thf(fact_10163_DERIV__isconst__end,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67         => ( ! [X6: real] :
% 0.32/0.67                ( ( ord_less_real @ A @ X6 )
% 0.32/0.67               => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67           => ( ( F @ B )
% 0.32/0.67              = ( F @ A ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_isconst_end
% 0.32/0.67  thf(fact_10164_DERIV__neg__imp__decreasing__open,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 0.32/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_neg_imp_decreasing_open
% 0.32/0.67  thf(fact_10165_DERIV__pos__imp__increasing__open,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ! [X6: real] :
% 0.32/0.67              ( ( ord_less_real @ A @ X6 )
% 0.32/0.67             => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67               => ? [Y2: real] :
% 0.32/0.67                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 0.32/0.67                    & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 0.32/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_pos_imp_increasing_open
% 0.32/0.67  thf(fact_10166_continuous__on__artanh,axiom,
% 0.32/0.67      ! [A2: set_real] :
% 0.32/0.67        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 0.32/0.67       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % continuous_on_artanh
% 0.32/0.67  thf(fact_10167_DERIV__isconst2,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real,X: real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67         => ( ! [X6: real] :
% 0.32/0.67                ( ( ord_less_real @ A @ X6 )
% 0.32/0.67               => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67           => ( ( ord_less_eq_real @ A @ X )
% 0.32/0.67             => ( ( ord_less_eq_real @ X @ B )
% 0.32/0.67               => ( ( F @ X )
% 0.32/0.67                  = ( F @ A ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % DERIV_isconst2
% 0.32/0.67  thf(fact_10168_Rolle,axiom,
% 0.32/0.67      ! [A: real,B: real,F: real > real] :
% 0.32/0.67        ( ( ord_less_real @ A @ B )
% 0.32/0.67       => ( ( ( F @ A )
% 0.32/0.67            = ( F @ B ) )
% 0.32/0.67         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 0.32/0.67           => ( ! [X6: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ X6 )
% 0.32/0.67                 => ( ( ord_less_real @ X6 @ B )
% 0.32/0.67                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 0.32/0.67             => ? [Z5: real] :
% 0.32/0.67                  ( ( ord_less_real @ A @ Z5 )
% 0.32/0.67                  & ( ord_less_real @ Z5 @ B )
% 0.32/0.67                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % Rolle
% 0.32/0.67  thf(fact_10169_uniformity__real__def,axiom,
% 0.32/0.67      ( topolo1511823702728130853y_real
% 0.32/0.67      = ( comple2936214249959783750l_real
% 0.32/0.67        @ ( image_2178119161166701260l_real
% 0.32/0.67          @ ^ [E3: real] :
% 0.32/0.67              ( princi6114159922880469582l_real
% 0.32/0.67              @ ( collec3799799289383736868l_real
% 0.32/0.67                @ ( produc5414030515140494994real_o
% 0.32/0.67                  @ ^ [X3: real,Y3: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X3 @ Y3 ) @ E3 ) ) ) )
% 0.32/0.67          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % uniformity_real_def
% 0.32/0.67  thf(fact_10170_uniformity__complex__def,axiom,
% 0.32/0.67      ( topolo896644834953643431omplex
% 0.32/0.67      = ( comple8358262395181532106omplex
% 0.32/0.67        @ ( image_5971271580939081552omplex
% 0.32/0.67          @ ^ [E3: real] :
% 0.32/0.67              ( princi3496590319149328850omplex
% 0.32/0.67              @ ( collec8663557070575231912omplex
% 0.32/0.67                @ ( produc6771430404735790350plex_o
% 0.32/0.67                  @ ^ [X3: complex,Y3: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X3 @ Y3 ) @ E3 ) ) ) )
% 0.32/0.67          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % uniformity_complex_def
% 0.32/0.67  thf(fact_10171_eventually__prod__sequentially,axiom,
% 0.32/0.67      ! [P: product_prod_nat_nat > $o] :
% 0.32/0.67        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.32/0.67        = ( ? [N6: nat] :
% 0.32/0.67            ! [M3: nat] :
% 0.32/0.67              ( ( ord_less_eq_nat @ N6 @ M3 )
% 0.32/0.67             => ! [N2: nat] :
% 0.32/0.67                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.32/0.67                 => ( P @ ( product_Pair_nat_nat @ N2 @ M3 ) ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % eventually_prod_sequentially
% 0.32/0.67  thf(fact_10172_mono__times__nat,axiom,
% 0.32/0.67      ! [N: nat] :
% 0.32/0.67        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.67       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mono_times_nat
% 0.32/0.67  thf(fact_10173_mono__Suc,axiom,
% 0.32/0.67      order_mono_nat_nat @ suc ).
% 0.32/0.67  
% 0.32/0.67  % mono_Suc
% 0.32/0.67  thf(fact_10174_incseq__bounded,axiom,
% 0.32/0.67      ! [X8: nat > real,B3: real] :
% 0.32/0.67        ( ( order_mono_nat_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 0.32/0.67         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % incseq_bounded
% 0.32/0.67  thf(fact_10175_filtermap__at__right__shift,axiom,
% 0.32/0.67      ! [D: real,A: real] :
% 0.32/0.67        ( ( filtermap_real_real
% 0.32/0.67          @ ^ [X3: real] : ( minus_minus_real @ X3 @ D )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 0.32/0.67        = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % filtermap_at_right_shift
% 0.32/0.67  thf(fact_10176_incseq__convergent,axiom,
% 0.32/0.67      ! [X8: nat > real,B3: real] :
% 0.32/0.67        ( ( order_mono_nat_real @ X8 )
% 0.32/0.67       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 0.32/0.67         => ~ ! [L6: real] :
% 0.32/0.67                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 0.32/0.67               => ~ ! [I2: nat] : ( ord_less_eq_real @ ( X8 @ I2 ) @ L6 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % incseq_convergent
% 0.32/0.67  thf(fact_10177_at__right__to__0,axiom,
% 0.32/0.67      ! [A: real] :
% 0.32/0.67        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 0.32/0.67        = ( filtermap_real_real
% 0.32/0.67          @ ^ [X3: real] : ( plus_plus_real @ X3 @ A )
% 0.32/0.67          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % at_right_to_0
% 0.32/0.67  thf(fact_10178_at__right__to__top,axiom,
% 0.32/0.67      ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 0.32/0.67      = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 0.32/0.67  
% 0.32/0.67  % at_right_to_top
% 0.32/0.67  thf(fact_10179_at__top__to__right,axiom,
% 0.32/0.67      ( at_top_real
% 0.32/0.67      = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % at_top_to_right
% 0.32/0.67  thf(fact_10180_filtermap__ln__at__right,axiom,
% 0.32/0.67      ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 0.32/0.67      = at_bot_real ) ).
% 0.32/0.67  
% 0.32/0.67  % filtermap_ln_at_right
% 0.32/0.67  thf(fact_10181_mono__ge2__power__minus__self,axiom,
% 0.32/0.67      ! [K: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.32/0.67       => ( order_mono_nat_nat
% 0.32/0.67          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % mono_ge2_power_minus_self
% 0.32/0.67  thf(fact_10182_remdups__upt,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( remdups_nat @ ( upt @ M @ N ) )
% 0.32/0.67        = ( upt @ M @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % remdups_upt
% 0.32/0.67  thf(fact_10183_length__upt,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 0.32/0.67        = ( minus_minus_nat @ J @ I ) ) ).
% 0.32/0.67  
% 0.32/0.67  % length_upt
% 0.32/0.67  thf(fact_10184_upt__conv__Nil,axiom,
% 0.32/0.67      ! [J: nat,I: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ J @ I )
% 0.32/0.67       => ( ( upt @ I @ J )
% 0.32/0.67          = nil_nat ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_conv_Nil
% 0.32/0.67  thf(fact_10185_sorted__list__of__set__range,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.32/0.67        = ( upt @ M @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sorted_list_of_set_range
% 0.32/0.67  thf(fact_10186_upt__eq__Nil__conv,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ( upt @ I @ J )
% 0.32/0.67          = nil_nat )
% 0.32/0.67        = ( ( J = zero_zero_nat )
% 0.32/0.67          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_eq_Nil_conv
% 0.32/0.67  thf(fact_10187_nth__upt,axiom,
% 0.32/0.67      ! [I: nat,K: nat,J: nat] :
% 0.32/0.67        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.32/0.67       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.32/0.67          = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % nth_upt
% 0.32/0.67  thf(fact_10188_upt__rec__numeral,axiom,
% 0.32/0.67      ! [M: num,N: num] :
% 0.32/0.67        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.67         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.67            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.67         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.32/0.67            = nil_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_rec_numeral
% 0.32/0.67  thf(fact_10189_atLeast__upt,axiom,
% 0.32/0.67      ( set_ord_lessThan_nat
% 0.32/0.67      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeast_upt
% 0.32/0.67  thf(fact_10190_atMost__upto,axiom,
% 0.32/0.67      ( set_ord_atMost_nat
% 0.32/0.67      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atMost_upto
% 0.32/0.67  thf(fact_10191_atLeastAtMost__upt,axiom,
% 0.32/0.67      ( set_or1269000886237332187st_nat
% 0.32/0.67      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastAtMost_upt
% 0.32/0.67  thf(fact_10192_greaterThanLessThan__upt,axiom,
% 0.32/0.67      ( set_or5834768355832116004an_nat
% 0.32/0.67      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThanLessThan_upt
% 0.32/0.67  thf(fact_10193_greaterThanAtMost__upt,axiom,
% 0.32/0.67      ( set_or6659071591806873216st_nat
% 0.32/0.67      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M3 ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % greaterThanAtMost_upt
% 0.32/0.67  thf(fact_10194_atLeastLessThan__upt,axiom,
% 0.32/0.67      ( set_or4665077453230672383an_nat
% 0.32/0.67      = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % atLeastLessThan_upt
% 0.32/0.67  thf(fact_10195_upt__0,axiom,
% 0.32/0.67      ! [I: nat] :
% 0.32/0.67        ( ( upt @ I @ zero_zero_nat )
% 0.32/0.67        = nil_nat ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_0
% 0.32/0.67  thf(fact_10196_upt__conv__Cons__Cons,axiom,
% 0.32/0.67      ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 0.32/0.67        ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 0.32/0.67          = ( upt @ M @ Q2 ) )
% 0.32/0.67        = ( ( cons_nat @ N @ Ns )
% 0.32/0.67          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_conv_Cons_Cons
% 0.32/0.67  thf(fact_10197_upt__conv__Cons,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ord_less_nat @ I @ J )
% 0.32/0.67       => ( ( upt @ I @ J )
% 0.32/0.67          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_conv_Cons
% 0.32/0.67  thf(fact_10198_distinct__upt,axiom,
% 0.32/0.67      ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 0.32/0.67  
% 0.32/0.67  % distinct_upt
% 0.32/0.67  thf(fact_10199_map__add__upt,axiom,
% 0.32/0.67      ! [N: nat,M: nat] :
% 0.32/0.67        ( ( map_nat_nat
% 0.32/0.67          @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N )
% 0.32/0.67          @ ( upt @ zero_zero_nat @ M ) )
% 0.32/0.67        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % map_add_upt
% 0.32/0.67  thf(fact_10200_map__Suc__upt,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 0.32/0.67        = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % map_Suc_upt
% 0.32/0.67  thf(fact_10201_map__decr__upt,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( map_nat_nat
% 0.32/0.67          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.32/0.67          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.32/0.67        = ( upt @ M @ N ) ) ).
% 0.32/0.67  
% 0.32/0.67  % map_decr_upt
% 0.32/0.67  thf(fact_10202_upt__add__eq__append,axiom,
% 0.32/0.67      ! [I: nat,J: nat,K: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.67       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.32/0.67          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_add_eq_append
% 0.32/0.67  thf(fact_10203_upt__eq__Cons__conv,axiom,
% 0.32/0.67      ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 0.32/0.67        ( ( ( upt @ I @ J )
% 0.32/0.67          = ( cons_nat @ X @ Xs ) )
% 0.32/0.67        = ( ( ord_less_nat @ I @ J )
% 0.32/0.67          & ( I = X )
% 0.32/0.67          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.32/0.67            = Xs ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_eq_Cons_conv
% 0.32/0.67  thf(fact_10204_upt__rec,axiom,
% 0.32/0.67      ( upt
% 0.32/0.67      = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_rec
% 0.32/0.67  thf(fact_10205_upt__Suc__append,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.67       => ( ( upt @ I @ ( suc @ J ) )
% 0.32/0.67          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_Suc_append
% 0.32/0.67  thf(fact_10206_upt__Suc,axiom,
% 0.32/0.67      ! [I: nat,J: nat] :
% 0.32/0.67        ( ( ( ord_less_eq_nat @ I @ J )
% 0.32/0.67         => ( ( upt @ I @ ( suc @ J ) )
% 0.32/0.67            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.32/0.67        & ( ~ ( ord_less_eq_nat @ I @ J )
% 0.32/0.67         => ( ( upt @ I @ ( suc @ J ) )
% 0.32/0.67            = nil_nat ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % upt_Suc
% 0.32/0.67  thf(fact_10207_sum__list__upt,axiom,
% 0.32/0.67      ! [M: nat,N: nat] :
% 0.32/0.67        ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.67       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.32/0.67          = ( groups3542108847815614940at_nat
% 0.32/0.67            @ ^ [X3: nat] : X3
% 0.32/0.67            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  % sum_list_upt
% 0.32/0.67  
% 0.32/0.67  % Helper facts (40)
% 0.32/0.67  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.32/0.67      ! [X: int,Y: int] :
% 0.32/0.67        ( ( if_int @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.32/0.67      ! [X: int,Y: int] :
% 0.32/0.67        ( ( if_int @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.32/0.67      ! [X: nat,Y: nat] :
% 0.32/0.67        ( ( if_nat @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.32/0.67      ! [X: nat,Y: nat] :
% 0.32/0.67        ( ( if_nat @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.32/0.67      ! [X: num,Y: num] :
% 0.32/0.67        ( ( if_num @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.32/0.67      ! [X: num,Y: num] :
% 0.32/0.67        ( ( if_num @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.32/0.67      ! [X: rat,Y: rat] :
% 0.32/0.67        ( ( if_rat @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.32/0.67      ! [X: rat,Y: rat] :
% 0.32/0.67        ( ( if_rat @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.32/0.67      ! [X: real,Y: real] :
% 0.32/0.67        ( ( if_real @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.32/0.67      ! [X: real,Y: real] :
% 0.32/0.67        ( ( if_real @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 0.32/0.67      ! [P: real > $o] :
% 0.32/0.67        ( ( P @ ( fChoice_real @ P ) )
% 0.32/0.67        = ( ? [X2: real] : ( P @ X2 ) ) ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.32/0.67      ! [X: complex,Y: complex] :
% 0.32/0.67        ( ( if_complex @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.32/0.67      ! [X: complex,Y: complex] :
% 0.32/0.67        ( ( if_complex @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.32/0.67      ! [X: extended_enat,Y: extended_enat] :
% 0.32/0.67        ( ( if_Extended_enat @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.32/0.67      ! [X: extended_enat,Y: extended_enat] :
% 0.32/0.67        ( ( if_Extended_enat @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.32/0.67      ! [X: code_integer,Y: code_integer] :
% 0.32/0.67        ( ( if_Code_integer @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.32/0.67      ! [X: code_integer,Y: code_integer] :
% 0.32/0.67        ( ( if_Code_integer @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: set_int,Y: set_int] :
% 0.32/0.67        ( ( if_set_int @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: set_int,Y: set_int] :
% 0.32/0.67        ( ( if_set_int @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.32/0.67        ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.32/0.67      ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.32/0.67        ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: list_int,Y: list_int] :
% 0.32/0.67        ( ( if_list_int @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: list_int,Y: list_int] :
% 0.32/0.67        ( ( if_list_int @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.32/0.67      ! [X: list_nat,Y: list_nat] :
% 0.32/0.67        ( ( if_list_nat @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.32/0.67      ! [X: list_nat,Y: list_nat] :
% 0.32/0.67        ( ( if_list_nat @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: int > int,Y: int > int] :
% 0.32/0.67        ( ( if_int_int @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: int > int,Y: int > int] :
% 0.32/0.67        ( ( if_int_int @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.32/0.67      ! [X: option_nat,Y: option_nat] :
% 0.32/0.67        ( ( if_option_nat @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.32/0.67      ! [X: option_nat,Y: option_nat] :
% 0.32/0.67        ( ( if_option_nat @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.32/0.67      ! [X: option_num,Y: option_num] :
% 0.32/0.67        ( ( if_option_num @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.32/0.67      ! [X: option_num,Y: option_num] :
% 0.32/0.67        ( ( if_option_num @ $true @ X @ Y )
% 0.32/0.67        = X ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.32/0.67        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 0.32/0.67        = Y ) ).
% 0.32/0.67  
% 0.32/0.67  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.32/0.67      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.32/0.67        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 0.32/0.68        = X ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.32/0.68      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.32/0.68        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 0.32/0.68        = Y ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.32/0.68      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.32/0.68        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 0.32/0.68        = X ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.32/0.68      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.32/0.68        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 0.32/0.68        = Y ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 0.32/0.68      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 0.32/0.68        ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 0.32/0.68        = X ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.32/0.68      ! [P: $o] :
% 0.32/0.68        ( ( P = $true )
% 0.32/0.68        | ( P = $false ) ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.32/0.68      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.32/0.68        ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 0.32/0.68        = Y ) ).
% 0.32/0.68  
% 0.32/0.68  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.32/0.68      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.32/0.68        ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 0.32/0.68        = X ) ).
% 0.32/0.68  
% 0.32/0.68  % Conjectures (1)
% 0.32/0.68  thf(conj_0,conjecture,
% 0.32/0.68      ? [Y2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ Y2 ) ).
% 0.32/0.68  
% 0.32/0.68  %------------------------------------------------------------------------------
% 0.32/0.68  ------------------------
% 6.45/2.62  ---- Embedded in THF ---
% 6.45/2.62  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 6.45/2.62  %%% Generated on Fri Feb 27 06:07:46 EST 2026
% 6.45/2.62  %%% using '$$dhol' embedding, version 1.3.0.
% 6.45/2.62  %%% Logic specification used:
% 6.45/2.62  %%% thf(spec, logic, $$dhol).
% 6.45/2.62  
% 6.45/2.62  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2DTF3754.p
% See solution above
% 6.45/2.65  ------------------------
% 8.68/4.80  ---- Cleaned THF ---
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.68/4.80      produc5542196010084753463at_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 8.68/4.80      produc1908205239877642774nteger: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.68/4.80      produc5491161045314408544at_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.68/4.80      produc2285326912895808259nt_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 8.68/4.80      produc8763457246119570046nteger: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.68/4.80      produc7773217078559923341nt_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 8.68/4.80      produc1193250871479095198on_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 8.68/4.80      produc8306885398267862888on_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.68/4.80      produc6121120109295599847at_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 8.68/4.80      produc7036089656553540234on_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 8.68/4.80      produc2233624965454879586on_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J,type,
% 8.68/4.80      produc6241069584506657477e_term: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J_J,type,
% 8.68/4.80      set_fi4554929511873752355omplex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.80      list_P7413028617227757229T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J,type,
% 8.68/4.80      produc8551481072490612790e_term: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
% 8.68/4.80      option6357759511663192854e_term: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 8.68/4.80      produc3447558737645232053on_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 8.68/4.80      produc4953844613479565601on_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J_J,type,
% 8.68/4.80      set_fi7789364187291644575l_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 8.68/4.80      filter6041513312241820739omplex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 8.68/4.80      list_P7037539587688870467BT_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 8.68/4.80      list_P4547456442757143711BT_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.80      list_P5647936690300460905T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.80      produc8243902056947475879T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 8.68/4.80      set_Pr5085853215250843933omplex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.68/4.80      produc8923325533196201883nteger: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 8.68/4.80      list_P3126845725202233233VEBT_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.80      list_P7495141550334521929T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 8.68/4.80      filter2146258269922977983l_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.68/4.80      option4927543243414619207at_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Filter__Ofilter_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.68/4.80      filter1242075044329608583at_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 8.68/4.80      set_Pr6218003697084177305l_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 8.68/4.80      produc9072475918466114483BT_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 8.68/4.80      produc4894624898956917775BT_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.80      produc8025551001238799321T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.68/4.80      set_Pr958786334691620121nt_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 8.68/4.80      produc4411394909380815293omplex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 8.68/4.80      list_P7333126701944960589_nat_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 8.68/4.80      list_P6285523579766656935_o_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 8.68/4.80      list_P3795440434834930179_o_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.80      set_list_VEBT_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 8.68/4.80      produc334124729049499915VEBT_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.80      produc2504756804600209347T_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 8.68/4.80      produc6271795597528267376eger_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 8.68/4.80      produc2422161461964618553l_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 8.68/4.80      product_prod_num_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 8.68/4.80      product_prod_nat_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.80      product_prod_nat_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.80      product_prod_int_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 8.68/4.80      list_P4002435161011370285od_o_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__List__Olist_It__Complex__Ocomplex_J_J,type,
% 8.68/4.80      set_list_complex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Complex__Ocomplex_J_J,type,
% 8.68/4.80      set_set_complex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.80      list_VEBT_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 8.68/4.80      set_list_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
% 8.68/4.80      set_list_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 8.68/4.80      product_prod_nat_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 8.68/4.80      product_prod_o_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 8.68/4.80      product_prod_o_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.80      list_set_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.80      set_VEBT_VEBT: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.80      set_set_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 8.68/4.80      set_set_int: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 8.68/4.80      set_Code_integer: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
% 8.68/4.80      set_Product_unit: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Extended____Nat__Oenat_J,type,
% 8.68/4.80      set_Extended_enat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
% 8.68/4.80      list_complex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
% 8.68/4.80      set_list_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 8.68/4.80      product_prod_o_o: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.80      set_complex: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
% 8.68/4.80      filter_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.80      option_num: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
% 8.68/4.80      option_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
% 8.68/4.80      filter_nat: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 8.68/4.80      set_char: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
% 8.68/4.80      list_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.80      set_real: $tType ).
% 8.68/4.80  
% 8.68/4.80  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      list_nat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      list_int: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      vEBT_VEBT: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 8.68/4.81      set_rat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
% 8.68/4.81      set_num: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      set_nat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      set_int: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Code____Numeral__Ointeger,type,
% 8.68/4.81      code_integer: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Extended____Nat__Oenat,type,
% 8.68/4.81      extended_enat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__List__Olist_I_Eo_J,type,
% 8.68/4.81      list_o: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Complex__Ocomplex,type,
% 8.68/4.81      complex: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 8.68/4.81      set_o: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__String__Ochar,type,
% 8.68/4.81      char: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Real__Oreal,type,
% 8.68/4.81      real: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Rat__Orat,type,
% 8.68/4.81      rat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Num__Onum,type,
% 8.68/4.81      num: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Nat__Onat,type,
% 8.68/4.81      nat: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(ty_n_t__Int__Oint,type,
% 8.68/4.81      int: $tType ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 8.68/4.81      archim7802044766580827645g_real: real > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 8.68/4.81      archim3151403230148437115or_rat: rat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 8.68/4.81      archim6058952711729229775r_real: real > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 8.68/4.81      archim7778729529865785530nd_rat: rat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 8.68/4.81      archim8280529875227126926d_real: real > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Binomial_Obinomial,type,
% 8.68/4.81      binomial: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 8.68/4.81      bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oand__not__num,type,
% 8.68/4.81      bit_and_not_num: num > num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 8.68/4.81      bit_concat_bit: nat > int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 8.68/4.81      bit_or_not_num_neg: num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 8.68/4.81      bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 8.68/4.81      bit_ri7919022796975470100ot_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_ri631733984087533419it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 8.68/4.81      bit_se725231765392027082nd_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 8.68/4.81      bit_se727722235901077358nd_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se8568078237143864401it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se8570568707652914677it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se2159334234014336723it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se2161824704523386999it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se2119862282449309892nteger: nat > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 8.68/4.81      bit_se2000444600071755411sk_int: nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 8.68/4.81      bit_se2002935070580805687sk_nat: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 8.68/4.81      bit_se1409905431419307370or_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 8.68/4.81      bit_se1412395901928357646or_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se545348938243370406it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se547839408752420682it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se7879613467334960850it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se7882103937844011126it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se2923211474154528505it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se2925701944663578781it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      bit_se8260200283734997820nteger: nat > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
% 8.68/4.81      bit_se4203085406695923979it_int: nat > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se4205575877204974255it_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
% 8.68/4.81      bit_se6526347334894502574or_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
% 8.68/4.81      bit_se6528837805403552850or_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
% 8.68/4.81      bit_se1146084159140164899it_int: int > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
% 8.68/4.81      bit_se1148574629649215175it_nat: nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 8.68/4.81      bit_take_bit_num: nat > num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 8.68/4.81      code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Odivmod__abs,type,
% 8.68/4.81      code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 8.68/4.81      code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
% 8.68/4.81      code_int_of_integer: code_integer > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 8.68/4.81      code_integer_of_int: int > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 8.68/4.81      code_integer_of_num: num > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 8.68/4.81      code_nat_of_integer: code_integer > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Onegative,type,
% 8.68/4.81      code_negative: num > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Onum__of__integer,type,
% 8.68/4.81      code_num_of_integer: code_integer > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Numeral_Opositive,type,
% 8.68/4.81      code_positive: num > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Target__Int_Onegative,type,
% 8.68/4.81      code_Target_negative: num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Code__Target__Int_Opositive,type,
% 8.68/4.81      code_Target_positive: num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 8.68/4.81      comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 8.68/4.81      comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Real__Oreal,type,
% 8.68/4.81      comple4887499456419720421f_real: set_real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 8.68/4.81      complete_Sup_Sup_int: set_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
% 8.68/4.81      complete_Sup_Sup_nat: set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
% 8.68/4.81      comple1385675409528146559p_real: set_real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      comple7399068483239264473et_nat: set_set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_OArg,type,
% 8.68/4.81      arg: complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocis,type,
% 8.68/4.81      cis: real > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocnj,type,
% 8.68/4.81      cnj: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocomplex_OComplex,type,
% 8.68/4.81      complex2: real > real > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocomplex_OIm,type,
% 8.68/4.81      im: complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocomplex_ORe,type,
% 8.68/4.81      re: complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Ocsqrt,type,
% 8.68/4.81      csqrt: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Complex_Oimaginary__unit,type,
% 8.68/4.81      imaginary_unit: complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Deriv_Odifferentiable_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Deriv_Ohas__derivative_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Deriv_Ohas__field__derivative_001t__Real__Oreal,type,
% 8.68/4.81      has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Oadjust__div,type,
% 8.68/4.81      adjust_div: product_prod_int_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Oadjust__mod,type,
% 8.68/4.81      adjust_mod: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Odivmod__nat,type,
% 8.68/4.81      divmod_nat: nat > nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Oeucl__rel__int,type,
% 8.68/4.81      eucl_rel_int: int > int > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 8.68/4.81      unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 8.68/4.81      unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 8.68/4.81      unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 8.68/4.81      unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 8.68/4.81      unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 8.68/4.81      unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 8.68/4.81      semiri5044797733671781792omplex: nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 8.68/4.81      semiri1408675320244567234ct_nat: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 8.68/4.81      semiri2265585572941072030t_real: nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 8.68/4.81      invers8013647133539491842omplex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 8.68/4.81      inverse_inverse_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 8.68/4.81      inverse_inverse_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 8.68/4.81      at_bot_real: filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 8.68/4.81      at_top_nat: filter_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 8.68/4.81      at_top_real: filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 8.68/4.81      eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 8.68/4.81      eventually_real: ( real > $o ) > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 8.68/4.81      princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 8.68/4.81      princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 8.68/4.81      finite_card_o: set_o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 8.68/4.81      finite_card_complex: set_complex > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 8.68/4.81      finite_card_int: set_int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 8.68/4.81      finite_card_nat: set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 8.68/4.81      finite410649719033368117t_unit: set_Product_unit > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      finite_card_set_nat: set_set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 8.68/4.81      finite_card_char: set_char > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 8.68/4.81      finite_finite_o: set_o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 8.68/4.81      finite3207457112153483333omplex: set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 8.68/4.81      finite_finite_int: set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 8.68/4.81      finite_finite_list_o: set_list_o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 8.68/4.81      finite8712137658972009173omplex: set_list_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      finite3922522038869484883st_int: set_list_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      finite8100373058378681591st_nat: set_list_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 8.68/4.81      finite_finite_nat: set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 8.68/4.81      finite_finite_num: set_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 8.68/4.81      finite_finite_rat: set_rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 8.68/4.81      finite_finite_real: set_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      finite6551019134538273531omplex: set_set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      finite6197958912794628473et_int: set_set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      finite1152437895449049373et_nat: set_set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 8.68/4.81      bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 8.68/4.81      bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 8.68/4.81      comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 8.68/4.81      comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Oid_001_Eo,type,
% 8.68/4.81      id_o: $o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 8.68/4.81      id_nat: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 8.68/4.81      map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 8.68/4.81      map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.68/4.81      map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 8.68/4.81      gcd_Gcd_int: set_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 8.68/4.81      gcd_Gcd_nat: set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Obezw,type,
% 8.68/4.81      bezw: nat > nat > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Obezw__rel,type,
% 8.68/4.81      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 8.68/4.81      gcd_gcd_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 8.68/4.81      gcd_gcd_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 8.68/4.81      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      abs_abs_Code_integer: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 8.68/4.81      abs_abs_complex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 8.68/4.81      abs_abs_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 8.68/4.81      abs_abs_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 8.68/4.81      abs_abs_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 8.68/4.81      minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 8.68/4.81      minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.68/4.81      minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 8.68/4.81      minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
% 8.68/4.81      minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 8.68/4.81      minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 8.68/4.81      minus_minus_complex: complex > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 8.68/4.81      minus_minus_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 8.68/4.81      minus_minus_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 8.68/4.81      minus_minus_rat: rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 8.68/4.81      minus_minus_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      minus_minus_set_int: set_int > set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.68/4.81      minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      minus_minus_set_real: set_real > set_real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      one_one_Code_integer: code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 8.68/4.81      one_one_complex: complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      one_on7984719198319812577d_enat: extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 8.68/4.81      one_one_int: int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 8.68/4.81      one_one_nat: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 8.68/4.81      one_one_rat: rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 8.68/4.81      one_one_real: real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 8.68/4.81      plus_plus_complex: complex > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 8.68/4.81      plus_plus_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 8.68/4.81      plus_plus_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 8.68/4.81      plus_plus_num: num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 8.68/4.81      plus_plus_rat: rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 8.68/4.81      plus_plus_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      sgn_sgn_Code_integer: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Osgn__class_Osgn_001t__Complex__Ocomplex,type,
% 8.68/4.81      sgn_sgn_complex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 8.68/4.81      sgn_sgn_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 8.68/4.81      sgn_sgn_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 8.68/4.81      sgn_sgn_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 8.68/4.81      times_times_complex: complex > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 8.68/4.81      times_times_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 8.68/4.81      times_times_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 8.68/4.81      times_times_num: num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 8.68/4.81      times_times_rat: rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 8.68/4.81      times_times_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      uminus1351360451143612070nteger: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 8.68/4.81      uminus1482373934393186551omplex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 8.68/4.81      uminus_uminus_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 8.68/4.81      uminus_uminus_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 8.68/4.81      uminus_uminus_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      uminus8566677241136511917omplex: set_complex > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      uminus1532241313380277803et_int: set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      uminus5710092332889474511et_nat: set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      uminus612125837232591019t_real: set_real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      zero_z3403309356797280102nteger: code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 8.68/4.81      zero_zero_complex: complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      zero_z5237406670263579293d_enat: extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 8.68/4.81      zero_zero_int: int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 8.68/4.81      zero_zero_nat: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 8.68/4.81      zero_zero_rat: rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 8.68/4.81      zero_zero_real: real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 8.68/4.81      groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 8.68/4.81      groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 8.68/4.81      groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Rat__Orat,type,
% 8.68/4.81      groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 8.68/4.81      groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 8.68/4.81      groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Nat__Onat,type,
% 8.68/4.81      groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Rat__Orat,type,
% 8.68/4.81      groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Real__Oreal,type,
% 8.68/4.81      groups8778361861064173332t_real: ( int > real ) > set_int > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 8.68/4.81      groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Int__Oint,type,
% 8.68/4.81      groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Rat__Orat,type,
% 8.68/4.81      groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 8.68/4.81      groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 8.68/4.81      groups1932886352136224148al_int: ( real > int ) > set_real > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Nat__Onat,type,
% 8.68/4.81      groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Rat__Orat,type,
% 8.68/4.81      groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      groups8097168146408367636l_real: ( real > real ) > set_real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Complex__Ocomplex,type,
% 8.68/4.81      groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 8.68/4.81      groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Real__Oreal,type,
% 8.68/4.81      groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
% 8.68/4.81      groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__List_Ocomm__semiring__0__class_Ohorner__sum_001_Eo_001t__Int__Oint,type,
% 8.68/4.81      groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Nat__Onat,type,
% 8.68/4.81      groups4561878855575611511st_nat: list_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_HOL_OThe_001t__Int__Oint,type,
% 8.68/4.81      the_int: ( int > $o ) > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
% 8.68/4.81      the_real: ( real > $o ) > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Complex__Ocomplex,type,
% 8.68/4.81      if_complex: $o > complex > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Int__Oint,type,
% 8.68/4.81      if_int: $o > int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      if_list_int: $o > list_int > list_int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      if_list_nat: $o > list_nat > list_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Nat__Onat,type,
% 8.68/4.81      if_nat: $o > nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Num__Onum,type,
% 8.68/4.81      if_num: $o > num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 8.68/4.81      if_option_nat: $o > option_nat > option_nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      if_option_num: $o > option_num > option_num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 8.68/4.81      if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.68/4.81      if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Rat__Orat,type,
% 8.68/4.81      if_rat: $o > rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Real__Oreal,type,
% 8.68/4.81      if_real: $o > real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      if_set_int: $o > set_int > set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_OAbs__Integ,type,
% 8.68/4.81      abs_Integ: product_prod_nat_nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_ORep__Integ,type,
% 8.68/4.81      rep_Integ: int > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oint__ge__less__than,type,
% 8.68/4.81      int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oint__ge__less__than2,type,
% 8.68/4.81      int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Onat,type,
% 8.68/4.81      nat2: int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 8.68/4.81      ring_1_Ints_complex: set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 8.68/4.81      ring_1_Ints_real: set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      ring_18347121197199848620nteger: int > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 8.68/4.81      ring_17405671764205052669omplex: int > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 8.68/4.81      ring_1_of_int_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 8.68/4.81      ring_1_of_int_rat: int > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 8.68/4.81      ring_1_of_int_real: int > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 8.68/4.81      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 8.68/4.81      sup_sup_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 8.68/4.81      lattic8263393255366662781ax_int: set_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 8.68/4.81      lattic8265883725875713057ax_nat: set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 8.68/4.81      at_infinity_real: filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 8.68/4.81      append_int: list_int > list_int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 8.68/4.81      append_nat: list_nat > list_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 8.68/4.81      distinct_int: list_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 8.68/4.81      distinct_nat: list_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 8.68/4.81      linord2614967742042102400et_nat: set_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 8.68/4.81      cons_int: int > list_int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 8.68/4.81      cons_nat: nat > list_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 8.68/4.81      nil_int: list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 8.68/4.81      nil_nat: list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001_Eo,type,
% 8.68/4.81      set_o2: list_o > set_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 8.68/4.81      set_complex2: list_complex > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 8.68/4.81      set_int2: list_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 8.68/4.81      set_nat2: list_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 8.68/4.81      set_real2: list_real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      set_set_nat2: list_set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001_Eo,type,
% 8.68/4.81      list_update_o: list_o > nat > $o > list_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 8.68/4.81      list_update_complex: list_complex > nat > complex > list_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 8.68/4.81      list_update_int: list_int > nat > int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 8.68/4.81      list_update_nat: list_nat > nat > nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 8.68/4.81      list_update_real: list_real > nat > real > list_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001_Eo,type,
% 8.68/4.81      nth_o: list_o > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 8.68/4.81      nth_complex: list_complex > nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Int__Oint,type,
% 8.68/4.81      nth_int: list_int > nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 8.68/4.81      nth_nat: list_nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 8.68/4.81      nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 8.68/4.81      nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 8.68/4.81      nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 8.68/4.81      nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 8.68/4.81      nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 8.68/4.81      nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 8.68/4.81      nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 8.68/4.81      nth_real: list_real > nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      nth_set_nat: list_set_nat > nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 8.68/4.81      product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 8.68/4.81      product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 8.68/4.81      product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 8.68/4.81      product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 8.68/4.81      product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 8.68/4.81      produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 8.68/4.81      produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 8.68/4.81      remdups_nat: list_nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001_Eo,type,
% 8.68/4.81      replicate_o: nat > $o > list_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 8.68/4.81      replicate_complex: nat > complex > list_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 8.68/4.81      replicate_int: nat > int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 8.68/4.81      replicate_nat: nat > nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 8.68/4.81      replicate_real: nat > real > list_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      replicate_set_nat: nat > set_nat > list_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oupt,type,
% 8.68/4.81      upt: nat > nat > list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oupto,type,
% 8.68/4.81      upto: int > int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oupto__aux,type,
% 8.68/4.81      upto_aux: int > int > list_int > list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_List_Oupto__rel,type,
% 8.68/4.81      upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_OSuc,type,
% 8.68/4.81      suc: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 8.68/4.81      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 8.68/4.81      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Onat_Opred,type,
% 8.68/4.81      pred: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      semiri4939895301339042750nteger: nat > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 8.68/4.81      semiri8010041392384452111omplex: nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      semiri4216267220026989637d_enat: nat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 8.68/4.81      semiri1314217659103216013at_int: nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 8.68/4.81      semiri1316708129612266289at_nat: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 8.68/4.81      semiri681578069525770553at_rat: nat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 8.68/4.81      semiri5074537144036343181t_real: nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 8.68/4.81      size_size_list_o: list_o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 8.68/4.81      size_s3451745648224563538omplex: list_complex > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      size_size_list_int: list_int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      size_size_list_nat: list_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 8.68/4.81      size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 8.68/4.81      size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 8.68/4.81      size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.81      size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 8.68/4.81      size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.68/4.81      size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 8.68/4.81      size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 8.68/4.81      size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 8.68/4.81      size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 8.68/4.81      size_size_list_real: list_real > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      size_s3254054031482475050et_nat: list_set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 8.68/4.81      size_size_num: num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 8.68/4.81      size_size_option_nat: option_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      size_size_option_num: option_num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.68/4.81      size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 8.68/4.81      size_size_char: char > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 8.68/4.81      nat_list_encode: list_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 8.68/4.81      nat_list_encode_rel: list_nat > list_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 8.68/4.81      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 8.68/4.81      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 8.68/4.81      nat_prod_encode: product_prod_nat_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 8.68/4.81      nat_set_decode: nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 8.68/4.81      nat_set_encode: set_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Nat__Bijection_Otriangle,type,
% 8.68/4.81      nat_triangle: nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_NthRoot_Oroot,type,
% 8.68/4.81      root: nat > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_NthRoot_Osqrt,type,
% 8.68/4.81      sqrt: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_OBitM,type,
% 8.68/4.81      bitM: num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oinc,type,
% 8.68/4.81      inc: num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 8.68/4.81      neg_nu7009210354673126013omplex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 8.68/4.81      neg_numeral_dbl_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 8.68/4.81      neg_numeral_dbl_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 8.68/4.81      neg_numeral_dbl_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 8.68/4.81      neg_nu6511756317524482435omplex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 8.68/4.81      neg_nu3811975205180677377ec_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 8.68/4.81      neg_nu3179335615603231917ec_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 8.68/4.81      neg_nu6075765906172075777c_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 8.68/4.81      neg_nu8557863876264182079omplex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 8.68/4.81      neg_nu5851722552734809277nc_int: int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 8.68/4.81      neg_nu5219082963157363817nc_rat: rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 8.68/4.81      neg_nu8295874005876285629c_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 8.68/4.81      neg_numeral_sub_int: num > num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum_OBit0,type,
% 8.68/4.81      bit0: num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum_OBit1,type,
% 8.68/4.81      bit1: num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum_OOne,type,
% 8.68/4.81      one: num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum_Osize__num,type,
% 8.68/4.81      size_num: num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onum__of__nat,type,
% 8.68/4.81      num_of_nat: nat > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      numera6620942414471956472nteger: num > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 8.68/4.81      numera6690914467698888265omplex: num > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      numera1916890842035813515d_enat: num > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 8.68/4.81      numeral_numeral_int: num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 8.68/4.81      numeral_numeral_nat: num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 8.68/4.81      numeral_numeral_rat: num > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 8.68/4.81      numeral_numeral_real: num > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Opow,type,
% 8.68/4.81      pow: num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Opred__numeral,type,
% 8.68/4.81      pred_numeral: num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Num_Osqr,type,
% 8.68/4.81      sqr: num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 8.68/4.81      none_nat: option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 8.68/4.81      none_num: option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 8.68/4.81      some_nat: nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 8.68/4.81      some_num: num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 8.68/4.81      case_option_int_num: int > ( num > int ) > option_num > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 8.68/4.81      case_option_num_num: num > ( num > num ) > option_num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 8.68/4.81      case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
% 8.68/4.81      size_option_nat: ( nat > nat ) > option_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 8.68/4.81      size_option_num: ( num > nat ) > option_num > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 8.68/4.81      the_nat: option_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 8.68/4.81      the_num: option_num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      bot_bo4199563552545308370d_enat: extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 8.68/4.81      bot_bot_nat: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      bot_bot_set_complex: set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
% 8.68/4.81      bot_bo7653980558646680370d_enat: set_Extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      bot_bot_set_int: set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      bot_bot_set_nat: set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
% 8.68/4.81      bot_bot_set_num: set_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
% 8.68/4.81      bot_bot_set_rat: set_rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      bot_bot_set_real: set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 8.68/4.81      bot_bot_set_set_int: set_set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      bot_bot_set_set_nat: set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 8.68/4.81      ord_less_int: int > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 8.68/4.81      ord_less_nat: nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 8.68/4.81      ord_less_num: num > num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 8.68/4.81      ord_less_rat: rat > rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 8.68/4.81      ord_less_real: real > real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 8.68/4.81      ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      ord_less_set_complex: set_complex > set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      ord_less_set_int: set_int > set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      ord_less_set_nat: set_nat > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
% 8.68/4.81      ord_less_set_num: set_num > set_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
% 8.68/4.81      ord_less_set_rat: set_rat > set_rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      ord_less_set_real: set_real > set_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 8.68/4.81      ord_less_set_set_int: set_set_int > set_set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 8.68/4.81      ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 8.68/4.81      ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_Eo_J,type,
% 8.68/4.81      ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.68/4.81      ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 8.68/4.81      ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 8.68/4.81      ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 8.68/4.81      ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Real__Oreal_J,type,
% 8.68/4.81      ord_le4104064031414453916r_real: filter_real > filter_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 8.68/4.81      ord_less_eq_int: int > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 8.68/4.81      ord_less_eq_nat: nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 8.68/4.81      ord_less_eq_num: num > num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 8.68/4.81      ord_less_eq_rat: rat > rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 8.68/4.81      ord_less_eq_real: real > real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
% 8.68/4.81      ord_less_eq_set_o: set_o > set_o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 8.68/4.81      ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      ord_less_eq_set_int: set_int > set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
% 8.68/4.81      ord_less_eq_set_num: set_num > set_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.68/4.81      ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
% 8.68/4.81      ord_less_eq_set_rat: set_rat > set_rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      ord_less_eq_set_real: set_real > set_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 8.68/4.81      ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 8.68/4.81      ord_max_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 8.68/4.81      ord_max_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 8.68/4.81      ord_max_num: num > num > num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 8.68/4.81      ord_max_rat: rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 8.68/4.81      ord_max_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      ord_max_set_int: set_int > set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 8.68/4.81      order_Greatest_nat: ( nat > $o ) > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      order_9091379641038594480t_real: ( nat > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      order_mono_nat_nat: ( nat > nat ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      order_mono_nat_real: ( nat > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 8.68/4.81      top_top_set_o: set_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      top_top_set_nat: set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 8.68/4.81      top_to1996260823553986621t_unit: set_Product_unit ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      top_top_set_real: set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 8.68/4.81      top_top_set_char: set_char ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 8.68/4.81      power_power_complex: complex > nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 8.68/4.81      power_power_int: int > nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 8.68/4.81      power_power_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 8.68/4.81      power_power_rat: rat > nat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 8.68/4.81      power_power_real: real > nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.68/4.81      produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 8.68/4.81      produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 8.68/4.81      produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 8.68/4.81      produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 8.68/4.81      produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.68/4.81      produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.68/4.81      produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.68/4.81      produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 8.68/4.81      product_Pair_o_o: $o > $o > product_prod_o_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 8.68/4.81      product_Pair_o_int: $o > int > product_prod_o_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 8.68/4.81      product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 8.68/4.81      produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      product_Pair_int_int: int > int > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 8.68/4.81      product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 8.68/4.81      product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 8.68/4.81      product_Pair_num_num: num > num > product_prod_num_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 8.68/4.81      produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.68/4.81      produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 8.68/4.81      produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 8.68/4.81      produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 8.68/4.81      produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 8.68/4.81      produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 8.68/4.81      produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      produc7959293469001253456omplex: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > produc7773217078559923341nt_int > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 8.68/4.81      produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 8.68/4.81      produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 8.68/4.81      produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 8.68/4.81      produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 8.68/4.81      produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 8.68/4.81      produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 8.68/4.81      produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Real__Oreal_J,type,
% 8.68/4.81      produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.68/4.81      produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 8.68/4.81      produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 8.68/4.81      produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 8.68/4.81      produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  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,
% 8.68/4.81      produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 8.68/4.81      produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.68/4.81      produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 8.68/4.81      produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      product_fst_int_int: product_prod_int_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      product_fst_nat_nat: product_prod_nat_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      product_snd_int_int: product_prod_int_int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      product_snd_nat_nat: product_prod_nat_nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rat_OFract,type,
% 8.68/4.81      fract: int > int > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rat_OFrct,type,
% 8.68/4.81      frct: product_prod_int_int > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rat_Onormalize,type,
% 8.68/4.81      normalize: product_prod_int_int > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rat_Oof__int,type,
% 8.68/4.81      of_int: int > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rat_Oquotient__of,type,
% 8.68/4.81      quotient_of: rat > product_prod_int_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 8.68/4.81      real_V2521375963428798218omplex: set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      real_V5970128139526366754l_real: ( real > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 8.68/4.81      real_V3694042436643373181omplex: complex > complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 8.68/4.81      real_V975177566351809787t_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 8.68/4.81      real_V1022390504157884413omplex: complex > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 8.68/4.81      real_V7735802525324610683m_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 8.68/4.81      real_V4546457046886955230omplex: real > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 8.68/4.81      real_V2046097035970521341omplex: real > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 8.68/4.81      real_V1485227260804924795R_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 8.68/4.81      divide1717551699836669952omplex: complex > complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 8.68/4.81      divide_divide_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 8.68/4.81      divide_divide_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 8.68/4.81      divide_divide_rat: rat > rat > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 8.68/4.81      divide_divide_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 8.68/4.81      dvd_dvd_complex: complex > complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 8.68/4.81      dvd_dvd_int: int > int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 8.68/4.81      dvd_dvd_nat: nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 8.68/4.81      dvd_dvd_rat: rat > rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 8.68/4.81      dvd_dvd_real: real > real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 8.68/4.81      modulo_modulo_int: int > int > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 8.68/4.81      modulo_modulo_nat: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      zero_n356916108424825756nteger: $o > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 8.68/4.81      zero_n1201886186963655149omplex: $o > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 8.68/4.81      zero_n2684676970156552555ol_int: $o > int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 8.68/4.81      zero_n2687167440665602831ol_nat: $o > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 8.68/4.81      zero_n2052037380579107095ol_rat: $o > rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 8.68/4.81      zero_n3304061248610475627l_real: $o > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 8.68/4.81      suminf_complex: ( nat > complex ) > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 8.68/4.81      suminf_real: ( nat > real ) > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 8.68/4.81      summable_real: ( nat > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 8.68/4.81      sums_real: ( nat > real ) > real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 8.68/4.81      collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 8.68/4.81      collect_complex: ( complex > $o ) > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 8.68/4.81      collect_int: ( int > $o ) > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 8.68/4.81      collect_list_o: ( list_o > $o ) > set_list_o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 8.68/4.81      collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      collect_list_int: ( list_int > $o ) > set_list_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 8.68/4.81      collect_nat: ( nat > $o ) > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Num__Onum,type,
% 8.68/4.81      collect_num: ( num > $o ) > set_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 8.68/4.81      collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 8.68/4.81      collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 8.68/4.81      collect_rat: ( rat > $o ) > set_rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 8.68/4.81      collect_real: ( real > $o ) > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 8.68/4.81      collect_set_complex: ( set_complex > $o ) > set_set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      collect_set_int: ( set_int > $o ) > set_set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 8.68/4.81      pow_nat: set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 8.68/4.81      image_int_int: ( int > int ) > set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 8.68/4.81      image_nat_int: ( nat > int ) > set_nat > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.68/4.81      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.68/4.81      image_nat_real: ( nat > real ) > set_nat > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 8.68/4.81      image_nat_char: ( nat > char ) > set_nat > set_char ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
% 8.68/4.81      image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 8.68/4.81      image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      image_real_real: ( real > real ) > set_real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 8.68/4.81      image_char_nat: ( char > nat ) > set_char > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 8.68/4.81      insert_complex: complex > set_complex > set_complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 8.68/4.81      insert_int: int > set_int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 8.68/4.81      insert_nat: nat > set_nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 8.68/4.81      insert_num: num > set_num > set_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 8.68/4.81      insert_rat: rat > set_rat > set_rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 8.68/4.81      insert_real: real > set_real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 8.68/4.81      set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 8.68/4.81      set_or1266510415728281911st_int: int > int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 8.68/4.81      set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 8.68/4.81      set_or7049704709247886629st_num: num > num > set_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 8.68/4.81      set_or633870826150836451st_rat: rat > rat > set_rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 8.68/4.81      set_or1222579329274155063t_real: real > real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 8.68/4.81      set_or4662586982721622107an_int: int > int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 8.68/4.81      set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 8.68/4.81      set_ord_atLeast_nat: nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 8.68/4.81      set_ord_atLeast_real: real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 8.68/4.81      set_ord_atMost_int: int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 8.68/4.81      set_ord_atMost_nat: nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 8.68/4.81      set_or6656581121297822940st_int: int > int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 8.68/4.81      set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 8.68/4.81      set_or5832277885323065728an_int: int > int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 8.68/4.81      set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 8.68/4.81      set_or1633881224788618240n_real: real > real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 8.68/4.81      set_or1210151606488870762an_nat: nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 8.68/4.81      set_or5849166863359141190n_real: real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Extended____Nat__Oenat,type,
% 8.68/4.81      set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 8.68/4.81      set_ord_lessThan_int: int > set_int ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 8.68/4.81      set_ord_lessThan_nat: nat > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 8.68/4.81      set_ord_lessThan_num: num > set_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 8.68/4.81      set_ord_lessThan_rat: rat > set_rat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 8.68/4.81      set_or5984915006950818249n_real: real > set_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Oascii__of,type,
% 8.68/4.81      ascii_of: char > char ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Ochar_OChar,type,
% 8.68/4.81      char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Ochar_Osize__char,type,
% 8.68/4.81      size_char: char > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 8.68/4.81      comm_s629917340098488124ar_nat: char > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Ointeger__of__char,type,
% 8.68/4.81      integer_of_char: char > code_integer ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 8.68/4.81      unique3096191561947761185of_nat: nat > char ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.68/4.81      topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 8.68/4.81      topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 8.68/4.81      topolo2177554685111907308n_real: real > set_real > filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 8.68/4.81      topolo2815343760600316023s_real: real > filter_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 8.68/4.81      topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 8.68/4.81      topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 8.68/4.81      topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oarccos,type,
% 8.68/4.81      arccos: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 8.68/4.81      arcosh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oarcsin,type,
% 8.68/4.81      arcsin: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oarctan,type,
% 8.68/4.81      arctan: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 8.68/4.81      arsinh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 8.68/4.81      artanh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 8.68/4.81      cos_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Ocos__coeff,type,
% 8.68/4.81      cos_coeff: nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 8.68/4.81      cosh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 8.68/4.81      cot_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 8.68/4.81      exp_complex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 8.68/4.81      exp_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 8.68/4.81      ln_ln_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Olog,type,
% 8.68/4.81      log: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Opi,type,
% 8.68/4.81      pi: real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 8.68/4.81      powr_real: real > real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 8.68/4.81      sin_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Osin__coeff,type,
% 8.68/4.81      sin_coeff: nat > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 8.68/4.81      sinh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 8.68/4.81      tan_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 8.68/4.81      tanh_complex: complex > complex ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 8.68/4.81      tanh_real: real > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 8.68/4.81      vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 8.68/4.81      vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 8.68/4.81      vEBT_size_VEBT: vEBT_VEBT > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 8.68/4.81      vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 8.68/4.81      vEBT_VEBT_high: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 8.68/4.81      vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 8.68/4.81      vEBT_VEBT_low: nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 8.68/4.81      vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 8.68/4.81      vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 8.68/4.81      vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 8.68/4.81      vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 8.68/4.81      vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 8.68/4.81      vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 8.68/4.81      vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 8.68/4.81      vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 8.68/4.81      vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 8.68/4.81      vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 8.68/4.81      vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 8.68/4.81      vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 8.68/4.81      vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 8.68/4.81      vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 8.68/4.81      vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 8.68/4.81      vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 8.68/4.81      vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 8.68/4.81      vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_Ovebt__member,type,
% 8.68/4.81      vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 8.68/4.81      vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 8.68/4.81      vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 8.68/4.81      vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 8.68/4.81      vEBT_VEBT_less: option_nat > option_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 8.68/4.81      vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 8.68/4.81      vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 8.68/4.81      vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 8.68/4.81      vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 8.68/4.81      vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 8.68/4.81      vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 8.68/4.81      vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 8.68/4.81      vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 8.68/4.81      vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 8.68/4.81      vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 8.68/4.81      vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 8.68/4.81      vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 8.68/4.81      vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 8.68/4.81      vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 8.68/4.81      vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 8.68/4.81      vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 8.68/4.81      vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 8.68/4.81      accp_nat: ( nat > nat > $o ) > nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.68/4.81      accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 8.68/4.81      accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 8.68/4.81      accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_fChoice_001t__Real__Oreal,type,
% 8.68/4.81      fChoice_real: ( real > $o ) > real ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001_Eo,type,
% 8.68/4.81      member_o: $o > set_o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Complex__Ocomplex,type,
% 8.68/4.81      member_complex: complex > set_complex > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Int__Oint,type,
% 8.68/4.81      member_int: int > set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 8.68/4.81      member_list_o: list_o > set_list_o > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 8.68/4.81      member_list_int: list_int > set_list_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 8.68/4.81      member_list_nat: list_nat > set_list_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.68/4.81      member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Nat__Onat,type,
% 8.68/4.81      member_nat: nat > set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Num__Onum,type,
% 8.68/4.81      member_num: num > set_num > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.68/4.81      member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Rat__Orat,type,
% 8.68/4.81      member_rat: rat > set_rat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Real__Oreal,type,
% 8.68/4.81      member_real: real > set_real > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 8.68/4.81      member_set_int: set_int > set_set_int > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.68/4.81      member_set_nat: set_nat > set_set_nat > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 8.68/4.81      member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_deg____,type,
% 8.68/4.81      deg: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_m____,type,
% 8.68/4.81      m: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_ma____,type,
% 8.68/4.81      ma: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_maxs____,type,
% 8.68/4.81      maxs: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_mi____,type,
% 8.68/4.81      mi: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_na____,type,
% 8.68/4.81      na: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_summary____,type,
% 8.68/4.81      summary: vEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_treeList____,type,
% 8.68/4.81      treeList: list_VEBT_VEBT ).
% 8.68/4.81  
% 8.68/4.81  thf(sy_v_xa____,type,
% 8.68/4.81      xa: nat ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_0__C1_C,axiom,
% 8.68/4.81      vEBT_invar_vebt @ summary @ m ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062,axiom,
% 8.68/4.81      vEBT_V8194947554948674370ptions @ summary @ maxs ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_2__C8_C,axiom,
% 8.68/4.81      na = m ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_3_bit__split__inv,axiom,
% 8.68/4.81      ! [X: nat,D: nat] :
% 8.68/4.81        ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 8.68/4.81        = X ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_4_dele__bmo__cont__corr,axiom,
% 8.68/4.81      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.68/4.81        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.81       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 8.68/4.81          = ( ( X != Y )
% 8.68/4.81            & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_5__092_060open_062invar__vebt_A_ItreeList_091high_Ax_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_Ax_An_J_A_Ilow_Ax_An_J_093_A_B_Amaxs_J_An_092_060close_062,axiom,
% 8.68/4.81      vEBT_invar_vebt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ na ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_6_xnotmi,axiom,
% 8.68/4.81      xa != mi ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_7_hlist,axiom,
% 8.68/4.81      ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( vEBT_VEBT_high @ xa @ na ) )
% 8.68/4.81      = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_8_nnvalid,axiom,
% 8.68/4.81      vEBT_invar_vebt @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_9_ninNullc,axiom,
% 8.68/4.81      vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_10_bb,axiom,
% 8.68/4.81      ( ( maxs
% 8.68/4.81       != ( vEBT_VEBT_high @ xa @ na ) )
% 8.68/4.81      & ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_11_True,axiom,
% 8.68/4.81      xa = ma ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_12_nothlist,axiom,
% 8.68/4.81      ! [I: nat] :
% 8.68/4.81        ( ( I
% 8.68/4.81         != ( vEBT_VEBT_high @ xa @ na ) )
% 8.68/4.81       => ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81         => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I )
% 8.68/4.81            = ( nth_VEBT_VEBT @ treeList @ I ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_13__C4_C,axiom,
% 8.68/4.81      ! [I2: nat] :
% 8.68/4.81        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X2 ) )
% 8.68/4.81          = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_14_in__children__def,axiom,
% 8.68/4.81      ( vEBT_V5917875025757280293ildren
% 8.68/4.81      = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ N2 ) ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_15_newsummvalid,axiom,
% 8.68/4.81      vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ m ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_16__C4_OIH_C_I1_J,axiom,
% 8.68/4.81      ! [X4: vEBT_VEBT] :
% 8.68/4.81        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 8.68/4.81       => ( ( vEBT_invar_vebt @ X4 @ na )
% 8.68/4.81          & ! [Xa: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ X4 @ Xa ) @ na ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_17_list__update__id,axiom,
% 8.68/4.81      ! [Xs: list_nat,I: nat] :
% 8.68/4.81        ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 8.68/4.81        = Xs ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_18_list__update__id,axiom,
% 8.68/4.81      ! [Xs: list_int,I: nat] :
% 8.68/4.81        ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 8.68/4.81        = Xs ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_19_list__update__id,axiom,
% 8.68/4.81      ! [Xs: list_VEBT_VEBT,I: nat] :
% 8.68/4.81        ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 8.68/4.81        = Xs ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_20_nth__list__update__neq,axiom,
% 8.68/4.81      ! [I: nat,J: nat,Xs: list_nat,X: nat] :
% 8.68/4.81        ( ( I != J )
% 8.68/4.81       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 8.68/4.81          = ( nth_nat @ Xs @ J ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_21_nth__list__update__neq,axiom,
% 8.68/4.81      ! [I: nat,J: nat,Xs: list_int,X: int] :
% 8.68/4.81        ( ( I != J )
% 8.68/4.81       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 8.68/4.81          = ( nth_int @ Xs @ J ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_22_nth__list__update__neq,axiom,
% 8.68/4.81      ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.68/4.81        ( ( I != J )
% 8.68/4.81       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 8.68/4.81          = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_23__092_060open_062treeList_A_B_Ahigh_Ax_An_A_092_060in_062_Aset_AtreeList_092_060close_062,axiom,
% 8.68/4.81      member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_24_allvalidinlist,axiom,
% 8.68/4.81      ! [X4: vEBT_VEBT] :
% 8.68/4.81        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ) )
% 8.68/4.81       => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_25__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062,axiom,
% 8.68/4.81      vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( vEBT_VEBT_low @ ma @ na ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_26__C111_C,axiom,
% 8.68/4.81      ! [I2: nat] :
% 8.68/4.81        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I2 ) @ X2 ) )
% 8.68/4.81          = ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ I2 ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_27__C4_OIH_C_I2_J,axiom,
% 8.68/4.81      ! [X: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ X ) @ m ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_28_list__update__overwrite,axiom,
% 8.68/4.81      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.68/4.81        ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
% 8.68/4.81        = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_29_not__min__Null__member,axiom,
% 8.68/4.81      ! [T: vEBT_VEBT] :
% 8.68/4.81        ( ~ ( vEBT_VEBT_minNull @ T )
% 8.68/4.81       => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_30__C5_C,axiom,
% 8.68/4.81      ( ( mi = ma )
% 8.68/4.81     => ! [X4: vEBT_VEBT] :
% 8.68/4.81          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 8.68/4.81         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_31__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 8.68/4.81      ( ( xa != mi )
% 8.68/4.81      | ( xa != ma ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_32__C0_C,axiom,
% 8.68/4.81      ! [X4: vEBT_VEBT] :
% 8.68/4.81        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 8.68/4.81       => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_33_hlbound,axiom,
% 8.68/4.81      ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81      & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_34__C4_Ohyps_C_I7_J,axiom,
% 8.68/4.81      ord_less_eq_nat @ mi @ ma ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_35__C4_Ohyps_C_I8_J,axiom,
% 8.68/4.81      ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_36__C2_C,axiom,
% 8.68/4.81      ( ( size_s6755466524823107622T_VEBT @ treeList )
% 8.68/4.81      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_37__C7_C,axiom,
% 8.68/4.81      ( ( mi != ma )
% 8.68/4.81     => ! [I2: nat] :
% 8.68/4.81          ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81         => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 8.68/4.81                = I2 )
% 8.68/4.81             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 8.68/4.81            & ! [Y2: nat] :
% 8.68/4.81                ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 8.68/4.81                    = I2 )
% 8.68/4.81                  & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 8.68/4.81               => ( ( ord_less_nat @ mi @ Y2 )
% 8.68/4.81                  & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_38_list__update__swap,axiom,
% 8.68/4.81      ! [I: nat,I3: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X5: vEBT_VEBT] :
% 8.68/4.81        ( ( I != I3 )
% 8.68/4.81       => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I3 @ X5 )
% 8.68/4.81          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X5 ) @ I @ X ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_39_yhelper,axiom,
% 8.68/4.81      ! [Y: nat] :
% 8.68/4.81        ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ Y @ na ) ) @ ( vEBT_VEBT_low @ Y @ na ) )
% 8.68/4.81       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81         => ( ( ord_less_nat @ mi @ Y )
% 8.68/4.81            & ( ord_less_eq_nat @ Y @ ma )
% 8.68/4.81            & ( ord_less_nat @ ( vEBT_VEBT_low @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_40__C7b_C,axiom,
% 8.68/4.81      ! [I2: nat] :
% 8.68/4.81        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.68/4.81       => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 8.68/4.81              = I2 )
% 8.68/4.81           => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 8.68/4.81          & ! [Y2: nat] :
% 8.68/4.81              ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 8.68/4.81                  = I2 )
% 8.68/4.81                & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 8.68/4.81             => ( ( ord_less_nat @ mi @ Y2 )
% 8.68/4.81                & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_41_valid__insert__both__member__options__pres,axiom,
% 8.68/4.81      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.68/4.81        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.81       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.81         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.81           => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.68/4.81             => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_42_valid__insert__both__member__options__add,axiom,
% 8.68/4.81      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.81        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.81       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.81         => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_43_newlistlength,axiom,
% 8.68/4.81      ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) )
% 8.68/4.81      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_44__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 8.68/4.81      ( ( mi != ma )
% 8.68/4.81      & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_45_member__bound,axiom,
% 8.68/4.81      ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 8.68/4.81        ( ( vEBT_vebt_member @ Tree @ X )
% 8.68/4.81       => ( ( vEBT_invar_vebt @ Tree @ N )
% 8.68/4.81         => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_46_less__exp,axiom,
% 8.68/4.81      ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_47_semiring__norm_I85_J,axiom,
% 8.68/4.81      ! [M: num] :
% 8.68/4.81        ( ( bit0 @ M )
% 8.68/4.81       != one ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_48_semiring__norm_I83_J,axiom,
% 8.68/4.81      ! [N: num] :
% 8.68/4.81        ( one
% 8.68/4.81       != ( bit0 @ N ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_49_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: real,P: real > $o] :
% 8.68/4.81        ( ( member_real @ A @ ( collect_real @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_50_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 8.68/4.81        ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_51_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: complex,P: complex > $o] :
% 8.68/4.81        ( ( member_complex @ A @ ( collect_complex @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_52_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: set_nat,P: set_nat > $o] :
% 8.68/4.81        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_53_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: nat,P: nat > $o] :
% 8.68/4.81        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_54_mem__Collect__eq,axiom,
% 8.68/4.81      ! [A: int,P: int > $o] :
% 8.68/4.81        ( ( member_int @ A @ ( collect_int @ P ) )
% 8.68/4.81        = ( P @ A ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_55_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_real] :
% 8.68/4.81        ( ( collect_real
% 8.68/4.81          @ ^ [X3: real] : ( member_real @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_56_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_Pr958786334691620121nt_int] :
% 8.68/4.81        ( ( collec213857154873943460nt_int
% 8.68/4.81          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_57_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_complex] :
% 8.68/4.81        ( ( collect_complex
% 8.68/4.81          @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_58_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_set_nat] :
% 8.68/4.81        ( ( collect_set_nat
% 8.68/4.81          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_59_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_nat] :
% 8.68/4.81        ( ( collect_nat
% 8.68/4.81          @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_60_Collect__mem__eq,axiom,
% 8.68/4.81      ! [A2: set_int] :
% 8.68/4.81        ( ( collect_int
% 8.68/4.81          @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 8.68/4.81        = A2 ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_61_Collect__cong,axiom,
% 8.68/4.81      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 8.68/4.81        ( ! [X6: product_prod_int_int] :
% 8.68/4.81            ( ( P @ X6 )
% 8.68/4.81            = ( Q @ X6 ) )
% 8.68/4.81       => ( ( collec213857154873943460nt_int @ P )
% 8.68/4.81          = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 8.68/4.81  
% 8.68/4.81  thf(fact_62_Collect__cong,axiom,
% 8.68/4.81      ! [P: complex > $o,Q: complex > $o] :
% 8.68/4.81        ( ! [X6: complex] :
% 8.68/4.81            ( ( P @ X6 )
% 8.68/4.81            = ( Q @ X6 ) )
% 8.68/4.81       => ( ( collect_complex @ P )
% 8.68/4.81          = ( collect_complex @ Q ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_63_Collect__cong,axiom,
% 8.68/4.82      ! [P: set_nat > $o,Q: set_nat > $o] :
% 8.68/4.82        ( ! [X6: set_nat] :
% 8.68/4.82            ( ( P @ X6 )
% 8.68/4.82            = ( Q @ X6 ) )
% 8.68/4.82       => ( ( collect_set_nat @ P )
% 8.68/4.82          = ( collect_set_nat @ Q ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_64_Collect__cong,axiom,
% 8.68/4.82      ! [P: nat > $o,Q: nat > $o] :
% 8.68/4.82        ( ! [X6: nat] :
% 8.68/4.82            ( ( P @ X6 )
% 8.68/4.82            = ( Q @ X6 ) )
% 8.68/4.82       => ( ( collect_nat @ P )
% 8.68/4.82          = ( collect_nat @ Q ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_65_Collect__cong,axiom,
% 8.68/4.82      ! [P: int > $o,Q: int > $o] :
% 8.68/4.82        ( ! [X6: int] :
% 8.68/4.82            ( ( P @ X6 )
% 8.68/4.82            = ( Q @ X6 ) )
% 8.68/4.82       => ( ( collect_int @ P )
% 8.68/4.82          = ( collect_int @ Q ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_66_numeral__less__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( ord_less_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_67_numeral__less__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( ord_less_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_68_numeral__less__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( ord_less_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_69_numeral__less__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( ord_less_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_70_high__bound__aux,axiom,
% 8.68/4.82      ! [Ma: nat,N: nat,M: nat] :
% 8.68/4.82        ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 8.68/4.82       => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_71_min__Null__member,axiom,
% 8.68/4.82      ! [T: vEBT_VEBT,X: nat] :
% 8.68/4.82        ( ( vEBT_VEBT_minNull @ T )
% 8.68/4.82       => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_72__C3_C,axiom,
% 8.68/4.82      ( deg
% 8.68/4.82      = ( plus_plus_nat @ na @ m ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_73_both__member__options__equiv__member,axiom,
% 8.68/4.82      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.82        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.82       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.68/4.82          = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_74_valid__member__both__member__options,axiom,
% 8.68/4.82      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.82        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.82       => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.68/4.82         => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_75_min__in__set__def,axiom,
% 8.68/4.82      ( vEBT_VEBT_min_in_set
% 8.68/4.82      = ( ^ [Xs2: set_nat,X3: nat] :
% 8.68/4.82            ( ( member_nat @ X3 @ Xs2 )
% 8.68/4.82            & ! [Y3: nat] :
% 8.68/4.82                ( ( member_nat @ Y3 @ Xs2 )
% 8.68/4.82               => ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_76_max__in__set__def,axiom,
% 8.68/4.82      ( vEBT_VEBT_max_in_set
% 8.68/4.82      = ( ^ [Xs2: set_nat,X3: nat] :
% 8.68/4.82            ( ( member_nat @ X3 @ Xs2 )
% 8.68/4.82            & ! [Y3: nat] :
% 8.68/4.82                ( ( member_nat @ Y3 @ Xs2 )
% 8.68/4.82               => ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_77_inthall,axiom,
% 8.68/4.82      ! [Xs: list_complex,P: complex > $o,N: nat] :
% 8.68/4.82        ( ! [X6: complex] :
% 8.68/4.82            ( ( member_complex @ X6 @ ( set_complex2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_78_inthall,axiom,
% 8.68/4.82      ! [Xs: list_real,P: real > $o,N: nat] :
% 8.68/4.82        ( ! [X6: real] :
% 8.68/4.82            ( ( member_real @ X6 @ ( set_real2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_79_inthall,axiom,
% 8.68/4.82      ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 8.68/4.82        ( ! [X6: set_nat] :
% 8.68/4.82            ( ( member_set_nat @ X6 @ ( set_set_nat2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_80_inthall,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 8.68/4.82        ( ! [X6: vEBT_VEBT] :
% 8.68/4.82            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_81_inthall,axiom,
% 8.68/4.82      ! [Xs: list_o,P: $o > $o,N: nat] :
% 8.68/4.82        ( ! [X6: $o] :
% 8.68/4.82            ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_82_inthall,axiom,
% 8.68/4.82      ! [Xs: list_nat,P: nat > $o,N: nat] :
% 8.68/4.82        ( ! [X6: nat] :
% 8.68/4.82            ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_83_inthall,axiom,
% 8.68/4.82      ! [Xs: list_int,P: int > $o,N: nat] :
% 8.68/4.82        ( ! [X6: int] :
% 8.68/4.82            ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 8.68/4.82           => ( P @ X6 ) )
% 8.68/4.82       => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.68/4.82         => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_84_numeral__eq__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( numera6690914467698888265omplex @ M )
% 8.68/4.82          = ( numera6690914467698888265omplex @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_85_numeral__eq__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_real @ M )
% 8.68/4.82          = ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_86_numeral__eq__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_rat @ M )
% 8.68/4.82          = ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_87_numeral__eq__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_nat @ M )
% 8.68/4.82          = ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_88_numeral__eq__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_int @ M )
% 8.68/4.82          = ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_89_semiring__norm_I87_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ( bit0 @ M )
% 8.68/4.82          = ( bit0 @ N ) )
% 8.68/4.82        = ( M = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_90__C12_C,axiom,
% 8.68/4.82      ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_91_inrg,axiom,
% 8.68/4.82      ( ( ord_less_eq_nat @ mi @ xa )
% 8.68/4.82      & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_92_numeral__le__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_93_numeral__le__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_94_numeral__le__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_95_numeral__le__iff,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_96_numeral__plus__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 8.68/4.82        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_97_numeral__plus__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_98_numeral__plus__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_99_numeral__plus__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_100_numeral__plus__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_101_add__numeral__left,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: complex] :
% 8.68/4.82        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 8.68/4.82        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_102_add__numeral__left,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: real] :
% 8.68/4.82        ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 8.68/4.82        = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_103_add__numeral__left,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: rat] :
% 8.68/4.82        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 8.68/4.82        = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_104_add__numeral__left,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: nat] :
% 8.68/4.82        ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 8.68/4.82        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_105_add__numeral__left,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: int] :
% 8.68/4.82        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 8.68/4.82        = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_106_post__member__pre__member,axiom,
% 8.68/4.82      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.68/4.82        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.82       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.82         => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.82           => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 8.68/4.82             => ( ( vEBT_vebt_member @ T @ Y )
% 8.68/4.82                | ( X = Y ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_107_member__correct,axiom,
% 8.68/4.82      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.82        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.82       => ( ( vEBT_vebt_member @ T @ X )
% 8.68/4.82          = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_108_length__list__update,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 8.68/4.82        ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
% 8.68/4.82        = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_109_length__list__update,axiom,
% 8.68/4.82      ! [Xs: list_o,I: nat,X: $o] :
% 8.68/4.82        ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X ) )
% 8.68/4.82        = ( size_size_list_o @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_110_length__list__update,axiom,
% 8.68/4.82      ! [Xs: list_nat,I: nat,X: nat] :
% 8.68/4.82        ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X ) )
% 8.68/4.82        = ( size_size_list_nat @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_111_length__list__update,axiom,
% 8.68/4.82      ! [Xs: list_int,I: nat,X: int] :
% 8.68/4.82        ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X ) )
% 8.68/4.82        = ( size_size_list_int @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_112_semiring__norm_I78_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.68/4.82        = ( ord_less_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_113_semiring__norm_I75_J,axiom,
% 8.68/4.82      ! [M: num] :
% 8.68/4.82        ~ ( ord_less_num @ M @ one ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_114__C6_C,axiom,
% 8.68/4.82      ( ( ord_less_eq_nat @ mi @ ma )
% 8.68/4.82      & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_115_list__update__beyond,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 8.68/4.82       => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 8.68/4.82          = Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_116_list__update__beyond,axiom,
% 8.68/4.82      ! [Xs: list_o,I: nat,X: $o] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 8.68/4.82       => ( ( list_update_o @ Xs @ I @ X )
% 8.68/4.82          = Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_117_list__update__beyond,axiom,
% 8.68/4.82      ! [Xs: list_nat,I: nat,X: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 8.68/4.82       => ( ( list_update_nat @ Xs @ I @ X )
% 8.68/4.82          = Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_118_list__update__beyond,axiom,
% 8.68/4.82      ! [Xs: list_int,I: nat,X: int] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 8.68/4.82       => ( ( list_update_int @ Xs @ I @ X )
% 8.68/4.82          = Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_119_semiring__norm_I76_J,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_120_nth__list__update__eq,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 8.68/4.82          = X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_121_nth__list__update__eq,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_o,X: $o] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ I )
% 8.68/4.82          = X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_122_nth__list__update__eq,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_nat,X: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 8.68/4.82          = X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_123_nth__list__update__eq,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_int,X: int] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 8.68/4.82          = X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_124_set__swap,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82         => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 8.68/4.82            = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_125_set__swap,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_o,J: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 8.68/4.82         => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 8.68/4.82            = ( set_o2 @ Xs ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_126_set__swap,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_nat,J: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82         => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 8.68/4.82            = ( set_nat2 @ Xs ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_127_set__swap,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_int,J: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 8.68/4.82         => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 8.68/4.82            = ( set_int2 @ Xs ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_128_Ex__list__of__length,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82      ? [Xs3: list_VEBT_VEBT] :
% 8.68/4.82        ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_129_Ex__list__of__length,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82      ? [Xs3: list_o] :
% 8.68/4.82        ( ( size_size_list_o @ Xs3 )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_130_Ex__list__of__length,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82      ? [Xs3: list_nat] :
% 8.68/4.82        ( ( size_size_list_nat @ Xs3 )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_131_Ex__list__of__length,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82      ? [Xs3: list_int] :
% 8.68/4.82        ( ( size_size_list_int @ Xs3 )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_132_neq__if__length__neq,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.68/4.82        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.68/4.82         != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.68/4.82       => ( Xs != Ys ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_133_neq__if__length__neq,axiom,
% 8.68/4.82      ! [Xs: list_o,Ys: list_o] :
% 8.68/4.82        ( ( ( size_size_list_o @ Xs )
% 8.68/4.82         != ( size_size_list_o @ Ys ) )
% 8.68/4.82       => ( Xs != Ys ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_134_neq__if__length__neq,axiom,
% 8.68/4.82      ! [Xs: list_nat,Ys: list_nat] :
% 8.68/4.82        ( ( ( size_size_list_nat @ Xs )
% 8.68/4.82         != ( size_size_list_nat @ Ys ) )
% 8.68/4.82       => ( Xs != Ys ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_135_neq__if__length__neq,axiom,
% 8.68/4.82      ! [Xs: list_int,Ys: list_int] :
% 8.68/4.82        ( ( ( size_size_list_int @ Xs )
% 8.68/4.82         != ( size_size_list_int @ Ys ) )
% 8.68/4.82       => ( Xs != Ys ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_136_is__num__normalize_I1_J,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_137_is__num__normalize_I1_J,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_138_is__num__normalize_I1_J,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_139_length__induct,axiom,
% 8.68/4.82      ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 8.68/4.82        ( ! [Xs3: list_VEBT_VEBT] :
% 8.68/4.82            ( ! [Ys2: list_VEBT_VEBT] :
% 8.68/4.82                ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 8.68/4.82               => ( P @ Ys2 ) )
% 8.68/4.82           => ( P @ Xs3 ) )
% 8.68/4.82       => ( P @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_140_length__induct,axiom,
% 8.68/4.82      ! [P: list_o > $o,Xs: list_o] :
% 8.68/4.82        ( ! [Xs3: list_o] :
% 8.68/4.82            ( ! [Ys2: list_o] :
% 8.68/4.82                ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 8.68/4.82               => ( P @ Ys2 ) )
% 8.68/4.82           => ( P @ Xs3 ) )
% 8.68/4.82       => ( P @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_141_length__induct,axiom,
% 8.68/4.82      ! [P: list_nat > $o,Xs: list_nat] :
% 8.68/4.82        ( ! [Xs3: list_nat] :
% 8.68/4.82            ( ! [Ys2: list_nat] :
% 8.68/4.82                ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 8.68/4.82               => ( P @ Ys2 ) )
% 8.68/4.82           => ( P @ Xs3 ) )
% 8.68/4.82       => ( P @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_142_length__induct,axiom,
% 8.68/4.82      ! [P: list_int > $o,Xs: list_int] :
% 8.68/4.82        ( ! [Xs3: list_int] :
% 8.68/4.82            ( ! [Ys2: list_int] :
% 8.68/4.82                ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 8.68/4.82               => ( P @ Ys2 ) )
% 8.68/4.82           => ( P @ Xs3 ) )
% 8.68/4.82       => ( P @ Xs ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_143_numeral__Bit0,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 8.68/4.82        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_144_numeral__Bit0,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 8.68/4.82        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_145_numeral__Bit0,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 8.68/4.82        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_146_numeral__Bit0,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.68/4.82        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_147_numeral__Bit0,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 8.68/4.82        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_148_nth__equalityI,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.68/4.82        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.68/4.82          = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.68/4.82       => ( ! [I4: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82             => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 8.68/4.82                = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 8.68/4.82         => ( Xs = Ys ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_149_nth__equalityI,axiom,
% 8.68/4.82      ! [Xs: list_o,Ys: list_o] :
% 8.68/4.82        ( ( ( size_size_list_o @ Xs )
% 8.68/4.82          = ( size_size_list_o @ Ys ) )
% 8.68/4.82       => ( ! [I4: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 8.68/4.82             => ( ( nth_o @ Xs @ I4 )
% 8.68/4.82                = ( nth_o @ Ys @ I4 ) ) )
% 8.68/4.82         => ( Xs = Ys ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_150_nth__equalityI,axiom,
% 8.68/4.82      ! [Xs: list_nat,Ys: list_nat] :
% 8.68/4.82        ( ( ( size_size_list_nat @ Xs )
% 8.68/4.82          = ( size_size_list_nat @ Ys ) )
% 8.68/4.82       => ( ! [I4: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82             => ( ( nth_nat @ Xs @ I4 )
% 8.68/4.82                = ( nth_nat @ Ys @ I4 ) ) )
% 8.68/4.82         => ( Xs = Ys ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_151_nth__equalityI,axiom,
% 8.68/4.82      ! [Xs: list_int,Ys: list_int] :
% 8.68/4.82        ( ( ( size_size_list_int @ Xs )
% 8.68/4.82          = ( size_size_list_int @ Ys ) )
% 8.68/4.82       => ( ! [I4: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 8.68/4.82             => ( ( nth_int @ Xs @ I4 )
% 8.68/4.82                = ( nth_int @ Ys @ I4 ) ) )
% 8.68/4.82         => ( Xs = Ys ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_152_Skolem__list__nth,axiom,
% 8.68/4.82      ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 8.68/4.82        ( ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82             => ? [X2: vEBT_VEBT] : ( P @ I5 @ X2 ) ) )
% 8.68/4.82        = ( ? [Xs2: list_VEBT_VEBT] :
% 8.68/4.82              ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.68/4.82                = K )
% 8.68/4.82              & ! [I5: nat] :
% 8.68/4.82                  ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82                 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs2 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_153_Skolem__list__nth,axiom,
% 8.68/4.82      ! [K: nat,P: nat > $o > $o] :
% 8.68/4.82        ( ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82             => ? [X2: $o] : ( P @ I5 @ X2 ) ) )
% 8.68/4.82        = ( ? [Xs2: list_o] :
% 8.68/4.82              ( ( ( size_size_list_o @ Xs2 )
% 8.68/4.82                = K )
% 8.68/4.82              & ! [I5: nat] :
% 8.68/4.82                  ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82                 => ( P @ I5 @ ( nth_o @ Xs2 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_154_Skolem__list__nth,axiom,
% 8.68/4.82      ! [K: nat,P: nat > nat > $o] :
% 8.68/4.82        ( ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82             => ? [X2: nat] : ( P @ I5 @ X2 ) ) )
% 8.68/4.82        = ( ? [Xs2: list_nat] :
% 8.68/4.82              ( ( ( size_size_list_nat @ Xs2 )
% 8.68/4.82                = K )
% 8.68/4.82              & ! [I5: nat] :
% 8.68/4.82                  ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82                 => ( P @ I5 @ ( nth_nat @ Xs2 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_155_Skolem__list__nth,axiom,
% 8.68/4.82      ! [K: nat,P: nat > int > $o] :
% 8.68/4.82        ( ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82             => ? [X2: int] : ( P @ I5 @ X2 ) ) )
% 8.68/4.82        = ( ? [Xs2: list_int] :
% 8.68/4.82              ( ( ( size_size_list_int @ Xs2 )
% 8.68/4.82                = K )
% 8.68/4.82              & ! [I5: nat] :
% 8.68/4.82                  ( ( ord_less_nat @ I5 @ K )
% 8.68/4.82                 => ( P @ I5 @ ( nth_int @ Xs2 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_156_list__eq__iff__nth__eq,axiom,
% 8.68/4.82      ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 8.68/4.82      = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 8.68/4.82            ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.68/4.82              = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 8.68/4.82            & ! [I5: nat] :
% 8.68/4.82                ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.68/4.82               => ( ( nth_VEBT_VEBT @ Xs2 @ I5 )
% 8.68/4.82                  = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_157_list__eq__iff__nth__eq,axiom,
% 8.68/4.82      ( ( ^ [Y4: list_o,Z2: list_o] : ( Y4 = Z2 ) )
% 8.68/4.82      = ( ^ [Xs2: list_o,Ys3: list_o] :
% 8.68/4.82            ( ( ( size_size_list_o @ Xs2 )
% 8.68/4.82              = ( size_size_list_o @ Ys3 ) )
% 8.68/4.82            & ! [I5: nat] :
% 8.68/4.82                ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 8.68/4.82               => ( ( nth_o @ Xs2 @ I5 )
% 8.68/4.82                  = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_158_list__eq__iff__nth__eq,axiom,
% 8.68/4.82      ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 8.68/4.82      = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 8.68/4.82            ( ( ( size_size_list_nat @ Xs2 )
% 8.68/4.82              = ( size_size_list_nat @ Ys3 ) )
% 8.68/4.82            & ! [I5: nat] :
% 8.68/4.82                ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 8.68/4.82               => ( ( nth_nat @ Xs2 @ I5 )
% 8.68/4.82                  = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_159_list__eq__iff__nth__eq,axiom,
% 8.68/4.82      ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 8.68/4.82      = ( ^ [Xs2: list_int,Ys3: list_int] :
% 8.68/4.82            ( ( ( size_size_list_int @ Xs2 )
% 8.68/4.82              = ( size_size_list_int @ Ys3 ) )
% 8.68/4.82            & ! [I5: nat] :
% 8.68/4.82                ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 8.68/4.82               => ( ( nth_int @ Xs2 @ I5 )
% 8.68/4.82                  = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_160_power2__nat__le__imp__le,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 8.68/4.82       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_161_power2__nat__le__eq__le,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.82        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_162_self__le__ge2__pow,axiom,
% 8.68/4.82      ! [K: nat,M: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.68/4.82       => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_163_all__set__conv__all__nth,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 8.68/4.82        ( ( ! [X3: vEBT_VEBT] :
% 8.68/4.82              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82             => ( P @ X3 ) ) )
% 8.68/4.82        = ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82             => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_164_all__set__conv__all__nth,axiom,
% 8.68/4.82      ! [Xs: list_o,P: $o > $o] :
% 8.68/4.82        ( ( ! [X3: $o] :
% 8.68/4.82              ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 8.68/4.82             => ( P @ X3 ) ) )
% 8.68/4.82        = ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 8.68/4.82             => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_165_all__set__conv__all__nth,axiom,
% 8.68/4.82      ! [Xs: list_nat,P: nat > $o] :
% 8.68/4.82        ( ( ! [X3: nat] :
% 8.68/4.82              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 8.68/4.82             => ( P @ X3 ) ) )
% 8.68/4.82        = ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82             => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_166_all__set__conv__all__nth,axiom,
% 8.68/4.82      ! [Xs: list_int,P: int > $o] :
% 8.68/4.82        ( ( ! [X3: int] :
% 8.68/4.82              ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 8.68/4.82             => ( P @ X3 ) ) )
% 8.68/4.82        = ( ! [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 8.68/4.82             => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_167_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_complex,P: complex > $o,X: complex] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_168_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_real,P: real > $o,X: real] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_169_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_set_nat @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_170_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_171_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_o,P: $o > $o,X: $o] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_172_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_nat,P: nat > $o,X: nat] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_173_all__nth__imp__all__set,axiom,
% 8.68/4.82      ! [Xs: list_int,P: int > $o,X: int] :
% 8.68/4.82        ( ! [I4: nat] :
% 8.68/4.82            ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 8.68/4.82           => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 8.68/4.82       => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 8.68/4.82         => ( P @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_174_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: complex,Xs: list_complex] :
% 8.68/4.82        ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs ) )
% 8.68/4.82              & ( ( nth_complex @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_175_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: real,Xs: list_real] :
% 8.68/4.82        ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 8.68/4.82              & ( ( nth_real @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_176_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: set_nat,Xs: list_set_nat] :
% 8.68/4.82        ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 8.68/4.82              & ( ( nth_set_nat @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_177_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 8.68/4.82        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82              & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_178_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: $o,Xs: list_o] :
% 8.68/4.82        ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 8.68/4.82              & ( ( nth_o @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_179_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: nat,Xs: list_nat] :
% 8.68/4.82        ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82              & ( ( nth_nat @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_180_in__set__conv__nth,axiom,
% 8.68/4.82      ! [X: int,Xs: list_int] :
% 8.68/4.82        ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 8.68/4.82        = ( ? [I5: nat] :
% 8.68/4.82              ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 8.68/4.82              & ( ( nth_int @ Xs @ I5 )
% 8.68/4.82                = X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_181_list__ball__nth,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( ! [X6: vEBT_VEBT] :
% 8.68/4.82              ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82             => ( P @ X6 ) )
% 8.68/4.82         => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_182_list__ball__nth,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_o,P: $o > $o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( ! [X6: $o] :
% 8.68/4.82              ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 8.68/4.82             => ( P @ X6 ) )
% 8.68/4.82         => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_183_list__ball__nth,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_nat,P: nat > $o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( ! [X6: nat] :
% 8.68/4.82              ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 8.68/4.82             => ( P @ X6 ) )
% 8.68/4.82         => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_184_list__ball__nth,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_int,P: int > $o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( ! [X6: int] :
% 8.68/4.82              ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 8.68/4.82             => ( P @ X6 ) )
% 8.68/4.82         => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_185_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_complex] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 8.68/4.82       => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_186_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_real] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 8.68/4.82       => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_187_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_set_nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 8.68/4.82       => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_188_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_VEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_189_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_190_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_191_nth__mem,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_int] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_192_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_complex,X: complex] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 8.68/4.82       => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_193_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_real,X: real] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 8.68/4.82       => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_194_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 8.68/4.82       => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_195_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_196_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_o,X: $o] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_197_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_nat,X: nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_198_set__update__memI,axiom,
% 8.68/4.82      ! [N: nat,Xs: list_int,X: int] :
% 8.68/4.82        ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_199_nth__list__update,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( ( ( I = J )
% 8.68/4.82           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 8.68/4.82              = X ) )
% 8.68/4.82          & ( ( I != J )
% 8.68/4.82           => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 8.68/4.82              = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_200_nth__list__update,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_o,X: $o,J: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ J )
% 8.68/4.82          = ( ( ( I = J )
% 8.68/4.82             => X )
% 8.68/4.82            & ( ( I != J )
% 8.68/4.82             => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_201_nth__list__update,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( ( ( I = J )
% 8.68/4.82           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 8.68/4.82              = X ) )
% 8.68/4.82          & ( ( I != J )
% 8.68/4.82           => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 8.68/4.82              = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_202_nth__list__update,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_int,J: nat,X: int] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( ( ( I = J )
% 8.68/4.82           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 8.68/4.82              = X ) )
% 8.68/4.82          & ( ( I != J )
% 8.68/4.82           => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 8.68/4.82              = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_203_list__update__same__conv,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.68/4.82       => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 8.68/4.82            = Xs )
% 8.68/4.82          = ( ( nth_VEBT_VEBT @ Xs @ I )
% 8.68/4.82            = X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_204_list__update__same__conv,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_o,X: $o] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.68/4.82       => ( ( ( list_update_o @ Xs @ I @ X )
% 8.68/4.82            = Xs )
% 8.68/4.82          = ( ( nth_o @ Xs @ I )
% 8.68/4.82            = X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_205_list__update__same__conv,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_nat,X: nat] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.68/4.82       => ( ( ( list_update_nat @ Xs @ I @ X )
% 8.68/4.82            = Xs )
% 8.68/4.82          = ( ( nth_nat @ Xs @ I )
% 8.68/4.82            = X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_206_list__update__same__conv,axiom,
% 8.68/4.82      ! [I: nat,Xs: list_int,X: int] :
% 8.68/4.82        ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.68/4.82       => ( ( ( list_update_int @ Xs @ I @ X )
% 8.68/4.82            = Xs )
% 8.68/4.82          = ( ( nth_int @ Xs @ I )
% 8.68/4.82            = X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_207_set__n__deg__not__0,axiom,
% 8.68/4.82      ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 8.68/4.82        ( ! [X6: vEBT_VEBT] :
% 8.68/4.82            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.82           => ( vEBT_invar_vebt @ X6 @ N ) )
% 8.68/4.82       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.68/4.82            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.82         => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_208_bit__concat__def,axiom,
% 8.68/4.82      ( vEBT_VEBT_bit_concat
% 8.68/4.82      = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_209_low__inv,axiom,
% 8.68/4.82      ! [X: nat,N: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.82       => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 8.68/4.82          = X ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_210_high__inv,axiom,
% 8.68/4.82      ! [X: nat,N: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.82       => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 8.68/4.82          = Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_211__C9_C,axiom,
% 8.68/4.82      ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.82      = na ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_212_nat__add__left__cancel__le,axiom,
% 8.68/4.82      ! [K: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.68/4.82        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_213_nat__add__left__cancel__less,axiom,
% 8.68/4.82      ! [K: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.68/4.82        = ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_214_enat__ord__number_I2_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.68/4.82        = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_215_add__less__cancel__right,axiom,
% 8.68/4.82      ! [A: real,C: real,B: real] :
% 8.68/4.82        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.82        = ( ord_less_real @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_216_add__less__cancel__right,axiom,
% 8.68/4.82      ! [A: rat,C: rat,B: rat] :
% 8.68/4.82        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.82        = ( ord_less_rat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_217_add__less__cancel__right,axiom,
% 8.68/4.82      ! [A: nat,C: nat,B: nat] :
% 8.68/4.82        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.82        = ( ord_less_nat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_218_add__less__cancel__right,axiom,
% 8.68/4.82      ! [A: int,C: int,B: int] :
% 8.68/4.82        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.82        = ( ord_less_int @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_219_add__less__cancel__left,axiom,
% 8.68/4.82      ! [C: real,A: real,B: real] :
% 8.68/4.82        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 8.68/4.82        = ( ord_less_real @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_220_add__less__cancel__left,axiom,
% 8.68/4.82      ! [C: rat,A: rat,B: rat] :
% 8.68/4.82        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.68/4.82        = ( ord_less_rat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_221_add__less__cancel__left,axiom,
% 8.68/4.82      ! [C: nat,A: nat,B: nat] :
% 8.68/4.82        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.68/4.82        = ( ord_less_nat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_222_add__less__cancel__left,axiom,
% 8.68/4.82      ! [C: int,A: int,B: int] :
% 8.68/4.82        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.68/4.82        = ( ord_less_int @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_223_add__le__cancel__right,axiom,
% 8.68/4.82      ! [A: real,C: real,B: real] :
% 8.68/4.82        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.82        = ( ord_less_eq_real @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_224_add__le__cancel__right,axiom,
% 8.68/4.82      ! [A: rat,C: rat,B: rat] :
% 8.68/4.82        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.82        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_225_add__le__cancel__right,axiom,
% 8.68/4.82      ! [A: nat,C: nat,B: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.82        = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_226_add__le__cancel__right,axiom,
% 8.68/4.82      ! [A: int,C: int,B: int] :
% 8.68/4.82        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.82        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_227_add__le__cancel__left,axiom,
% 8.68/4.82      ! [C: real,A: real,B: real] :
% 8.68/4.82        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 8.68/4.82        = ( ord_less_eq_real @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_228_add__le__cancel__left,axiom,
% 8.68/4.82      ! [C: rat,A: rat,B: rat] :
% 8.68/4.82        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.68/4.82        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_229_add__le__cancel__left,axiom,
% 8.68/4.82      ! [C: nat,A: nat,B: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.68/4.82        = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_230_add__le__cancel__left,axiom,
% 8.68/4.82      ! [C: int,A: int,B: int] :
% 8.68/4.82        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.68/4.82        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_231__C11_C,axiom,
% 8.68/4.82      ord_less_eq_nat @ one_one_nat @ na ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_232_add__left__cancel,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ A @ B )
% 8.68/4.82          = ( plus_plus_real @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_233_add__left__cancel,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ A @ B )
% 8.68/4.82          = ( plus_plus_rat @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_234_add__left__cancel,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( ( plus_plus_nat @ A @ B )
% 8.68/4.82          = ( plus_plus_nat @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_235_add__left__cancel,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ A @ B )
% 8.68/4.82          = ( plus_plus_int @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_236_add__right__cancel,axiom,
% 8.68/4.82      ! [B: real,A: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ B @ A )
% 8.68/4.82          = ( plus_plus_real @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_237_add__right__cancel,axiom,
% 8.68/4.82      ! [B: rat,A: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ B @ A )
% 8.68/4.82          = ( plus_plus_rat @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_238_add__right__cancel,axiom,
% 8.68/4.82      ! [B: nat,A: nat,C: nat] :
% 8.68/4.82        ( ( ( plus_plus_nat @ B @ A )
% 8.68/4.82          = ( plus_plus_nat @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_239_add__right__cancel,axiom,
% 8.68/4.82      ! [B: int,A: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ B @ A )
% 8.68/4.82          = ( plus_plus_int @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_240_pow__sum,axiom,
% 8.68/4.82      ! [A: nat,B: nat] :
% 8.68/4.82        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 8.68/4.82        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_241_high__def,axiom,
% 8.68/4.82      ( vEBT_VEBT_high
% 8.68/4.82      = ( ^ [X3: nat,N2: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_242_mult__numeral__left__semiring__numeral,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: complex] :
% 8.68/4.82        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 8.68/4.82        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_243_mult__numeral__left__semiring__numeral,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: real] :
% 8.68/4.82        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 8.68/4.82        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_244_mult__numeral__left__semiring__numeral,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 8.68/4.82        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_245_mult__numeral__left__semiring__numeral,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 8.68/4.82        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_246_mult__numeral__left__semiring__numeral,axiom,
% 8.68/4.82      ! [V: num,W: num,Z: int] :
% 8.68/4.82        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 8.68/4.82        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_247_numeral__times__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 8.68/4.82        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_248_numeral__times__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_249_numeral__times__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_250_numeral__times__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_251_numeral__times__numeral,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_252_mult_Oright__neutral,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ A @ one_one_complex )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_253_mult_Oright__neutral,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ A @ one_one_real )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_254_mult_Oright__neutral,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ A @ one_one_rat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_255_mult_Oright__neutral,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_256_mult_Oright__neutral,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ A @ one_one_int )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_257_mult__1,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ one_one_complex @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_258_mult__1,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ one_one_real @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_259_mult__1,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ one_one_rat @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_260_mult__1,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ one_one_nat @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_261_mult__1,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ one_one_int @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_262_power__one,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( power_power_rat @ one_one_rat @ N )
% 8.68/4.82        = one_one_rat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_263_power__one,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( power_power_nat @ one_one_nat @ N )
% 8.68/4.82        = one_one_nat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_264_power__one,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( power_power_real @ one_one_real @ N )
% 8.68/4.82        = one_one_real ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_265_power__one,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( power_power_int @ one_one_int @ N )
% 8.68/4.82        = one_one_int ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_266_power__one,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( power_power_complex @ one_one_complex @ N )
% 8.68/4.82        = one_one_complex ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_267_power__one__right,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( power_power_nat @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_268_power__one__right,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( power_power_real @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_269_power__one__right,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( power_power_int @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_270_power__one__right,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( power_power_complex @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_271_nat__1__eq__mult__iff,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( one_one_nat
% 8.68/4.82          = ( times_times_nat @ M @ N ) )
% 8.68/4.82        = ( ( M = one_one_nat )
% 8.68/4.82          & ( N = one_one_nat ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_272_nat__mult__eq__1__iff,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( ( times_times_nat @ M @ N )
% 8.68/4.82          = one_one_nat )
% 8.68/4.82        = ( ( M = one_one_nat )
% 8.68/4.82          & ( N = one_one_nat ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_273_semiring__norm_I6_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.68/4.82        = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_274_semiring__norm_I71_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.68/4.82        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_275_semiring__norm_I68_J,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_276_distrib__right__numeral,axiom,
% 8.68/4.82      ! [A: complex,B: complex,V: num] :
% 8.68/4.82        ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 8.68/4.82        = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_277_distrib__right__numeral,axiom,
% 8.68/4.82      ! [A: real,B: real,V: num] :
% 8.68/4.82        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.82        = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_278_distrib__right__numeral,axiom,
% 8.68/4.82      ! [A: rat,B: rat,V: num] :
% 8.68/4.82        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.82        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_279_distrib__right__numeral,axiom,
% 8.68/4.82      ! [A: nat,B: nat,V: num] :
% 8.68/4.82        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 8.68/4.82        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_280_distrib__right__numeral,axiom,
% 8.68/4.82      ! [A: int,B: int,V: num] :
% 8.68/4.82        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.82        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_281_distrib__left__numeral,axiom,
% 8.68/4.82      ! [V: num,B: complex,C: complex] :
% 8.68/4.82        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 8.68/4.82        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_282_distrib__left__numeral,axiom,
% 8.68/4.82      ! [V: num,B: real,C: real] :
% 8.68/4.82        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.82        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_283_distrib__left__numeral,axiom,
% 8.68/4.82      ! [V: num,B: rat,C: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.82        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_284_distrib__left__numeral,axiom,
% 8.68/4.82      ! [V: num,B: nat,C: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.82        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_285_distrib__left__numeral,axiom,
% 8.68/4.82      ! [V: num,B: int,C: int] :
% 8.68/4.82        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.82        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_286_numeral__eq__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ( numera6690914467698888265omplex @ N )
% 8.68/4.82          = one_one_complex )
% 8.68/4.82        = ( N = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_287_numeral__eq__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_real @ N )
% 8.68/4.82          = one_one_real )
% 8.68/4.82        = ( N = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_288_numeral__eq__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_rat @ N )
% 8.68/4.82          = one_one_rat )
% 8.68/4.82        = ( N = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_289_numeral__eq__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_nat @ N )
% 8.68/4.82          = one_one_nat )
% 8.68/4.82        = ( N = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_290_numeral__eq__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ( numeral_numeral_int @ N )
% 8.68/4.82          = one_one_int )
% 8.68/4.82        = ( N = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_291_one__eq__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( one_one_complex
% 8.68/4.82          = ( numera6690914467698888265omplex @ N ) )
% 8.68/4.82        = ( one = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_292_one__eq__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( one_one_real
% 8.68/4.82          = ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( one = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_293_one__eq__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( one_one_rat
% 8.68/4.82          = ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( one = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_294_one__eq__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( one_one_nat
% 8.68/4.82          = ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( one = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_295_one__eq__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( one_one_int
% 8.68/4.82          = ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( one = N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_296_power__inject__exp,axiom,
% 8.68/4.82      ! [A: real,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.82       => ( ( ( power_power_real @ A @ M )
% 8.68/4.82            = ( power_power_real @ A @ N ) )
% 8.68/4.82          = ( M = N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_297_power__inject__exp,axiom,
% 8.68/4.82      ! [A: rat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.82       => ( ( ( power_power_rat @ A @ M )
% 8.68/4.82            = ( power_power_rat @ A @ N ) )
% 8.68/4.82          = ( M = N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_298_power__inject__exp,axiom,
% 8.68/4.82      ! [A: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.82       => ( ( ( power_power_nat @ A @ M )
% 8.68/4.82            = ( power_power_nat @ A @ N ) )
% 8.68/4.82          = ( M = N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_299_power__inject__exp,axiom,
% 8.68/4.82      ! [A: int,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.82       => ( ( ( power_power_int @ A @ M )
% 8.68/4.82            = ( power_power_int @ A @ N ) )
% 8.68/4.82          = ( M = N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_300_semiring__norm_I2_J,axiom,
% 8.68/4.82      ( ( plus_plus_num @ one @ one )
% 8.68/4.82      = ( bit0 @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_301_semiring__norm_I69_J,axiom,
% 8.68/4.82      ! [M: num] :
% 8.68/4.82        ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_302_enat__ord__number_I1_J,axiom,
% 8.68/4.82      ! [M: num,N: num] :
% 8.68/4.82        ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.68/4.82        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_303_le__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [A: real,B: real,W: num] :
% 8.68/4.82        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 8.68/4.82        = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_304_le__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [A: rat,B: rat,W: num] :
% 8.68/4.82        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 8.68/4.82        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_305_divide__le__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [B: real,W: num,A: real] :
% 8.68/4.82        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 8.68/4.82        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_306_divide__le__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [B: rat,W: num,A: rat] :
% 8.68/4.82        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 8.68/4.82        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_307_divide__less__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [B: real,W: num,A: real] :
% 8.68/4.82        ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 8.68/4.82        = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_308_divide__less__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [B: rat,W: num,A: rat] :
% 8.68/4.82        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 8.68/4.82        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_309_less__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [A: real,B: real,W: num] :
% 8.68/4.82        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 8.68/4.82        = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_310_less__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.82      ! [A: rat,B: rat,W: num] :
% 8.68/4.82        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 8.68/4.82        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_311_power__strict__increasing__iff,axiom,
% 8.68/4.82      ! [B: real,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ B )
% 8.68/4.82       => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 8.68/4.82          = ( ord_less_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_312_power__strict__increasing__iff,axiom,
% 8.68/4.82      ! [B: rat,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ B )
% 8.68/4.82       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 8.68/4.82          = ( ord_less_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_313_power__strict__increasing__iff,axiom,
% 8.68/4.82      ! [B: nat,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ B )
% 8.68/4.82       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 8.68/4.82          = ( ord_less_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_314_power__strict__increasing__iff,axiom,
% 8.68/4.82      ! [B: int,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ B )
% 8.68/4.82       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 8.68/4.82          = ( ord_less_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_315_power__add__numeral,axiom,
% 8.68/4.82      ! [A: complex,M: num,N: num] :
% 8.68/4.82        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.68/4.82        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_316_power__add__numeral,axiom,
% 8.68/4.82      ! [A: real,M: num,N: num] :
% 8.68/4.82        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.68/4.82        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_317_power__add__numeral,axiom,
% 8.68/4.82      ! [A: rat,M: num,N: num] :
% 8.68/4.82        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.68/4.82        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_318_power__add__numeral,axiom,
% 8.68/4.82      ! [A: nat,M: num,N: num] :
% 8.68/4.82        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.68/4.82        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_319_power__add__numeral,axiom,
% 8.68/4.82      ! [A: int,M: num,N: num] :
% 8.68/4.82        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.68/4.82        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_320_power__add__numeral2,axiom,
% 8.68/4.82      ! [A: complex,M: num,N: num,B: complex] :
% 8.68/4.82        ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.68/4.82        = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_321_power__add__numeral2,axiom,
% 8.68/4.82      ! [A: real,M: num,N: num,B: real] :
% 8.68/4.82        ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.68/4.82        = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_322_power__add__numeral2,axiom,
% 8.68/4.82      ! [A: rat,M: num,N: num,B: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.68/4.82        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_323_power__add__numeral2,axiom,
% 8.68/4.82      ! [A: nat,M: num,N: num,B: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.68/4.82        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_324_power__add__numeral2,axiom,
% 8.68/4.82      ! [A: int,M: num,N: num,B: int] :
% 8.68/4.82        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.68/4.82        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_325_one__add__one,axiom,
% 8.68/4.82      ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 8.68/4.82      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_326_one__add__one,axiom,
% 8.68/4.82      ( ( plus_plus_real @ one_one_real @ one_one_real )
% 8.68/4.82      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_327_one__add__one,axiom,
% 8.68/4.82      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 8.68/4.82      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_328_one__add__one,axiom,
% 8.68/4.82      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 8.68/4.82      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_329_one__add__one,axiom,
% 8.68/4.82      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 8.68/4.82      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_330_power__increasing__iff,axiom,
% 8.68/4.82      ! [B: real,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ B )
% 8.68/4.82       => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 8.68/4.82          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_331_power__increasing__iff,axiom,
% 8.68/4.82      ! [B: rat,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ B )
% 8.68/4.82       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 8.68/4.82          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_332_power__increasing__iff,axiom,
% 8.68/4.82      ! [B: nat,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ B )
% 8.68/4.82       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 8.68/4.82          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_333_power__increasing__iff,axiom,
% 8.68/4.82      ! [B: int,X: nat,Y: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ B )
% 8.68/4.82       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 8.68/4.82          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_334_numeral__plus__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 8.68/4.82        = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_335_numeral__plus__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 8.68/4.82        = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_336_numeral__plus__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 8.68/4.82        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_337_numeral__plus__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 8.68/4.82        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_338_numeral__plus__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 8.68/4.82        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_339_one__plus__numeral,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 8.68/4.82        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_340_one__plus__numeral,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_341_one__plus__numeral,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_342_one__plus__numeral,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_343_one__plus__numeral,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_344_numeral__le__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 8.68/4.82        = ( ord_less_eq_num @ N @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_345_numeral__le__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 8.68/4.82        = ( ord_less_eq_num @ N @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_346_numeral__le__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 8.68/4.82        = ( ord_less_eq_num @ N @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_347_numeral__le__one__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 8.68/4.82        = ( ord_less_eq_num @ N @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_348_one__less__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 8.68/4.82        = ( ord_less_num @ one @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_349_one__less__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 8.68/4.82        = ( ord_less_num @ one @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_350_one__less__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 8.68/4.82        = ( ord_less_num @ one @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_351_one__less__numeral__iff,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 8.68/4.82        = ( ord_less_num @ one @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_352_enat__less__induct,axiom,
% 8.68/4.82      ! [P: extended_enat > $o,N: extended_enat] :
% 8.68/4.82        ( ! [N3: extended_enat] :
% 8.68/4.82            ( ! [M2: extended_enat] :
% 8.68/4.82                ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 8.68/4.82               => ( P @ M2 ) )
% 8.68/4.82           => ( P @ N3 ) )
% 8.68/4.82       => ( P @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_353_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_354_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_355_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_356_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_357_comm__monoid__mult__class_Omult__1,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ one_one_complex @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_358_comm__monoid__mult__class_Omult__1,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ one_one_real @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_359_comm__monoid__mult__class_Omult__1,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ one_one_rat @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_360_comm__monoid__mult__class_Omult__1,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ one_one_nat @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_361_comm__monoid__mult__class_Omult__1,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ one_one_int @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_362_mult_Oassoc,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_363_mult_Oassoc,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_364_mult_Oassoc,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_365_mult_Oassoc,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 8.68/4.82        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_366_mult_Ocommute,axiom,
% 8.68/4.82      ( times_times_real
% 8.68/4.82      = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_367_mult_Ocommute,axiom,
% 8.68/4.82      ( times_times_rat
% 8.68/4.82      = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_368_mult_Ocommute,axiom,
% 8.68/4.82      ( times_times_nat
% 8.68/4.82      = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_369_mult_Ocommute,axiom,
% 8.68/4.82      ( times_times_int
% 8.68/4.82      = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_370_mult_Ocomm__neutral,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ A @ one_one_complex )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_371_mult_Ocomm__neutral,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ A @ one_one_real )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_372_mult_Ocomm__neutral,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ A @ one_one_rat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_373_mult_Ocomm__neutral,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ A @ one_one_nat )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_374_mult_Ocomm__neutral,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ A @ one_one_int )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_375_mult_Oleft__commute,axiom,
% 8.68/4.82      ! [B: real,A: real,C: real] :
% 8.68/4.82        ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 8.68/4.82        = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_376_mult_Oleft__commute,axiom,
% 8.68/4.82      ! [B: rat,A: rat,C: rat] :
% 8.68/4.82        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 8.68/4.82        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_377_mult_Oleft__commute,axiom,
% 8.68/4.82      ! [B: nat,A: nat,C: nat] :
% 8.68/4.82        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 8.68/4.82        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_378_mult_Oleft__commute,axiom,
% 8.68/4.82      ! [B: int,A: int,C: int] :
% 8.68/4.82        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 8.68/4.82        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_379_nat__mult__1,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( times_times_nat @ one_one_nat @ N )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_380_one__reorient,axiom,
% 8.68/4.82      ! [X: complex] :
% 8.68/4.82        ( ( one_one_complex = X )
% 8.68/4.82        = ( X = one_one_complex ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_381_one__reorient,axiom,
% 8.68/4.82      ! [X: real] :
% 8.68/4.82        ( ( one_one_real = X )
% 8.68/4.82        = ( X = one_one_real ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_382_one__reorient,axiom,
% 8.68/4.82      ! [X: rat] :
% 8.68/4.82        ( ( one_one_rat = X )
% 8.68/4.82        = ( X = one_one_rat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_383_one__reorient,axiom,
% 8.68/4.82      ! [X: nat] :
% 8.68/4.82        ( ( one_one_nat = X )
% 8.68/4.82        = ( X = one_one_nat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_384_one__reorient,axiom,
% 8.68/4.82      ! [X: int] :
% 8.68/4.82        ( ( one_one_int = X )
% 8.68/4.82        = ( X = one_one_int ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_385_nat__mult__1__right,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ( ( times_times_nat @ N @ one_one_nat )
% 8.68/4.82        = N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_386_power__one__over,axiom,
% 8.68/4.82      ! [A: complex,N: nat] :
% 8.68/4.82        ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 8.68/4.82        = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_387_power__one__over,axiom,
% 8.68/4.82      ! [A: real,N: nat] :
% 8.68/4.82        ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 8.68/4.82        = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_388_power__one__over,axiom,
% 8.68/4.82      ! [A: rat,N: nat] :
% 8.68/4.82        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 8.68/4.82        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_389_left__right__inverse__power,axiom,
% 8.68/4.82      ! [X: complex,Y: complex,N: nat] :
% 8.68/4.82        ( ( ( times_times_complex @ X @ Y )
% 8.68/4.82          = one_one_complex )
% 8.68/4.82       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 8.68/4.82          = one_one_complex ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_390_left__right__inverse__power,axiom,
% 8.68/4.82      ! [X: real,Y: real,N: nat] :
% 8.68/4.82        ( ( ( times_times_real @ X @ Y )
% 8.68/4.82          = one_one_real )
% 8.68/4.82       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 8.68/4.82          = one_one_real ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_391_left__right__inverse__power,axiom,
% 8.68/4.82      ! [X: rat,Y: rat,N: nat] :
% 8.68/4.82        ( ( ( times_times_rat @ X @ Y )
% 8.68/4.82          = one_one_rat )
% 8.68/4.82       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 8.68/4.82          = one_one_rat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_392_left__right__inverse__power,axiom,
% 8.68/4.82      ! [X: nat,Y: nat,N: nat] :
% 8.68/4.82        ( ( ( times_times_nat @ X @ Y )
% 8.68/4.82          = one_one_nat )
% 8.68/4.82       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 8.68/4.82          = one_one_nat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_393_left__right__inverse__power,axiom,
% 8.68/4.82      ! [X: int,Y: int,N: nat] :
% 8.68/4.82        ( ( ( times_times_int @ X @ Y )
% 8.68/4.82          = one_one_int )
% 8.68/4.82       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 8.68/4.82          = one_one_int ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_394_le__cube,axiom,
% 8.68/4.82      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_395_le__square,axiom,
% 8.68/4.82      ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_396_mult__le__mono,axiom,
% 8.68/4.82      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.82       => ( ( ord_less_eq_nat @ K @ L2 )
% 8.68/4.82         => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_397_mult__le__mono1,axiom,
% 8.68/4.82      ! [I: nat,J: nat,K: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.82       => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_398_mult__le__mono2,axiom,
% 8.68/4.82      ! [I: nat,J: nat,K: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.82       => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_399_add__mult__distrib,axiom,
% 8.68/4.82      ! [M: nat,N: nat,K: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 8.68/4.82        = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_400_add__mult__distrib2,axiom,
% 8.68/4.82      ! [K: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_401_power__gt1__lemma,axiom,
% 8.68/4.82      ! [A: real,N: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.82       => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_402_power__gt1__lemma,axiom,
% 8.68/4.82      ! [A: rat,N: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.82       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_403_power__gt1__lemma,axiom,
% 8.68/4.82      ! [A: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.82       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_404_power__gt1__lemma,axiom,
% 8.68/4.82      ! [A: int,N: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.82       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_405_power__less__power__Suc,axiom,
% 8.68/4.82      ! [A: real,N: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.82       => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_406_power__less__power__Suc,axiom,
% 8.68/4.82      ! [A: rat,N: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.82       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_407_power__less__power__Suc,axiom,
% 8.68/4.82      ! [A: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.82       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_408_power__less__power__Suc,axiom,
% 8.68/4.82      ! [A: int,N: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.82       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_409_power__divide,axiom,
% 8.68/4.82      ! [A: complex,B: complex,N: nat] :
% 8.68/4.82        ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 8.68/4.82        = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_410_power__divide,axiom,
% 8.68/4.82      ! [A: real,B: real,N: nat] :
% 8.68/4.82        ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 8.68/4.82        = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_411_power__divide,axiom,
% 8.68/4.82      ! [A: rat,B: rat,N: nat] :
% 8.68/4.82        ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 8.68/4.82        = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_412_add__One__commute,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ( ( plus_plus_num @ one @ N )
% 8.68/4.82        = ( plus_plus_num @ N @ one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_413_le__num__One__iff,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( ord_less_eq_num @ X @ one )
% 8.68/4.82        = ( X = one ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_414_power__commutes,axiom,
% 8.68/4.82      ! [A: complex,N: nat] :
% 8.68/4.82        ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 8.68/4.82        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_415_power__commutes,axiom,
% 8.68/4.82      ! [A: real,N: nat] :
% 8.68/4.82        ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 8.68/4.82        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_416_power__commutes,axiom,
% 8.68/4.82      ! [A: rat,N: nat] :
% 8.68/4.82        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 8.68/4.82        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_417_power__commutes,axiom,
% 8.68/4.82      ! [A: nat,N: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 8.68/4.82        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_418_power__commutes,axiom,
% 8.68/4.82      ! [A: int,N: nat] :
% 8.68/4.82        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 8.68/4.82        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_419_power__mult__distrib,axiom,
% 8.68/4.82      ! [A: complex,B: complex,N: nat] :
% 8.68/4.82        ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 8.68/4.82        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_420_power__mult__distrib,axiom,
% 8.68/4.82      ! [A: real,B: real,N: nat] :
% 8.68/4.82        ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 8.68/4.82        = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_421_power__mult__distrib,axiom,
% 8.68/4.82      ! [A: rat,B: rat,N: nat] :
% 8.68/4.82        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 8.68/4.82        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_422_power__mult__distrib,axiom,
% 8.68/4.82      ! [A: nat,B: nat,N: nat] :
% 8.68/4.82        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 8.68/4.82        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_423_power__mult__distrib,axiom,
% 8.68/4.82      ! [A: int,B: int,N: nat] :
% 8.68/4.82        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 8.68/4.82        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_424_power__commuting__commutes,axiom,
% 8.68/4.82      ! [X: complex,Y: complex,N: nat] :
% 8.68/4.82        ( ( ( times_times_complex @ X @ Y )
% 8.68/4.82          = ( times_times_complex @ Y @ X ) )
% 8.68/4.82       => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 8.68/4.82          = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_425_power__commuting__commutes,axiom,
% 8.68/4.82      ! [X: real,Y: real,N: nat] :
% 8.68/4.82        ( ( ( times_times_real @ X @ Y )
% 8.68/4.82          = ( times_times_real @ Y @ X ) )
% 8.68/4.82       => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 8.68/4.82          = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_426_power__commuting__commutes,axiom,
% 8.68/4.82      ! [X: rat,Y: rat,N: nat] :
% 8.68/4.82        ( ( ( times_times_rat @ X @ Y )
% 8.68/4.82          = ( times_times_rat @ Y @ X ) )
% 8.68/4.82       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 8.68/4.82          = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_427_power__commuting__commutes,axiom,
% 8.68/4.82      ! [X: nat,Y: nat,N: nat] :
% 8.68/4.82        ( ( ( times_times_nat @ X @ Y )
% 8.68/4.82          = ( times_times_nat @ Y @ X ) )
% 8.68/4.82       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 8.68/4.82          = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_428_power__commuting__commutes,axiom,
% 8.68/4.82      ! [X: int,Y: int,N: nat] :
% 8.68/4.82        ( ( ( times_times_int @ X @ Y )
% 8.68/4.82          = ( times_times_int @ Y @ X ) )
% 8.68/4.82       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 8.68/4.82          = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_429_power__mult,axiom,
% 8.68/4.82      ! [A: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 8.68/4.82        = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_430_power__mult,axiom,
% 8.68/4.82      ! [A: real,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 8.68/4.82        = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_431_power__mult,axiom,
% 8.68/4.82      ! [A: int,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 8.68/4.82        = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_432_power__mult,axiom,
% 8.68/4.82      ! [A: complex,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 8.68/4.82        = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_433_le__numeral__extra_I4_J,axiom,
% 8.68/4.82      ord_less_eq_real @ one_one_real @ one_one_real ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_434_le__numeral__extra_I4_J,axiom,
% 8.68/4.82      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_435_le__numeral__extra_I4_J,axiom,
% 8.68/4.82      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_436_le__numeral__extra_I4_J,axiom,
% 8.68/4.82      ord_less_eq_int @ one_one_int @ one_one_int ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_437_less__numeral__extra_I4_J,axiom,
% 8.68/4.82      ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_438_less__numeral__extra_I4_J,axiom,
% 8.68/4.82      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_439_less__numeral__extra_I4_J,axiom,
% 8.68/4.82      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_440_less__numeral__extra_I4_J,axiom,
% 8.68/4.82      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_441_left__add__mult__distrib,axiom,
% 8.68/4.82      ! [I: nat,U: nat,J: nat,K: nat] :
% 8.68/4.82        ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 8.68/4.82        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_442_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_complex,B3: set_complex] :
% 8.68/4.82        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: complex] :
% 8.68/4.82              ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 8.68/4.82             => ( member_complex @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_443_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_real,B3: set_real] :
% 8.68/4.82        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: real] :
% 8.68/4.82              ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 8.68/4.82             => ( member_real @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_444_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_set_nat,B3: set_set_nat] :
% 8.68/4.82        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: set_nat] :
% 8.68/4.82              ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 8.68/4.82             => ( member_set_nat @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_445_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 8.68/4.82        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: vEBT_VEBT] :
% 8.68/4.82              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.82             => ( member_VEBT_VEBT @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_446_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_nat,B3: set_nat] :
% 8.68/4.82        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: nat] :
% 8.68/4.82              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 8.68/4.82             => ( member_nat @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_447_subset__code_I1_J,axiom,
% 8.68/4.82      ! [Xs: list_int,B3: set_int] :
% 8.68/4.82        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 8.68/4.82        = ( ! [X3: int] :
% 8.68/4.82              ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 8.68/4.82             => ( member_int @ X3 @ B3 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_448_divide__numeral__1,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_449_divide__numeral__1,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_450_divide__numeral__1,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_451_mult__numeral__1,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_452_mult__numeral__1,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_453_mult__numeral__1,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_454_mult__numeral__1,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_455_mult__numeral__1,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_456_mult__numeral__1__right,axiom,
% 8.68/4.82      ! [A: complex] :
% 8.68/4.82        ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_457_mult__numeral__1__right,axiom,
% 8.68/4.82      ! [A: real] :
% 8.68/4.82        ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_458_mult__numeral__1__right,axiom,
% 8.68/4.82      ! [A: rat] :
% 8.68/4.82        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_459_mult__numeral__1__right,axiom,
% 8.68/4.82      ! [A: nat] :
% 8.68/4.82        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_460_mult__numeral__1__right,axiom,
% 8.68/4.82      ! [A: int] :
% 8.68/4.82        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 8.68/4.82        = A ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_461_power__add,axiom,
% 8.68/4.82      ! [A: complex,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_462_power__add,axiom,
% 8.68/4.82      ! [A: real,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_463_power__add,axiom,
% 8.68/4.82      ! [A: rat,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_464_power__add,axiom,
% 8.68/4.82      ! [A: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_465_power__add,axiom,
% 8.68/4.82      ! [A: int,M: nat,N: nat] :
% 8.68/4.82        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.82        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_466_one__le__numeral,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_467_one__le__numeral,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_468_one__le__numeral,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_469_one__le__numeral,axiom,
% 8.68/4.82      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_470_not__numeral__less__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_471_not__numeral__less__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_472_not__numeral__less__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_473_not__numeral__less__one,axiom,
% 8.68/4.82      ! [N: num] :
% 8.68/4.82        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_474_one__plus__numeral__commute,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 8.68/4.82        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_475_one__plus__numeral__commute,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 8.68/4.82        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_476_one__plus__numeral__commute,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 8.68/4.82        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_477_one__plus__numeral__commute,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 8.68/4.82        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_478_one__plus__numeral__commute,axiom,
% 8.68/4.82      ! [X: num] :
% 8.68/4.82        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 8.68/4.82        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_479_numeral__One,axiom,
% 8.68/4.82      ( ( numera6690914467698888265omplex @ one )
% 8.68/4.82      = one_one_complex ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_480_numeral__One,axiom,
% 8.68/4.82      ( ( numeral_numeral_real @ one )
% 8.68/4.82      = one_one_real ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_481_numeral__One,axiom,
% 8.68/4.82      ( ( numeral_numeral_rat @ one )
% 8.68/4.82      = one_one_rat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_482_numeral__One,axiom,
% 8.68/4.82      ( ( numeral_numeral_nat @ one )
% 8.68/4.82      = one_one_nat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_483_numeral__One,axiom,
% 8.68/4.82      ( ( numeral_numeral_int @ one )
% 8.68/4.82      = one_one_int ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_484_one__le__power,axiom,
% 8.68/4.82      ! [A: real,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_real @ one_one_real @ A )
% 8.68/4.82       => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_485_one__le__power,axiom,
% 8.68/4.82      ! [A: rat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.68/4.82       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_486_one__le__power,axiom,
% 8.68/4.82      ! [A: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.68/4.82       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_487_one__le__power,axiom,
% 8.68/4.82      ! [A: int,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_int @ one_one_int @ A )
% 8.68/4.82       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_488_numerals_I1_J,axiom,
% 8.68/4.82      ( ( numeral_numeral_nat @ one )
% 8.68/4.82      = one_one_nat ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_489_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_complex,A2: set_complex,X: complex,I: nat] :
% 8.68/4.82        ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_complex @ X @ A2 )
% 8.68/4.82         => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_490_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_real,A2: set_real,X: real,I: nat] :
% 8.68/4.82        ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_real @ X @ A2 )
% 8.68/4.82         => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_491_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 8.68/4.82        ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_set_nat @ X @ A2 )
% 8.68/4.82         => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_492_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_nat,A2: set_nat,X: nat,I: nat] :
% 8.68/4.82        ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_nat @ X @ A2 )
% 8.68/4.82         => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_493_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 8.68/4.82        ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_VEBT_VEBT @ X @ A2 )
% 8.68/4.82         => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_494_set__update__subsetI,axiom,
% 8.68/4.82      ! [Xs: list_int,A2: set_int,X: int,I: nat] :
% 8.68/4.82        ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 8.68/4.82       => ( ( member_int @ X @ A2 )
% 8.68/4.82         => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_495_power__less__imp__less__exp,axiom,
% 8.68/4.82      ! [A: real,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.82       => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 8.68/4.82         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_496_power__less__imp__less__exp,axiom,
% 8.68/4.82      ! [A: rat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.82       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 8.68/4.82         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_497_power__less__imp__less__exp,axiom,
% 8.68/4.82      ! [A: nat,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.82       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.68/4.82         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_498_power__less__imp__less__exp,axiom,
% 8.68/4.82      ! [A: int,M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.82       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.68/4.82         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_499_power__strict__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: real] :
% 8.68/4.82        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.82         => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_500_power__strict__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: rat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.82         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_501_power__strict__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.82         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_502_power__strict__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: int] :
% 8.68/4.82        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.82         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_504_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_505_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_506_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_507_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.68/4.82      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.82        ( ( ( I = J )
% 8.68/4.82          & ( K = L2 ) )
% 8.68/4.82       => ( ( plus_plus_real @ I @ K )
% 8.68/4.82          = ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_508_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.68/4.82      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.82        ( ( ( I = J )
% 8.68/4.82          & ( K = L2 ) )
% 8.68/4.82       => ( ( plus_plus_rat @ I @ K )
% 8.68/4.82          = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_509_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.68/4.82      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.82        ( ( ( I = J )
% 8.68/4.82          & ( K = L2 ) )
% 8.68/4.82       => ( ( plus_plus_nat @ I @ K )
% 8.68/4.82          = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_510_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.68/4.82      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.82        ( ( ( I = J )
% 8.68/4.82          & ( K = L2 ) )
% 8.68/4.82       => ( ( plus_plus_int @ I @ K )
% 8.68/4.82          = ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_511_group__cancel_Oadd1,axiom,
% 8.68/4.82      ! [A2: real,K: real,A: real,B: real] :
% 8.68/4.82        ( ( A2
% 8.68/4.82          = ( plus_plus_real @ K @ A ) )
% 8.68/4.82       => ( ( plus_plus_real @ A2 @ B )
% 8.68/4.82          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_512_group__cancel_Oadd1,axiom,
% 8.68/4.82      ! [A2: rat,K: rat,A: rat,B: rat] :
% 8.68/4.82        ( ( A2
% 8.68/4.82          = ( plus_plus_rat @ K @ A ) )
% 8.68/4.82       => ( ( plus_plus_rat @ A2 @ B )
% 8.68/4.82          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_513_group__cancel_Oadd1,axiom,
% 8.68/4.82      ! [A2: nat,K: nat,A: nat,B: nat] :
% 8.68/4.82        ( ( A2
% 8.68/4.82          = ( plus_plus_nat @ K @ A ) )
% 8.68/4.82       => ( ( plus_plus_nat @ A2 @ B )
% 8.68/4.82          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_514_group__cancel_Oadd1,axiom,
% 8.68/4.82      ! [A2: int,K: int,A: int,B: int] :
% 8.68/4.82        ( ( A2
% 8.68/4.82          = ( plus_plus_int @ K @ A ) )
% 8.68/4.82       => ( ( plus_plus_int @ A2 @ B )
% 8.68/4.82          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_515_group__cancel_Oadd2,axiom,
% 8.68/4.82      ! [B3: real,K: real,B: real,A: real] :
% 8.68/4.82        ( ( B3
% 8.68/4.82          = ( plus_plus_real @ K @ B ) )
% 8.68/4.82       => ( ( plus_plus_real @ A @ B3 )
% 8.68/4.82          = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_516_group__cancel_Oadd2,axiom,
% 8.68/4.82      ! [B3: rat,K: rat,B: rat,A: rat] :
% 8.68/4.82        ( ( B3
% 8.68/4.82          = ( plus_plus_rat @ K @ B ) )
% 8.68/4.82       => ( ( plus_plus_rat @ A @ B3 )
% 8.68/4.82          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_517_group__cancel_Oadd2,axiom,
% 8.68/4.82      ! [B3: nat,K: nat,B: nat,A: nat] :
% 8.68/4.82        ( ( B3
% 8.68/4.82          = ( plus_plus_nat @ K @ B ) )
% 8.68/4.82       => ( ( plus_plus_nat @ A @ B3 )
% 8.68/4.82          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_518_group__cancel_Oadd2,axiom,
% 8.68/4.82      ! [B3: int,K: int,B: int,A: int] :
% 8.68/4.82        ( ( B3
% 8.68/4.82          = ( plus_plus_int @ K @ B ) )
% 8.68/4.82       => ( ( plus_plus_int @ A @ B3 )
% 8.68/4.82          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_519_add_Oassoc,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_520_add_Oassoc,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_521_add_Oassoc,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_522_add_Oassoc,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.82        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_523_add_Oleft__cancel,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ A @ B )
% 8.68/4.82          = ( plus_plus_real @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_524_add_Oleft__cancel,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ A @ B )
% 8.68/4.82          = ( plus_plus_rat @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_525_add_Oleft__cancel,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ A @ B )
% 8.68/4.82          = ( plus_plus_int @ A @ C ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_526_add_Oright__cancel,axiom,
% 8.68/4.82      ! [B: real,A: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ B @ A )
% 8.68/4.82          = ( plus_plus_real @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_527_add_Oright__cancel,axiom,
% 8.68/4.82      ! [B: rat,A: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ B @ A )
% 8.68/4.82          = ( plus_plus_rat @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_528_add_Oright__cancel,axiom,
% 8.68/4.82      ! [B: int,A: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ B @ A )
% 8.68/4.82          = ( plus_plus_int @ C @ A ) )
% 8.68/4.82        = ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_529_add_Ocommute,axiom,
% 8.68/4.82      ( plus_plus_real
% 8.68/4.82      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_530_add_Ocommute,axiom,
% 8.68/4.82      ( plus_plus_rat
% 8.68/4.82      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_531_add_Ocommute,axiom,
% 8.68/4.82      ( plus_plus_nat
% 8.68/4.82      = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_532_add_Ocommute,axiom,
% 8.68/4.82      ( plus_plus_int
% 8.68/4.82      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_533_add_Oleft__commute,axiom,
% 8.68/4.82      ! [B: real,A: real,C: real] :
% 8.68/4.82        ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 8.68/4.82        = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_534_add_Oleft__commute,axiom,
% 8.68/4.82      ! [B: rat,A: rat,C: rat] :
% 8.68/4.82        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 8.68/4.82        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_535_add_Oleft__commute,axiom,
% 8.68/4.82      ! [B: nat,A: nat,C: nat] :
% 8.68/4.82        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 8.68/4.82        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_536_add_Oleft__commute,axiom,
% 8.68/4.82      ! [B: int,A: int,C: int] :
% 8.68/4.82        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 8.68/4.82        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_537_add__left__imp__eq,axiom,
% 8.68/4.82      ! [A: real,B: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ A @ B )
% 8.68/4.82          = ( plus_plus_real @ A @ C ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_538_add__left__imp__eq,axiom,
% 8.68/4.82      ! [A: rat,B: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ A @ B )
% 8.68/4.82          = ( plus_plus_rat @ A @ C ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_539_add__left__imp__eq,axiom,
% 8.68/4.82      ! [A: nat,B: nat,C: nat] :
% 8.68/4.82        ( ( ( plus_plus_nat @ A @ B )
% 8.68/4.82          = ( plus_plus_nat @ A @ C ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_540_add__left__imp__eq,axiom,
% 8.68/4.82      ! [A: int,B: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ A @ B )
% 8.68/4.82          = ( plus_plus_int @ A @ C ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_541_add__right__imp__eq,axiom,
% 8.68/4.82      ! [B: real,A: real,C: real] :
% 8.68/4.82        ( ( ( plus_plus_real @ B @ A )
% 8.68/4.82          = ( plus_plus_real @ C @ A ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_542_add__right__imp__eq,axiom,
% 8.68/4.82      ! [B: rat,A: rat,C: rat] :
% 8.68/4.82        ( ( ( plus_plus_rat @ B @ A )
% 8.68/4.82          = ( plus_plus_rat @ C @ A ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_543_add__right__imp__eq,axiom,
% 8.68/4.82      ! [B: nat,A: nat,C: nat] :
% 8.68/4.82        ( ( ( plus_plus_nat @ B @ A )
% 8.68/4.82          = ( plus_plus_nat @ C @ A ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_544_add__right__imp__eq,axiom,
% 8.68/4.82      ! [B: int,A: int,C: int] :
% 8.68/4.82        ( ( ( plus_plus_int @ B @ A )
% 8.68/4.82          = ( plus_plus_int @ C @ A ) )
% 8.68/4.82       => ( B = C ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_545_power__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: real] :
% 8.68/4.82        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_eq_real @ one_one_real @ A )
% 8.68/4.82         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_546_power__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: rat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.68/4.82         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_547_power__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.68/4.82         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_548_power__increasing,axiom,
% 8.68/4.82      ! [N: nat,N4: nat,A: int] :
% 8.68/4.82        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.82       => ( ( ord_less_eq_int @ one_one_int @ A )
% 8.68/4.82         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_549_nat__neq__iff,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( M != N )
% 8.68/4.82        = ( ( ord_less_nat @ M @ N )
% 8.68/4.82          | ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_550_less__not__refl,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ~ ( ord_less_nat @ N @ N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_551_less__not__refl2,axiom,
% 8.68/4.82      ! [N: nat,M: nat] :
% 8.68/4.82        ( ( ord_less_nat @ N @ M )
% 8.68/4.82       => ( M != N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_552_less__not__refl3,axiom,
% 8.68/4.82      ! [S: nat,T: nat] :
% 8.68/4.82        ( ( ord_less_nat @ S @ T )
% 8.68/4.82       => ( S != T ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_553_less__irrefl__nat,axiom,
% 8.68/4.82      ! [N: nat] :
% 8.68/4.82        ~ ( ord_less_nat @ N @ N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_554_nat__less__induct,axiom,
% 8.68/4.82      ! [P: nat > $o,N: nat] :
% 8.68/4.82        ( ! [N3: nat] :
% 8.68/4.82            ( ! [M2: nat] :
% 8.68/4.82                ( ( ord_less_nat @ M2 @ N3 )
% 8.68/4.82               => ( P @ M2 ) )
% 8.68/4.82           => ( P @ N3 ) )
% 8.68/4.82       => ( P @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_555_infinite__descent,axiom,
% 8.68/4.82      ! [P: nat > $o,N: nat] :
% 8.68/4.82        ( ! [N3: nat] :
% 8.68/4.82            ( ~ ( P @ N3 )
% 8.68/4.82           => ? [M2: nat] :
% 8.68/4.82                ( ( ord_less_nat @ M2 @ N3 )
% 8.68/4.82                & ~ ( P @ M2 ) ) )
% 8.68/4.82       => ( P @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_556_linorder__neqE__nat,axiom,
% 8.68/4.82      ! [X: nat,Y: nat] :
% 8.68/4.82        ( ( X != Y )
% 8.68/4.82       => ( ~ ( ord_less_nat @ X @ Y )
% 8.68/4.82         => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_557_le__refl,axiom,
% 8.68/4.82      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_558_le__trans,axiom,
% 8.68/4.82      ! [I: nat,J: nat,K: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.82       => ( ( ord_less_eq_nat @ J @ K )
% 8.68/4.82         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_559_eq__imp__le,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( M = N )
% 8.68/4.82       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_560_le__antisym,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.82       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.82         => ( M = N ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_561_nat__le__linear,axiom,
% 8.68/4.82      ! [M: nat,N: nat] :
% 8.68/4.82        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.82        | ( ord_less_eq_nat @ N @ M ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_562_Nat_Oex__has__greatest__nat,axiom,
% 8.68/4.82      ! [P: nat > $o,K: nat,B: nat] :
% 8.68/4.82        ( ( P @ K )
% 8.68/4.82       => ( ! [Y5: nat] :
% 8.68/4.82              ( ( P @ Y5 )
% 8.68/4.82             => ( ord_less_eq_nat @ Y5 @ B ) )
% 8.68/4.82         => ? [X6: nat] :
% 8.68/4.82              ( ( P @ X6 )
% 8.68/4.82              & ! [Y2: nat] :
% 8.68/4.82                  ( ( P @ Y2 )
% 8.68/4.82                 => ( ord_less_eq_nat @ Y2 @ X6 ) ) ) ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_563_size__neq__size__imp__neq,axiom,
% 8.68/4.82      ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 8.68/4.82        ( ( ( size_s6755466524823107622T_VEBT @ X )
% 8.68/4.82         != ( size_s6755466524823107622T_VEBT @ Y ) )
% 8.68/4.82       => ( X != Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_564_size__neq__size__imp__neq,axiom,
% 8.68/4.82      ! [X: list_o,Y: list_o] :
% 8.68/4.82        ( ( ( size_size_list_o @ X )
% 8.68/4.82         != ( size_size_list_o @ Y ) )
% 8.68/4.82       => ( X != Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_565_size__neq__size__imp__neq,axiom,
% 8.68/4.82      ! [X: list_nat,Y: list_nat] :
% 8.68/4.82        ( ( ( size_size_list_nat @ X )
% 8.68/4.82         != ( size_size_list_nat @ Y ) )
% 8.68/4.82       => ( X != Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_566_size__neq__size__imp__neq,axiom,
% 8.68/4.82      ! [X: list_int,Y: list_int] :
% 8.68/4.82        ( ( ( size_size_list_int @ X )
% 8.68/4.82         != ( size_size_list_int @ Y ) )
% 8.68/4.82       => ( X != Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_567_size__neq__size__imp__neq,axiom,
% 8.68/4.82      ! [X: num,Y: num] :
% 8.68/4.82        ( ( ( size_size_num @ X )
% 8.68/4.82         != ( size_size_num @ Y ) )
% 8.68/4.82       => ( X != Y ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_568_mult__2,axiom,
% 8.68/4.82      ! [Z: complex] :
% 8.68/4.82        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 8.68/4.82        = ( plus_plus_complex @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_569_mult__2,axiom,
% 8.68/4.82      ! [Z: real] :
% 8.68/4.82        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 8.68/4.82        = ( plus_plus_real @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_570_mult__2,axiom,
% 8.68/4.82      ! [Z: rat] :
% 8.68/4.82        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 8.68/4.82        = ( plus_plus_rat @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_571_mult__2,axiom,
% 8.68/4.82      ! [Z: nat] :
% 8.68/4.82        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 8.68/4.82        = ( plus_plus_nat @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_572_mult__2,axiom,
% 8.68/4.82      ! [Z: int] :
% 8.68/4.82        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 8.68/4.82        = ( plus_plus_int @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_573_mult__2__right,axiom,
% 8.68/4.82      ! [Z: complex] :
% 8.68/4.82        ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 8.68/4.82        = ( plus_plus_complex @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_574_mult__2__right,axiom,
% 8.68/4.82      ! [Z: real] :
% 8.68/4.82        ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.68/4.82        = ( plus_plus_real @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_575_mult__2__right,axiom,
% 8.68/4.82      ! [Z: rat] :
% 8.68/4.82        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 8.68/4.82        = ( plus_plus_rat @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_576_mult__2__right,axiom,
% 8.68/4.82      ! [Z: nat] :
% 8.68/4.82        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.82        = ( plus_plus_nat @ Z @ Z ) ) ).
% 8.68/4.82  
% 8.68/4.82  thf(fact_577_mult__2__right,axiom,
% 8.68/4.82      ! [Z: int] :
% 8.68/4.82        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.82        = ( plus_plus_int @ Z @ Z ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_578_left__add__twice,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 8.68/4.83        = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_579_left__add__twice,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_580_left__add__twice,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_581_left__add__twice,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.68/4.83        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_582_left__add__twice,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_583_power4__eq__xxxx,axiom,
% 8.68/4.83      ! [X: complex] :
% 8.68/4.83        ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_584_power4__eq__xxxx,axiom,
% 8.68/4.83      ! [X: real] :
% 8.68/4.83        ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_585_power4__eq__xxxx,axiom,
% 8.68/4.83      ! [X: rat] :
% 8.68/4.83        ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_586_power4__eq__xxxx,axiom,
% 8.68/4.83      ! [X: nat] :
% 8.68/4.83        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_587_power4__eq__xxxx,axiom,
% 8.68/4.83      ! [X: int] :
% 8.68/4.83        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_588_power2__eq__square,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( times_times_complex @ A @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_589_power2__eq__square,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( times_times_real @ A @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_590_power2__eq__square,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( times_times_rat @ A @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_591_power2__eq__square,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( times_times_nat @ A @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_592_power2__eq__square,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( times_times_int @ A @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_593_power__even__eq,axiom,
% 8.68/4.83      ! [A: nat,N: nat] :
% 8.68/4.83        ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_594_power__even__eq,axiom,
% 8.68/4.83      ! [A: real,N: nat] :
% 8.68/4.83        ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_595_power__even__eq,axiom,
% 8.68/4.83      ! [A: int,N: nat] :
% 8.68/4.83        ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_596_power__even__eq,axiom,
% 8.68/4.83      ! [A: complex,N: nat] :
% 8.68/4.83        ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_597_power__le__imp__le__exp,axiom,
% 8.68/4.83      ! [A: real,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.83       => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 8.68/4.83         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_598_power__le__imp__le__exp,axiom,
% 8.68/4.83      ! [A: rat,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.83       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 8.68/4.83         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_599_power__le__imp__le__exp,axiom,
% 8.68/4.83      ! [A: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.83       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.68/4.83         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_600_power__le__imp__le__exp,axiom,
% 8.68/4.83      ! [A: int,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.83       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.68/4.83         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_601_one__power2,axiom,
% 8.68/4.83      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83      = one_one_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_602_one__power2,axiom,
% 8.68/4.83      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83      = one_one_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_603_one__power2,axiom,
% 8.68/4.83      ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83      = one_one_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_604_one__power2,axiom,
% 8.68/4.83      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83      = one_one_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_605_one__power2,axiom,
% 8.68/4.83      ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83      = one_one_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_606_nat__1__add__1,axiom,
% 8.68/4.83      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 8.68/4.83      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_607_power2__sum,axiom,
% 8.68/4.83      ! [X: complex,Y: complex] :
% 8.68/4.83        ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_608_power2__sum,axiom,
% 8.68/4.83      ! [X: real,Y: real] :
% 8.68/4.83        ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_609_power2__sum,axiom,
% 8.68/4.83      ! [X: rat,Y: rat] :
% 8.68/4.83        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_610_power2__sum,axiom,
% 8.68/4.83      ! [X: nat,Y: nat] :
% 8.68/4.83        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_611_power2__sum,axiom,
% 8.68/4.83      ! [X: int,Y: int] :
% 8.68/4.83        ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_612_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_eq_real @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_613_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_eq_rat @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_614_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_615_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_eq_int @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_616_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_eq_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_617_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_eq_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_618_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_eq_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_619_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_eq_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_620_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_eq_real @ I @ J )
% 8.68/4.83          & ( ord_less_eq_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_621_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_eq_rat @ I @ J )
% 8.68/4.83          & ( ord_less_eq_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_622_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83          & ( ord_less_eq_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_623_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_eq_int @ I @ J )
% 8.68/4.83          & ( ord_less_eq_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_624_add__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_real @ C @ D )
% 8.68/4.83         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_625_add__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_rat @ C @ D )
% 8.68/4.83         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_626_add__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_nat @ C @ D )
% 8.68/4.83         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_627_add__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_int @ C @ D )
% 8.68/4.83         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_628_add__left__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.83       => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_629_add__left__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.83       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_630_add__left__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_631_add__left__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.83       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_632_less__eqE,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.83       => ~ ! [C2: nat] :
% 8.68/4.83              ( B
% 8.68/4.83             != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_633_add__right__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.83       => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_634_add__right__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.83       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_635_add__right__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_636_add__right__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.83       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_637_le__iff__add,axiom,
% 8.68/4.83      ( ord_less_eq_nat
% 8.68/4.83      = ( ^ [A3: nat,B2: nat] :
% 8.68/4.83          ? [C3: nat] :
% 8.68/4.83            ( B2
% 8.68/4.83            = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_638_add__le__imp__le__left,axiom,
% 8.68/4.83      ! [C: real,A: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 8.68/4.83       => ( ord_less_eq_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_639_add__le__imp__le__left,axiom,
% 8.68/4.83      ! [C: rat,A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.68/4.83       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_640_add__le__imp__le__left,axiom,
% 8.68/4.83      ! [C: nat,A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.68/4.83       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_641_add__le__imp__le__left,axiom,
% 8.68/4.83      ! [C: int,A: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.68/4.83       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_642_add__le__imp__le__right,axiom,
% 8.68/4.83      ! [A: real,C: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.83       => ( ord_less_eq_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_643_add__le__imp__le__right,axiom,
% 8.68/4.83      ! [A: rat,C: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.83       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_644_add__le__imp__le__right,axiom,
% 8.68/4.83      ! [A: nat,C: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.83       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_645_add__le__imp__le__right,axiom,
% 8.68/4.83      ! [A: int,C: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.83       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_646_add__mono__thms__linordered__field_I5_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_real @ I @ J )
% 8.68/4.83          & ( ord_less_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_647_add__mono__thms__linordered__field_I5_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_rat @ I @ J )
% 8.68/4.83          & ( ord_less_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_648_add__mono__thms__linordered__field_I5_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_nat @ I @ J )
% 8.68/4.83          & ( ord_less_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_649_add__mono__thms__linordered__field_I5_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_int @ I @ J )
% 8.68/4.83          & ( ord_less_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_650_add__mono__thms__linordered__field_I2_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_651_add__mono__thms__linordered__field_I2_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_652_add__mono__thms__linordered__field_I2_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_653_add__mono__thms__linordered__field_I2_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( I = J )
% 8.68/4.83          & ( ord_less_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_654_add__mono__thms__linordered__field_I1_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_real @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_655_add__mono__thms__linordered__field_I1_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_rat @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_656_add__mono__thms__linordered__field_I1_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_nat @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_657_add__mono__thms__linordered__field_I1_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_int @ I @ J )
% 8.68/4.83          & ( K = L2 ) )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_658_add__strict__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ( ord_less_real @ C @ D )
% 8.68/4.83         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_659_add__strict__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ( ord_less_rat @ C @ D )
% 8.68/4.83         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_660_add__strict__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ B )
% 8.68/4.83       => ( ( ord_less_nat @ C @ D )
% 8.68/4.83         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_661_add__strict__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ B )
% 8.68/4.83       => ( ( ord_less_int @ C @ D )
% 8.68/4.83         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_662_add__strict__left__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_663_add__strict__left__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_664_add__strict__left__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ B )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_665_add__strict__left__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ B )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_666_add__strict__right__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_667_add__strict__right__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_668_add__strict__right__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ B )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_669_add__strict__right__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ B )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_670_add__less__imp__less__left,axiom,
% 8.68/4.83      ! [C: real,A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 8.68/4.83       => ( ord_less_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_671_add__less__imp__less__left,axiom,
% 8.68/4.83      ! [C: rat,A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.68/4.83       => ( ord_less_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_672_add__less__imp__less__left,axiom,
% 8.68/4.83      ! [C: nat,A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.68/4.83       => ( ord_less_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_673_add__less__imp__less__left,axiom,
% 8.68/4.83      ! [C: int,A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.68/4.83       => ( ord_less_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_674_add__less__imp__less__right,axiom,
% 8.68/4.83      ! [A: real,C: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.83       => ( ord_less_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_675_add__less__imp__less__right,axiom,
% 8.68/4.83      ! [A: rat,C: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.83       => ( ord_less_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_676_add__less__imp__less__right,axiom,
% 8.68/4.83      ! [A: nat,C: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.83       => ( ord_less_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_677_add__less__imp__less__right,axiom,
% 8.68/4.83      ! [A: int,C: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.83       => ( ord_less_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_678_nat__less__le,axiom,
% 8.68/4.83      ( ord_less_nat
% 8.68/4.83      = ( ^ [M3: nat,N2: nat] :
% 8.68/4.83            ( ( ord_less_eq_nat @ M3 @ N2 )
% 8.68/4.83            & ( M3 != N2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_679_less__imp__le__nat,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ M @ N )
% 8.68/4.83       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_680_le__eq__less__or__eq,axiom,
% 8.68/4.83      ( ord_less_eq_nat
% 8.68/4.83      = ( ^ [M3: nat,N2: nat] :
% 8.68/4.83            ( ( ord_less_nat @ M3 @ N2 )
% 8.68/4.83            | ( M3 = N2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_681_less__or__eq__imp__le,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ( ord_less_nat @ M @ N )
% 8.68/4.83          | ( M = N ) )
% 8.68/4.83       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_682_le__neq__implies__less,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.83       => ( ( M != N )
% 8.68/4.83         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_683_less__mono__imp__le__mono,axiom,
% 8.68/4.83      ! [F: nat > nat,I: nat,J: nat] :
% 8.68/4.83        ( ! [I4: nat,J2: nat] :
% 8.68/4.83            ( ( ord_less_nat @ I4 @ J2 )
% 8.68/4.83           => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 8.68/4.83       => ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83         => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_684_add__lessD1,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 8.68/4.83       => ( ord_less_nat @ I @ K ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_685_add__less__mono,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ord_less_nat @ I @ J )
% 8.68/4.83       => ( ( ord_less_nat @ K @ L2 )
% 8.68/4.83         => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_686_not__add__less1,axiom,
% 8.68/4.83      ! [I: nat,J: nat] :
% 8.68/4.83        ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_687_not__add__less2,axiom,
% 8.68/4.83      ! [J: nat,I: nat] :
% 8.68/4.83        ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_688_add__less__mono1,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_nat @ I @ J )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_689_trans__less__add1,axiom,
% 8.68/4.83      ! [I: nat,J: nat,M: nat] :
% 8.68/4.83        ( ( ord_less_nat @ I @ J )
% 8.68/4.83       => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_690_trans__less__add2,axiom,
% 8.68/4.83      ! [I: nat,J: nat,M: nat] :
% 8.68/4.83        ( ( ord_less_nat @ I @ J )
% 8.68/4.83       => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_691_less__add__eq__less,axiom,
% 8.68/4.83      ! [K: nat,L2: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ K @ L2 )
% 8.68/4.83       => ( ( ( plus_plus_nat @ M @ L2 )
% 8.68/4.83            = ( plus_plus_nat @ K @ N ) )
% 8.68/4.83         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_692_add__leE,axiom,
% 8.68/4.83      ! [M: nat,K: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.68/4.83       => ~ ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.83           => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_693_le__add1,axiom,
% 8.68/4.83      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_694_le__add2,axiom,
% 8.68/4.83      ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_695_add__leD1,axiom,
% 8.68/4.83      ! [M: nat,K: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.68/4.83       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_696_add__leD2,axiom,
% 8.68/4.83      ! [M: nat,K: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 8.68/4.83       => ( ord_less_eq_nat @ K @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_697_le__Suc__ex,axiom,
% 8.68/4.83      ! [K: nat,L2: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ K @ L2 )
% 8.68/4.83       => ? [N3: nat] :
% 8.68/4.83            ( L2
% 8.68/4.83            = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_698_add__le__mono,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83       => ( ( ord_less_eq_nat @ K @ L2 )
% 8.68/4.83         => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_699_add__le__mono1,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_700_trans__le__add1,axiom,
% 8.68/4.83      ! [I: nat,J: nat,M: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_701_trans__le__add2,axiom,
% 8.68/4.83      ! [I: nat,J: nat,M: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83       => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_702_nat__le__iff__add,axiom,
% 8.68/4.83      ( ord_less_eq_nat
% 8.68/4.83      = ( ^ [M3: nat,N2: nat] :
% 8.68/4.83          ? [K2: nat] :
% 8.68/4.83            ( N2
% 8.68/4.83            = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_703_ex__power__ivl1,axiom,
% 8.68/4.83      ! [B: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.68/4.83       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 8.68/4.83         => ? [N3: nat] :
% 8.68/4.83              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 8.68/4.83              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_704_ex__power__ivl2,axiom,
% 8.68/4.83      ! [B: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.68/4.83       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.68/4.83         => ? [N3: nat] :
% 8.68/4.83              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 8.68/4.83              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_705_add__less__le__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_real @ C @ D )
% 8.68/4.83         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_706_add__less__le__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_rat @ C @ D )
% 8.68/4.83         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_707_add__less__le__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_nat @ C @ D )
% 8.68/4.83         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_708_add__less__le__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ B )
% 8.68/4.83       => ( ( ord_less_eq_int @ C @ D )
% 8.68/4.83         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_709_add__le__less__mono,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.83       => ( ( ord_less_real @ C @ D )
% 8.68/4.83         => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_710_add__le__less__mono,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.83       => ( ( ord_less_rat @ C @ D )
% 8.68/4.83         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_711_add__le__less__mono,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.83       => ( ( ord_less_nat @ C @ D )
% 8.68/4.83         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_712_add__le__less__mono,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.83       => ( ( ord_less_int @ C @ D )
% 8.68/4.83         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_713_add__mono__thms__linordered__field_I3_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_real @ I @ J )
% 8.68/4.83          & ( ord_less_eq_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_714_add__mono__thms__linordered__field_I3_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_rat @ I @ J )
% 8.68/4.83          & ( ord_less_eq_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_715_add__mono__thms__linordered__field_I3_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_nat @ I @ J )
% 8.68/4.83          & ( ord_less_eq_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_716_add__mono__thms__linordered__field_I3_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_int @ I @ J )
% 8.68/4.83          & ( ord_less_eq_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_717_add__mono__thms__linordered__field_I4_J,axiom,
% 8.68/4.83      ! [I: real,J: real,K: real,L2: real] :
% 8.68/4.83        ( ( ( ord_less_eq_real @ I @ J )
% 8.68/4.83          & ( ord_less_real @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_718_add__mono__thms__linordered__field_I4_J,axiom,
% 8.68/4.83      ! [I: rat,J: rat,K: rat,L2: rat] :
% 8.68/4.83        ( ( ( ord_less_eq_rat @ I @ J )
% 8.68/4.83          & ( ord_less_rat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_719_add__mono__thms__linordered__field_I4_J,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat,L2: nat] :
% 8.68/4.83        ( ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.83          & ( ord_less_nat @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_720_add__mono__thms__linordered__field_I4_J,axiom,
% 8.68/4.83      ! [I: int,J: int,K: int,L2: int] :
% 8.68/4.83        ( ( ( ord_less_eq_int @ I @ J )
% 8.68/4.83          & ( ord_less_int @ K @ L2 ) )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_721_mono__nat__linear__lb,axiom,
% 8.68/4.83      ! [F: nat > nat,M: nat,K: nat] :
% 8.68/4.83        ( ! [M4: nat,N3: nat] :
% 8.68/4.83            ( ( ord_less_nat @ M4 @ N3 )
% 8.68/4.83           => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 8.68/4.83       => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_722_set__vebt__set__vebt_H__valid,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ( vEBT_set_vebt @ T )
% 8.68/4.83          = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_723_add__self__div__2,axiom,
% 8.68/4.83      ! [M: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_724_both__member__options__ding,axiom,
% 8.68/4.83      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.83       => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.68/4.83         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 8.68/4.83           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_725_sum__squares__bound,axiom,
% 8.68/4.83      ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_726_sum__squares__bound,axiom,
% 8.68/4.83      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_727_div__exp__eq,axiom,
% 8.68/4.83      ! [A: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_728_div__exp__eq,axiom,
% 8.68/4.83      ! [A: int,M: nat,N: nat] :
% 8.68/4.83        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.83        = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_729_field__less__half__sum,axiom,
% 8.68/4.83      ! [X: real,Y: real] :
% 8.68/4.83        ( ( ord_less_real @ X @ Y )
% 8.68/4.83       => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_730_field__less__half__sum,axiom,
% 8.68/4.83      ! [X: rat,Y: rat] :
% 8.68/4.83        ( ( ord_less_rat @ X @ Y )
% 8.68/4.83       => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_731_div__by__1,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_732_div__by__1,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( divide_divide_real @ A @ one_one_real )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_733_div__by__1,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ A @ one_one_rat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_734_div__by__1,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ A @ one_one_nat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_735_div__by__1,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ A @ one_one_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_736_bits__div__by__1,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ A @ one_one_nat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_737_bits__div__by__1,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ A @ one_one_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_738_times__divide__eq__left,axiom,
% 8.68/4.83      ! [B: complex,C: complex,A: complex] :
% 8.68/4.83        ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 8.68/4.83        = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_739_times__divide__eq__left,axiom,
% 8.68/4.83      ! [B: real,C: real,A: real] :
% 8.68/4.83        ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.83        = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_740_times__divide__eq__left,axiom,
% 8.68/4.83      ! [B: rat,C: rat,A: rat] :
% 8.68/4.83        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.83        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_741_divide__divide__eq__left,axiom,
% 8.68/4.83      ! [A: complex,B: complex,C: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 8.68/4.83        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_742_divide__divide__eq__left,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 8.68/4.83        = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_743_divide__divide__eq__left,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 8.68/4.83        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_744_divide__divide__eq__right,axiom,
% 8.68/4.83      ! [A: complex,B: complex,C: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.83        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_745_divide__divide__eq__right,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.83        = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_746_divide__divide__eq__right,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.83        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_747_times__divide__eq__right,axiom,
% 8.68/4.83      ! [A: complex,B: complex,C: complex] :
% 8.68/4.83        ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.83        = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_748_times__divide__eq__right,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.83        = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_749_times__divide__eq__right,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.83        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_750_deg__deg__n,axiom,
% 8.68/4.83      ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.83       => ( Deg = N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_751_semiring__norm_I13_J,axiom,
% 8.68/4.83      ! [M: num,N: num] :
% 8.68/4.83        ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.68/4.83        = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_752_semiring__norm_I11_J,axiom,
% 8.68/4.83      ! [M: num] :
% 8.68/4.83        ( ( times_times_num @ M @ one )
% 8.68/4.83        = M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_753_semiring__norm_I12_J,axiom,
% 8.68/4.83      ! [N: num] :
% 8.68/4.83        ( ( times_times_num @ one @ N )
% 8.68/4.83        = N ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_754_num__double,axiom,
% 8.68/4.83      ! [N: num] :
% 8.68/4.83        ( ( times_times_num @ ( bit0 @ one ) @ N )
% 8.68/4.83        = ( bit0 @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_755_power__mult__numeral,axiom,
% 8.68/4.83      ! [A: nat,M: num,N: num] :
% 8.68/4.83        ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.83        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_756_power__mult__numeral,axiom,
% 8.68/4.83      ! [A: real,M: num,N: num] :
% 8.68/4.83        ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.83        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_757_power__mult__numeral,axiom,
% 8.68/4.83      ! [A: int,M: num,N: num] :
% 8.68/4.83        ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.83        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_758_power__mult__numeral,axiom,
% 8.68/4.83      ! [A: complex,M: num,N: num] :
% 8.68/4.83        ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 8.68/4.83        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_759_succ__member,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 8.68/4.83        ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 8.68/4.83        = ( ( vEBT_vebt_member @ T @ Y )
% 8.68/4.83          & ( ord_less_nat @ X @ Y )
% 8.68/4.83          & ! [Z3: nat] :
% 8.68/4.83              ( ( ( vEBT_vebt_member @ T @ Z3 )
% 8.68/4.83                & ( ord_less_nat @ X @ Z3 ) )
% 8.68/4.83             => ( ord_less_eq_nat @ Y @ Z3 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_760_pred__member,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 8.68/4.83        ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 8.68/4.83        = ( ( vEBT_vebt_member @ T @ Y )
% 8.68/4.83          & ( ord_less_nat @ Y @ X )
% 8.68/4.83          & ! [Z3: nat] :
% 8.68/4.83              ( ( ( vEBT_vebt_member @ T @ Z3 )
% 8.68/4.83                & ( ord_less_nat @ Z3 @ X ) )
% 8.68/4.83             => ( ord_less_eq_nat @ Z3 @ Y ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_761_two__realpow__ge__one,axiom,
% 8.68/4.83      ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_762_four__x__squared,axiom,
% 8.68/4.83      ! [X: real] :
% 8.68/4.83        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_763_L2__set__mult__ineq__lemma,axiom,
% 8.68/4.83      ! [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 ) ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_764_div__mult2__numeral__eq,axiom,
% 8.68/4.83      ! [A: nat,K: num,L2: num] :
% 8.68/4.83        ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_765_div__mult2__numeral__eq,axiom,
% 8.68/4.83      ! [A: int,K: num,L2: num] :
% 8.68/4.83        ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 8.68/4.83        = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_766_linorder__neqE__linordered__idom,axiom,
% 8.68/4.83      ! [X: real,Y: real] :
% 8.68/4.83        ( ( X != Y )
% 8.68/4.83       => ( ~ ( ord_less_real @ X @ Y )
% 8.68/4.83         => ( ord_less_real @ Y @ X ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_767_linorder__neqE__linordered__idom,axiom,
% 8.68/4.83      ! [X: rat,Y: rat] :
% 8.68/4.83        ( ( X != Y )
% 8.68/4.83       => ( ~ ( ord_less_rat @ X @ Y )
% 8.68/4.83         => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_768_linorder__neqE__linordered__idom,axiom,
% 8.68/4.83      ! [X: int,Y: int] :
% 8.68/4.83        ( ( X != Y )
% 8.68/4.83       => ( ~ ( ord_less_int @ X @ Y )
% 8.68/4.83         => ( ord_less_int @ Y @ X ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_769_linordered__field__no__ub,axiom,
% 8.68/4.83      ! [X4: real] :
% 8.68/4.83      ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_770_linordered__field__no__ub,axiom,
% 8.68/4.83      ! [X4: rat] :
% 8.68/4.83      ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_771_linordered__field__no__lb,axiom,
% 8.68/4.83      ! [X4: real] :
% 8.68/4.83      ? [Y5: real] : ( ord_less_real @ Y5 @ X4 ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_772_linordered__field__no__lb,axiom,
% 8.68/4.83      ! [X4: rat] :
% 8.68/4.83      ? [Y5: rat] : ( ord_less_rat @ Y5 @ X4 ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_773_combine__common__factor,axiom,
% 8.68/4.83      ! [A: real,E: real,B: real,C: real] :
% 8.68/4.83        ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_774_combine__common__factor,axiom,
% 8.68/4.83      ! [A: rat,E: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_775_combine__common__factor,axiom,
% 8.68/4.83      ! [A: nat,E: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 8.68/4.83        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_776_combine__common__factor,axiom,
% 8.68/4.83      ! [A: int,E: int,B: int,C: int] :
% 8.68/4.83        ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_777_distrib__right,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_778_distrib__right,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_779_distrib__right,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_780_distrib__right,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_781_distrib__left,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_782_distrib__left,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_783_distrib__left,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.83        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_784_distrib__left,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_785_comm__semiring__class_Odistrib,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_786_comm__semiring__class_Odistrib,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_787_comm__semiring__class_Odistrib,axiom,
% 8.68/4.83      ! [A: nat,B: nat,C: nat] :
% 8.68/4.83        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_788_comm__semiring__class_Odistrib,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_789_ring__class_Oring__distribs_I1_J,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_790_ring__class_Oring__distribs_I1_J,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_791_ring__class_Oring__distribs_I1_J,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_792_ring__class_Oring__distribs_I2_J,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_793_ring__class_Oring__distribs_I2_J,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_794_ring__class_Oring__distribs_I2_J,axiom,
% 8.68/4.83      ! [A: int,B: int,C: int] :
% 8.68/4.83        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_795_divide__divide__eq__left_H,axiom,
% 8.68/4.83      ! [A: complex,B: complex,C: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 8.68/4.83        = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_796_divide__divide__eq__left_H,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 8.68/4.83        = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_797_divide__divide__eq__left_H,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 8.68/4.83        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_798_divide__divide__times__eq,axiom,
% 8.68/4.83      ! [X: complex,Y: complex,Z: complex,W: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 8.68/4.83        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_799_divide__divide__times__eq,axiom,
% 8.68/4.83      ! [X: real,Y: real,Z: real,W: real] :
% 8.68/4.83        ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 8.68/4.83        = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_800_divide__divide__times__eq,axiom,
% 8.68/4.83      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 8.68/4.83        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_801_times__divide__times__eq,axiom,
% 8.68/4.83      ! [X: complex,Y: complex,Z: complex,W: complex] :
% 8.68/4.83        ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 8.68/4.83        = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_802_times__divide__times__eq,axiom,
% 8.68/4.83      ! [X: real,Y: real,Z: real,W: real] :
% 8.68/4.83        ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 8.68/4.83        = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_803_times__divide__times__eq,axiom,
% 8.68/4.83      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 8.68/4.83        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 8.68/4.83        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_804_add__divide__distrib,axiom,
% 8.68/4.83      ! [A: complex,B: complex,C: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_805_add__divide__distrib,axiom,
% 8.68/4.83      ! [A: real,B: real,C: real] :
% 8.68/4.83        ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_806_add__divide__distrib,axiom,
% 8.68/4.83      ! [A: rat,B: rat,C: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 8.68/4.83        = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_807_div__le__dividend,axiom,
% 8.68/4.83      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_808_div__le__mono,axiom,
% 8.68/4.83      ! [M: nat,N: nat,K: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.83       => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_809_div__mult2__eq,axiom,
% 8.68/4.83      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 8.68/4.83        = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_810_less__1__mult,axiom,
% 8.68/4.83      ! [M: real,N: real] :
% 8.68/4.83        ( ( ord_less_real @ one_one_real @ M )
% 8.68/4.83       => ( ( ord_less_real @ one_one_real @ N )
% 8.68/4.83         => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_811_less__1__mult,axiom,
% 8.68/4.83      ! [M: rat,N: rat] :
% 8.68/4.83        ( ( ord_less_rat @ one_one_rat @ M )
% 8.68/4.83       => ( ( ord_less_rat @ one_one_rat @ N )
% 8.68/4.83         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_812_less__1__mult,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ one_one_nat @ M )
% 8.68/4.83       => ( ( ord_less_nat @ one_one_nat @ N )
% 8.68/4.83         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_813_less__1__mult,axiom,
% 8.68/4.83      ! [M: int,N: int] :
% 8.68/4.83        ( ( ord_less_int @ one_one_int @ M )
% 8.68/4.83       => ( ( ord_less_int @ one_one_int @ N )
% 8.68/4.83         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_814_less__add__one,axiom,
% 8.68/4.83      ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_815_less__add__one,axiom,
% 8.68/4.83      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_816_less__add__one,axiom,
% 8.68/4.83      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_817_less__add__one,axiom,
% 8.68/4.83      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_818_add__mono1,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_819_add__mono1,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_820_add__mono1,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ B )
% 8.68/4.83       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_821_add__mono1,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ B )
% 8.68/4.83       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_822_less__mult__imp__div__less,axiom,
% 8.68/4.83      ! [M: nat,I: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 8.68/4.83       => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_823_div__times__less__eq__dividend,axiom,
% 8.68/4.83      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_824_times__div__less__eq__dividend,axiom,
% 8.68/4.83      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_825_gt__half__sum,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_826_gt__half__sum,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_827_less__half__sum,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ B )
% 8.68/4.83       => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_828_less__half__sum,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ B )
% 8.68/4.83       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_829_numeral__Bit0__div__2,axiom,
% 8.68/4.83      ! [N: num] :
% 8.68/4.83        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( numeral_numeral_nat @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_830_numeral__Bit0__div__2,axiom,
% 8.68/4.83      ! [N: num] :
% 8.68/4.83        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.83        = ( numeral_numeral_int @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_831_field__sum__of__halves,axiom,
% 8.68/4.83      ! [X: real] :
% 8.68/4.83        ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = X ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_832_field__sum__of__halves,axiom,
% 8.68/4.83      ! [X: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = X ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_833_power__minus__is__div,axiom,
% 8.68/4.83      ! [B: nat,A: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.83       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 8.68/4.83          = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_834_discrete,axiom,
% 8.68/4.83      ( ord_less_nat
% 8.68/4.83      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_835_discrete,axiom,
% 8.68/4.83      ( ord_less_int
% 8.68/4.83      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_836_low__def,axiom,
% 8.68/4.83      ( vEBT_VEBT_low
% 8.68/4.83      = ( ^ [X3: nat,N2: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_837__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_092_060close_062,axiom,
% 8.68/4.83      ( ( some_nat @ maxs )
% 8.68/4.83      = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_838_dbl__simps_I3_J,axiom,
% 8.68/4.83      ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 8.68/4.83      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_839_dbl__simps_I3_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_real @ one_one_real )
% 8.68/4.83      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_840_dbl__simps_I3_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 8.68/4.83      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_841_dbl__simps_I3_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_int @ one_one_int )
% 8.68/4.83      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_842_power__numeral,axiom,
% 8.68/4.83      ! [K: num,L2: num] :
% 8.68/4.83        ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_843_power__numeral,axiom,
% 8.68/4.83      ! [K: num,L2: num] :
% 8.68/4.83        ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_844_power__numeral,axiom,
% 8.68/4.83      ! [K: num,L2: num] :
% 8.68/4.83        ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_845_power__numeral,axiom,
% 8.68/4.83      ! [K: num,L2: num] :
% 8.68/4.83        ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_846_power__numeral,axiom,
% 8.68/4.83      ! [K: num,L2: num] :
% 8.68/4.83        ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 8.68/4.83        = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_847_both__member__options__from__chilf__to__complete__tree,axiom,
% 8.68/4.83      ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.68/4.83        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.83       => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 8.68/4.83         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 8.68/4.83           => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_848_arith__geo__mean,axiom,
% 8.68/4.83      ! [U: real,X: real,Y: real] :
% 8.68/4.83        ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83          = ( times_times_real @ X @ Y ) )
% 8.68/4.83       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.83         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.83           => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_849_arith__geo__mean,axiom,
% 8.68/4.83      ! [U: rat,X: rat,Y: rat] :
% 8.68/4.83        ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.83          = ( times_times_rat @ X @ Y ) )
% 8.68/4.83       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.83         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.83           => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_850_False,axiom,
% 8.68/4.83      ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 8.68/4.83     != none_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_851_valid__tree__deg__neq__0,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT] :
% 8.68/4.83        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_852_valid__0__not,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT] :
% 8.68/4.83        ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_853_deg__not__0,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_854_maxbmo,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,X: nat] :
% 8.68/4.83        ( ( ( vEBT_vebt_maxt @ T )
% 8.68/4.83          = ( some_nat @ X ) )
% 8.68/4.83       => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_855_power__shift,axiom,
% 8.68/4.83      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.83        ( ( ( power_power_nat @ X @ Y )
% 8.68/4.83          = Z )
% 8.68/4.83        = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.68/4.83          = ( some_nat @ Z ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_856_maxt__member,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ( ( vEBT_vebt_maxt @ T )
% 8.68/4.83            = ( some_nat @ Maxi ) )
% 8.68/4.83         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_857_zdiv__numeral__Bit0,axiom,
% 8.68/4.83      ! [V: num,W: num] :
% 8.68/4.83        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 8.68/4.83        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_858_bot__nat__0_Onot__eq__extremum,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( A != zero_zero_nat )
% 8.68/4.83        = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_859_neq0__conv,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ( ( N != zero_zero_nat )
% 8.68/4.83        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_860_less__nat__zero__code,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_861_bot__nat__0_Oextremum,axiom,
% 8.68/4.83      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_862_le0,axiom,
% 8.68/4.83      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_863_add__is__0,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ( plus_plus_nat @ M @ N )
% 8.68/4.83          = zero_zero_nat )
% 8.68/4.83        = ( ( M = zero_zero_nat )
% 8.68/4.83          & ( N = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_864_Nat_Oadd__0__right,axiom,
% 8.68/4.83      ! [M: nat] :
% 8.68/4.83        ( ( plus_plus_nat @ M @ zero_zero_nat )
% 8.68/4.83        = M ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_865_mod__mod__trivial,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.68/4.83        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_866_mod__mod__trivial,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.68/4.83        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_867_mod__mod__trivial,axiom,
% 8.68/4.83      ! [A: code_integer,B: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 8.68/4.83        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_868_diff__self__eq__0,axiom,
% 8.68/4.83      ! [M: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ M @ M )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_869_diff__0__eq__0,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ zero_zero_nat @ N )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_870_mult__is__0,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ M @ N )
% 8.68/4.83          = zero_zero_nat )
% 8.68/4.83        = ( ( M = zero_zero_nat )
% 8.68/4.83          | ( N = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_871_mult__0__right,axiom,
% 8.68/4.83      ! [M: nat] :
% 8.68/4.83        ( ( times_times_nat @ M @ zero_zero_nat )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_872_mult__cancel1,axiom,
% 8.68/4.83      ! [K: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ K @ M )
% 8.68/4.83          = ( times_times_nat @ K @ N ) )
% 8.68/4.83        = ( ( M = N )
% 8.68/4.83          | ( K = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_873_mult__cancel2,axiom,
% 8.68/4.83      ! [M: nat,K: nat,N: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ M @ K )
% 8.68/4.83          = ( times_times_nat @ N @ K ) )
% 8.68/4.83        = ( ( M = N )
% 8.68/4.83          | ( K = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_874_not__real__square__gt__zero,axiom,
% 8.68/4.83      ! [X: real] :
% 8.68/4.83        ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 8.68/4.83        = ( X = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_875_real__divide__square__eq,axiom,
% 8.68/4.83      ! [R: real,A: real] :
% 8.68/4.83        ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 8.68/4.83        = ( divide_divide_real @ A @ R ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_876_i0__less,axiom,
% 8.68/4.83      ! [N: extended_enat] :
% 8.68/4.83        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 8.68/4.83        = ( N != zero_z5237406670263579293d_enat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_877_maxt__corr__help,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ( ( vEBT_vebt_maxt @ T )
% 8.68/4.83            = ( some_nat @ Maxi ) )
% 8.68/4.83         => ( ( vEBT_vebt_member @ T @ X )
% 8.68/4.83           => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_878_maxt__corr,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ( ( vEBT_vebt_maxt @ T )
% 8.68/4.83            = ( some_nat @ X ) )
% 8.68/4.83         => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_879_maxt__sound,axiom,
% 8.68/4.83      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.83       => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 8.68/4.83         => ( ( vEBT_vebt_maxt @ T )
% 8.68/4.83            = ( some_nat @ X ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_880_mi__eq__ma__no__ch,axiom,
% 8.68/4.83      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 8.68/4.83       => ( ( Mi = Ma )
% 8.68/4.83         => ( ! [X4: vEBT_VEBT] :
% 8.68/4.83                ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.83               => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 8.68/4.83            & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_881_le__zero__eq,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.68/4.83        = ( N = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_882_not__gr__zero,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.68/4.83        = ( N = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_883_mult__zero__left,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( times_times_complex @ zero_zero_complex @ A )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_884_mult__zero__left,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( times_times_real @ zero_zero_real @ A )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_885_mult__zero__left,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( times_times_rat @ zero_zero_rat @ A )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_886_mult__zero__left,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( times_times_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_887_mult__zero__left,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( times_times_int @ zero_zero_int @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_888_mult__zero__right,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( times_times_complex @ A @ zero_zero_complex )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_889_mult__zero__right,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( times_times_real @ A @ zero_zero_real )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_890_mult__zero__right,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( times_times_rat @ A @ zero_zero_rat )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_891_mult__zero__right,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( times_times_nat @ A @ zero_zero_nat )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_892_mult__zero__right,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( times_times_int @ A @ zero_zero_int )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_893_mult__eq__0__iff,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( ( times_times_complex @ A @ B )
% 8.68/4.83          = zero_zero_complex )
% 8.68/4.83        = ( ( A = zero_zero_complex )
% 8.68/4.83          | ( B = zero_zero_complex ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_894_mult__eq__0__iff,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ( times_times_real @ A @ B )
% 8.68/4.83          = zero_zero_real )
% 8.68/4.83        = ( ( A = zero_zero_real )
% 8.68/4.83          | ( B = zero_zero_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_895_mult__eq__0__iff,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ( times_times_rat @ A @ B )
% 8.68/4.83          = zero_zero_rat )
% 8.68/4.83        = ( ( A = zero_zero_rat )
% 8.68/4.83          | ( B = zero_zero_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_896_mult__eq__0__iff,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ A @ B )
% 8.68/4.83          = zero_zero_nat )
% 8.68/4.83        = ( ( A = zero_zero_nat )
% 8.68/4.83          | ( B = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_897_mult__eq__0__iff,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ( times_times_int @ A @ B )
% 8.68/4.83          = zero_zero_int )
% 8.68/4.83        = ( ( A = zero_zero_int )
% 8.68/4.83          | ( B = zero_zero_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_898_mult__cancel__left,axiom,
% 8.68/4.83      ! [C: complex,A: complex,B: complex] :
% 8.68/4.83        ( ( ( times_times_complex @ C @ A )
% 8.68/4.83          = ( times_times_complex @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_899_mult__cancel__left,axiom,
% 8.68/4.83      ! [C: real,A: real,B: real] :
% 8.68/4.83        ( ( ( times_times_real @ C @ A )
% 8.68/4.83          = ( times_times_real @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_900_mult__cancel__left,axiom,
% 8.68/4.83      ! [C: rat,A: rat,B: rat] :
% 8.68/4.83        ( ( ( times_times_rat @ C @ A )
% 8.68/4.83          = ( times_times_rat @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_901_mult__cancel__left,axiom,
% 8.68/4.83      ! [C: nat,A: nat,B: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ C @ A )
% 8.68/4.83          = ( times_times_nat @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_nat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_902_mult__cancel__left,axiom,
% 8.68/4.83      ! [C: int,A: int,B: int] :
% 8.68/4.83        ( ( ( times_times_int @ C @ A )
% 8.68/4.83          = ( times_times_int @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_int )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_903_mult__cancel__right,axiom,
% 8.68/4.83      ! [A: complex,C: complex,B: complex] :
% 8.68/4.83        ( ( ( times_times_complex @ A @ C )
% 8.68/4.83          = ( times_times_complex @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_904_mult__cancel__right,axiom,
% 8.68/4.83      ! [A: real,C: real,B: real] :
% 8.68/4.83        ( ( ( times_times_real @ A @ C )
% 8.68/4.83          = ( times_times_real @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_905_mult__cancel__right,axiom,
% 8.68/4.83      ! [A: rat,C: rat,B: rat] :
% 8.68/4.83        ( ( ( times_times_rat @ A @ C )
% 8.68/4.83          = ( times_times_rat @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_906_mult__cancel__right,axiom,
% 8.68/4.83      ! [A: nat,C: nat,B: nat] :
% 8.68/4.83        ( ( ( times_times_nat @ A @ C )
% 8.68/4.83          = ( times_times_nat @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_nat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_907_mult__cancel__right,axiom,
% 8.68/4.83      ! [A: int,C: int,B: int] :
% 8.68/4.83        ( ( ( times_times_int @ A @ C )
% 8.68/4.83          = ( times_times_int @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_int )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_908_add_Oright__neutral,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_909_add_Oright__neutral,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( plus_plus_real @ A @ zero_zero_real )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_910_add_Oright__neutral,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_911_add_Oright__neutral,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_912_add_Oright__neutral,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_913_double__zero__sym,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( zero_zero_real
% 8.68/4.83          = ( plus_plus_real @ A @ A ) )
% 8.68/4.83        = ( A = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_914_double__zero__sym,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( zero_zero_rat
% 8.68/4.83          = ( plus_plus_rat @ A @ A ) )
% 8.68/4.83        = ( A = zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_915_double__zero__sym,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( zero_zero_int
% 8.68/4.83          = ( plus_plus_int @ A @ A ) )
% 8.68/4.83        = ( A = zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_916_add__cancel__left__left,axiom,
% 8.68/4.83      ! [B: complex,A: complex] :
% 8.68/4.83        ( ( ( plus_plus_complex @ B @ A )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_complex ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_917_add__cancel__left__left,axiom,
% 8.68/4.83      ! [B: real,A: real] :
% 8.68/4.83        ( ( ( plus_plus_real @ B @ A )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_918_add__cancel__left__left,axiom,
% 8.68/4.83      ! [B: rat,A: rat] :
% 8.68/4.83        ( ( ( plus_plus_rat @ B @ A )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_919_add__cancel__left__left,axiom,
% 8.68/4.83      ! [B: nat,A: nat] :
% 8.68/4.83        ( ( ( plus_plus_nat @ B @ A )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_920_add__cancel__left__left,axiom,
% 8.68/4.83      ! [B: int,A: int] :
% 8.68/4.83        ( ( ( plus_plus_int @ B @ A )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_921_add__cancel__left__right,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( ( plus_plus_complex @ A @ B )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_complex ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_922_add__cancel__left__right,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ( plus_plus_real @ A @ B )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_923_add__cancel__left__right,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ( plus_plus_rat @ A @ B )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_924_add__cancel__left__right,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ( plus_plus_nat @ A @ B )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_925_add__cancel__left__right,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ( plus_plus_int @ A @ B )
% 8.68/4.83          = A )
% 8.68/4.83        = ( B = zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_926_add__cancel__right__left,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_complex @ B @ A ) )
% 8.68/4.83        = ( B = zero_zero_complex ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_927_add__cancel__right__left,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_real @ B @ A ) )
% 8.68/4.83        = ( B = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_928_add__cancel__right__left,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_rat @ B @ A ) )
% 8.68/4.83        = ( B = zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_929_add__cancel__right__left,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_nat @ B @ A ) )
% 8.68/4.83        = ( B = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_930_add__cancel__right__left,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_int @ B @ A ) )
% 8.68/4.83        = ( B = zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_931_add__cancel__right__right,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_complex @ A @ B ) )
% 8.68/4.83        = ( B = zero_zero_complex ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_932_add__cancel__right__right,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_real @ A @ B ) )
% 8.68/4.83        = ( B = zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_933_add__cancel__right__right,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_rat @ A @ B ) )
% 8.68/4.83        = ( B = zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_934_add__cancel__right__right,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_nat @ A @ B ) )
% 8.68/4.83        = ( B = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_935_add__cancel__right__right,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( A
% 8.68/4.83          = ( plus_plus_int @ A @ B ) )
% 8.68/4.83        = ( B = zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_936_add__eq__0__iff__both__eq__0,axiom,
% 8.68/4.83      ! [X: nat,Y: nat] :
% 8.68/4.83        ( ( ( plus_plus_nat @ X @ Y )
% 8.68/4.83          = zero_zero_nat )
% 8.68/4.83        = ( ( X = zero_zero_nat )
% 8.68/4.83          & ( Y = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_937_zero__eq__add__iff__both__eq__0,axiom,
% 8.68/4.83      ! [X: nat,Y: nat] :
% 8.68/4.83        ( ( zero_zero_nat
% 8.68/4.83          = ( plus_plus_nat @ X @ Y ) )
% 8.68/4.83        = ( ( X = zero_zero_nat )
% 8.68/4.83          & ( Y = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_938_add__0,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_939_add__0,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( plus_plus_real @ zero_zero_real @ A )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_940_add__0,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_941_add__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_942_add__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_943_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( minus_minus_complex @ A @ A )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_944_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( minus_minus_real @ A @ A )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_945_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ A @ A )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_946_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ A @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_947_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( minus_minus_int @ A @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_948_diff__zero,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_949_diff__zero,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( minus_minus_real @ A @ zero_zero_real )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_950_diff__zero,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_951_diff__zero,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_952_diff__zero,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( minus_minus_int @ A @ zero_zero_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_953_zero__diff,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_954_diff__0__right,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( minus_minus_complex @ A @ zero_zero_complex )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_955_diff__0__right,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( minus_minus_real @ A @ zero_zero_real )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_956_diff__0__right,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_957_diff__0__right,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( minus_minus_int @ A @ zero_zero_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_958_diff__self,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( minus_minus_complex @ A @ A )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_959_diff__self,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( minus_minus_real @ A @ A )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_960_diff__self,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ A @ A )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_961_diff__self,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( minus_minus_int @ A @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_962_div__0,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_963_div__0,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( divide_divide_real @ zero_zero_real @ A )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_964_div__0,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ zero_zero_rat @ A )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_965_div__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_966_div__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ zero_zero_int @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_967_divide__eq__0__iff,axiom,
% 8.68/4.83      ! [A: complex,B: complex] :
% 8.68/4.83        ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.68/4.83          = zero_zero_complex )
% 8.68/4.83        = ( ( A = zero_zero_complex )
% 8.68/4.83          | ( B = zero_zero_complex ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_968_divide__eq__0__iff,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ( divide_divide_real @ A @ B )
% 8.68/4.83          = zero_zero_real )
% 8.68/4.83        = ( ( A = zero_zero_real )
% 8.68/4.83          | ( B = zero_zero_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_969_divide__eq__0__iff,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ( divide_divide_rat @ A @ B )
% 8.68/4.83          = zero_zero_rat )
% 8.68/4.83        = ( ( A = zero_zero_rat )
% 8.68/4.83          | ( B = zero_zero_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_970_div__by__0,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_971_div__by__0,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( divide_divide_real @ A @ zero_zero_real )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_972_div__by__0,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_973_div__by__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_974_div__by__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ A @ zero_zero_int )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_975_divide__cancel__left,axiom,
% 8.68/4.83      ! [C: complex,A: complex,B: complex] :
% 8.68/4.83        ( ( ( divide1717551699836669952omplex @ C @ A )
% 8.68/4.83          = ( divide1717551699836669952omplex @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_976_divide__cancel__left,axiom,
% 8.68/4.83      ! [C: real,A: real,B: real] :
% 8.68/4.83        ( ( ( divide_divide_real @ C @ A )
% 8.68/4.83          = ( divide_divide_real @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_977_divide__cancel__left,axiom,
% 8.68/4.83      ! [C: rat,A: rat,B: rat] :
% 8.68/4.83        ( ( ( divide_divide_rat @ C @ A )
% 8.68/4.83          = ( divide_divide_rat @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_978_divide__cancel__right,axiom,
% 8.68/4.83      ! [A: complex,C: complex,B: complex] :
% 8.68/4.83        ( ( ( divide1717551699836669952omplex @ A @ C )
% 8.68/4.83          = ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_979_divide__cancel__right,axiom,
% 8.68/4.83      ! [A: real,C: real,B: real] :
% 8.68/4.83        ( ( ( divide_divide_real @ A @ C )
% 8.68/4.83          = ( divide_divide_real @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_980_divide__cancel__right,axiom,
% 8.68/4.83      ! [A: rat,C: rat,B: rat] :
% 8.68/4.83        ( ( ( divide_divide_rat @ A @ C )
% 8.68/4.83          = ( divide_divide_rat @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( A = B ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_981_bits__div__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_982_bits__div__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ zero_zero_int @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_983_bits__div__by__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_984_bits__div__by__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( divide_divide_int @ A @ zero_zero_int )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_985_division__ring__divide__zero,axiom,
% 8.68/4.83      ! [A: complex] :
% 8.68/4.83        ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 8.68/4.83        = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_986_division__ring__divide__zero,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( divide_divide_real @ A @ zero_zero_real )
% 8.68/4.83        = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_987_division__ring__divide__zero,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.68/4.83        = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_988_half__nonnegative__int__iff,axiom,
% 8.68/4.83      ! [K: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.68/4.83        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_989_half__negative__int__iff,axiom,
% 8.68/4.83      ! [K: int] :
% 8.68/4.83        ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 8.68/4.83        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_990_add__diff__cancel,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_991_add__diff__cancel,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_992_add__diff__cancel,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_993_diff__add__cancel,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_994_diff__add__cancel,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_995_diff__add__cancel,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_996_add__diff__cancel__left,axiom,
% 8.68/4.83      ! [C: real,A: real,B: real] :
% 8.68/4.83        ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 8.68/4.83        = ( minus_minus_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_997_add__diff__cancel__left,axiom,
% 8.68/4.83      ! [C: rat,A: rat,B: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 8.68/4.83        = ( minus_minus_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_998_add__diff__cancel__left,axiom,
% 8.68/4.83      ! [C: nat,A: nat,B: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 8.68/4.83        = ( minus_minus_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_999_add__diff__cancel__left,axiom,
% 8.68/4.83      ! [C: int,A: int,B: int] :
% 8.68/4.83        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 8.68/4.83        = ( minus_minus_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1000_add__diff__cancel__left_H,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 8.68/4.83        = B ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1001_add__diff__cancel__left_H,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 8.68/4.83        = B ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1002_add__diff__cancel__left_H,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 8.68/4.83        = B ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1003_add__diff__cancel__left_H,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 8.68/4.83        = B ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1004_add__diff__cancel__right,axiom,
% 8.68/4.83      ! [A: real,C: real,B: real] :
% 8.68/4.83        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 8.68/4.83        = ( minus_minus_real @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1005_add__diff__cancel__right,axiom,
% 8.68/4.83      ! [A: rat,C: rat,B: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.83        = ( minus_minus_rat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1006_add__diff__cancel__right,axiom,
% 8.68/4.83      ! [A: nat,C: nat,B: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 8.68/4.83        = ( minus_minus_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1007_add__diff__cancel__right,axiom,
% 8.68/4.83      ! [A: int,C: int,B: int] :
% 8.68/4.83        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 8.68/4.83        = ( minus_minus_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1008_add__diff__cancel__right_H,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1009_add__diff__cancel__right_H,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1010_add__diff__cancel__right_H,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1011_add__diff__cancel__right_H,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1012_bits__mod__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1013_bits__mod__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1014_bits__mod__0,axiom,
% 8.68/4.83      ! [A: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.83        = zero_z3403309356797280102nteger ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1015_mod__self,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ A @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1016_mod__self,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ A @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1017_mod__self,axiom,
% 8.68/4.83      ! [A: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ A @ A )
% 8.68/4.83        = zero_z3403309356797280102nteger ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1018_mod__by__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1019_mod__by__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ A @ zero_zero_int )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1020_mod__by__0,axiom,
% 8.68/4.83      ! [A: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 8.68/4.83        = A ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1021_mod__0,axiom,
% 8.68/4.83      ! [A: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.68/4.83        = zero_zero_nat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1022_mod__0,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.68/4.83        = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1023_mod__0,axiom,
% 8.68/4.83      ! [A: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.83        = zero_z3403309356797280102nteger ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1024_insert__simp__mima,axiom,
% 8.68/4.83      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.83        ( ( ( X = Mi )
% 8.68/4.83          | ( X = Ma ) )
% 8.68/4.83       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.83         => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.83            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1025_mod__add__self1,axiom,
% 8.68/4.83      ! [B: nat,A: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.68/4.83        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1026_mod__add__self1,axiom,
% 8.68/4.83      ! [B: int,A: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.68/4.83        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1027_mod__add__self1,axiom,
% 8.68/4.83      ! [B: code_integer,A: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.68/4.83        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1028_mod__add__self2,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.68/4.83        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1029_mod__add__self2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.83        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1030_mod__add__self2,axiom,
% 8.68/4.83      ! [A: code_integer,B: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.68/4.83        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1031_minus__mod__self2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.68/4.83        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1032_minus__mod__self2,axiom,
% 8.68/4.83      ! [A: code_integer,B: code_integer] :
% 8.68/4.83        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 8.68/4.83        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1033_add__gr__0,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.83        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.83          | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1034_zero__less__diff,axiom,
% 8.68/4.83      ! [N: nat,M: nat] :
% 8.68/4.83        ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 8.68/4.83        = ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1035_mult__less__cancel2,axiom,
% 8.68/4.83      ! [M: nat,K: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 8.68/4.83        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.83          & ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1036_nat__0__less__mult__iff,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 8.68/4.83        = ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.83          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1037_nat__mult__less__cancel__disj,axiom,
% 8.68/4.83      ! [K: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.83        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.83          & ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1038_div__less,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ M @ N )
% 8.68/4.83       => ( ( divide_divide_nat @ M @ N )
% 8.68/4.83          = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1039_diff__is__0__eq_H,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.83       => ( ( minus_minus_nat @ M @ N )
% 8.68/4.83          = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1040_diff__is__0__eq,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ( minus_minus_nat @ M @ N )
% 8.68/4.83          = zero_zero_nat )
% 8.68/4.83        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1041_diff__diff__cancel,axiom,
% 8.68/4.83      ! [I: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ I @ N )
% 8.68/4.83       => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 8.68/4.83          = I ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1042_less__one,axiom,
% 8.68/4.83      ! [N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ N @ one_one_nat )
% 8.68/4.83        = ( N = zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1043_diff__diff__left,axiom,
% 8.68/4.83      ! [I: nat,J: nat,K: nat] :
% 8.68/4.83        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 8.68/4.83        = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1044_nat__zero__less__power__iff,axiom,
% 8.68/4.83      ! [X: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 8.68/4.83        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.68/4.83          | ( N = zero_zero_nat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1045_nat__mult__div__cancel__disj,axiom,
% 8.68/4.83      ! [K: nat,M: nat,N: nat] :
% 8.68/4.83        ( ( ( K = zero_zero_nat )
% 8.68/4.83         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.83            = zero_zero_nat ) )
% 8.68/4.83        & ( ( K != zero_zero_nat )
% 8.68/4.83         => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.83            = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1046_mod__less,axiom,
% 8.68/4.83      ! [M: nat,N: nat] :
% 8.68/4.83        ( ( ord_less_nat @ M @ N )
% 8.68/4.83       => ( ( modulo_modulo_nat @ M @ N )
% 8.68/4.83          = M ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1047_delt__out__of__range,axiom,
% 8.68/4.83      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.83        ( ( ( ord_less_nat @ X @ Mi )
% 8.68/4.83          | ( ord_less_nat @ Ma @ X ) )
% 8.68/4.83       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.83         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.83            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1048_dbl__simps_I2_J,axiom,
% 8.68/4.83      ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 8.68/4.83      = zero_zero_complex ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1049_dbl__simps_I2_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_real @ zero_zero_real )
% 8.68/4.83      = zero_zero_real ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1050_dbl__simps_I2_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 8.68/4.83      = zero_zero_rat ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1051_dbl__simps_I2_J,axiom,
% 8.68/4.83      ( ( neg_numeral_dbl_int @ zero_zero_int )
% 8.68/4.83      = zero_zero_int ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1052__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 8.68/4.83      ~ ! [Maxs: nat] :
% 8.68/4.83          ( ( some_nat @ Maxs )
% 8.68/4.83         != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1053_mi__ma__2__deg,axiom,
% 8.68/4.83      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.68/4.83        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.83       => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.68/4.83          & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1054_add__le__same__cancel1,axiom,
% 8.68/4.83      ! [B: real,A: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1055_add__le__same__cancel1,axiom,
% 8.68/4.83      ! [B: rat,A: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1056_add__le__same__cancel1,axiom,
% 8.68/4.83      ! [B: nat,A: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1057_add__le__same__cancel1,axiom,
% 8.68/4.83      ! [B: int,A: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1058_add__le__same__cancel2,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1059_add__le__same__cancel2,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1060_add__le__same__cancel2,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1061_add__le__same__cancel2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1062_le__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1063_le__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1064_le__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1065_le__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1066_le__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.68/4.83        = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1067_le__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.68/4.83        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1068_le__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.68/4.83        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1069_le__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.68/4.83        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1070_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 8.68/4.83        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1071_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.68/4.83        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1072_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.68/4.83        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1073_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 8.68/4.83        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1074_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.68/4.83        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1075_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.68/4.83        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1076_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 8.68/4.83        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1077_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.68/4.83        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1078_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.68/4.83        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1079_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.68/4.83      ! [A: real] :
% 8.68/4.83        ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 8.68/4.83        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1080_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.68/4.83      ! [A: rat] :
% 8.68/4.83        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.68/4.83        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1081_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.68/4.83      ! [A: int] :
% 8.68/4.83        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.68/4.83        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1082_less__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.68/4.83        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1083_less__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.68/4.83        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1084_less__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.68/4.83        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1085_less__add__same__cancel2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.68/4.83        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1086_less__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.68/4.83        = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1087_less__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.68/4.83        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1088_less__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.68/4.83        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1089_less__add__same__cancel1,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.68/4.83        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1090_add__less__same__cancel2,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1091_add__less__same__cancel2,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1092_add__less__same__cancel2,axiom,
% 8.68/4.83      ! [A: nat,B: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1093_add__less__same__cancel2,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.83        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1094_add__less__same__cancel1,axiom,
% 8.68/4.83      ! [B: real,A: real] :
% 8.68/4.83        ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1095_add__less__same__cancel1,axiom,
% 8.68/4.83      ! [B: rat,A: rat] :
% 8.68/4.83        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1096_add__less__same__cancel1,axiom,
% 8.68/4.83      ! [B: nat,A: nat] :
% 8.68/4.83        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1097_add__less__same__cancel1,axiom,
% 8.68/4.83      ! [B: int,A: int] :
% 8.68/4.83        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.68/4.83        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1098_diff__ge__0__iff__ge,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_real @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1099_diff__ge__0__iff__ge,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_rat @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1100_diff__ge__0__iff__ge,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.68/4.83        = ( ord_less_eq_int @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1101_diff__gt__0__iff__gt,axiom,
% 8.68/4.83      ! [A: real,B: real] :
% 8.68/4.83        ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 8.68/4.83        = ( ord_less_real @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1102_diff__gt__0__iff__gt,axiom,
% 8.68/4.83      ! [A: rat,B: rat] :
% 8.68/4.83        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.68/4.83        = ( ord_less_rat @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1103_diff__gt__0__iff__gt,axiom,
% 8.68/4.83      ! [A: int,B: int] :
% 8.68/4.83        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.68/4.83        = ( ord_less_int @ B @ A ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1104_sum__squares__eq__zero__iff,axiom,
% 8.68/4.83      ! [X: real,Y: real] :
% 8.68/4.83        ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 8.68/4.83          = zero_zero_real )
% 8.68/4.83        = ( ( X = zero_zero_real )
% 8.68/4.83          & ( Y = zero_zero_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1105_sum__squares__eq__zero__iff,axiom,
% 8.68/4.83      ! [X: rat,Y: rat] :
% 8.68/4.83        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 8.68/4.83          = zero_zero_rat )
% 8.68/4.83        = ( ( X = zero_zero_rat )
% 8.68/4.83          & ( Y = zero_zero_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1106_sum__squares__eq__zero__iff,axiom,
% 8.68/4.83      ! [X: int,Y: int] :
% 8.68/4.83        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 8.68/4.83          = zero_zero_int )
% 8.68/4.83        = ( ( X = zero_zero_int )
% 8.68/4.83          & ( Y = zero_zero_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1107_mult__cancel__left1,axiom,
% 8.68/4.83      ! [C: complex,B: complex] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_complex @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( B = one_one_complex ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1108_mult__cancel__left1,axiom,
% 8.68/4.83      ! [C: real,B: real] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_real @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( B = one_one_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1109_mult__cancel__left1,axiom,
% 8.68/4.83      ! [C: rat,B: rat] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_rat @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( B = one_one_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1110_mult__cancel__left1,axiom,
% 8.68/4.83      ! [C: int,B: int] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_int @ C @ B ) )
% 8.68/4.83        = ( ( C = zero_zero_int )
% 8.68/4.83          | ( B = one_one_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1111_mult__cancel__left2,axiom,
% 8.68/4.83      ! [C: complex,A: complex] :
% 8.68/4.83        ( ( ( times_times_complex @ C @ A )
% 8.68/4.83          = C )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( A = one_one_complex ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1112_mult__cancel__left2,axiom,
% 8.68/4.83      ! [C: real,A: real] :
% 8.68/4.83        ( ( ( times_times_real @ C @ A )
% 8.68/4.83          = C )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( A = one_one_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1113_mult__cancel__left2,axiom,
% 8.68/4.83      ! [C: rat,A: rat] :
% 8.68/4.83        ( ( ( times_times_rat @ C @ A )
% 8.68/4.83          = C )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( A = one_one_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1114_mult__cancel__left2,axiom,
% 8.68/4.83      ! [C: int,A: int] :
% 8.68/4.83        ( ( ( times_times_int @ C @ A )
% 8.68/4.83          = C )
% 8.68/4.83        = ( ( C = zero_zero_int )
% 8.68/4.83          | ( A = one_one_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1115_mult__cancel__right1,axiom,
% 8.68/4.83      ! [C: complex,B: complex] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_complex @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_complex )
% 8.68/4.83          | ( B = one_one_complex ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1116_mult__cancel__right1,axiom,
% 8.68/4.83      ! [C: real,B: real] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_real @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_real )
% 8.68/4.83          | ( B = one_one_real ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1117_mult__cancel__right1,axiom,
% 8.68/4.83      ! [C: rat,B: rat] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_rat @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_rat )
% 8.68/4.83          | ( B = one_one_rat ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1118_mult__cancel__right1,axiom,
% 8.68/4.83      ! [C: int,B: int] :
% 8.68/4.83        ( ( C
% 8.68/4.83          = ( times_times_int @ B @ C ) )
% 8.68/4.83        = ( ( C = zero_zero_int )
% 8.68/4.83          | ( B = one_one_int ) ) ) ).
% 8.68/4.83  
% 8.68/4.83  thf(fact_1119_mult__cancel__right2,axiom,
% 8.68/4.84      ! [A: complex,C: complex] :
% 8.68/4.84        ( ( ( times_times_complex @ A @ C )
% 8.68/4.84          = C )
% 8.68/4.84        = ( ( C = zero_zero_complex )
% 8.68/4.84          | ( A = one_one_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1120_mult__cancel__right2,axiom,
% 8.68/4.84      ! [A: real,C: real] :
% 8.68/4.84        ( ( ( times_times_real @ A @ C )
% 8.68/4.84          = C )
% 8.68/4.84        = ( ( C = zero_zero_real )
% 8.68/4.84          | ( A = one_one_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1121_mult__cancel__right2,axiom,
% 8.68/4.84      ! [A: rat,C: rat] :
% 8.68/4.84        ( ( ( times_times_rat @ A @ C )
% 8.68/4.84          = C )
% 8.68/4.84        = ( ( C = zero_zero_rat )
% 8.68/4.84          | ( A = one_one_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1122_mult__cancel__right2,axiom,
% 8.68/4.84      ! [A: int,C: int] :
% 8.68/4.84        ( ( ( times_times_int @ A @ C )
% 8.68/4.84          = C )
% 8.68/4.84        = ( ( C = zero_zero_int )
% 8.68/4.84          | ( A = one_one_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1123_mult__divide__mult__cancel__left__if,axiom,
% 8.68/4.84      ! [C: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( ( C = zero_zero_complex )
% 8.68/4.84         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 8.68/4.84            = zero_zero_complex ) )
% 8.68/4.84        & ( ( C != zero_zero_complex )
% 8.68/4.84         => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 8.68/4.84            = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1124_mult__divide__mult__cancel__left__if,axiom,
% 8.68/4.84      ! [C: real,A: real,B: real] :
% 8.68/4.84        ( ( ( C = zero_zero_real )
% 8.68/4.84         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.84            = zero_zero_real ) )
% 8.68/4.84        & ( ( C != zero_zero_real )
% 8.68/4.84         => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.84            = ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1125_mult__divide__mult__cancel__left__if,axiom,
% 8.68/4.84      ! [C: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( ( C = zero_zero_rat )
% 8.68/4.84         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.84            = zero_zero_rat ) )
% 8.68/4.84        & ( ( C != zero_zero_rat )
% 8.68/4.84         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.84            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1126_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [C: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( C != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1127_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [C: real,A: real,B: real] :
% 8.68/4.84        ( ( C != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.84          = ( divide_divide_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1128_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [C: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( C != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.84          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1129_nonzero__mult__div__cancel__left,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( A != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 8.68/4.84          = B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1130_nonzero__mult__div__cancel__left,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( A != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 8.68/4.84          = B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1131_nonzero__mult__div__cancel__left,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( A != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 8.68/4.84          = B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1132_nonzero__mult__div__cancel__left,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( A != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 8.68/4.84          = B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1133_nonzero__mult__div__cancel__left,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( A != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 8.68/4.84          = B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1134_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.68/4.84      ! [C: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( C != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1135_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.68/4.84      ! [C: real,A: real,B: real] :
% 8.68/4.84        ( ( C != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 8.68/4.84          = ( divide_divide_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1136_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.68/4.84      ! [C: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( C != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.84          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1137_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [C: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( C != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1138_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [C: real,A: real,B: real] :
% 8.68/4.84        ( ( C != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.84          = ( divide_divide_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1139_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [C: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( C != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.84          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1140_nonzero__mult__div__cancel__right,axiom,
% 8.68/4.84      ! [B: complex,A: complex] :
% 8.68/4.84        ( ( B != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1141_nonzero__mult__div__cancel__right,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( B != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1142_nonzero__mult__div__cancel__right,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( B != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1143_nonzero__mult__div__cancel__right,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( B != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1144_nonzero__mult__div__cancel__right,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( B != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1145_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.68/4.84      ! [C: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( C != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1146_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.68/4.84      ! [C: real,A: real,B: real] :
% 8.68/4.84        ( ( C != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 8.68/4.84          = ( divide_divide_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1147_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.68/4.84      ! [C: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( C != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.84          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1148_div__mult__mult1,axiom,
% 8.68/4.84      ! [C: nat,A: nat,B: nat] :
% 8.68/4.84        ( ( C != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.68/4.84          = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1149_div__mult__mult1,axiom,
% 8.68/4.84      ! [C: int,A: int,B: int] :
% 8.68/4.84        ( ( C != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.84          = ( divide_divide_int @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1150_div__mult__mult2,axiom,
% 8.68/4.84      ! [C: nat,A: nat,B: nat] :
% 8.68/4.84        ( ( C != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.68/4.84          = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1151_div__mult__mult2,axiom,
% 8.68/4.84      ! [C: int,A: int,B: int] :
% 8.68/4.84        ( ( C != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.84          = ( divide_divide_int @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1152_div__mult__mult1__if,axiom,
% 8.68/4.84      ! [C: nat,A: nat,B: nat] :
% 8.68/4.84        ( ( ( C = zero_zero_nat )
% 8.68/4.84         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.68/4.84            = zero_zero_nat ) )
% 8.68/4.84        & ( ( C != zero_zero_nat )
% 8.68/4.84         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.68/4.84            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1153_div__mult__mult1__if,axiom,
% 8.68/4.84      ! [C: int,A: int,B: int] :
% 8.68/4.84        ( ( ( C = zero_zero_int )
% 8.68/4.84         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.84            = zero_zero_int ) )
% 8.68/4.84        & ( ( C != zero_zero_int )
% 8.68/4.84         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.84            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1154_le__add__diff__inverse,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.84       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1155_le__add__diff__inverse,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.84       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1156_le__add__diff__inverse,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.84       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1157_le__add__diff__inverse,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.84       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1158_le__add__diff__inverse2,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.84       => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1159_le__add__diff__inverse2,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.84       => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1160_le__add__diff__inverse2,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.84       => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1161_le__add__diff__inverse2,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.84       => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.68/4.84          = A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1162_diff__add__zero,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1163_diff__numeral__special_I9_J,axiom,
% 8.68/4.84      ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 8.68/4.84      = zero_zero_complex ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1164_diff__numeral__special_I9_J,axiom,
% 8.68/4.84      ( ( minus_minus_real @ one_one_real @ one_one_real )
% 8.68/4.84      = zero_zero_real ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1165_diff__numeral__special_I9_J,axiom,
% 8.68/4.84      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 8.68/4.84      = zero_zero_rat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1166_diff__numeral__special_I9_J,axiom,
% 8.68/4.84      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 8.68/4.84      = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1167_divide__eq__1__iff,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.68/4.84          = one_one_complex )
% 8.68/4.84        = ( ( B != zero_zero_complex )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1168_divide__eq__1__iff,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ( divide_divide_real @ A @ B )
% 8.68/4.84          = one_one_real )
% 8.68/4.84        = ( ( B != zero_zero_real )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1169_divide__eq__1__iff,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ( divide_divide_rat @ A @ B )
% 8.68/4.84          = one_one_rat )
% 8.68/4.84        = ( ( B != zero_zero_rat )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1170_div__self,axiom,
% 8.68/4.84      ! [A: complex] :
% 8.68/4.84        ( ( A != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ A @ A )
% 8.68/4.84          = one_one_complex ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1171_div__self,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( A != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ A @ A )
% 8.68/4.84          = one_one_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1172_div__self,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( A != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ A @ A )
% 8.68/4.84          = one_one_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1173_div__self,axiom,
% 8.68/4.84      ! [A: nat] :
% 8.68/4.84        ( ( A != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ A @ A )
% 8.68/4.84          = one_one_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1174_div__self,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( A != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ A @ A )
% 8.68/4.84          = one_one_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1175_one__eq__divide__iff,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( one_one_complex
% 8.68/4.84          = ( divide1717551699836669952omplex @ A @ B ) )
% 8.68/4.84        = ( ( B != zero_zero_complex )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1176_one__eq__divide__iff,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( one_one_real
% 8.68/4.84          = ( divide_divide_real @ A @ B ) )
% 8.68/4.84        = ( ( B != zero_zero_real )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1177_one__eq__divide__iff,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( one_one_rat
% 8.68/4.84          = ( divide_divide_rat @ A @ B ) )
% 8.68/4.84        = ( ( B != zero_zero_rat )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1178_divide__self,axiom,
% 8.68/4.84      ! [A: complex] :
% 8.68/4.84        ( ( A != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ A @ A )
% 8.68/4.84          = one_one_complex ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1179_divide__self,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( A != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ A @ A )
% 8.68/4.84          = one_one_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1180_divide__self,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( A != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ A @ A )
% 8.68/4.84          = one_one_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1181_divide__self__if,axiom,
% 8.68/4.84      ! [A: complex] :
% 8.68/4.84        ( ( ( A = zero_zero_complex )
% 8.68/4.84         => ( ( divide1717551699836669952omplex @ A @ A )
% 8.68/4.84            = zero_zero_complex ) )
% 8.68/4.84        & ( ( A != zero_zero_complex )
% 8.68/4.84         => ( ( divide1717551699836669952omplex @ A @ A )
% 8.68/4.84            = one_one_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1182_divide__self__if,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ( A = zero_zero_real )
% 8.68/4.84         => ( ( divide_divide_real @ A @ A )
% 8.68/4.84            = zero_zero_real ) )
% 8.68/4.84        & ( ( A != zero_zero_real )
% 8.68/4.84         => ( ( divide_divide_real @ A @ A )
% 8.68/4.84            = one_one_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1183_divide__self__if,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ( A = zero_zero_rat )
% 8.68/4.84         => ( ( divide_divide_rat @ A @ A )
% 8.68/4.84            = zero_zero_rat ) )
% 8.68/4.84        & ( ( A != zero_zero_rat )
% 8.68/4.84         => ( ( divide_divide_rat @ A @ A )
% 8.68/4.84            = one_one_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1184_divide__eq__eq__1,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( ( divide_divide_real @ B @ A )
% 8.68/4.84          = one_one_real )
% 8.68/4.84        = ( ( A != zero_zero_real )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1185_divide__eq__eq__1,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( ( divide_divide_rat @ B @ A )
% 8.68/4.84          = one_one_rat )
% 8.68/4.84        = ( ( A != zero_zero_rat )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1186_eq__divide__eq__1,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( one_one_real
% 8.68/4.84          = ( divide_divide_real @ B @ A ) )
% 8.68/4.84        = ( ( A != zero_zero_real )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1187_eq__divide__eq__1,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( one_one_rat
% 8.68/4.84          = ( divide_divide_rat @ B @ A ) )
% 8.68/4.84        = ( ( A != zero_zero_rat )
% 8.68/4.84          & ( A = B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1188_one__divide__eq__0__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ( divide_divide_real @ one_one_real @ A )
% 8.68/4.84          = zero_zero_real )
% 8.68/4.84        = ( A = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1189_one__divide__eq__0__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 8.68/4.84          = zero_zero_rat )
% 8.68/4.84        = ( A = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1190_zero__eq__1__divide__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( zero_zero_real
% 8.68/4.84          = ( divide_divide_real @ one_one_real @ A ) )
% 8.68/4.84        = ( A = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1191_zero__eq__1__divide__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( zero_zero_rat
% 8.68/4.84          = ( divide_divide_rat @ one_one_rat @ A ) )
% 8.68/4.84        = ( A = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1192_right__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [V: num,B: complex,C: complex] :
% 8.68/4.84        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 8.68/4.84        = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1193_right__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [V: num,B: real,C: real] :
% 8.68/4.84        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1194_right__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [V: num,B: rat,C: rat] :
% 8.68/4.84        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1195_right__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [V: num,B: int,C: int] :
% 8.68/4.84        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1196_left__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [A: complex,B: complex,V: num] :
% 8.68/4.84        ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 8.68/4.84        = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1197_left__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [A: real,B: real,V: num] :
% 8.68/4.84        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1198_left__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [A: rat,B: rat,V: num] :
% 8.68/4.84        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1199_left__diff__distrib__numeral,axiom,
% 8.68/4.84      ! [A: int,B: int,V: num] :
% 8.68/4.84        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1200_power__zero__numeral,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 8.68/4.84        = zero_zero_rat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1201_power__zero__numeral,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1202_power__zero__numeral,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 8.68/4.84        = zero_zero_real ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1203_power__zero__numeral,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1204_power__zero__numeral,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 8.68/4.84        = zero_zero_complex ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1205_power__eq__0__iff,axiom,
% 8.68/4.84      ! [A: rat,N: nat] :
% 8.68/4.84        ( ( ( power_power_rat @ A @ N )
% 8.68/4.84          = zero_zero_rat )
% 8.68/4.84        = ( ( A = zero_zero_rat )
% 8.68/4.84          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1206_power__eq__0__iff,axiom,
% 8.68/4.84      ! [A: nat,N: nat] :
% 8.68/4.84        ( ( ( power_power_nat @ A @ N )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84        = ( ( A = zero_zero_nat )
% 8.68/4.84          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1207_power__eq__0__iff,axiom,
% 8.68/4.84      ! [A: real,N: nat] :
% 8.68/4.84        ( ( ( power_power_real @ A @ N )
% 8.68/4.84          = zero_zero_real )
% 8.68/4.84        = ( ( A = zero_zero_real )
% 8.68/4.84          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1208_power__eq__0__iff,axiom,
% 8.68/4.84      ! [A: int,N: nat] :
% 8.68/4.84        ( ( ( power_power_int @ A @ N )
% 8.68/4.84          = zero_zero_int )
% 8.68/4.84        = ( ( A = zero_zero_int )
% 8.68/4.84          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1209_power__eq__0__iff,axiom,
% 8.68/4.84      ! [A: complex,N: nat] :
% 8.68/4.84        ( ( ( power_power_complex @ A @ N )
% 8.68/4.84          = zero_zero_complex )
% 8.68/4.84        = ( ( A = zero_zero_complex )
% 8.68/4.84          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1210_mod__mult__self2__is__0,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1211_mod__mult__self2__is__0,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1212_mod__mult__self2__is__0,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1213_mod__mult__self1__is__0,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1214_mod__mult__self1__is__0,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1215_mod__mult__self1__is__0,axiom,
% 8.68/4.84      ! [B: code_integer,A: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1216_bits__mod__by__1,axiom,
% 8.68/4.84      ! [A: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1217_bits__mod__by__1,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ A @ one_one_int )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1218_bits__mod__by__1,axiom,
% 8.68/4.84      ! [A: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1219_mod__by__1,axiom,
% 8.68/4.84      ! [A: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1220_mod__by__1,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ A @ one_one_int )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1221_mod__by__1,axiom,
% 8.68/4.84      ! [A: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1222_mod__div__trivial,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1223_mod__div__trivial,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1224_mod__div__trivial,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1225_bits__mod__div__trivial,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1226_bits__mod__div__trivial,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1227_bits__mod__div__trivial,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1228_mod__mult__self4,axiom,
% 8.68/4.84      ! [B: nat,C: nat,A: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1229_mod__mult__self4,axiom,
% 8.68/4.84      ! [B: int,C: int,A: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1230_mod__mult__self4,axiom,
% 8.68/4.84      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1231_mod__mult__self3,axiom,
% 8.68/4.84      ! [C: nat,B: nat,A: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1232_mod__mult__self3,axiom,
% 8.68/4.84      ! [C: int,B: int,A: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1233_mod__mult__self3,axiom,
% 8.68/4.84      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1234_mod__mult__self2,axiom,
% 8.68/4.84      ! [A: nat,B: nat,C: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1235_mod__mult__self2,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1236_mod__mult__self2,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1237_mod__mult__self1,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1238_mod__mult__self1,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1239_mod__mult__self1,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1240_mult__le__cancel2,axiom,
% 8.68/4.84      ! [M: nat,K: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 8.68/4.84        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.84         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1241_nat__mult__le__cancel__disj,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.84        = ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.84         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1242_Nat_Oadd__diff__assoc,axiom,
% 8.68/4.84      ! [K: nat,J: nat,I: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.84       => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.68/4.84          = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1243_Nat_Oadd__diff__assoc2,axiom,
% 8.68/4.84      ! [K: nat,J: nat,I: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.84       => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.68/4.84          = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1244_Nat_Odiff__diff__right,axiom,
% 8.68/4.84      ! [K: nat,J: nat,I: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.84       => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.68/4.84          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1245_div__mult__self__is__m,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 8.68/4.84          = M ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1246_div__mult__self1__is__m,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 8.68/4.84          = M ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1247_dbl__simps_I5_J,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 8.68/4.84        = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1248_dbl__simps_I5_J,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 8.68/4.84        = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1249_dbl__simps_I5_J,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 8.68/4.84        = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1250_dbl__simps_I5_J,axiom,
% 8.68/4.84      ! [K: num] :
% 8.68/4.84        ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 8.68/4.84        = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1251_both__member__options__from__complete__tree__to__child,axiom,
% 8.68/4.84      ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 8.68/4.84       => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.84         => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) )
% 8.68/4.84            | ( X = Mi )
% 8.68/4.84            | ( X = Ma ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1252__C10_C,axiom,
% 8.68/4.84      vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1253_member__inv,axiom,
% 8.68/4.84      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.68/4.84        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.84       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.84          & ( ( X = Mi )
% 8.68/4.84            | ( X = Ma )
% 8.68/4.84            | ( ( ord_less_nat @ X @ Ma )
% 8.68/4.84              & ( ord_less_nat @ Mi @ X )
% 8.68/4.84              & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.84              & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1254_zero__le__divide__1__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 8.68/4.84        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1255_zero__le__divide__1__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.68/4.84        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1256_divide__le__0__1__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 8.68/4.84        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1257_divide__le__0__1__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.68/4.84        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1258_divide__less__0__1__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 8.68/4.84        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1259_divide__less__0__1__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.68/4.84        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1260_divide__less__eq__1__neg,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.84       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.84          = ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1261_divide__less__eq__1__neg,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.84       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.84          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1262_divide__less__eq__1__pos,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84       => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.84          = ( ord_less_real @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1263_divide__less__eq__1__pos,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.84       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.84          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1264_less__divide__eq__1__neg,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.84       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.84          = ( ord_less_real @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1265_less__divide__eq__1__neg,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.84       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.84          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1266_less__divide__eq__1__pos,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84       => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.84          = ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1267_less__divide__eq__1__pos,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.84       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.84          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1268_zero__less__divide__1__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 8.68/4.84        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1269_zero__less__divide__1__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.68/4.84        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1270_divide__eq__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [B: complex,W: num,A: complex] :
% 8.68/4.84        ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( ( ( numera6690914467698888265omplex @ W )
% 8.68/4.84             != zero_zero_complex )
% 8.68/4.84           => ( B
% 8.68/4.84              = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 8.68/4.84          & ( ( ( numera6690914467698888265omplex @ W )
% 8.68/4.84              = zero_zero_complex )
% 8.68/4.84           => ( A = zero_zero_complex ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1271_divide__eq__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [B: real,W: num,A: real] :
% 8.68/4.84        ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( ( ( numeral_numeral_real @ W )
% 8.68/4.84             != zero_zero_real )
% 8.68/4.84           => ( B
% 8.68/4.84              = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 8.68/4.84          & ( ( ( numeral_numeral_real @ W )
% 8.68/4.84              = zero_zero_real )
% 8.68/4.84           => ( A = zero_zero_real ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1272_divide__eq__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [B: rat,W: num,A: rat] :
% 8.68/4.84        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( ( ( numeral_numeral_rat @ W )
% 8.68/4.84             != zero_zero_rat )
% 8.68/4.84           => ( B
% 8.68/4.84              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 8.68/4.84          & ( ( ( numeral_numeral_rat @ W )
% 8.68/4.84              = zero_zero_rat )
% 8.68/4.84           => ( A = zero_zero_rat ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1273_eq__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [A: complex,B: complex,W: num] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 8.68/4.84        = ( ( ( ( numera6690914467698888265omplex @ W )
% 8.68/4.84             != zero_zero_complex )
% 8.68/4.84           => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 8.68/4.84              = B ) )
% 8.68/4.84          & ( ( ( numera6690914467698888265omplex @ W )
% 8.68/4.84              = zero_zero_complex )
% 8.68/4.84           => ( A = zero_zero_complex ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1274_eq__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [A: real,B: real,W: num] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 8.68/4.84        = ( ( ( ( numeral_numeral_real @ W )
% 8.68/4.84             != zero_zero_real )
% 8.68/4.84           => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 8.68/4.84              = B ) )
% 8.68/4.84          & ( ( ( numeral_numeral_real @ W )
% 8.68/4.84              = zero_zero_real )
% 8.68/4.84           => ( A = zero_zero_real ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1275_eq__divide__eq__numeral1_I1_J,axiom,
% 8.68/4.84      ! [A: rat,B: rat,W: num] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 8.68/4.84        = ( ( ( ( numeral_numeral_rat @ W )
% 8.68/4.84             != zero_zero_rat )
% 8.68/4.84           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 8.68/4.84              = B ) )
% 8.68/4.84          & ( ( ( numeral_numeral_rat @ W )
% 8.68/4.84              = zero_zero_rat )
% 8.68/4.84           => ( A = zero_zero_rat ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1276_div__mult__self4,axiom,
% 8.68/4.84      ! [B: nat,C: nat,A: nat] :
% 8.68/4.84        ( ( B != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 8.68/4.84          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1277_div__mult__self4,axiom,
% 8.68/4.84      ! [B: int,C: int,A: int] :
% 8.68/4.84        ( ( B != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 8.68/4.84          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1278_div__mult__self3,axiom,
% 8.68/4.84      ! [B: nat,C: nat,A: nat] :
% 8.68/4.84        ( ( B != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 8.68/4.84          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1279_div__mult__self3,axiom,
% 8.68/4.84      ! [B: int,C: int,A: int] :
% 8.68/4.84        ( ( B != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 8.68/4.84          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1280_div__mult__self2,axiom,
% 8.68/4.84      ! [B: nat,A: nat,C: nat] :
% 8.68/4.84        ( ( B != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 8.68/4.84          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1281_div__mult__self2,axiom,
% 8.68/4.84      ! [B: int,A: int,C: int] :
% 8.68/4.84        ( ( B != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 8.68/4.84          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1282_div__mult__self1,axiom,
% 8.68/4.84      ! [B: nat,A: nat,C: nat] :
% 8.68/4.84        ( ( B != zero_zero_nat )
% 8.68/4.84       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 8.68/4.84          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1283_div__mult__self1,axiom,
% 8.68/4.84      ! [B: int,A: int,C: int] :
% 8.68/4.84        ( ( B != zero_zero_int )
% 8.68/4.84       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 8.68/4.84          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1284_nonzero__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( A != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1285_nonzero__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( A != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 8.68/4.84          = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1286_nonzero__divide__mult__cancel__left,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( A != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 8.68/4.84          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1287_nonzero__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [B: complex,A: complex] :
% 8.68/4.84        ( ( B != zero_zero_complex )
% 8.68/4.84       => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1288_nonzero__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [B: real,A: real] :
% 8.68/4.84        ( ( B != zero_zero_real )
% 8.68/4.84       => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 8.68/4.84          = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1289_nonzero__divide__mult__cancel__right,axiom,
% 8.68/4.84      ! [B: rat,A: rat] :
% 8.68/4.84        ( ( B != zero_zero_rat )
% 8.68/4.84       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 8.68/4.84          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1290_power__mono__iff,axiom,
% 8.68/4.84      ! [A: real,B: real,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.84       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.84         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84           => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 8.68/4.84              = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1291_power__mono__iff,axiom,
% 8.68/4.84      ! [A: rat,B: rat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.84       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.84         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84           => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.68/4.84              = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1292_power__mono__iff,axiom,
% 8.68/4.84      ! [A: nat,B: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.84       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.84         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84           => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.68/4.84              = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1293_power__mono__iff,axiom,
% 8.68/4.84      ! [A: int,B: int,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.84       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.84         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84           => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.68/4.84              = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1294_lesseq__shift,axiom,
% 8.68/4.84      ( ord_less_eq_nat
% 8.68/4.84      = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1295_le__divide__eq__1__pos,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.84          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1296_le__divide__eq__1__pos,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.84       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.84          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1297_le__divide__eq__1__neg,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.84       => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.84          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1298_le__divide__eq__1__neg,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.84       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.84          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1299_divide__le__eq__1__pos,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.84          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1300_divide__le__eq__1__pos,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.84       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.84          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1301_divide__le__eq__1__neg,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.84       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.84          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1302_divide__le__eq__1__neg,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.84       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.84          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1303_power__strict__decreasing__iff,axiom,
% 8.68/4.84      ! [B: real,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.84       => ( ( ord_less_real @ B @ one_one_real )
% 8.68/4.84         => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 8.68/4.84            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1304_power__strict__decreasing__iff,axiom,
% 8.68/4.84      ! [B: rat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.84       => ( ( ord_less_rat @ B @ one_one_rat )
% 8.68/4.84         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 8.68/4.84            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1305_power__strict__decreasing__iff,axiom,
% 8.68/4.84      ! [B: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.84       => ( ( ord_less_nat @ B @ one_one_nat )
% 8.68/4.84         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 8.68/4.84            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1306_power__strict__decreasing__iff,axiom,
% 8.68/4.84      ! [B: int,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.84       => ( ( ord_less_int @ B @ one_one_int )
% 8.68/4.84         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 8.68/4.84            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1307_zero__eq__power2,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = zero_zero_rat )
% 8.68/4.84        = ( A = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1308_zero__eq__power2,axiom,
% 8.68/4.84      ! [A: nat] :
% 8.68/4.84        ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84        = ( A = zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1309_zero__eq__power2,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = zero_zero_real )
% 8.68/4.84        = ( A = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1310_zero__eq__power2,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = zero_zero_int )
% 8.68/4.84        = ( A = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1311_zero__eq__power2,axiom,
% 8.68/4.84      ! [A: complex] :
% 8.68/4.84        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = zero_zero_complex )
% 8.68/4.84        = ( A = zero_zero_complex ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1312_bits__one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1313_bits__one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1314_bits__one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_Code_integer ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1315_one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1316_one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1317_one__mod__two__eq__one,axiom,
% 8.68/4.84      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.84      = one_one_Code_integer ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1318_add__self__mod__2,axiom,
% 8.68/4.84      ! [M: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1319_bits__1__div__2,axiom,
% 8.68/4.84      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84      = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1320_bits__1__div__2,axiom,
% 8.68/4.84      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.84      = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1321_one__div__two__eq__zero,axiom,
% 8.68/4.84      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84      = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1322_one__div__two__eq__zero,axiom,
% 8.68/4.84      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.84      = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1323_power2__less__eq__zero__iff,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 8.68/4.84        = ( A = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1324_power2__less__eq__zero__iff,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 8.68/4.84        = ( A = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1325_power2__less__eq__zero__iff,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 8.68/4.84        = ( A = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1326_power2__eq__iff__nonneg,axiom,
% 8.68/4.84      ! [X: real,Y: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.84       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.84         => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84              = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84            = ( X = Y ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1327_power2__eq__iff__nonneg,axiom,
% 8.68/4.84      ! [X: rat,Y: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.84       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.84         => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84              = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84            = ( X = Y ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1328_power2__eq__iff__nonneg,axiom,
% 8.68/4.84      ! [X: nat,Y: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.68/4.84       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.68/4.84         => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84              = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84            = ( X = Y ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1329_power2__eq__iff__nonneg,axiom,
% 8.68/4.84      ! [X: int,Y: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.84       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.84         => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84              = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84            = ( X = Y ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1330_power__decreasing__iff,axiom,
% 8.68/4.84      ! [B: real,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.84       => ( ( ord_less_real @ B @ one_one_real )
% 8.68/4.84         => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 8.68/4.84            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1331_power__decreasing__iff,axiom,
% 8.68/4.84      ! [B: rat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.84       => ( ( ord_less_rat @ B @ one_one_rat )
% 8.68/4.84         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 8.68/4.84            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1332_power__decreasing__iff,axiom,
% 8.68/4.84      ! [B: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.84       => ( ( ord_less_nat @ B @ one_one_nat )
% 8.68/4.84         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 8.68/4.84            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1333_power__decreasing__iff,axiom,
% 8.68/4.84      ! [B: int,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.84       => ( ( ord_less_int @ B @ one_one_int )
% 8.68/4.84         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 8.68/4.84            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1334_zero__less__power2,axiom,
% 8.68/4.84      ! [A: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84        = ( A != zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1335_zero__less__power2,axiom,
% 8.68/4.84      ! [A: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84        = ( A != zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1336_zero__less__power2,axiom,
% 8.68/4.84      ! [A: int] :
% 8.68/4.84        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84        = ( A != zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1337_sum__power2__eq__zero__iff,axiom,
% 8.68/4.84      ! [X: rat,Y: rat] :
% 8.68/4.84        ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84          = zero_zero_rat )
% 8.68/4.84        = ( ( X = zero_zero_rat )
% 8.68/4.84          & ( Y = zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1338_sum__power2__eq__zero__iff,axiom,
% 8.68/4.84      ! [X: real,Y: real] :
% 8.68/4.84        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84          = zero_zero_real )
% 8.68/4.84        = ( ( X = zero_zero_real )
% 8.68/4.84          & ( Y = zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1339_sum__power2__eq__zero__iff,axiom,
% 8.68/4.84      ! [X: int,Y: int] :
% 8.68/4.84        ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84          = zero_zero_int )
% 8.68/4.84        = ( ( X = zero_zero_int )
% 8.68/4.84          & ( Y = zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1340_mod2__gr__0,axiom,
% 8.68/4.84      ! [M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.84        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.84          = one_one_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1341_real__arch__pow,axiom,
% 8.68/4.84      ! [X: real,Y: real] :
% 8.68/4.84        ( ( ord_less_real @ one_one_real @ X )
% 8.68/4.84       => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N3 ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1342_less__eq__real__def,axiom,
% 8.68/4.84      ( ord_less_eq_real
% 8.68/4.84      = ( ^ [X3: real,Y3: real] :
% 8.68/4.84            ( ( ord_less_real @ X3 @ Y3 )
% 8.68/4.84            | ( X3 = Y3 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1343_real__arch__pow__inv,axiom,
% 8.68/4.84      ! [Y: real,X: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.84       => ( ( ord_less_real @ X @ one_one_real )
% 8.68/4.84         => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1344_complete__real,axiom,
% 8.68/4.84      ! [S2: set_real] :
% 8.68/4.84        ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 8.68/4.84       => ( ? [Z4: real] :
% 8.68/4.84            ! [X6: real] :
% 8.68/4.84              ( ( member_real @ X6 @ S2 )
% 8.68/4.84             => ( ord_less_eq_real @ X6 @ Z4 ) )
% 8.68/4.84         => ? [Y5: real] :
% 8.68/4.84              ( ! [X4: real] :
% 8.68/4.84                  ( ( member_real @ X4 @ S2 )
% 8.68/4.84                 => ( ord_less_eq_real @ X4 @ Y5 ) )
% 8.68/4.84              & ! [Z4: real] :
% 8.68/4.84                  ( ! [X6: real] :
% 8.68/4.84                      ( ( member_real @ X6 @ S2 )
% 8.68/4.84                     => ( ord_less_eq_real @ X6 @ Z4 ) )
% 8.68/4.84                 => ( ord_less_eq_real @ Y5 @ Z4 ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1345_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.84       => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1346_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.84       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1347_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.84       => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1348_mod__eq__0D,axiom,
% 8.68/4.84      ! [M: nat,D: nat] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ M @ D )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84       => ? [Q3: nat] :
% 8.68/4.84            ( M
% 8.68/4.84            = ( times_times_nat @ D @ Q3 ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1349_mod__diff__right__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1350_mod__diff__right__eq,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1351_mod__diff__left__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1352_mod__diff__left__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1353_mod__diff__cong,axiom,
% 8.68/4.84      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ A @ C )
% 8.68/4.84          = ( modulo_modulo_int @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo_modulo_int @ B @ C )
% 8.68/4.84            = ( modulo_modulo_int @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.84            = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1354_mod__diff__cong,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.68/4.84          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1355_mod__diff__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1356_mod__diff__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1357_diffs0__imp__equal,axiom,
% 8.68/4.84      ! [M: nat,N: nat] :
% 8.68/4.84        ( ( ( minus_minus_nat @ M @ N )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84       => ( ( ( minus_minus_nat @ N @ M )
% 8.68/4.84            = zero_zero_nat )
% 8.68/4.84         => ( M = N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1358_zero__reorient,axiom,
% 8.68/4.84      ! [X: complex] :
% 8.68/4.84        ( ( zero_zero_complex = X )
% 8.68/4.84        = ( X = zero_zero_complex ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1359_zero__reorient,axiom,
% 8.68/4.84      ! [X: real] :
% 8.68/4.84        ( ( zero_zero_real = X )
% 8.68/4.84        = ( X = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1360_zero__reorient,axiom,
% 8.68/4.84      ! [X: rat] :
% 8.68/4.84        ( ( zero_zero_rat = X )
% 8.68/4.84        = ( X = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1361_zero__reorient,axiom,
% 8.68/4.84      ! [X: nat] :
% 8.68/4.84        ( ( zero_zero_nat = X )
% 8.68/4.84        = ( X = zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1362_zero__reorient,axiom,
% 8.68/4.84      ! [X: int] :
% 8.68/4.84        ( ( zero_zero_int = X )
% 8.68/4.84        = ( X = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1363_diff__commute,axiom,
% 8.68/4.84      ! [I: nat,J: nat,K: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 8.68/4.84        = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1364_diff__right__commute,axiom,
% 8.68/4.84      ! [A: real,C: real,B: real] :
% 8.68/4.84        ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 8.68/4.84        = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1365_diff__right__commute,axiom,
% 8.68/4.84      ! [A: rat,C: rat,B: rat] :
% 8.68/4.84        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 8.68/4.84        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1366_diff__right__commute,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 8.68/4.84        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1367_diff__right__commute,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 8.68/4.84        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1368_eq__iff__diff__eq__0,axiom,
% 8.68/4.84      ( ( ^ [Y4: complex,Z2: complex] : ( Y4 = Z2 ) )
% 8.68/4.84      = ( ^ [A3: complex,B2: complex] :
% 8.68/4.84            ( ( minus_minus_complex @ A3 @ B2 )
% 8.68/4.84            = zero_zero_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1369_eq__iff__diff__eq__0,axiom,
% 8.68/4.84      ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 8.68/4.84      = ( ^ [A3: real,B2: real] :
% 8.68/4.84            ( ( minus_minus_real @ A3 @ B2 )
% 8.68/4.84            = zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1370_eq__iff__diff__eq__0,axiom,
% 8.68/4.84      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 8.68/4.84      = ( ^ [A3: rat,B2: rat] :
% 8.68/4.84            ( ( minus_minus_rat @ A3 @ B2 )
% 8.68/4.84            = zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1371_eq__iff__diff__eq__0,axiom,
% 8.68/4.84      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 8.68/4.84      = ( ^ [A3: int,B2: int] :
% 8.68/4.84            ( ( minus_minus_int @ A3 @ B2 )
% 8.68/4.84            = zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1372_diff__eq__diff__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.84        ( ( ( minus_minus_real @ A @ B )
% 8.68/4.84          = ( minus_minus_real @ C @ D ) )
% 8.68/4.84       => ( ( A = B )
% 8.68/4.84          = ( C = D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1373_diff__eq__diff__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.84        ( ( ( minus_minus_rat @ A @ B )
% 8.68/4.84          = ( minus_minus_rat @ C @ D ) )
% 8.68/4.84       => ( ( A = B )
% 8.68/4.84          = ( C = D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1374_diff__eq__diff__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.84        ( ( ( minus_minus_int @ A @ B )
% 8.68/4.84          = ( minus_minus_int @ C @ D ) )
% 8.68/4.84       => ( ( A = B )
% 8.68/4.84          = ( C = D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1375_minus__nat_Odiff__0,axiom,
% 8.68/4.84      ! [M: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ M @ zero_zero_nat )
% 8.68/4.84        = M ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1376_mod__geq,axiom,
% 8.68/4.84      ! [M: nat,N: nat] :
% 8.68/4.84        ( ~ ( ord_less_nat @ M @ N )
% 8.68/4.84       => ( ( modulo_modulo_nat @ M @ N )
% 8.68/4.84          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1377_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.84       => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1378_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.84       => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1379_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.68/4.84      ! [B: code_integer,A: code_integer] :
% 8.68/4.84        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.84       => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1380_mod__if,axiom,
% 8.68/4.84      ( modulo_modulo_nat
% 8.68/4.84      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N2 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1381_le__mod__geq,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.84       => ( ( modulo_modulo_nat @ M @ N )
% 8.68/4.84          = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1382_mod__eq__self__iff__div__eq__0,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ A @ B )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( divide_divide_nat @ A @ B )
% 8.68/4.84          = zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1383_mod__eq__self__iff__div__eq__0,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ A @ B )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( divide_divide_int @ A @ B )
% 8.68/4.84          = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1384_mod__eq__self__iff__div__eq__0,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ A @ B )
% 8.68/4.84          = A )
% 8.68/4.84        = ( ( divide6298287555418463151nteger @ A @ B )
% 8.68/4.84          = zero_z3403309356797280102nteger ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1385_le__iff__diff__le__0,axiom,
% 8.68/4.84      ( ord_less_eq_real
% 8.68/4.84      = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1386_le__iff__diff__le__0,axiom,
% 8.68/4.84      ( ord_less_eq_rat
% 8.68/4.84      = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1387_le__iff__diff__le__0,axiom,
% 8.68/4.84      ( ord_less_eq_int
% 8.68/4.84      = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1388_less__iff__diff__less__0,axiom,
% 8.68/4.84      ( ord_less_real
% 8.68/4.84      = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1389_less__iff__diff__less__0,axiom,
% 8.68/4.84      ( ord_less_rat
% 8.68/4.84      = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1390_less__iff__diff__less__0,axiom,
% 8.68/4.84      ( ord_less_int
% 8.68/4.84      = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1391_mod__less__divisor,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1392_diff__less,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.84         => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1393_diff__add__0,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1394_realpow__pos__nth__unique,axiom,
% 8.68/4.84      ! [N: nat,A: real] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84         => ? [X6: real] :
% 8.68/4.84              ( ( ord_less_real @ zero_zero_real @ X6 )
% 8.68/4.84              & ( ( power_power_real @ X6 @ N )
% 8.68/4.84                = A )
% 8.68/4.84              & ! [Y2: real] :
% 8.68/4.84                  ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 8.68/4.84                    & ( ( power_power_real @ Y2 @ N )
% 8.68/4.84                      = A ) )
% 8.68/4.84                 => ( Y2 = X6 ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1395_realpow__pos__nth,axiom,
% 8.68/4.84      ! [N: nat,A: real] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.84         => ? [R2: real] :
% 8.68/4.84              ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.68/4.84              & ( ( power_power_real @ R2 @ N )
% 8.68/4.84                = A ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1396_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.68/4.84      ! [B: code_integer,A: code_integer] :
% 8.68/4.84        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.84       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1397_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.68/4.84      ! [B: nat,A: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.84       => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1398_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.68/4.84      ! [B: int,A: int] :
% 8.68/4.84        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.84       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1399_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.84       => ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.68/4.84         => ( ( modulo364778990260209775nteger @ A @ B )
% 8.68/4.84            = A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1400_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.84       => ( ( ord_less_nat @ A @ B )
% 8.68/4.84         => ( ( modulo_modulo_nat @ A @ B )
% 8.68/4.84            = A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1401_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.84       => ( ( ord_less_int @ A @ B )
% 8.68/4.84         => ( ( modulo_modulo_int @ A @ B )
% 8.68/4.84            = A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1402_cong__exp__iff__simps_I2_J,axiom,
% 8.68/4.84      ! [N: num,Q2: num] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.68/4.84          = zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1403_cong__exp__iff__simps_I2_J,axiom,
% 8.68/4.84      ! [N: num,Q2: num] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = zero_zero_int )
% 8.68/4.84        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 8.68/4.84          = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1404_cong__exp__iff__simps_I2_J,axiom,
% 8.68/4.84      ! [N: num,Q2: num] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = zero_z3403309356797280102nteger )
% 8.68/4.84        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 8.68/4.84          = zero_z3403309356797280102nteger ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1405_cong__exp__iff__simps_I1_J,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 8.68/4.84        = zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1406_cong__exp__iff__simps_I1_J,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 8.68/4.84        = zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1407_cong__exp__iff__simps_I1_J,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 8.68/4.84        = zero_z3403309356797280102nteger ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1408_minus__div__mult__eq__mod,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1409_minus__div__mult__eq__mod,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1410_minus__div__mult__eq__mod,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1411_minus__mod__eq__div__mult,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 8.68/4.84        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1412_minus__mod__eq__div__mult,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.84        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1413_minus__mod__eq__div__mult,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.68/4.84        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1414_minus__mod__eq__mult__div,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 8.68/4.84        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1415_minus__mod__eq__mult__div,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.84        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1416_minus__mod__eq__mult__div,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.68/4.84        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1417_minus__mult__div__eq__mod,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 8.68/4.84        = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1418_minus__mult__div__eq__mod,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 8.68/4.84        = ( modulo_modulo_int @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1419_minus__mult__div__eq__mod,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 8.68/4.84        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1420_add__divide__eq__if__simps_I4_J,axiom,
% 8.68/4.84      ! [Z: complex,A: complex,B: complex] :
% 8.68/4.84        ( ( ( Z = zero_zero_complex )
% 8.68/4.84         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 8.68/4.84            = A ) )
% 8.68/4.84        & ( ( Z != zero_zero_complex )
% 8.68/4.84         => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 8.68/4.84            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1421_add__divide__eq__if__simps_I4_J,axiom,
% 8.68/4.84      ! [Z: real,A: real,B: real] :
% 8.68/4.84        ( ( ( Z = zero_zero_real )
% 8.68/4.84         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 8.68/4.84            = A ) )
% 8.68/4.84        & ( ( Z != zero_zero_real )
% 8.68/4.84         => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 8.68/4.84            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1422_add__divide__eq__if__simps_I4_J,axiom,
% 8.68/4.84      ! [Z: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( ( Z = zero_zero_rat )
% 8.68/4.84         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 8.68/4.84            = A ) )
% 8.68/4.84        & ( ( Z != zero_zero_rat )
% 8.68/4.84         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 8.68/4.84            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1423_diff__frac__eq,axiom,
% 8.68/4.84      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 8.68/4.84        ( ( Y != zero_zero_complex )
% 8.68/4.84       => ( ( Z != zero_zero_complex )
% 8.68/4.84         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 8.68/4.84            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1424_diff__frac__eq,axiom,
% 8.68/4.84      ! [Y: real,Z: real,X: real,W: real] :
% 8.68/4.84        ( ( Y != zero_zero_real )
% 8.68/4.84       => ( ( Z != zero_zero_real )
% 8.68/4.84         => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 8.68/4.84            = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1425_diff__frac__eq,axiom,
% 8.68/4.84      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 8.68/4.84        ( ( Y != zero_zero_rat )
% 8.68/4.84       => ( ( Z != zero_zero_rat )
% 8.68/4.84         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 8.68/4.84            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1426_diff__divide__eq__iff,axiom,
% 8.68/4.84      ! [Z: complex,X: complex,Y: complex] :
% 8.68/4.84        ( ( Z != zero_zero_complex )
% 8.68/4.84       => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 8.68/4.84          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1427_diff__divide__eq__iff,axiom,
% 8.68/4.84      ! [Z: real,X: real,Y: real] :
% 8.68/4.84        ( ( Z != zero_zero_real )
% 8.68/4.84       => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 8.68/4.84          = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1428_diff__divide__eq__iff,axiom,
% 8.68/4.84      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.84        ( ( Z != zero_zero_rat )
% 8.68/4.84       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 8.68/4.84          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1429_divide__diff__eq__iff,axiom,
% 8.68/4.84      ! [Z: complex,X: complex,Y: complex] :
% 8.68/4.84        ( ( Z != zero_zero_complex )
% 8.68/4.84       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 8.68/4.84          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1430_divide__diff__eq__iff,axiom,
% 8.68/4.84      ! [Z: real,X: real,Y: real] :
% 8.68/4.84        ( ( Z != zero_zero_real )
% 8.68/4.84       => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 8.68/4.84          = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1431_divide__diff__eq__iff,axiom,
% 8.68/4.84      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.84        ( ( Z != zero_zero_rat )
% 8.68/4.84       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 8.68/4.84          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1432_modulo__nat__def,axiom,
% 8.68/4.84      ( modulo_modulo_nat
% 8.68/4.84      = ( ^ [M3: nat,N2: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1433_mod__le__divisor,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1434_nat__diff__split__asm,axiom,
% 8.68/4.84      ! [P: nat > $o,A: nat,B: nat] :
% 8.68/4.84        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 8.68/4.84        = ( ~ ( ( ( ord_less_nat @ A @ B )
% 8.68/4.84                & ~ ( P @ zero_zero_nat ) )
% 8.68/4.84              | ? [D2: nat] :
% 8.68/4.84                  ( ( A
% 8.68/4.84                    = ( plus_plus_nat @ B @ D2 ) )
% 8.68/4.84                  & ~ ( P @ D2 ) ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1435_nat__diff__split,axiom,
% 8.68/4.84      ! [P: nat > $o,A: nat,B: nat] :
% 8.68/4.84        ( ( P @ ( minus_minus_nat @ A @ B ) )
% 8.68/4.84        = ( ( ( ord_less_nat @ A @ B )
% 8.68/4.84           => ( P @ zero_zero_nat ) )
% 8.68/4.84          & ! [D2: nat] :
% 8.68/4.84              ( ( A
% 8.68/4.84                = ( plus_plus_nat @ B @ D2 ) )
% 8.68/4.84             => ( P @ D2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1436_power__0__left,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ( N = zero_zero_nat )
% 8.68/4.84         => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.68/4.84            = one_one_rat ) )
% 8.68/4.84        & ( ( N != zero_zero_nat )
% 8.68/4.84         => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.68/4.84            = zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1437_power__0__left,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ( N = zero_zero_nat )
% 8.68/4.84         => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.68/4.84            = one_one_nat ) )
% 8.68/4.84        & ( ( N != zero_zero_nat )
% 8.68/4.84         => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.68/4.84            = zero_zero_nat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1438_power__0__left,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ( N = zero_zero_nat )
% 8.68/4.84         => ( ( power_power_real @ zero_zero_real @ N )
% 8.68/4.84            = one_one_real ) )
% 8.68/4.84        & ( ( N != zero_zero_nat )
% 8.68/4.84         => ( ( power_power_real @ zero_zero_real @ N )
% 8.68/4.84            = zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1439_power__0__left,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ( N = zero_zero_nat )
% 8.68/4.84         => ( ( power_power_int @ zero_zero_int @ N )
% 8.68/4.84            = one_one_int ) )
% 8.68/4.84        & ( ( N != zero_zero_nat )
% 8.68/4.84         => ( ( power_power_int @ zero_zero_int @ N )
% 8.68/4.84            = zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1440_power__0__left,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ( N = zero_zero_nat )
% 8.68/4.84         => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.68/4.84            = one_one_complex ) )
% 8.68/4.84        & ( ( N != zero_zero_nat )
% 8.68/4.84         => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.68/4.84            = zero_zero_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1441_zero__power,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.68/4.84          = zero_zero_rat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1442_zero__power,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.68/4.84          = zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1443_zero__power,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( power_power_real @ zero_zero_real @ N )
% 8.68/4.84          = zero_zero_real ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1444_zero__power,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( power_power_int @ zero_zero_int @ N )
% 8.68/4.84          = zero_zero_int ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1445_zero__power,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84       => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.68/4.84          = zero_zero_complex ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1446_mod__mult__eq,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1447_mod__mult__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1448_mod__mult__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1449_mod__mult__cong,axiom,
% 8.68/4.84      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ A @ C )
% 8.68/4.84          = ( modulo_modulo_nat @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo_modulo_nat @ B @ C )
% 8.68/4.84            = ( modulo_modulo_nat @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.68/4.84            = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1450_mod__mult__cong,axiom,
% 8.68/4.84      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ A @ C )
% 8.68/4.84          = ( modulo_modulo_int @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo_modulo_int @ B @ C )
% 8.68/4.84            = ( modulo_modulo_int @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 8.68/4.84            = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1451_mod__mult__cong,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.68/4.84          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1452_mod__mult__mult2,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.68/4.84        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1453_mod__mult__mult2,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.84        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1454_mod__mult__mult2,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.68/4.84        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1455_mult__mod__right,axiom,
% 8.68/4.84      ! [C: nat,A: nat,B: nat] :
% 8.68/4.84        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 8.68/4.84        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1456_mult__mod__right,axiom,
% 8.68/4.84      ! [C: int,A: int,B: int] :
% 8.68/4.84        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.84        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1457_mult__mod__right,axiom,
% 8.68/4.84      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.68/4.84        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1458_mod__mult__left__eq,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1459_mod__mult__left__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1460_mod__mult__left__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1461_mod__mult__right__eq,axiom,
% 8.68/4.84      ! [A: nat,B: nat,C: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1462_mod__mult__right__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1463_mod__mult__right__eq,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1464_mod__add__eq,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1465_mod__add__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1466_mod__add__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1467_mod__add__cong,axiom,
% 8.68/4.84      ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ A @ C )
% 8.68/4.84          = ( modulo_modulo_nat @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo_modulo_nat @ B @ C )
% 8.68/4.84            = ( modulo_modulo_nat @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.84            = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1468_mod__add__cong,axiom,
% 8.68/4.84      ! [A: int,C: int,A4: int,B: int,B4: int] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ A @ C )
% 8.68/4.84          = ( modulo_modulo_int @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo_modulo_int @ B @ C )
% 8.68/4.84            = ( modulo_modulo_int @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.84            = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1469_mod__add__cong,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.68/4.84          = ( modulo364778990260209775nteger @ A4 @ C ) )
% 8.68/4.84       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ B4 @ C ) )
% 8.68/4.84         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.68/4.84            = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1470_mod__add__left__eq,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1471_mod__add__left__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1472_mod__add__left__eq,axiom,
% 8.68/4.84      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1473_mod__add__right__eq,axiom,
% 8.68/4.84      ! [A: nat,B: nat,C: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1474_mod__add__right__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1475_mod__add__right__eq,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1476_power__mod,axiom,
% 8.68/4.84      ! [A: nat,B: nat,N: nat] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 8.68/4.84        = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1477_power__mod,axiom,
% 8.68/4.84      ! [A: int,B: int,N: nat] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 8.68/4.84        = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1478_power__mod,axiom,
% 8.68/4.84      ! [A: code_integer,B: code_integer,N: nat] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1479_diff__mono,axiom,
% 8.68/4.84      ! [A: real,B: real,D: real,C: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.84       => ( ( ord_less_eq_real @ D @ C )
% 8.68/4.84         => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1480_diff__mono,axiom,
% 8.68/4.84      ! [A: rat,B: rat,D: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.84       => ( ( ord_less_eq_rat @ D @ C )
% 8.68/4.84         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1481_diff__mono,axiom,
% 8.68/4.84      ! [A: int,B: int,D: int,C: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.84       => ( ( ord_less_eq_int @ D @ C )
% 8.68/4.84         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1482_diff__left__mono,axiom,
% 8.68/4.84      ! [B: real,A: real,C: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.84       => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1483_diff__left__mono,axiom,
% 8.68/4.84      ! [B: rat,A: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.84       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1484_diff__left__mono,axiom,
% 8.68/4.84      ! [B: int,A: int,C: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.84       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1485_diff__right__mono,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.84       => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1486_diff__right__mono,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.84       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1487_diff__right__mono,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.84       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1488_diff__eq__diff__less__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.84        ( ( ( minus_minus_real @ A @ B )
% 8.68/4.84          = ( minus_minus_real @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_eq_real @ A @ B )
% 8.68/4.84          = ( ord_less_eq_real @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1489_diff__eq__diff__less__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.84        ( ( ( minus_minus_rat @ A @ B )
% 8.68/4.84          = ( minus_minus_rat @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.84          = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1490_diff__eq__diff__less__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.84        ( ( ( minus_minus_int @ A @ B )
% 8.68/4.84          = ( minus_minus_int @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_eq_int @ A @ B )
% 8.68/4.84          = ( ord_less_eq_int @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1491_diff__strict__mono,axiom,
% 8.68/4.84      ! [A: real,B: real,D: real,C: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ B )
% 8.68/4.84       => ( ( ord_less_real @ D @ C )
% 8.68/4.84         => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1492_diff__strict__mono,axiom,
% 8.68/4.84      ! [A: rat,B: rat,D: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ B )
% 8.68/4.84       => ( ( ord_less_rat @ D @ C )
% 8.68/4.84         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1493_diff__strict__mono,axiom,
% 8.68/4.84      ! [A: int,B: int,D: int,C: int] :
% 8.68/4.84        ( ( ord_less_int @ A @ B )
% 8.68/4.84       => ( ( ord_less_int @ D @ C )
% 8.68/4.84         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1494_diff__eq__diff__less,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.84        ( ( ( minus_minus_real @ A @ B )
% 8.68/4.84          = ( minus_minus_real @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_real @ A @ B )
% 8.68/4.84          = ( ord_less_real @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1495_diff__eq__diff__less,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.84        ( ( ( minus_minus_rat @ A @ B )
% 8.68/4.84          = ( minus_minus_rat @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_rat @ A @ B )
% 8.68/4.84          = ( ord_less_rat @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1496_diff__eq__diff__less,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.84        ( ( ( minus_minus_int @ A @ B )
% 8.68/4.84          = ( minus_minus_int @ C @ D ) )
% 8.68/4.84       => ( ( ord_less_int @ A @ B )
% 8.68/4.84          = ( ord_less_int @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1497_diff__strict__left__mono,axiom,
% 8.68/4.84      ! [B: real,A: real,C: real] :
% 8.68/4.84        ( ( ord_less_real @ B @ A )
% 8.68/4.84       => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1498_diff__strict__left__mono,axiom,
% 8.68/4.84      ! [B: rat,A: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_rat @ B @ A )
% 8.68/4.84       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1499_diff__strict__left__mono,axiom,
% 8.68/4.84      ! [B: int,A: int,C: int] :
% 8.68/4.84        ( ( ord_less_int @ B @ A )
% 8.68/4.84       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1500_diff__strict__right__mono,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( ord_less_real @ A @ B )
% 8.68/4.84       => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1501_diff__strict__right__mono,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( ord_less_rat @ A @ B )
% 8.68/4.84       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1502_diff__strict__right__mono,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( ord_less_int @ A @ B )
% 8.68/4.84       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1503_left__diff__distrib,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1504_left__diff__distrib,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1505_left__diff__distrib,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1506_right__diff__distrib,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1507_right__diff__distrib,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1508_right__diff__distrib,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1509_left__diff__distrib_H,axiom,
% 8.68/4.84      ! [B: real,C: real,A: real] :
% 8.68/4.84        ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1510_left__diff__distrib_H,axiom,
% 8.68/4.84      ! [B: rat,C: rat,A: rat] :
% 8.68/4.84        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1511_left__diff__distrib_H,axiom,
% 8.68/4.84      ! [B: nat,C: nat,A: nat] :
% 8.68/4.84        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 8.68/4.84        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1512_left__diff__distrib_H,axiom,
% 8.68/4.84      ! [B: int,C: int,A: int] :
% 8.68/4.84        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1513_right__diff__distrib_H,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1514_right__diff__distrib_H,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1515_right__diff__distrib_H,axiom,
% 8.68/4.84      ! [A: nat,B: nat,C: nat] :
% 8.68/4.84        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1516_right__diff__distrib_H,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1517_group__cancel_Osub1,axiom,
% 8.68/4.84      ! [A2: real,K: real,A: real,B: real] :
% 8.68/4.84        ( ( A2
% 8.68/4.84          = ( plus_plus_real @ K @ A ) )
% 8.68/4.84       => ( ( minus_minus_real @ A2 @ B )
% 8.68/4.84          = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1518_group__cancel_Osub1,axiom,
% 8.68/4.84      ! [A2: rat,K: rat,A: rat,B: rat] :
% 8.68/4.84        ( ( A2
% 8.68/4.84          = ( plus_plus_rat @ K @ A ) )
% 8.68/4.84       => ( ( minus_minus_rat @ A2 @ B )
% 8.68/4.84          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1519_group__cancel_Osub1,axiom,
% 8.68/4.84      ! [A2: int,K: int,A: int,B: int] :
% 8.68/4.84        ( ( A2
% 8.68/4.84          = ( plus_plus_int @ K @ A ) )
% 8.68/4.84       => ( ( minus_minus_int @ A2 @ B )
% 8.68/4.84          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1520_diff__eq__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( ( minus_minus_real @ A @ B )
% 8.68/4.84          = C )
% 8.68/4.84        = ( A
% 8.68/4.84          = ( plus_plus_real @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1521_diff__eq__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( ( minus_minus_rat @ A @ B )
% 8.68/4.84          = C )
% 8.68/4.84        = ( A
% 8.68/4.84          = ( plus_plus_rat @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1522_diff__eq__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( ( minus_minus_int @ A @ B )
% 8.68/4.84          = C )
% 8.68/4.84        = ( A
% 8.68/4.84          = ( plus_plus_int @ C @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1523_eq__diff__eq,axiom,
% 8.68/4.84      ! [A: real,C: real,B: real] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( minus_minus_real @ C @ B ) )
% 8.68/4.84        = ( ( plus_plus_real @ A @ B )
% 8.68/4.84          = C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1524_eq__diff__eq,axiom,
% 8.68/4.84      ! [A: rat,C: rat,B: rat] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( minus_minus_rat @ C @ B ) )
% 8.68/4.84        = ( ( plus_plus_rat @ A @ B )
% 8.68/4.84          = C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1525_eq__diff__eq,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int] :
% 8.68/4.84        ( ( A
% 8.68/4.84          = ( minus_minus_int @ C @ B ) )
% 8.68/4.84        = ( ( plus_plus_int @ A @ B )
% 8.68/4.84          = C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1526_add__diff__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1527_add__diff__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1528_add__diff__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1529_diff__diff__eq2,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1530_diff__diff__eq2,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1531_diff__diff__eq2,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1532_diff__add__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1533_diff__add__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1534_diff__add__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1535_diff__add__eq__diff__diff__swap,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 8.68/4.84        = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1536_diff__add__eq__diff__diff__swap,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.68/4.84        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1537_diff__add__eq__diff__diff__swap,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.68/4.84        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1538_add__implies__diff,axiom,
% 8.68/4.84      ! [C: real,B: real,A: real] :
% 8.68/4.84        ( ( ( plus_plus_real @ C @ B )
% 8.68/4.84          = A )
% 8.68/4.84       => ( C
% 8.68/4.84          = ( minus_minus_real @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1539_add__implies__diff,axiom,
% 8.68/4.84      ! [C: rat,B: rat,A: rat] :
% 8.68/4.84        ( ( ( plus_plus_rat @ C @ B )
% 8.68/4.84          = A )
% 8.68/4.84       => ( C
% 8.68/4.84          = ( minus_minus_rat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1540_add__implies__diff,axiom,
% 8.68/4.84      ! [C: nat,B: nat,A: nat] :
% 8.68/4.84        ( ( ( plus_plus_nat @ C @ B )
% 8.68/4.84          = A )
% 8.68/4.84       => ( C
% 8.68/4.84          = ( minus_minus_nat @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1541_add__implies__diff,axiom,
% 8.68/4.84      ! [C: int,B: int,A: int] :
% 8.68/4.84        ( ( ( plus_plus_int @ C @ B )
% 8.68/4.84          = A )
% 8.68/4.84       => ( C
% 8.68/4.84          = ( minus_minus_int @ A @ B ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1542_diff__diff__eq,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1543_diff__diff__eq,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1544_diff__diff__eq,axiom,
% 8.68/4.84      ! [A: nat,B: nat,C: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1545_diff__diff__eq,axiom,
% 8.68/4.84      ! [A: int,B: int,C: int] :
% 8.68/4.84        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1546_add__diff__add,axiom,
% 8.68/4.84      ! [A: real,C: real,B: real,D: real] :
% 8.68/4.84        ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 8.68/4.84        = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1547_add__diff__add,axiom,
% 8.68/4.84      ! [A: rat,C: rat,B: rat,D: rat] :
% 8.68/4.84        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 8.68/4.84        = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1548_add__diff__add,axiom,
% 8.68/4.84      ! [A: int,C: int,B: int,D: int] :
% 8.68/4.84        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 8.68/4.84        = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1549_mod__less__eq__dividend,axiom,
% 8.68/4.84      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1550_diff__divide__distrib,axiom,
% 8.68/4.84      ! [A: complex,B: complex,C: complex] :
% 8.68/4.84        ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1551_diff__divide__distrib,axiom,
% 8.68/4.84      ! [A: real,B: real,C: real] :
% 8.68/4.84        ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1552_diff__divide__distrib,axiom,
% 8.68/4.84      ! [A: rat,B: rat,C: rat] :
% 8.68/4.84        ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.84        = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1553_diff__less__mono2,axiom,
% 8.68/4.84      ! [M: nat,N: nat,L2: nat] :
% 8.68/4.84        ( ( ord_less_nat @ M @ N )
% 8.68/4.84       => ( ( ord_less_nat @ M @ L2 )
% 8.68/4.84         => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1554_less__imp__diff__less,axiom,
% 8.68/4.84      ! [J: nat,K: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ J @ K )
% 8.68/4.84       => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1555_eq__diff__iff,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ M )
% 8.68/4.84       => ( ( ord_less_eq_nat @ K @ N )
% 8.68/4.84         => ( ( ( minus_minus_nat @ M @ K )
% 8.68/4.84              = ( minus_minus_nat @ N @ K ) )
% 8.68/4.84            = ( M = N ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1556_le__diff__iff,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ M )
% 8.68/4.84       => ( ( ord_less_eq_nat @ K @ N )
% 8.68/4.84         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.68/4.84            = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1557_Nat_Odiff__diff__eq,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ K @ M )
% 8.68/4.84       => ( ( ord_less_eq_nat @ K @ N )
% 8.68/4.84         => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.68/4.84            = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1558_diff__le__mono,axiom,
% 8.68/4.84      ! [M: nat,N: nat,L2: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.84       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1559_diff__le__self,axiom,
% 8.68/4.84      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1560_le__diff__iff_H,axiom,
% 8.68/4.84      ! [A: nat,C: nat,B: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ A @ C )
% 8.68/4.84       => ( ( ord_less_eq_nat @ B @ C )
% 8.68/4.84         => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 8.68/4.84            = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1561_diff__le__mono2,axiom,
% 8.68/4.84      ! [M: nat,N: nat,L2: nat] :
% 8.68/4.84        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.84       => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1562_Nat_Odiff__cancel,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 8.68/4.84        = ( minus_minus_nat @ M @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1563_diff__cancel2,axiom,
% 8.68/4.84      ! [M: nat,K: nat,N: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 8.68/4.84        = ( minus_minus_nat @ M @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1564_diff__add__inverse,axiom,
% 8.68/4.84      ! [N: nat,M: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 8.68/4.84        = M ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1565_diff__add__inverse2,axiom,
% 8.68/4.84      ! [M: nat,N: nat] :
% 8.68/4.84        ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 8.68/4.84        = M ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1566_diff__mult__distrib,axiom,
% 8.68/4.84      ! [M: nat,N: nat,K: nat] :
% 8.68/4.84        ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 8.68/4.84        = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1567_diff__mult__distrib2,axiom,
% 8.68/4.84      ! [K: nat,M: nat,N: nat] :
% 8.68/4.84        ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.84        = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1568_zero__le,axiom,
% 8.68/4.84      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1569_le__numeral__extra_I3_J,axiom,
% 8.68/4.84      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1570_le__numeral__extra_I3_J,axiom,
% 8.68/4.84      ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1571_le__numeral__extra_I3_J,axiom,
% 8.68/4.84      ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1572_le__numeral__extra_I3_J,axiom,
% 8.68/4.84      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1573_gr__zeroI,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( N != zero_zero_nat )
% 8.68/4.84       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1574_not__less__zero,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1575_gr__implies__not__zero,axiom,
% 8.68/4.84      ! [M: nat,N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ M @ N )
% 8.68/4.84       => ( N != zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1576_zero__less__iff__neq__zero,axiom,
% 8.68/4.84      ! [N: nat] :
% 8.68/4.84        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.84        = ( N != zero_zero_nat ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1577_less__numeral__extra_I3_J,axiom,
% 8.68/4.84      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1578_less__numeral__extra_I3_J,axiom,
% 8.68/4.84      ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1579_less__numeral__extra_I3_J,axiom,
% 8.68/4.84      ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1580_less__numeral__extra_I3_J,axiom,
% 8.68/4.84      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1581_field__lbound__gt__zero,axiom,
% 8.68/4.84      ! [D1: real,D22: real] :
% 8.68/4.84        ( ( ord_less_real @ zero_zero_real @ D1 )
% 8.68/4.84       => ( ( ord_less_real @ zero_zero_real @ D22 )
% 8.68/4.84         => ? [E2: real] :
% 8.68/4.84              ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.68/4.84              & ( ord_less_real @ E2 @ D1 )
% 8.68/4.84              & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1582_field__lbound__gt__zero,axiom,
% 8.68/4.84      ! [D1: rat,D22: rat] :
% 8.68/4.84        ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 8.68/4.84       => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 8.68/4.84         => ? [E2: rat] :
% 8.68/4.84              ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.68/4.84              & ( ord_less_rat @ E2 @ D1 )
% 8.68/4.84              & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1583_zero__neq__numeral,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( zero_zero_complex
% 8.68/4.84       != ( numera6690914467698888265omplex @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1584_zero__neq__numeral,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( zero_zero_real
% 8.68/4.84       != ( numeral_numeral_real @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1585_zero__neq__numeral,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( zero_zero_rat
% 8.68/4.84       != ( numeral_numeral_rat @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1586_zero__neq__numeral,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( zero_zero_nat
% 8.68/4.84       != ( numeral_numeral_nat @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1587_zero__neq__numeral,axiom,
% 8.68/4.84      ! [N: num] :
% 8.68/4.84        ( zero_zero_int
% 8.68/4.84       != ( numeral_numeral_int @ N ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1588_cong__exp__iff__simps_I9_J,axiom,
% 8.68/4.84      ! [M: num,Q2: num,N: num] :
% 8.68/4.84        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.68/4.84        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.68/4.84          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1589_cong__exp__iff__simps_I9_J,axiom,
% 8.68/4.84      ! [M: num,Q2: num,N: num] :
% 8.68/4.84        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.68/4.84        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 8.68/4.84          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1590_cong__exp__iff__simps_I9_J,axiom,
% 8.68/4.84      ! [M: num,Q2: num,N: num] :
% 8.68/4.84        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.68/4.84          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 8.68/4.84        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 8.68/4.84          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1591_cong__exp__iff__simps_I4_J,axiom,
% 8.68/4.84      ! [M: num,N: num] :
% 8.68/4.84        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 8.68/4.84        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1592_cong__exp__iff__simps_I4_J,axiom,
% 8.68/4.84      ! [M: num,N: num] :
% 8.68/4.84        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 8.68/4.84        = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1593_cong__exp__iff__simps_I4_J,axiom,
% 8.68/4.84      ! [M: num,N: num] :
% 8.68/4.84        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 8.68/4.84        = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1594_mult__not__zero,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( ( times_times_complex @ A @ B )
% 8.68/4.84         != zero_zero_complex )
% 8.68/4.84       => ( ( A != zero_zero_complex )
% 8.68/4.84          & ( B != zero_zero_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1595_mult__not__zero,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ( times_times_real @ A @ B )
% 8.68/4.84         != zero_zero_real )
% 8.68/4.84       => ( ( A != zero_zero_real )
% 8.68/4.84          & ( B != zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1596_mult__not__zero,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ( times_times_rat @ A @ B )
% 8.68/4.84         != zero_zero_rat )
% 8.68/4.84       => ( ( A != zero_zero_rat )
% 8.68/4.84          & ( B != zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1597_mult__not__zero,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( ( times_times_nat @ A @ B )
% 8.68/4.84         != zero_zero_nat )
% 8.68/4.84       => ( ( A != zero_zero_nat )
% 8.68/4.84          & ( B != zero_zero_nat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1598_mult__not__zero,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( ( times_times_int @ A @ B )
% 8.68/4.84         != zero_zero_int )
% 8.68/4.84       => ( ( A != zero_zero_int )
% 8.68/4.84          & ( B != zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1599_divisors__zero,axiom,
% 8.68/4.84      ! [A: complex,B: complex] :
% 8.68/4.84        ( ( ( times_times_complex @ A @ B )
% 8.68/4.84          = zero_zero_complex )
% 8.68/4.84       => ( ( A = zero_zero_complex )
% 8.68/4.84          | ( B = zero_zero_complex ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1600_divisors__zero,axiom,
% 8.68/4.84      ! [A: real,B: real] :
% 8.68/4.84        ( ( ( times_times_real @ A @ B )
% 8.68/4.84          = zero_zero_real )
% 8.68/4.84       => ( ( A = zero_zero_real )
% 8.68/4.84          | ( B = zero_zero_real ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1601_divisors__zero,axiom,
% 8.68/4.84      ! [A: rat,B: rat] :
% 8.68/4.84        ( ( ( times_times_rat @ A @ B )
% 8.68/4.84          = zero_zero_rat )
% 8.68/4.84       => ( ( A = zero_zero_rat )
% 8.68/4.84          | ( B = zero_zero_rat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1602_divisors__zero,axiom,
% 8.68/4.84      ! [A: nat,B: nat] :
% 8.68/4.84        ( ( ( times_times_nat @ A @ B )
% 8.68/4.84          = zero_zero_nat )
% 8.68/4.84       => ( ( A = zero_zero_nat )
% 8.68/4.84          | ( B = zero_zero_nat ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1603_divisors__zero,axiom,
% 8.68/4.84      ! [A: int,B: int] :
% 8.68/4.84        ( ( ( times_times_int @ A @ B )
% 8.68/4.84          = zero_zero_int )
% 8.68/4.84       => ( ( A = zero_zero_int )
% 8.68/4.84          | ( B = zero_zero_int ) ) ) ).
% 8.68/4.84  
% 8.68/4.84  thf(fact_1604_no__zero__divisors,axiom,
% 8.68/4.85      ! [A: complex,B: complex] :
% 8.68/4.85        ( ( A != zero_zero_complex )
% 8.68/4.85       => ( ( B != zero_zero_complex )
% 8.68/4.85         => ( ( times_times_complex @ A @ B )
% 8.68/4.85           != zero_zero_complex ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1605_no__zero__divisors,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( A != zero_zero_real )
% 8.68/4.85       => ( ( B != zero_zero_real )
% 8.68/4.85         => ( ( times_times_real @ A @ B )
% 8.68/4.85           != zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1606_no__zero__divisors,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( A != zero_zero_rat )
% 8.68/4.85       => ( ( B != zero_zero_rat )
% 8.68/4.85         => ( ( times_times_rat @ A @ B )
% 8.68/4.85           != zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1607_no__zero__divisors,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( A != zero_zero_nat )
% 8.68/4.85       => ( ( B != zero_zero_nat )
% 8.68/4.85         => ( ( times_times_nat @ A @ B )
% 8.68/4.85           != zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1608_no__zero__divisors,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( A != zero_zero_int )
% 8.68/4.85       => ( ( B != zero_zero_int )
% 8.68/4.85         => ( ( times_times_int @ A @ B )
% 8.68/4.85           != zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1609_mult__left__cancel,axiom,
% 8.68/4.85      ! [C: complex,A: complex,B: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( ( times_times_complex @ C @ A )
% 8.68/4.85            = ( times_times_complex @ C @ B ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1610_mult__left__cancel,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( ( times_times_real @ C @ A )
% 8.68/4.85            = ( times_times_real @ C @ B ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1611_mult__left__cancel,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( ( times_times_rat @ C @ A )
% 8.68/4.85            = ( times_times_rat @ C @ B ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1612_mult__left__cancel,axiom,
% 8.68/4.85      ! [C: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( C != zero_zero_nat )
% 8.68/4.85       => ( ( ( times_times_nat @ C @ A )
% 8.68/4.85            = ( times_times_nat @ C @ B ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1613_mult__left__cancel,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( C != zero_zero_int )
% 8.68/4.85       => ( ( ( times_times_int @ C @ A )
% 8.68/4.85            = ( times_times_int @ C @ B ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1614_mult__right__cancel,axiom,
% 8.68/4.85      ! [C: complex,A: complex,B: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( ( times_times_complex @ A @ C )
% 8.68/4.85            = ( times_times_complex @ B @ C ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1615_mult__right__cancel,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( ( times_times_real @ A @ C )
% 8.68/4.85            = ( times_times_real @ B @ C ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1616_mult__right__cancel,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( ( times_times_rat @ A @ C )
% 8.68/4.85            = ( times_times_rat @ B @ C ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1617_mult__right__cancel,axiom,
% 8.68/4.85      ! [C: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( C != zero_zero_nat )
% 8.68/4.85       => ( ( ( times_times_nat @ A @ C )
% 8.68/4.85            = ( times_times_nat @ B @ C ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1618_mult__right__cancel,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( C != zero_zero_int )
% 8.68/4.85       => ( ( ( times_times_int @ A @ C )
% 8.68/4.85            = ( times_times_int @ B @ C ) )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1619_comm__monoid__add__class_Oadd__0,axiom,
% 8.68/4.85      ! [A: complex] :
% 8.68/4.85        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1620_comm__monoid__add__class_Oadd__0,axiom,
% 8.68/4.85      ! [A: real] :
% 8.68/4.85        ( ( plus_plus_real @ zero_zero_real @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1621_comm__monoid__add__class_Oadd__0,axiom,
% 8.68/4.85      ! [A: rat] :
% 8.68/4.85        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1622_comm__monoid__add__class_Oadd__0,axiom,
% 8.68/4.85      ! [A: nat] :
% 8.68/4.85        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1623_comm__monoid__add__class_Oadd__0,axiom,
% 8.68/4.85      ! [A: int] :
% 8.68/4.85        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1624_add_Ocomm__neutral,axiom,
% 8.68/4.85      ! [A: complex] :
% 8.68/4.85        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1625_add_Ocomm__neutral,axiom,
% 8.68/4.85      ! [A: real] :
% 8.68/4.85        ( ( plus_plus_real @ A @ zero_zero_real )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1626_add_Ocomm__neutral,axiom,
% 8.68/4.85      ! [A: rat] :
% 8.68/4.85        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1627_add_Ocomm__neutral,axiom,
% 8.68/4.85      ! [A: nat] :
% 8.68/4.85        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1628_add_Ocomm__neutral,axiom,
% 8.68/4.85      ! [A: int] :
% 8.68/4.85        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1629_add_Ogroup__left__neutral,axiom,
% 8.68/4.85      ! [A: complex] :
% 8.68/4.85        ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1630_add_Ogroup__left__neutral,axiom,
% 8.68/4.85      ! [A: real] :
% 8.68/4.85        ( ( plus_plus_real @ zero_zero_real @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1631_add_Ogroup__left__neutral,axiom,
% 8.68/4.85      ! [A: rat] :
% 8.68/4.85        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1632_add_Ogroup__left__neutral,axiom,
% 8.68/4.85      ! [A: int] :
% 8.68/4.85        ( ( plus_plus_int @ zero_zero_int @ A )
% 8.68/4.85        = A ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1633_zero__neq__one,axiom,
% 8.68/4.85      zero_zero_complex != one_one_complex ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1634_zero__neq__one,axiom,
% 8.68/4.85      zero_zero_real != one_one_real ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1635_zero__neq__one,axiom,
% 8.68/4.85      zero_zero_rat != one_one_rat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1636_zero__neq__one,axiom,
% 8.68/4.85      zero_zero_nat != one_one_nat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1637_zero__neq__one,axiom,
% 8.68/4.85      zero_zero_int != one_one_int ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1638_power__not__zero,axiom,
% 8.68/4.85      ! [A: rat,N: nat] :
% 8.68/4.85        ( ( A != zero_zero_rat )
% 8.68/4.85       => ( ( power_power_rat @ A @ N )
% 8.68/4.85         != zero_zero_rat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1639_power__not__zero,axiom,
% 8.68/4.85      ! [A: nat,N: nat] :
% 8.68/4.85        ( ( A != zero_zero_nat )
% 8.68/4.85       => ( ( power_power_nat @ A @ N )
% 8.68/4.85         != zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1640_power__not__zero,axiom,
% 8.68/4.85      ! [A: real,N: nat] :
% 8.68/4.85        ( ( A != zero_zero_real )
% 8.68/4.85       => ( ( power_power_real @ A @ N )
% 8.68/4.85         != zero_zero_real ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1641_power__not__zero,axiom,
% 8.68/4.85      ! [A: int,N: nat] :
% 8.68/4.85        ( ( A != zero_zero_int )
% 8.68/4.85       => ( ( power_power_int @ A @ N )
% 8.68/4.85         != zero_zero_int ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1642_power__not__zero,axiom,
% 8.68/4.85      ! [A: complex,N: nat] :
% 8.68/4.85        ( ( A != zero_zero_complex )
% 8.68/4.85       => ( ( power_power_complex @ A @ N )
% 8.68/4.85         != zero_zero_complex ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1643_num_Osize_I4_J,axiom,
% 8.68/4.85      ( ( size_size_num @ one )
% 8.68/4.85      = zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1644_bot__nat__0_Oextremum__strict,axiom,
% 8.68/4.85      ! [A: nat] :
% 8.68/4.85        ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1645_gr0I,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ( ( N != zero_zero_nat )
% 8.68/4.85       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1646_not__gr0,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.68/4.85        = ( N = zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1647_not__less0,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1648_less__zeroE,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1649_gr__implies__not0,axiom,
% 8.68/4.85      ! [M: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_nat @ M @ N )
% 8.68/4.85       => ( N != zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1650_infinite__descent0,axiom,
% 8.68/4.85      ! [P: nat > $o,N: nat] :
% 8.68/4.85        ( ( P @ zero_zero_nat )
% 8.68/4.85       => ( ! [N3: nat] :
% 8.68/4.85              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.68/4.85             => ( ~ ( P @ N3 )
% 8.68/4.85               => ? [M2: nat] :
% 8.68/4.85                    ( ( ord_less_nat @ M2 @ N3 )
% 8.68/4.85                    & ~ ( P @ M2 ) ) ) )
% 8.68/4.85         => ( P @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1651_less__eq__nat_Osimps_I1_J,axiom,
% 8.68/4.85      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1652_bot__nat__0_Oextremum__unique,axiom,
% 8.68/4.85      ! [A: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85        = ( A = zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1653_bot__nat__0_Oextremum__uniqueI,axiom,
% 8.68/4.85      ! [A: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( A = zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1654_le__0__eq,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.68/4.85        = ( N = zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1655_plus__nat_Oadd__0,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ( ( plus_plus_nat @ zero_zero_nat @ N )
% 8.68/4.85        = N ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1656_add__eq__self__zero,axiom,
% 8.68/4.85      ! [M: nat,N: nat] :
% 8.68/4.85        ( ( ( plus_plus_nat @ M @ N )
% 8.68/4.85          = M )
% 8.68/4.85       => ( N = zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1657_nat__mult__eq__cancel__disj,axiom,
% 8.68/4.85      ! [K: nat,M: nat,N: nat] :
% 8.68/4.85        ( ( ( times_times_nat @ K @ M )
% 8.68/4.85          = ( times_times_nat @ K @ N ) )
% 8.68/4.85        = ( ( K = zero_zero_nat )
% 8.68/4.85          | ( M = N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1658_mult__0,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ( ( times_times_nat @ zero_zero_nat @ N )
% 8.68/4.85        = zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1659_nat__mod__eq__iff,axiom,
% 8.68/4.85      ! [X: nat,N: nat,Y: nat] :
% 8.68/4.85        ( ( ( modulo_modulo_nat @ X @ N )
% 8.68/4.85          = ( modulo_modulo_nat @ Y @ N ) )
% 8.68/4.85        = ( ? [Q1: nat,Q22: nat] :
% 8.68/4.85              ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 8.68/4.85              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1660_pos__zdiv__mult__2,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( 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 ) )
% 8.68/4.85          = ( divide_divide_int @ B @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1661_neg__zdiv__mult__2,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( 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 ) )
% 8.68/4.85          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1662_frac__le__eq,axiom,
% 8.68/4.85      ! [Y: real,Z: real,X: real,W: real] :
% 8.68/4.85        ( ( Y != zero_zero_real )
% 8.68/4.85       => ( ( Z != zero_zero_real )
% 8.68/4.85         => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 8.68/4.85            = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1663_frac__le__eq,axiom,
% 8.68/4.85      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 8.68/4.85        ( ( Y != zero_zero_rat )
% 8.68/4.85       => ( ( Z != zero_zero_rat )
% 8.68/4.85         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 8.68/4.85            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1664_frac__less__eq,axiom,
% 8.68/4.85      ! [Y: real,Z: real,X: real,W: real] :
% 8.68/4.85        ( ( Y != zero_zero_real )
% 8.68/4.85       => ( ( Z != zero_zero_real )
% 8.68/4.85         => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 8.68/4.85            = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1665_frac__less__eq,axiom,
% 8.68/4.85      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 8.68/4.85        ( ( Y != zero_zero_rat )
% 8.68/4.85       => ( ( Z != zero_zero_rat )
% 8.68/4.85         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 8.68/4.85            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1666_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.68/4.85      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.68/4.85        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 8.68/4.85       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.68/4.85          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1667_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.68/4.85      ! [C: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.68/4.85          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1668_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 8.68/4.85          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1669_not__iless0,axiom,
% 8.68/4.85      ! [N: extended_enat] :
% 8.68/4.85        ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1670_enat__0__less__mult__iff,axiom,
% 8.68/4.85      ! [M: extended_enat,N: extended_enat] :
% 8.68/4.85        ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 8.68/4.85        = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 8.68/4.85          & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1671_power__diff,axiom,
% 8.68/4.85      ! [A: complex,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_complex )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85            = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1672_power__diff,axiom,
% 8.68/4.85      ! [A: real,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85            = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1673_power__diff,axiom,
% 8.68/4.85      ! [A: rat,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85            = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1674_power__diff,axiom,
% 8.68/4.85      ! [A: nat,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85            = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1675_power__diff,axiom,
% 8.68/4.85      ! [A: int,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85            = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1676_split__mod,axiom,
% 8.68/4.85      ! [P: nat > $o,M: nat,N: nat] :
% 8.68/4.85        ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 8.68/4.85        = ( ( ( N = zero_zero_nat )
% 8.68/4.85           => ( P @ M ) )
% 8.68/4.85          & ( ( N != zero_zero_nat )
% 8.68/4.85           => ! [I5: nat,J3: nat] :
% 8.68/4.85                ( ( ord_less_nat @ J3 @ N )
% 8.68/4.85               => ( ( M
% 8.68/4.85                    = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 8.68/4.85                 => ( P @ J3 ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1677_i0__lb,axiom,
% 8.68/4.85      ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1678_ile0__eq,axiom,
% 8.68/4.85      ! [N: extended_enat] :
% 8.68/4.85        ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 8.68/4.85        = ( N = zero_z5237406670263579293d_enat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1679_divmod__digit__1_I2_J,axiom,
% 8.68/4.85      ! [A: code_integer,B: code_integer] :
% 8.68/4.85        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.85       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.85         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.85           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1680_divmod__digit__1_I2_J,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.85           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1681_divmod__digit__1_I2_J,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.85           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1682_power__eq__iff__eq__base,axiom,
% 8.68/4.85      ! [N: nat,A: real,B: real] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85           => ( ( ( power_power_real @ A @ N )
% 8.68/4.85                = ( power_power_real @ B @ N ) )
% 8.68/4.85              = ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1683_power__eq__iff__eq__base,axiom,
% 8.68/4.85      ! [N: nat,A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85           => ( ( ( power_power_rat @ A @ N )
% 8.68/4.85                = ( power_power_rat @ B @ N ) )
% 8.68/4.85              = ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1684_power__eq__iff__eq__base,axiom,
% 8.68/4.85      ! [N: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85           => ( ( ( power_power_nat @ A @ N )
% 8.68/4.85                = ( power_power_nat @ B @ N ) )
% 8.68/4.85              = ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1685_power__eq__iff__eq__base,axiom,
% 8.68/4.85      ! [N: nat,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85           => ( ( ( power_power_int @ A @ N )
% 8.68/4.85                = ( power_power_int @ B @ N ) )
% 8.68/4.85              = ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1686_power__eq__imp__eq__base,axiom,
% 8.68/4.85      ! [A: real,N: nat,B: real] :
% 8.68/4.85        ( ( ( power_power_real @ A @ N )
% 8.68/4.85          = ( power_power_real @ B @ N ) )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85             => ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1687_power__eq__imp__eq__base,axiom,
% 8.68/4.85      ! [A: rat,N: nat,B: rat] :
% 8.68/4.85        ( ( ( power_power_rat @ A @ N )
% 8.68/4.85          = ( power_power_rat @ B @ N ) )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85             => ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1688_power__eq__imp__eq__base,axiom,
% 8.68/4.85      ! [A: nat,N: nat,B: nat] :
% 8.68/4.85        ( ( ( power_power_nat @ A @ N )
% 8.68/4.85          = ( power_power_nat @ B @ N ) )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85             => ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1689_power__eq__imp__eq__base,axiom,
% 8.68/4.85      ! [A: int,N: nat,B: int] :
% 8.68/4.85        ( ( ( power_power_int @ A @ N )
% 8.68/4.85          = ( power_power_int @ B @ N ) )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85           => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85             => ( A = B ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1690_mult__eq__if,axiom,
% 8.68/4.85      ( times_times_nat
% 8.68/4.85      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1691_divmod__digit__0_I2_J,axiom,
% 8.68/4.85      ! [B: nat,A: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 8.68/4.85            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1692_divmod__digit__0_I2_J,axiom,
% 8.68/4.85      ! [B: int,A: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 8.68/4.85            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1693_divmod__digit__0_I2_J,axiom,
% 8.68/4.85      ! [B: code_integer,A: code_integer] :
% 8.68/4.85        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.85       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.85         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 8.68/4.85            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1694_cong__exp__iff__simps_I8_J,axiom,
% 8.68/4.85      ! [M: num,Q2: num] :
% 8.68/4.85        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1695_cong__exp__iff__simps_I8_J,axiom,
% 8.68/4.85      ! [M: num,Q2: num] :
% 8.68/4.85        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1696_cong__exp__iff__simps_I8_J,axiom,
% 8.68/4.85      ! [M: num,Q2: num] :
% 8.68/4.85        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1697_cong__exp__iff__simps_I6_J,axiom,
% 8.68/4.85      ! [Q2: num,N: num] :
% 8.68/4.85        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1698_cong__exp__iff__simps_I6_J,axiom,
% 8.68/4.85      ! [Q2: num,N: num] :
% 8.68/4.85        ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1699_cong__exp__iff__simps_I6_J,axiom,
% 8.68/4.85      ! [Q2: num,N: num] :
% 8.68/4.85        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.68/4.85       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1700_scaling__mono,axiom,
% 8.68/4.85      ! [U: real,V: real,R: real,S: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ U @ V )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 8.68/4.85         => ( ( ord_less_eq_real @ R @ S )
% 8.68/4.85           => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1701_scaling__mono,axiom,
% 8.68/4.85      ! [U: rat,V: rat,R: rat,S: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ U @ V )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 8.68/4.85         => ( ( ord_less_eq_rat @ R @ S )
% 8.68/4.85           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1702_mod__eqE,axiom,
% 8.68/4.85      ! [A: int,C: int,B: int] :
% 8.68/4.85        ( ( ( modulo_modulo_int @ A @ C )
% 8.68/4.85          = ( modulo_modulo_int @ B @ C ) )
% 8.68/4.85       => ~ ! [D3: int] :
% 8.68/4.85              ( B
% 8.68/4.85             != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1703_mod__eqE,axiom,
% 8.68/4.85      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.68/4.85        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.68/4.85          = ( modulo364778990260209775nteger @ B @ C ) )
% 8.68/4.85       => ~ ! [D3: code_integer] :
% 8.68/4.85              ( B
% 8.68/4.85             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1704_div__add1__eq,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.68/4.85        = ( 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 ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1705_div__add1__eq,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.68/4.85        = ( 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 ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1706_div__add1__eq,axiom,
% 8.68/4.85      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.85        ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.68/4.85        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1707_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 8.68/4.85      ! [N: nat,M: nat] :
% 8.68/4.85        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.68/4.85         != zero_zero_nat )
% 8.68/4.85       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 8.68/4.85         != zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1708_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 8.68/4.85      ! [N: nat,M: nat] :
% 8.68/4.85        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.68/4.85         != zero_zero_int )
% 8.68/4.85       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 8.68/4.85         != zero_zero_int ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1709_power__diff__power__eq,axiom,
% 8.68/4.85      ! [A: nat,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_nat )
% 8.68/4.85       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.68/4.85              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.68/4.85          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.68/4.85           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 8.68/4.85              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1710_power__diff__power__eq,axiom,
% 8.68/4.85      ! [A: int,N: nat,M: nat] :
% 8.68/4.85        ( ( A != zero_zero_int )
% 8.68/4.85       => ( ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.68/4.85              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 8.68/4.85          & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.68/4.85           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 8.68/4.85              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1711_power__eq__if,axiom,
% 8.68/4.85      ( power_power_complex
% 8.68/4.85      = ( ^ [P2: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P2 @ ( power_power_complex @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1712_power__eq__if,axiom,
% 8.68/4.85      ( power_power_real
% 8.68/4.85      = ( ^ [P2: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P2 @ ( power_power_real @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1713_power__eq__if,axiom,
% 8.68/4.85      ( power_power_rat
% 8.68/4.85      = ( ^ [P2: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P2 @ ( power_power_rat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1714_power__eq__if,axiom,
% 8.68/4.85      ( power_power_nat
% 8.68/4.85      = ( ^ [P2: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P2 @ ( power_power_nat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1715_power__eq__if,axiom,
% 8.68/4.85      ( power_power_int
% 8.68/4.85      = ( ^ [P2: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P2 @ ( power_power_int @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1716_diff__le__eq,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1717_diff__le__eq,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1718_diff__le__eq,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1719_le__diff__eq,axiom,
% 8.68/4.85      ! [A: real,C: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 8.68/4.85        = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1720_le__diff__eq,axiom,
% 8.68/4.85      ! [A: rat,C: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 8.68/4.85        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1721_le__diff__eq,axiom,
% 8.68/4.85      ! [A: int,C: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 8.68/4.85        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1722_diff__add,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 8.68/4.85          = B ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1723_le__add__diff,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1724_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.68/4.85          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1725_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.68/4.85          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1726_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 8.68/4.85          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1727_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 8.68/4.85          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1728_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 8.68/4.85          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1729_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 8.68/4.85          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1730_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 8.68/4.85          = B ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1731_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85         => ( ( ( minus_minus_nat @ B @ A )
% 8.68/4.85              = C )
% 8.68/4.85            = ( B
% 8.68/4.85              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1732_add__le__imp__le__diff,axiom,
% 8.68/4.85      ! [I: real,K: real,N: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 8.68/4.85       => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1733_add__le__imp__le__diff,axiom,
% 8.68/4.85      ! [I: rat,K: rat,N: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.68/4.85       => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1734_add__le__imp__le__diff,axiom,
% 8.68/4.85      ! [I: nat,K: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.68/4.85       => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1735_add__le__imp__le__diff,axiom,
% 8.68/4.85      ! [I: int,K: int,N: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.68/4.85       => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1736_add__le__add__imp__diff__le,axiom,
% 8.68/4.85      ! [I: real,K: real,N: real,J: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 8.68/4.85       => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 8.68/4.85         => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 8.68/4.85           => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 8.68/4.85             => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1737_add__le__add__imp__diff__le,axiom,
% 8.68/4.85      ! [I: rat,K: rat,N: rat,J: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.68/4.85       => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 8.68/4.85         => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 8.68/4.85           => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 8.68/4.85             => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1738_add__le__add__imp__diff__le,axiom,
% 8.68/4.85      ! [I: nat,K: nat,N: nat,J: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 8.68/4.85         => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 8.68/4.85           => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 8.68/4.85             => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1739_add__le__add__imp__diff__le,axiom,
% 8.68/4.85      ! [I: int,K: int,N: int,J: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.68/4.85       => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 8.68/4.85         => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 8.68/4.85           => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 8.68/4.85             => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1740_power__minus__mult,axiom,
% 8.68/4.85      ! [N: nat,A: complex] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.68/4.85          = ( power_power_complex @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1741_power__minus__mult,axiom,
% 8.68/4.85      ! [N: nat,A: real] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.68/4.85          = ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1742_power__minus__mult,axiom,
% 8.68/4.85      ! [N: nat,A: rat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.68/4.85          = ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1743_power__minus__mult,axiom,
% 8.68/4.85      ! [N: nat,A: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.68/4.85          = ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1744_power__minus__mult,axiom,
% 8.68/4.85      ! [N: nat,A: int] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.68/4.85          = ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1745_less__diff__eq,axiom,
% 8.68/4.85      ! [A: real,C: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 8.68/4.85        = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1746_less__diff__eq,axiom,
% 8.68/4.85      ! [A: rat,C: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 8.68/4.85        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1747_less__diff__eq,axiom,
% 8.68/4.85      ! [A: int,C: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 8.68/4.85        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1748_diff__less__eq,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1749_diff__less__eq,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1750_diff__less__eq,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.68/4.85        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1751_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ~ ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 8.68/4.85          = A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1752_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ~ ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.68/4.85          = A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1753_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ~ ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.68/4.85          = A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1754_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ~ ( ord_less_int @ A @ B )
% 8.68/4.85       => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.68/4.85          = A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1755_mult__diff__mult,axiom,
% 8.68/4.85      ! [X: real,Y: real,A: real,B: real] :
% 8.68/4.85        ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 8.68/4.85        = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1756_mult__diff__mult,axiom,
% 8.68/4.85      ! [X: rat,Y: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 8.68/4.85        = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1757_mult__diff__mult,axiom,
% 8.68/4.85      ! [X: int,Y: int,A: int,B: int] :
% 8.68/4.85        ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 8.68/4.85        = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1758_square__diff__square__factored,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 8.68/4.85        = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1759_square__diff__square__factored,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 8.68/4.85        = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1760_square__diff__square__factored,axiom,
% 8.68/4.85      ! [X: int,Y: int] :
% 8.68/4.85        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 8.68/4.85        = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1761_eq__add__iff2,axiom,
% 8.68/4.85      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.85        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.85        = ( C
% 8.68/4.85          = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1762_eq__add__iff2,axiom,
% 8.68/4.85      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.85        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.85        = ( C
% 8.68/4.85          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1763_eq__add__iff2,axiom,
% 8.68/4.85      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.85        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.85        = ( C
% 8.68/4.85          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1764_eq__add__iff1,axiom,
% 8.68/4.85      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.85        ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.85        = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 8.68/4.85          = D ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1765_eq__add__iff1,axiom,
% 8.68/4.85      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.85        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.85        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 8.68/4.85          = D ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1766_eq__add__iff1,axiom,
% 8.68/4.85      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.85        ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 8.68/4.85          = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.85        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 8.68/4.85          = D ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1767_power__strict__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,N: nat] :
% 8.68/4.85        ( ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85           => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1768_power__strict__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,N: nat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85           => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1769_power__strict__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85           => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1770_power__strict__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,N: nat] :
% 8.68/4.85        ( ( ord_less_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.85           => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1771_mod__eq__nat1E,axiom,
% 8.68/4.85      ! [M: nat,Q2: nat,N: nat] :
% 8.68/4.85        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.68/4.85          = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.68/4.85       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.85         => ~ ! [S3: nat] :
% 8.68/4.85                ( M
% 8.68/4.85               != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1772_mod__eq__nat2E,axiom,
% 8.68/4.85      ! [M: nat,Q2: nat,N: nat] :
% 8.68/4.85        ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.68/4.85          = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.68/4.85       => ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.85         => ~ ! [S3: nat] :
% 8.68/4.85                ( N
% 8.68/4.85               != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1773_nat__mod__eq__lemma,axiom,
% 8.68/4.85      ! [X: nat,N: nat,Y: nat] :
% 8.68/4.85        ( ( ( modulo_modulo_nat @ X @ N )
% 8.68/4.85          = ( modulo_modulo_nat @ Y @ N ) )
% 8.68/4.85       => ( ( ord_less_eq_nat @ Y @ X )
% 8.68/4.85         => ? [Q3: nat] :
% 8.68/4.85              ( X
% 8.68/4.85              = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1774_div__positive,axiom,
% 8.68/4.85      ! [B: nat,A: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.85         => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1775_div__positive,axiom,
% 8.68/4.85      ! [B: int,A: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ A )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1776_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ A @ B )
% 8.68/4.85         => ( ( divide_divide_nat @ A @ B )
% 8.68/4.85            = zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1777_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ A @ B )
% 8.68/4.85         => ( ( divide_divide_int @ A @ B )
% 8.68/4.85            = zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1778_diff__less__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.85         => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1779_less__diff__iff,axiom,
% 8.68/4.85      ! [K: nat,M: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ K @ M )
% 8.68/4.85       => ( ( ord_less_eq_nat @ K @ N )
% 8.68/4.85         => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 8.68/4.85            = ( ord_less_nat @ M @ N ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1780_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.68/4.85      ! [C: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.68/4.85          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1781_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.68/4.85          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1782_add__diff__inverse__nat,axiom,
% 8.68/4.85      ! [M: nat,N: nat] :
% 8.68/4.85        ( ~ ( ord_less_nat @ M @ N )
% 8.68/4.85       => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 8.68/4.85          = M ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1783_less__diff__conv,axiom,
% 8.68/4.85      ! [I: nat,J: nat,K: nat] :
% 8.68/4.85        ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.68/4.85        = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1784_le__diff__conv,axiom,
% 8.68/4.85      ! [J: nat,K: nat,I: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.68/4.85        = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1785_Nat_Ole__diff__conv2,axiom,
% 8.68/4.85      ! [K: nat,J: nat,I: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.85       => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 8.68/4.85          = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1786_Nat_Odiff__add__assoc,axiom,
% 8.68/4.85      ! [K: nat,J: nat,I: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.85       => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 8.68/4.85          = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1787_Nat_Odiff__add__assoc2,axiom,
% 8.68/4.85      ! [K: nat,J: nat,I: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.85       => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 8.68/4.85          = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1788_Nat_Ole__imp__diff__is__add,axiom,
% 8.68/4.85      ! [I: nat,J: nat,K: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.85       => ( ( ( minus_minus_nat @ J @ I )
% 8.68/4.85            = K )
% 8.68/4.85          = ( J
% 8.68/4.85            = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1789_dbl__def,axiom,
% 8.68/4.85      ( neg_numeral_dbl_real
% 8.68/4.85      = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1790_dbl__def,axiom,
% 8.68/4.85      ( neg_numeral_dbl_rat
% 8.68/4.85      = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1791_dbl__def,axiom,
% 8.68/4.85      ( neg_numeral_dbl_int
% 8.68/4.85      = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1792_not__numeral__le__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1793_not__numeral__le__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1794_not__numeral__le__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1795_not__numeral__le__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1796_zero__le__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1797_zero__le__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1798_zero__le__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1799_zero__le__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1800_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1801_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1802_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1803_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1804_zero__le__mult__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1805_zero__le__mult__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1806_zero__le__mult__iff,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1807_mult__nonneg__nonpos2,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1808_mult__nonneg__nonpos2,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1809_mult__nonneg__nonpos2,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1810_mult__nonneg__nonpos2,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1811_mult__nonpos__nonneg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1812_mult__nonpos__nonneg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1813_mult__nonpos__nonneg,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1814_mult__nonpos__nonneg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1815_mult__nonneg__nonpos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1816_mult__nonneg__nonpos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1817_mult__nonneg__nonpos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1818_mult__nonneg__nonpos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1819_mult__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1820_mult__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1821_mult__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1822_mult__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1823_split__mult__neg__le,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 8.68/4.85       => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1824_split__mult__neg__le,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 8.68/4.85       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1825_split__mult__neg__le,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 8.68/4.85          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 8.68/4.85       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1826_split__mult__neg__le,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.68/4.85          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 8.68/4.85       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1827_mult__le__0__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 8.68/4.85        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1828_mult__le__0__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.68/4.85        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1829_mult__le__0__iff,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.68/4.85        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.68/4.85          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1830_mult__right__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1831_mult__right__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1832_mult__right__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1833_mult__right__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1834_mult__right__mono__neg,axiom,
% 8.68/4.85      ! [B: real,A: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1835_mult__right__mono__neg,axiom,
% 8.68/4.85      ! [B: rat,A: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1836_mult__right__mono__neg,axiom,
% 8.68/4.85      ! [B: int,A: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1837_mult__left__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1838_mult__left__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1839_mult__left__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1840_mult__left__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1841_mult__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1842_mult__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1843_mult__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1844_mult__left__mono__neg,axiom,
% 8.68/4.85      ! [B: real,A: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1845_mult__left__mono__neg,axiom,
% 8.68/4.85      ! [B: rat,A: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1846_mult__left__mono__neg,axiom,
% 8.68/4.85      ! [B: int,A: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1847_split__mult__pos__le,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 8.68/4.85       => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1848_split__mult__pos__le,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.68/4.85       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1849_split__mult__pos__le,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.68/4.85       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1850_zero__le__square,axiom,
% 8.68/4.85      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1851_zero__le__square,axiom,
% 8.68/4.85      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1852_zero__le__square,axiom,
% 8.68/4.85      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1853_mult__mono_H,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1854_mult__mono_H,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1855_mult__mono_H,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1856_mult__mono_H,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1857_mult__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85             => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1858_mult__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1859_mult__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1860_mult__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ C @ D )
% 8.68/4.85         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1861_zero__less__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1862_zero__less__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1863_zero__less__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1864_zero__less__numeral,axiom,
% 8.68/4.85      ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1865_not__numeral__less__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1866_not__numeral__less__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1867_not__numeral__less__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1868_not__numeral__less__zero,axiom,
% 8.68/4.85      ! [N: num] :
% 8.68/4.85        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1869_add__decreasing,axiom,
% 8.68/4.85      ! [A: real,C: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ B )
% 8.68/4.85         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1870_add__decreasing,axiom,
% 8.68/4.85      ! [A: rat,C: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ B )
% 8.68/4.85         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1871_add__decreasing,axiom,
% 8.68/4.85      ! [A: nat,C: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ C @ B )
% 8.68/4.85         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1872_add__decreasing,axiom,
% 8.68/4.85      ! [A: int,C: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ C @ B )
% 8.68/4.85         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1873_add__increasing,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ C )
% 8.68/4.85         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1874_add__increasing,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ C )
% 8.68/4.85         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1875_add__increasing,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ C )
% 8.68/4.85         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1876_add__increasing,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ C )
% 8.68/4.85         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1877_add__decreasing2,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85         => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1878_add__decreasing2,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1879_add__decreasing2,axiom,
% 8.68/4.85      ! [C: nat,A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1880_add__decreasing2,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1881_add__increasing2,axiom,
% 8.68/4.85      ! [C: real,B: real,A: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ A )
% 8.68/4.85         => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1882_add__increasing2,axiom,
% 8.68/4.85      ! [C: rat,B: rat,A: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.85         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1883_add__increasing2,axiom,
% 8.68/4.85      ! [C: nat,B: nat,A: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.85         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1884_add__increasing2,axiom,
% 8.68/4.85      ! [C: int,B: int,A: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ A )
% 8.68/4.85         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1885_add__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1886_add__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1887_add__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1888_add__nonneg__nonneg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1889_add__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1890_add__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1891_add__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1892_add__nonpos__nonpos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1893_add__nonneg__eq__0__iff,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.85         => ( ( ( plus_plus_real @ X @ Y )
% 8.68/4.85              = zero_zero_real )
% 8.68/4.85            = ( ( X = zero_zero_real )
% 8.68/4.85              & ( Y = zero_zero_real ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1894_add__nonneg__eq__0__iff,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.85         => ( ( ( plus_plus_rat @ X @ Y )
% 8.68/4.85              = zero_zero_rat )
% 8.68/4.85            = ( ( X = zero_zero_rat )
% 8.68/4.85              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1895_add__nonneg__eq__0__iff,axiom,
% 8.68/4.85      ! [X: nat,Y: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.68/4.85         => ( ( ( plus_plus_nat @ X @ Y )
% 8.68/4.85              = zero_zero_nat )
% 8.68/4.85            = ( ( X = zero_zero_nat )
% 8.68/4.85              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1896_add__nonneg__eq__0__iff,axiom,
% 8.68/4.85      ! [X: int,Y: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.85         => ( ( ( plus_plus_int @ X @ Y )
% 8.68/4.85              = zero_zero_int )
% 8.68/4.85            = ( ( X = zero_zero_int )
% 8.68/4.85              & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1897_add__nonpos__eq__0__iff,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.68/4.85         => ( ( ( plus_plus_real @ X @ Y )
% 8.68/4.85              = zero_zero_real )
% 8.68/4.85            = ( ( X = zero_zero_real )
% 8.68/4.85              & ( Y = zero_zero_real ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1898_add__nonpos__eq__0__iff,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.68/4.85         => ( ( ( plus_plus_rat @ X @ Y )
% 8.68/4.85              = zero_zero_rat )
% 8.68/4.85            = ( ( X = zero_zero_rat )
% 8.68/4.85              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1899_add__nonpos__eq__0__iff,axiom,
% 8.68/4.85      ! [X: nat,Y: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 8.68/4.85         => ( ( ( plus_plus_nat @ X @ Y )
% 8.68/4.85              = zero_zero_nat )
% 8.68/4.85            = ( ( X = zero_zero_nat )
% 8.68/4.85              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1900_add__nonpos__eq__0__iff,axiom,
% 8.68/4.85      ! [X: int,Y: int] :
% 8.68/4.85        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.68/4.85         => ( ( ( plus_plus_int @ X @ Y )
% 8.68/4.85              = zero_zero_int )
% 8.68/4.85            = ( ( X = zero_zero_int )
% 8.68/4.85              & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1901_not__one__le__zero,axiom,
% 8.68/4.85      ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1902_not__one__le__zero,axiom,
% 8.68/4.85      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1903_not__one__le__zero,axiom,
% 8.68/4.85      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1904_not__one__le__zero,axiom,
% 8.68/4.85      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1905_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1906_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1907_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1908_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1909_zero__less__one__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1910_zero__less__one__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1911_zero__less__one__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1912_zero__less__one__class_Ozero__le__one,axiom,
% 8.68/4.85      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1913_mult__neg__neg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1914_mult__neg__neg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1915_mult__neg__neg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1916_not__square__less__zero,axiom,
% 8.68/4.85      ! [A: real] :
% 8.68/4.85        ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1917_not__square__less__zero,axiom,
% 8.68/4.85      ! [A: rat] :
% 8.68/4.85        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1918_not__square__less__zero,axiom,
% 8.68/4.85      ! [A: int] :
% 8.68/4.85        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1919_mult__less__0__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_real @ B @ zero_zero_real ) )
% 8.68/4.85          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1920_mult__less__0__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.68/4.85          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1921_mult__less__0__iff,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.68/4.85        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_int @ B @ zero_zero_int ) )
% 8.68/4.85          | ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1922_mult__neg__pos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1923_mult__neg__pos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1924_mult__neg__pos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1925_mult__neg__pos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1926_mult__pos__neg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1927_mult__pos__neg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1928_mult__pos__neg,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1929_mult__pos__neg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1930_mult__pos__pos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1931_mult__pos__pos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1932_mult__pos__pos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1933_mult__pos__pos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1934_mult__pos__neg2,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1935_mult__pos__neg2,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1936_mult__pos__neg2,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1937_mult__pos__neg2,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1938_zero__less__mult__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_real @ zero_zero_real @ B ) )
% 8.68/4.85          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1939_zero__less__mult__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.68/4.85          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1940_zero__less__mult__iff,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85            & ( ord_less_int @ zero_zero_int @ B ) )
% 8.68/4.85          | ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.85            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1941_zero__less__mult__pos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1942_zero__less__mult__pos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1943_zero__less__mult__pos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1944_zero__less__mult__pos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1945_zero__less__mult__pos2,axiom,
% 8.68/4.85      ! [B: real,A: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1946_zero__less__mult__pos2,axiom,
% 8.68/4.85      ! [B: rat,A: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1947_zero__less__mult__pos2,axiom,
% 8.68/4.85      ! [B: nat,A: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1948_zero__less__mult__pos2,axiom,
% 8.68/4.85      ! [B: int,A: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1949_mult__less__cancel__left__neg,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.85          = ( ord_less_real @ B @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1950_mult__less__cancel__left__neg,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.85          = ( ord_less_rat @ B @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1951_mult__less__cancel__left__neg,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.85          = ( ord_less_int @ B @ A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1952_mult__less__cancel__left__pos,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85       => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.85          = ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1953_mult__less__cancel__left__pos,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.85          = ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1954_mult__less__cancel__left__pos,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.85          = ( ord_less_int @ A @ B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1955_mult__strict__left__mono__neg,axiom,
% 8.68/4.85      ! [B: real,A: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ B @ A )
% 8.68/4.85       => ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1956_mult__strict__left__mono__neg,axiom,
% 8.68/4.85      ! [B: rat,A: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ B @ A )
% 8.68/4.85       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1957_mult__strict__left__mono__neg,axiom,
% 8.68/4.85      ! [B: int,A: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ B @ A )
% 8.68/4.85       => ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1958_mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1959_mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1960_mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1961_mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1962_mult__less__cancel__left__disj,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85            & ( ord_less_real @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1963_mult__less__cancel__left__disj,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85            & ( ord_less_rat @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1964_mult__less__cancel__left__disj,axiom,
% 8.68/4.85      ! [C: int,A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.85        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85            & ( ord_less_int @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.85            & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1965_mult__strict__right__mono__neg,axiom,
% 8.68/4.85      ! [B: real,A: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ B @ A )
% 8.68/4.85       => ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1966_mult__strict__right__mono__neg,axiom,
% 8.68/4.85      ! [B: rat,A: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ B @ A )
% 8.68/4.85       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1967_mult__strict__right__mono__neg,axiom,
% 8.68/4.85      ! [B: int,A: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ B @ A )
% 8.68/4.85       => ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1968_mult__strict__right__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1969_mult__strict__right__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1970_mult__strict__right__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1971_mult__strict__right__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1972_mult__less__cancel__right__disj,axiom,
% 8.68/4.85      ! [A: real,C: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85            & ( ord_less_real @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1973_mult__less__cancel__right__disj,axiom,
% 8.68/4.85      ! [A: rat,C: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85            & ( ord_less_rat @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1974_mult__less__cancel__right__disj,axiom,
% 8.68/4.85      ! [A: int,C: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.85        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85            & ( ord_less_int @ A @ B ) )
% 8.68/4.85          | ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.85            & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1975_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1976_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1977_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.85         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1978_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.85         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1979_pos__add__strict,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_real @ B @ C )
% 8.68/4.85         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1980_pos__add__strict,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_rat @ B @ C )
% 8.68/4.85         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1981_pos__add__strict,axiom,
% 8.68/4.85      ! [A: nat,B: nat,C: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ B @ C )
% 8.68/4.85         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1982_pos__add__strict,axiom,
% 8.68/4.85      ! [A: int,B: int,C: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ B @ C )
% 8.68/4.85         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1983_canonically__ordered__monoid__add__class_OlessE,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ B )
% 8.68/4.85       => ~ ! [C2: nat] :
% 8.68/4.85              ( ( B
% 8.68/4.85                = ( plus_plus_nat @ A @ C2 ) )
% 8.68/4.85             => ( C2 = zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1984_add__pos__pos,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1985_add__pos__pos,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1986_add__pos__pos,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.85         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1987_add__pos__pos,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.85         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1988_add__neg__neg,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ B @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1989_add__neg__neg,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1990_add__neg__neg,axiom,
% 8.68/4.85      ! [A: nat,B: nat] :
% 8.68/4.85        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.68/4.85       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.68/4.85         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1991_add__neg__neg,axiom,
% 8.68/4.85      ! [A: int,B: int] :
% 8.68/4.85        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.85         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1992_add__less__zeroD,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ X @ zero_zero_real )
% 8.68/4.85          | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1993_add__less__zeroD,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.68/4.85          | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1994_add__less__zeroD,axiom,
% 8.68/4.85      ! [X: int,Y: int] :
% 8.68/4.85        ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 8.68/4.85       => ( ( ord_less_int @ X @ zero_zero_int )
% 8.68/4.85          | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1995_less__numeral__extra_I1_J,axiom,
% 8.68/4.85      ord_less_real @ zero_zero_real @ one_one_real ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1996_less__numeral__extra_I1_J,axiom,
% 8.68/4.85      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1997_less__numeral__extra_I1_J,axiom,
% 8.68/4.85      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1998_less__numeral__extra_I1_J,axiom,
% 8.68/4.85      ord_less_int @ zero_zero_int @ one_one_int ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_1999_zero__less__one,axiom,
% 8.68/4.85      ord_less_real @ zero_zero_real @ one_one_real ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2000_zero__less__one,axiom,
% 8.68/4.85      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2001_zero__less__one,axiom,
% 8.68/4.85      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2002_zero__less__one,axiom,
% 8.68/4.85      ord_less_int @ zero_zero_int @ one_one_int ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2003_not__one__less__zero,axiom,
% 8.68/4.85      ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2004_not__one__less__zero,axiom,
% 8.68/4.85      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2005_not__one__less__zero,axiom,
% 8.68/4.85      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2006_not__one__less__zero,axiom,
% 8.68/4.85      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2007_divide__right__mono__neg,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2008_divide__right__mono__neg,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2009_divide__nonpos__nonpos,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2010_divide__nonpos__nonpos,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2011_divide__nonpos__nonneg,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.85         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2012_divide__nonpos__nonneg,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.85         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2013_divide__nonneg__nonpos,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.85       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.68/4.85         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2014_divide__nonneg__nonpos,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.85       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2015_divide__nonneg__nonneg,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.85         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2016_divide__nonneg__nonneg,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.85         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2017_zero__le__divide__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2018_zero__le__divide__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2019_divide__right__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2020_divide__right__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2021_divide__le__0__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 8.68/4.85        = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.68/4.85          | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2022_divide__le__0__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.68/4.85        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.68/4.85          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2023_divide__neg__neg,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_real @ X @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2024_divide__neg__neg,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2025_divide__neg__pos,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_real @ X @ zero_zero_real )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.85         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2026_divide__neg__pos,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.85         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2027_divide__pos__neg,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ X )
% 8.68/4.85       => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2028_divide__pos__neg,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.68/4.85       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2029_divide__pos__pos,axiom,
% 8.68/4.85      ! [X: real,Y: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ X )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.85         => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2030_divide__pos__pos,axiom,
% 8.68/4.85      ! [X: rat,Y: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.85         => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2031_divide__less__0__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_real @ B @ zero_zero_real ) )
% 8.68/4.85          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2032_divide__less__0__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.68/4.85          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2033_divide__less__cancel,axiom,
% 8.68/4.85      ! [A: real,C: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85           => ( ord_less_real @ A @ B ) )
% 8.68/4.85          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85           => ( ord_less_real @ B @ A ) )
% 8.68/4.85          & ( C != zero_zero_real ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2034_divide__less__cancel,axiom,
% 8.68/4.85      ! [A: rat,C: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85           => ( ord_less_rat @ A @ B ) )
% 8.68/4.85          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85           => ( ord_less_rat @ B @ A ) )
% 8.68/4.85          & ( C != zero_zero_rat ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2035_zero__less__divide__iff,axiom,
% 8.68/4.85      ! [A: real,B: real] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85            & ( ord_less_real @ zero_zero_real @ B ) )
% 8.68/4.85          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.85            & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2036_zero__less__divide__iff,axiom,
% 8.68/4.85      ! [A: rat,B: rat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.68/4.85        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.68/4.85          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.85            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2037_divide__strict__right__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.85         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2038_divide__strict__right__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.85         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2039_divide__strict__right__mono__neg,axiom,
% 8.68/4.85      ! [B: real,A: real,C: real] :
% 8.68/4.85        ( ( ord_less_real @ B @ A )
% 8.68/4.85       => ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.85         => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2040_divide__strict__right__mono__neg,axiom,
% 8.68/4.85      ! [B: rat,A: rat,C: rat] :
% 8.68/4.85        ( ( ord_less_rat @ B @ A )
% 8.68/4.85       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.85         => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2041_zero__le__power,axiom,
% 8.68/4.85      ! [A: real,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2042_zero__le__power,axiom,
% 8.68/4.85      ! [A: rat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2043_zero__le__power,axiom,
% 8.68/4.85      ! [A: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2044_zero__le__power,axiom,
% 8.68/4.85      ! [A: int,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2045_power__mono,axiom,
% 8.68/4.85      ! [A: real,B: real,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.85         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2046_power__mono,axiom,
% 8.68/4.85      ! [A: rat,B: rat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.85         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2047_power__mono,axiom,
% 8.68/4.85      ! [A: nat,B: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.85         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2048_power__mono,axiom,
% 8.68/4.85      ! [A: int,B: int,N: nat] :
% 8.68/4.85        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.85       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.85         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2049_zero__less__power,axiom,
% 8.68/4.85      ! [A: real,N: nat] :
% 8.68/4.85        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.85       => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2050_zero__less__power,axiom,
% 8.68/4.85      ! [A: rat,N: nat] :
% 8.68/4.85        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.85       => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2051_zero__less__power,axiom,
% 8.68/4.85      ! [A: nat,N: nat] :
% 8.68/4.85        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.85       => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2052_zero__less__power,axiom,
% 8.68/4.85      ! [A: int,N: nat] :
% 8.68/4.85        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.85       => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2053_frac__eq__eq,axiom,
% 8.68/4.85      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 8.68/4.85        ( ( Y != zero_zero_complex )
% 8.68/4.85       => ( ( Z != zero_zero_complex )
% 8.68/4.85         => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 8.68/4.85              = ( divide1717551699836669952omplex @ W @ Z ) )
% 8.68/4.85            = ( ( times_times_complex @ X @ Z )
% 8.68/4.85              = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2054_frac__eq__eq,axiom,
% 8.68/4.85      ! [Y: real,Z: real,X: real,W: real] :
% 8.68/4.85        ( ( Y != zero_zero_real )
% 8.68/4.85       => ( ( Z != zero_zero_real )
% 8.68/4.85         => ( ( ( divide_divide_real @ X @ Y )
% 8.68/4.85              = ( divide_divide_real @ W @ Z ) )
% 8.68/4.85            = ( ( times_times_real @ X @ Z )
% 8.68/4.85              = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2055_frac__eq__eq,axiom,
% 8.68/4.85      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 8.68/4.85        ( ( Y != zero_zero_rat )
% 8.68/4.85       => ( ( Z != zero_zero_rat )
% 8.68/4.85         => ( ( ( divide_divide_rat @ X @ Y )
% 8.68/4.85              = ( divide_divide_rat @ W @ Z ) )
% 8.68/4.85            = ( ( times_times_rat @ X @ Z )
% 8.68/4.85              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2056_divide__eq__eq,axiom,
% 8.68/4.85      ! [B: complex,C: complex,A: complex] :
% 8.68/4.85        ( ( ( divide1717551699836669952omplex @ B @ C )
% 8.68/4.85          = A )
% 8.68/4.85        = ( ( ( C != zero_zero_complex )
% 8.68/4.85           => ( B
% 8.68/4.85              = ( times_times_complex @ A @ C ) ) )
% 8.68/4.85          & ( ( C = zero_zero_complex )
% 8.68/4.85           => ( A = zero_zero_complex ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2057_divide__eq__eq,axiom,
% 8.68/4.85      ! [B: real,C: real,A: real] :
% 8.68/4.85        ( ( ( divide_divide_real @ B @ C )
% 8.68/4.85          = A )
% 8.68/4.85        = ( ( ( C != zero_zero_real )
% 8.68/4.85           => ( B
% 8.68/4.85              = ( times_times_real @ A @ C ) ) )
% 8.68/4.85          & ( ( C = zero_zero_real )
% 8.68/4.85           => ( A = zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2058_divide__eq__eq,axiom,
% 8.68/4.85      ! [B: rat,C: rat,A: rat] :
% 8.68/4.85        ( ( ( divide_divide_rat @ B @ C )
% 8.68/4.85          = A )
% 8.68/4.85        = ( ( ( C != zero_zero_rat )
% 8.68/4.85           => ( B
% 8.68/4.85              = ( times_times_rat @ A @ C ) ) )
% 8.68/4.85          & ( ( C = zero_zero_rat )
% 8.68/4.85           => ( A = zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2059_eq__divide__eq,axiom,
% 8.68/4.85      ! [A: complex,B: complex,C: complex] :
% 8.68/4.85        ( ( A
% 8.68/4.85          = ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.85        = ( ( ( C != zero_zero_complex )
% 8.68/4.85           => ( ( times_times_complex @ A @ C )
% 8.68/4.85              = B ) )
% 8.68/4.85          & ( ( C = zero_zero_complex )
% 8.68/4.85           => ( A = zero_zero_complex ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2060_eq__divide__eq,axiom,
% 8.68/4.85      ! [A: real,B: real,C: real] :
% 8.68/4.85        ( ( A
% 8.68/4.85          = ( divide_divide_real @ B @ C ) )
% 8.68/4.85        = ( ( ( C != zero_zero_real )
% 8.68/4.85           => ( ( times_times_real @ A @ C )
% 8.68/4.85              = B ) )
% 8.68/4.85          & ( ( C = zero_zero_real )
% 8.68/4.85           => ( A = zero_zero_real ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2061_eq__divide__eq,axiom,
% 8.68/4.85      ! [A: rat,B: rat,C: rat] :
% 8.68/4.85        ( ( A
% 8.68/4.85          = ( divide_divide_rat @ B @ C ) )
% 8.68/4.85        = ( ( ( C != zero_zero_rat )
% 8.68/4.85           => ( ( times_times_rat @ A @ C )
% 8.68/4.85              = B ) )
% 8.68/4.85          & ( ( C = zero_zero_rat )
% 8.68/4.85           => ( A = zero_zero_rat ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2062_divide__eq__imp,axiom,
% 8.68/4.85      ! [C: complex,B: complex,A: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( B
% 8.68/4.85            = ( times_times_complex @ A @ C ) )
% 8.68/4.85         => ( ( divide1717551699836669952omplex @ B @ C )
% 8.68/4.85            = A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2063_divide__eq__imp,axiom,
% 8.68/4.85      ! [C: real,B: real,A: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( B
% 8.68/4.85            = ( times_times_real @ A @ C ) )
% 8.68/4.85         => ( ( divide_divide_real @ B @ C )
% 8.68/4.85            = A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2064_divide__eq__imp,axiom,
% 8.68/4.85      ! [C: rat,B: rat,A: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( B
% 8.68/4.85            = ( times_times_rat @ A @ C ) )
% 8.68/4.85         => ( ( divide_divide_rat @ B @ C )
% 8.68/4.85            = A ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2065_eq__divide__imp,axiom,
% 8.68/4.85      ! [C: complex,A: complex,B: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( ( times_times_complex @ A @ C )
% 8.68/4.85            = B )
% 8.68/4.85         => ( A
% 8.68/4.85            = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2066_eq__divide__imp,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( ( times_times_real @ A @ C )
% 8.68/4.85            = B )
% 8.68/4.85         => ( A
% 8.68/4.85            = ( divide_divide_real @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2067_eq__divide__imp,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( ( times_times_rat @ A @ C )
% 8.68/4.85            = B )
% 8.68/4.85         => ( A
% 8.68/4.85            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2068_nonzero__divide__eq__eq,axiom,
% 8.68/4.85      ! [C: complex,B: complex,A: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( ( divide1717551699836669952omplex @ B @ C )
% 8.68/4.85            = A )
% 8.68/4.85          = ( B
% 8.68/4.85            = ( times_times_complex @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2069_nonzero__divide__eq__eq,axiom,
% 8.68/4.85      ! [C: real,B: real,A: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( ( divide_divide_real @ B @ C )
% 8.68/4.85            = A )
% 8.68/4.85          = ( B
% 8.68/4.85            = ( times_times_real @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2070_nonzero__divide__eq__eq,axiom,
% 8.68/4.85      ! [C: rat,B: rat,A: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( ( divide_divide_rat @ B @ C )
% 8.68/4.85            = A )
% 8.68/4.85          = ( B
% 8.68/4.85            = ( times_times_rat @ A @ C ) ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2071_nonzero__eq__divide__eq,axiom,
% 8.68/4.85      ! [C: complex,A: complex,B: complex] :
% 8.68/4.85        ( ( C != zero_zero_complex )
% 8.68/4.85       => ( ( A
% 8.68/4.85            = ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.85          = ( ( times_times_complex @ A @ C )
% 8.68/4.85            = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2072_nonzero__eq__divide__eq,axiom,
% 8.68/4.85      ! [C: real,A: real,B: real] :
% 8.68/4.85        ( ( C != zero_zero_real )
% 8.68/4.85       => ( ( A
% 8.68/4.85            = ( divide_divide_real @ B @ C ) )
% 8.68/4.85          = ( ( times_times_real @ A @ C )
% 8.68/4.85            = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2073_nonzero__eq__divide__eq,axiom,
% 8.68/4.85      ! [C: rat,A: rat,B: rat] :
% 8.68/4.85        ( ( C != zero_zero_rat )
% 8.68/4.85       => ( ( A
% 8.68/4.85            = ( divide_divide_rat @ B @ C ) )
% 8.68/4.85          = ( ( times_times_rat @ A @ C )
% 8.68/4.85            = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2074_right__inverse__eq,axiom,
% 8.68/4.85      ! [B: complex,A: complex] :
% 8.68/4.85        ( ( B != zero_zero_complex )
% 8.68/4.85       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.68/4.85            = one_one_complex )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2075_right__inverse__eq,axiom,
% 8.68/4.85      ! [B: real,A: real] :
% 8.68/4.85        ( ( B != zero_zero_real )
% 8.68/4.85       => ( ( ( divide_divide_real @ A @ B )
% 8.68/4.85            = one_one_real )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2076_right__inverse__eq,axiom,
% 8.68/4.85      ! [B: rat,A: rat] :
% 8.68/4.85        ( ( B != zero_zero_rat )
% 8.68/4.85       => ( ( ( divide_divide_rat @ A @ B )
% 8.68/4.85            = one_one_rat )
% 8.68/4.85          = ( A = B ) ) ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2077_not__exp__less__eq__0__int,axiom,
% 8.68/4.85      ! [N: nat] :
% 8.68/4.85        ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 8.68/4.85  
% 8.68/4.85  thf(fact_2078_power__0,axiom,
% 8.68/4.85      ! [A: rat] :
% 8.68/4.86        ( ( power_power_rat @ A @ zero_zero_nat )
% 8.68/4.86        = one_one_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2079_power__0,axiom,
% 8.68/4.86      ! [A: nat] :
% 8.68/4.86        ( ( power_power_nat @ A @ zero_zero_nat )
% 8.68/4.86        = one_one_nat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2080_power__0,axiom,
% 8.68/4.86      ! [A: real] :
% 8.68/4.86        ( ( power_power_real @ A @ zero_zero_nat )
% 8.68/4.86        = one_one_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2081_power__0,axiom,
% 8.68/4.86      ! [A: int] :
% 8.68/4.86        ( ( power_power_int @ A @ zero_zero_nat )
% 8.68/4.86        = one_one_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2082_power__0,axiom,
% 8.68/4.86      ! [A: complex] :
% 8.68/4.86        ( ( power_power_complex @ A @ zero_zero_nat )
% 8.68/4.86        = one_one_complex ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2083_divmod__digit__0_I1_J,axiom,
% 8.68/4.86      ! [B: nat,A: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.86       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.86         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2084_divmod__digit__0_I1_J,axiom,
% 8.68/4.86      ! [B: int,A: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.86       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.86         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2085_divmod__digit__0_I1_J,axiom,
% 8.68/4.86      ! [B: code_integer,A: code_integer] :
% 8.68/4.86        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.86       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.68/4.86         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2086_ex__least__nat__le,axiom,
% 8.68/4.86      ! [P: nat > $o,N: nat] :
% 8.68/4.86        ( ( P @ N )
% 8.68/4.86       => ( ~ ( P @ zero_zero_nat )
% 8.68/4.86         => ? [K3: nat] :
% 8.68/4.86              ( ( ord_less_eq_nat @ K3 @ N )
% 8.68/4.86              & ! [I2: nat] :
% 8.68/4.86                  ( ( ord_less_nat @ I2 @ K3 )
% 8.68/4.86                 => ~ ( P @ I2 ) )
% 8.68/4.86              & ( P @ K3 ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2087_less__imp__add__positive,axiom,
% 8.68/4.86      ! [I: nat,J: nat] :
% 8.68/4.86        ( ( ord_less_nat @ I @ J )
% 8.68/4.86       => ? [K3: nat] :
% 8.68/4.86            ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 8.68/4.86            & ( ( plus_plus_nat @ I @ K3 )
% 8.68/4.86              = J ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2088_mult__less__mono1,axiom,
% 8.68/4.86      ! [I: nat,J: nat,K: nat] :
% 8.68/4.86        ( ( ord_less_nat @ I @ J )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86         => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2089_mult__less__mono2,axiom,
% 8.68/4.86      ! [I: nat,J: nat,K: nat] :
% 8.68/4.86        ( ( ord_less_nat @ I @ J )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86         => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2090_nat__mult__less__cancel1,axiom,
% 8.68/4.86      ! [K: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86       => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.86          = ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2091_nat__mult__eq__cancel1,axiom,
% 8.68/4.86      ! [K: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86       => ( ( ( times_times_nat @ K @ M )
% 8.68/4.86            = ( times_times_nat @ K @ N ) )
% 8.68/4.86          = ( M = N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2092_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ( divide_divide_nat @ M @ N )
% 8.68/4.86          = zero_zero_nat )
% 8.68/4.86        = ( ( ord_less_nat @ M @ N )
% 8.68/4.86          | ( N = zero_zero_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2093_nat__power__less__imp__less,axiom,
% 8.68/4.86      ! [I: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ I )
% 8.68/4.86       => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 8.68/4.86         => ( ord_less_nat @ M @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2094_bits__stable__imp__add__self,axiom,
% 8.68/4.86      ! [A: nat] :
% 8.68/4.86        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86          = A )
% 8.68/4.86       => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86          = zero_zero_nat ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2095_bits__stable__imp__add__self,axiom,
% 8.68/4.86      ! [A: int] :
% 8.68/4.86        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.86          = A )
% 8.68/4.86       => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.68/4.86          = zero_zero_int ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2096_bits__stable__imp__add__self,axiom,
% 8.68/4.86      ! [A: code_integer] :
% 8.68/4.86        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.86          = A )
% 8.68/4.86       => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 8.68/4.86          = zero_z3403309356797280102nteger ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2097_mult__eq__self__implies__10,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( M
% 8.68/4.86          = ( times_times_nat @ M @ N ) )
% 8.68/4.86       => ( ( N = one_one_nat )
% 8.68/4.86          | ( M = zero_zero_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2098_pow_Osimps_I1_J,axiom,
% 8.68/4.86      ! [X: num] :
% 8.68/4.86        ( ( pow @ X @ one )
% 8.68/4.86        = X ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2099_mod__double__modulus,axiom,
% 8.68/4.86      ! [M: code_integer,X: code_integer] :
% 8.68/4.86        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 8.68/4.86       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 8.68/4.86         => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( modulo364778990260209775nteger @ X @ M ) )
% 8.68/4.86            | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2100_mod__double__modulus,axiom,
% 8.68/4.86      ! [M: nat,X: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.68/4.86         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( modulo_modulo_nat @ X @ M ) )
% 8.68/4.86            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2101_mod__double__modulus,axiom,
% 8.68/4.86      ! [M: int,X: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ M )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.86         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( modulo_modulo_int @ X @ M ) )
% 8.68/4.86            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2102_mult__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [M: nat,N: nat,A: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.86       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.86          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2103_mult__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [M: nat,N: nat,A: int] :
% 8.68/4.86        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.86       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.86          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2104_mult__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [M: nat,N: nat,A: code_integer] :
% 8.68/4.86        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.86       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.68/4.86          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2105_div__mult1__eq,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat] :
% 8.68/4.86        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.68/4.86        = ( 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 ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2106_div__mult1__eq,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int] :
% 8.68/4.86        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 8.68/4.86        = ( 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 ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2107_div__mult1__eq,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.86        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.68/4.86        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2108_mult__div__mod__eq,axiom,
% 8.68/4.86      ! [B: nat,A: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2109_mult__div__mod__eq,axiom,
% 8.68/4.86      ! [B: int,A: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2110_mult__div__mod__eq,axiom,
% 8.68/4.86      ! [B: code_integer,A: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2111_mod__mult__div__eq,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2112_mod__mult__div__eq,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2113_mod__mult__div__eq,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2114_mod__div__mult__eq,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2115_mod__div__mult__eq,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2116_mod__div__mult__eq,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2117_div__mult__mod__eq,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2118_div__mult__mod__eq,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2119_div__mult__mod__eq,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.68/4.86        = A ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2120_mod__div__decomp,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( A
% 8.68/4.86        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2121_mod__div__decomp,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( A
% 8.68/4.86        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2122_mod__div__decomp,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer] :
% 8.68/4.86        ( A
% 8.68/4.86        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2123_cancel__div__mod__rules_I1_J,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_plus_nat @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2124_cancel__div__mod__rules_I1_J,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_plus_int @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2125_cancel__div__mod__rules_I1_J,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2126_cancel__div__mod__rules_I2_J,axiom,
% 8.68/4.86      ! [B: nat,A: nat,C: nat] :
% 8.68/4.86        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_plus_nat @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2127_cancel__div__mod__rules_I2_J,axiom,
% 8.68/4.86      ! [B: int,A: int,C: int] :
% 8.68/4.86        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_plus_int @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2128_cancel__div__mod__rules_I2_J,axiom,
% 8.68/4.86      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.68/4.86        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 8.68/4.86        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2129_ordered__ring__class_Ole__add__iff1,axiom,
% 8.68/4.86      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2130_ordered__ring__class_Ole__add__iff1,axiom,
% 8.68/4.86      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2131_ordered__ring__class_Ole__add__iff1,axiom,
% 8.68/4.86      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2132_ordered__ring__class_Ole__add__iff2,axiom,
% 8.68/4.86      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2133_ordered__ring__class_Ole__add__iff2,axiom,
% 8.68/4.86      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2134_ordered__ring__class_Ole__add__iff2,axiom,
% 8.68/4.86      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2135_less__add__iff2,axiom,
% 8.68/4.86      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.86        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2136_less__add__iff2,axiom,
% 8.68/4.86      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2137_less__add__iff2,axiom,
% 8.68/4.86      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.86        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2138_less__add__iff1,axiom,
% 8.68/4.86      ! [A: real,E: real,C: real,B: real,D: real] :
% 8.68/4.86        ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2139_less__add__iff1,axiom,
% 8.68/4.86      ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2140_less__add__iff1,axiom,
% 8.68/4.86      ! [A: int,E: int,C: int,B: int,D: int] :
% 8.68/4.86        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.68/4.86        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2141_square__diff__one__factored,axiom,
% 8.68/4.86      ! [X: complex] :
% 8.68/4.86        ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 8.68/4.86        = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2142_square__diff__one__factored,axiom,
% 8.68/4.86      ! [X: real] :
% 8.68/4.86        ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 8.68/4.86        = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2143_square__diff__one__factored,axiom,
% 8.68/4.86      ! [X: rat] :
% 8.68/4.86        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 8.68/4.86        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2144_square__diff__one__factored,axiom,
% 8.68/4.86      ! [X: int] :
% 8.68/4.86        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 8.68/4.86        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2145_mod__mult2__eq,axiom,
% 8.68/4.86      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.86        ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 8.68/4.86        = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2146_less__diff__conv2,axiom,
% 8.68/4.86      ! [K: nat,J: nat,I: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.86       => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 8.68/4.86          = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2147_nat__eq__add__iff1,axiom,
% 8.68/4.86      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ J @ I )
% 8.68/4.86       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 8.68/4.86            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 8.68/4.86            = N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2148_nat__eq__add__iff2,axiom,
% 8.68/4.86      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.86       => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 8.68/4.86            = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( M
% 8.68/4.86            = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2149_nat__le__add__iff1,axiom,
% 8.68/4.86      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ J @ I )
% 8.68/4.86       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2150_nat__le__add__iff2,axiom,
% 8.68/4.86      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.86       => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2151_nat__diff__add__eq1,axiom,
% 8.68/4.86      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ J @ I )
% 8.68/4.86       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2152_nat__diff__add__eq2,axiom,
% 8.68/4.86      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.86       => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2153_mult__less__le__imp__less,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_real @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86           => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2154_mult__less__le__imp__less,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_rat @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2155_mult__less__le__imp__less,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.86        ( ( ord_less_nat @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_nat @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.86             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2156_mult__less__le__imp__less,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.86        ( ( ord_less_int @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_int @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86           => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2157_mult__le__less__imp__less,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_real @ C @ D )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2158_mult__le__less__imp__less,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_rat @ C @ D )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2159_mult__le__less__imp__less,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.86       => ( ( ord_less_nat @ C @ D )
% 8.68/4.86         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.86           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.86             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2160_mult__le__less__imp__less,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.86       => ( ( ord_less_int @ C @ D )
% 8.68/4.86         => ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.86           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2161_mult__right__le__imp__le,axiom,
% 8.68/4.86      ! [A: real,C: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2162_mult__right__le__imp__le,axiom,
% 8.68/4.86      ! [A: rat,C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2163_mult__right__le__imp__le,axiom,
% 8.68/4.86      ! [A: nat,C: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.86         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2164_mult__right__le__imp__le,axiom,
% 8.68/4.86      ! [A: int,C: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2165_mult__left__le__imp__le,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2166_mult__left__le__imp__le,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2167_mult__left__le__imp__le,axiom,
% 8.68/4.86      ! [C: nat,A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.68/4.86         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2168_mult__left__le__imp__le,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2169_mult__le__cancel__left__pos,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2170_mult__le__cancel__left__pos,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2171_mult__le__cancel__left__pos,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2172_mult__le__cancel__left__neg,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2173_mult__le__cancel__left__neg,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2174_mult__le__cancel__left__neg,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2175_mult__less__cancel__right,axiom,
% 8.68/4.86      ! [A: real,C: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2176_mult__less__cancel__right,axiom,
% 8.68/4.86      ! [A: rat,C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2177_mult__less__cancel__right,axiom,
% 8.68/4.86      ! [A: int,C: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2178_mult__strict__mono_H,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_real @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2179_mult__strict__mono_H,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_rat @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2180_mult__strict__mono_H,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.86        ( ( ord_less_nat @ A @ B )
% 8.68/4.86       => ( ( ord_less_nat @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.86             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2181_mult__strict__mono_H,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.86        ( ( ord_less_int @ A @ B )
% 8.68/4.86       => ( ( ord_less_int @ C @ D )
% 8.68/4.86         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2182_mult__right__less__imp__less,axiom,
% 8.68/4.86      ! [A: real,C: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2183_mult__right__less__imp__less,axiom,
% 8.68/4.86      ! [A: rat,C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2184_mult__right__less__imp__less,axiom,
% 8.68/4.86      ! [A: nat,C: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.86         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2185_mult__right__less__imp__less,axiom,
% 8.68/4.86      ! [A: int,C: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86         => ( ord_less_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2186_mult__less__cancel__left,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2187_mult__less__cancel__left,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2188_mult__less__cancel__left,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2189_mult__strict__mono,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_real @ C @ D )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.86           => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86             => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2190_mult__strict__mono,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_rat @ C @ D )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.86           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2191_mult__strict__mono,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.86        ( ( ord_less_nat @ A @ B )
% 8.68/4.86       => ( ( ord_less_nat @ C @ D )
% 8.68/4.86         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.86           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.86             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2192_mult__strict__mono,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.86        ( ( ord_less_int @ A @ B )
% 8.68/4.86       => ( ( ord_less_int @ C @ D )
% 8.68/4.86         => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.86           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2193_mult__left__less__imp__less,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2194_mult__left__less__imp__less,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2195_mult__left__less__imp__less,axiom,
% 8.68/4.86      ! [C: nat,A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 8.68/4.86         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2196_mult__left__less__imp__less,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86         => ( ord_less_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2197_mult__le__cancel__right,axiom,
% 8.68/4.86      ! [A: real,C: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2198_mult__le__cancel__right,axiom,
% 8.68/4.86      ! [A: rat,C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2199_mult__le__cancel__right,axiom,
% 8.68/4.86      ! [A: int,C: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2200_mult__le__cancel__left,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2201_mult__le__cancel__left,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2202_mult__le__cancel__left,axiom,
% 8.68/4.86      ! [C: int,A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2203_add__strict__increasing2,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_real @ B @ C )
% 8.68/4.86         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2204_add__strict__increasing2,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_rat @ B @ C )
% 8.68/4.86         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2205_add__strict__increasing2,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ B @ C )
% 8.68/4.86         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2206_add__strict__increasing2,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_int @ B @ C )
% 8.68/4.86         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2207_add__strict__increasing,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_eq_real @ B @ C )
% 8.68/4.86         => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2208_add__strict__increasing,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_eq_rat @ B @ C )
% 8.68/4.86         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2209_add__strict__increasing,axiom,
% 8.68/4.86      ! [A: nat,B: nat,C: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_eq_nat @ B @ C )
% 8.68/4.86         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2210_add__strict__increasing,axiom,
% 8.68/4.86      ! [A: int,B: int,C: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_eq_int @ B @ C )
% 8.68/4.86         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2211_add__pos__nonneg,axiom,
% 8.68/4.86      ! [A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.86         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2212_add__pos__nonneg,axiom,
% 8.68/4.86      ! [A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.86         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2213_add__pos__nonneg,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.86         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2214_add__pos__nonneg,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.86         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2215_add__nonpos__neg,axiom,
% 8.68/4.86      ! [A: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_real @ B @ zero_zero_real )
% 8.68/4.86         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2216_add__nonpos__neg,axiom,
% 8.68/4.86      ! [A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.68/4.86         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2217_add__nonpos__neg,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.68/4.86       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.68/4.86         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2218_add__nonpos__neg,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.86       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.86         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2219_add__nonneg__pos,axiom,
% 8.68/4.86      ! [A: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.68/4.86         => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2220_add__nonneg__pos,axiom,
% 8.68/4.86      ! [A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.68/4.86         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2221_add__nonneg__pos,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.86         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2222_add__nonneg__pos,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.86         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2223_add__neg__nonpos,axiom,
% 8.68/4.86      ! [A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.68/4.86         => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2224_add__neg__nonpos,axiom,
% 8.68/4.86      ! [A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.68/4.86         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2225_add__neg__nonpos,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.68/4.86       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.68/4.86         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2226_add__neg__nonpos,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.86       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.68/4.86         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2227_field__le__epsilon,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ! [E2: real] :
% 8.68/4.86            ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.68/4.86           => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 8.68/4.86       => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2228_field__le__epsilon,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ! [E2: rat] :
% 8.68/4.86            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.68/4.86           => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 8.68/4.86       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2229_divide__nonpos__pos,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2230_divide__nonpos__pos,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2231_divide__nonpos__neg,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.68/4.86         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2232_divide__nonpos__neg,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.68/4.86         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2233_divide__nonneg__pos,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2234_divide__nonneg__pos,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2235_divide__nonneg__neg,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.68/4.86         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2236_divide__nonneg__neg,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.68/4.86         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2237_divide__le__cancel,axiom,
% 8.68/4.86      ! [A: real,C: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2238_divide__le__cancel,axiom,
% 8.68/4.86      ! [A: rat,C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ A @ B ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2239_frac__less2,axiom,
% 8.68/4.86      ! [X: real,Y: real,W: real,Z: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_eq_real @ X @ Y )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ W )
% 8.68/4.86           => ( ( ord_less_real @ W @ Z )
% 8.68/4.86             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2240_frac__less2,axiom,
% 8.68/4.86      ! [X: rat,Y: rat,W: rat,Z: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_eq_rat @ X @ Y )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 8.68/4.86           => ( ( ord_less_rat @ W @ Z )
% 8.68/4.86             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2241_frac__less,axiom,
% 8.68/4.86      ! [X: real,Y: real,W: real,Z: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_real @ X @ Y )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ W )
% 8.68/4.86           => ( ( ord_less_eq_real @ W @ Z )
% 8.68/4.86             => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2242_frac__less,axiom,
% 8.68/4.86      ! [X: rat,Y: rat,W: rat,Z: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_rat @ X @ Y )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 8.68/4.86           => ( ( ord_less_eq_rat @ W @ Z )
% 8.68/4.86             => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2243_frac__le,axiom,
% 8.68/4.86      ! [Y: real,X: real,W: real,Z: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86       => ( ( ord_less_eq_real @ X @ Y )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ W )
% 8.68/4.86           => ( ( ord_less_eq_real @ W @ Z )
% 8.68/4.86             => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2244_frac__le,axiom,
% 8.68/4.86      ! [Y: rat,X: rat,W: rat,Z: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86       => ( ( ord_less_eq_rat @ X @ Y )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ W )
% 8.68/4.86           => ( ( ord_less_eq_rat @ W @ Z )
% 8.68/4.86             => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2245_sum__squares__le__zero__iff,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 8.68/4.86        = ( ( X = zero_zero_real )
% 8.68/4.86          & ( Y = zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2246_sum__squares__le__zero__iff,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 8.68/4.86        = ( ( X = zero_zero_rat )
% 8.68/4.86          & ( Y = zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2247_sum__squares__le__zero__iff,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 8.68/4.86        = ( ( X = zero_zero_int )
% 8.68/4.86          & ( Y = zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2248_sum__squares__ge__zero,axiom,
% 8.68/4.86      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2249_sum__squares__ge__zero,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2250_sum__squares__ge__zero,axiom,
% 8.68/4.86      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2251_mult__left__le,axiom,
% 8.68/4.86      ! [C: real,A: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ C @ one_one_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86         => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2252_mult__left__le,axiom,
% 8.68/4.86      ! [C: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2253_mult__left__le,axiom,
% 8.68/4.86      ! [C: nat,A: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2254_mult__left__le,axiom,
% 8.68/4.86      ! [C: int,A: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ C @ one_one_int )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2255_mult__le__one,axiom,
% 8.68/4.86      ! [A: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ A @ one_one_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.86         => ( ( ord_less_eq_real @ B @ one_one_real )
% 8.68/4.86           => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2256_mult__le__one,axiom,
% 8.68/4.86      ! [A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.86         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2257_mult__le__one,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.86         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 8.68/4.86           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2258_mult__le__one,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ A @ one_one_int )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.86         => ( ( ord_less_eq_int @ B @ one_one_int )
% 8.68/4.86           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2259_mult__right__le__one__le,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.68/4.86           => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2260_mult__right__le__one__le,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2261_mult__right__le__one__le,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.86         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.68/4.86           => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2262_mult__left__le__one__le,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.68/4.86           => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2263_mult__left__le__one__le,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2264_mult__left__le__one__le,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.86         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.68/4.86           => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2265_power__less__imp__less__base,axiom,
% 8.68/4.86      ! [A: real,N: nat,B: real] :
% 8.68/4.86        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.86         => ( ord_less_real @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2266_power__less__imp__less__base,axiom,
% 8.68/4.86      ! [A: rat,N: nat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.86         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2267_power__less__imp__less__base,axiom,
% 8.68/4.86      ! [A: nat,N: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.86         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2268_power__less__imp__less__base,axiom,
% 8.68/4.86      ! [A: int,N: nat,B: int] :
% 8.68/4.86        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.86         => ( ord_less_int @ A @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2269_sum__squares__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 8.68/4.86        = ( ( X != zero_zero_real )
% 8.68/4.86          | ( Y != zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2270_sum__squares__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 8.68/4.86        = ( ( X != zero_zero_rat )
% 8.68/4.86          | ( Y != zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2271_sum__squares__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 8.68/4.86        = ( ( X != zero_zero_int )
% 8.68/4.86          | ( Y != zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2272_not__sum__squares__lt__zero,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2273_not__sum__squares__lt__zero,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2274_not__sum__squares__lt__zero,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2275_zero__less__two,axiom,
% 8.68/4.86      ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2276_zero__less__two,axiom,
% 8.68/4.86      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2277_zero__less__two,axiom,
% 8.68/4.86      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2278_zero__less__two,axiom,
% 8.68/4.86      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2279_divide__less__eq,axiom,
% 8.68/4.86      ! [B: real,C: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2280_divide__less__eq,axiom,
% 8.68/4.86      ! [B: rat,C: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2281_less__divide__eq,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2282_less__divide__eq,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2283_neg__divide__less__eq,axiom,
% 8.68/4.86      ! [C: real,B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2284_neg__divide__less__eq,axiom,
% 8.68/4.86      ! [C: rat,B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2285_neg__less__divide__eq,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2286_neg__less__divide__eq,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2287_pos__divide__less__eq,axiom,
% 8.68/4.86      ! [C: real,B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86       => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2288_pos__divide__less__eq,axiom,
% 8.68/4.86      ! [C: rat,B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2289_pos__less__divide__eq,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86       => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86          = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2290_pos__less__divide__eq,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2291_mult__imp__div__pos__less,axiom,
% 8.68/4.86      ! [Y: real,X: real,Z: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86       => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 8.68/4.86         => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2292_mult__imp__div__pos__less,axiom,
% 8.68/4.86      ! [Y: rat,X: rat,Z: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 8.68/4.86         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2293_mult__imp__less__div__pos,axiom,
% 8.68/4.86      ! [Y: real,Z: real,X: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86       => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 8.68/4.86         => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2294_mult__imp__less__div__pos,axiom,
% 8.68/4.86      ! [Y: rat,Z: rat,X: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 8.68/4.86         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2295_divide__strict__left__mono,axiom,
% 8.68/4.86      ! [B: real,A: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ B @ A )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.86           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2296_divide__strict__left__mono,axiom,
% 8.68/4.86      ! [B: rat,A: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ B @ A )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.86           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2297_divide__strict__left__mono__neg,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.86           => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2298_divide__strict__left__mono__neg,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.86           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2299_divide__less__eq__1,axiom,
% 8.68/4.86      ! [B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86            & ( ord_less_real @ B @ A ) )
% 8.68/4.86          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.86            & ( ord_less_real @ A @ B ) )
% 8.68/4.86          | ( A = zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2300_divide__less__eq__1,axiom,
% 8.68/4.86      ! [B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86            & ( ord_less_rat @ B @ A ) )
% 8.68/4.86          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.86            & ( ord_less_rat @ A @ B ) )
% 8.68/4.86          | ( A = zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2301_less__divide__eq__1,axiom,
% 8.68/4.86      ! [B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86            & ( ord_less_real @ A @ B ) )
% 8.68/4.86          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.86            & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2302_less__divide__eq__1,axiom,
% 8.68/4.86      ! [B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86            & ( ord_less_rat @ A @ B ) )
% 8.68/4.86          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.86            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2303_power__le__one,axiom,
% 8.68/4.86      ! [A: real,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.68/4.86         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2304_power__le__one,axiom,
% 8.68/4.86      ! [A: rat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.68/4.86         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2305_power__le__one,axiom,
% 8.68/4.86      ! [A: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.68/4.86         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2306_power__le__one,axiom,
% 8.68/4.86      ! [A: int,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.68/4.86         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2307_divide__eq__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: complex,C: complex,W: num] :
% 8.68/4.86        ( ( ( divide1717551699836669952omplex @ B @ C )
% 8.68/4.86          = ( numera6690914467698888265omplex @ W ) )
% 8.68/4.86        = ( ( ( C != zero_zero_complex )
% 8.68/4.86           => ( B
% 8.68/4.86              = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 8.68/4.86          & ( ( C = zero_zero_complex )
% 8.68/4.86           => ( ( numera6690914467698888265omplex @ W )
% 8.68/4.86              = zero_zero_complex ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2308_divide__eq__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: real,C: real,W: num] :
% 8.68/4.86        ( ( ( divide_divide_real @ B @ C )
% 8.68/4.86          = ( numeral_numeral_real @ W ) )
% 8.68/4.86        = ( ( ( C != zero_zero_real )
% 8.68/4.86           => ( B
% 8.68/4.86              = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 8.68/4.86          & ( ( C = zero_zero_real )
% 8.68/4.86           => ( ( numeral_numeral_real @ W )
% 8.68/4.86              = zero_zero_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2309_divide__eq__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: rat,C: rat,W: num] :
% 8.68/4.86        ( ( ( divide_divide_rat @ B @ C )
% 8.68/4.86          = ( numeral_numeral_rat @ W ) )
% 8.68/4.86        = ( ( ( C != zero_zero_rat )
% 8.68/4.86           => ( B
% 8.68/4.86              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 8.68/4.86          & ( ( C = zero_zero_rat )
% 8.68/4.86           => ( ( numeral_numeral_rat @ W )
% 8.68/4.86              = zero_zero_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2310_eq__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: complex,C: complex] :
% 8.68/4.86        ( ( ( numera6690914467698888265omplex @ W )
% 8.68/4.86          = ( divide1717551699836669952omplex @ B @ C ) )
% 8.68/4.86        = ( ( ( C != zero_zero_complex )
% 8.68/4.86           => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 8.68/4.86              = B ) )
% 8.68/4.86          & ( ( C = zero_zero_complex )
% 8.68/4.86           => ( ( numera6690914467698888265omplex @ W )
% 8.68/4.86              = zero_zero_complex ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2311_eq__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: real,C: real] :
% 8.68/4.86        ( ( ( numeral_numeral_real @ W )
% 8.68/4.86          = ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( C != zero_zero_real )
% 8.68/4.86           => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 8.68/4.86              = B ) )
% 8.68/4.86          & ( ( C = zero_zero_real )
% 8.68/4.86           => ( ( numeral_numeral_real @ W )
% 8.68/4.86              = zero_zero_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2312_eq__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: rat,C: rat] :
% 8.68/4.86        ( ( ( numeral_numeral_rat @ W )
% 8.68/4.86          = ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( C != zero_zero_rat )
% 8.68/4.86           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 8.68/4.86              = B ) )
% 8.68/4.86          & ( ( C = zero_zero_rat )
% 8.68/4.86           => ( ( numeral_numeral_rat @ W )
% 8.68/4.86              = zero_zero_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2313_divide__add__eq__iff,axiom,
% 8.68/4.86      ! [Z: complex,X: complex,Y: complex] :
% 8.68/4.86        ( ( Z != zero_zero_complex )
% 8.68/4.86       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 8.68/4.86          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2314_divide__add__eq__iff,axiom,
% 8.68/4.86      ! [Z: real,X: real,Y: real] :
% 8.68/4.86        ( ( Z != zero_zero_real )
% 8.68/4.86       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 8.68/4.86          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2315_divide__add__eq__iff,axiom,
% 8.68/4.86      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.86        ( ( Z != zero_zero_rat )
% 8.68/4.86       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 8.68/4.86          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2316_add__divide__eq__iff,axiom,
% 8.68/4.86      ! [Z: complex,X: complex,Y: complex] :
% 8.68/4.86        ( ( Z != zero_zero_complex )
% 8.68/4.86       => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 8.68/4.86          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2317_add__divide__eq__iff,axiom,
% 8.68/4.86      ! [Z: real,X: real,Y: real] :
% 8.68/4.86        ( ( Z != zero_zero_real )
% 8.68/4.86       => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 8.68/4.86          = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2318_add__divide__eq__iff,axiom,
% 8.68/4.86      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.86        ( ( Z != zero_zero_rat )
% 8.68/4.86       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 8.68/4.86          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2319_add__num__frac,axiom,
% 8.68/4.86      ! [Y: complex,Z: complex,X: complex] :
% 8.68/4.86        ( ( Y != zero_zero_complex )
% 8.68/4.86       => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.68/4.86          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2320_add__num__frac,axiom,
% 8.68/4.86      ! [Y: real,Z: real,X: real] :
% 8.68/4.86        ( ( Y != zero_zero_real )
% 8.68/4.86       => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 8.68/4.86          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2321_add__num__frac,axiom,
% 8.68/4.86      ! [Y: rat,Z: rat,X: rat] :
% 8.68/4.86        ( ( Y != zero_zero_rat )
% 8.68/4.86       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 8.68/4.86          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2322_add__frac__num,axiom,
% 8.68/4.86      ! [Y: complex,X: complex,Z: complex] :
% 8.68/4.86        ( ( Y != zero_zero_complex )
% 8.68/4.86       => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 8.68/4.86          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2323_add__frac__num,axiom,
% 8.68/4.86      ! [Y: real,X: real,Z: real] :
% 8.68/4.86        ( ( Y != zero_zero_real )
% 8.68/4.86       => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 8.68/4.86          = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2324_add__frac__num,axiom,
% 8.68/4.86      ! [Y: rat,X: rat,Z: rat] :
% 8.68/4.86        ( ( Y != zero_zero_rat )
% 8.68/4.86       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 8.68/4.86          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2325_add__frac__eq,axiom,
% 8.68/4.86      ! [Y: complex,Z: complex,X: complex,W: complex] :
% 8.68/4.86        ( ( Y != zero_zero_complex )
% 8.68/4.86       => ( ( Z != zero_zero_complex )
% 8.68/4.86         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 8.68/4.86            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2326_add__frac__eq,axiom,
% 8.68/4.86      ! [Y: real,Z: real,X: real,W: real] :
% 8.68/4.86        ( ( Y != zero_zero_real )
% 8.68/4.86       => ( ( Z != zero_zero_real )
% 8.68/4.86         => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 8.68/4.86            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2327_add__frac__eq,axiom,
% 8.68/4.86      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 8.68/4.86        ( ( Y != zero_zero_rat )
% 8.68/4.86       => ( ( Z != zero_zero_rat )
% 8.68/4.86         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 8.68/4.86            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2328_add__divide__eq__if__simps_I1_J,axiom,
% 8.68/4.86      ! [Z: complex,A: complex,B: complex] :
% 8.68/4.86        ( ( ( Z = zero_zero_complex )
% 8.68/4.86         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 8.68/4.86            = A ) )
% 8.68/4.86        & ( ( Z != zero_zero_complex )
% 8.68/4.86         => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 8.68/4.86            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2329_add__divide__eq__if__simps_I1_J,axiom,
% 8.68/4.86      ! [Z: real,A: real,B: real] :
% 8.68/4.86        ( ( ( Z = zero_zero_real )
% 8.68/4.86         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 8.68/4.86            = A ) )
% 8.68/4.86        & ( ( Z != zero_zero_real )
% 8.68/4.86         => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 8.68/4.86            = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2330_add__divide__eq__if__simps_I1_J,axiom,
% 8.68/4.86      ! [Z: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ( Z = zero_zero_rat )
% 8.68/4.86         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 8.68/4.86            = A ) )
% 8.68/4.86        & ( ( Z != zero_zero_rat )
% 8.68/4.86         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 8.68/4.86            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2331_add__divide__eq__if__simps_I2_J,axiom,
% 8.68/4.86      ! [Z: complex,A: complex,B: complex] :
% 8.68/4.86        ( ( ( Z = zero_zero_complex )
% 8.68/4.86         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 8.68/4.86            = B ) )
% 8.68/4.86        & ( ( Z != zero_zero_complex )
% 8.68/4.86         => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 8.68/4.86            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2332_add__divide__eq__if__simps_I2_J,axiom,
% 8.68/4.86      ! [Z: real,A: real,B: real] :
% 8.68/4.86        ( ( ( Z = zero_zero_real )
% 8.68/4.86         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 8.68/4.86            = B ) )
% 8.68/4.86        & ( ( Z != zero_zero_real )
% 8.68/4.86         => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 8.68/4.86            = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2333_add__divide__eq__if__simps_I2_J,axiom,
% 8.68/4.86      ! [Z: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ( Z = zero_zero_rat )
% 8.68/4.86         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 8.68/4.86            = B ) )
% 8.68/4.86        & ( ( Z != zero_zero_rat )
% 8.68/4.86         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 8.68/4.86            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2334_div__add__self2,axiom,
% 8.68/4.86      ! [B: nat,A: nat] :
% 8.68/4.86        ( ( B != zero_zero_nat )
% 8.68/4.86       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.68/4.86          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2335_div__add__self2,axiom,
% 8.68/4.86      ! [B: int,A: int] :
% 8.68/4.86        ( ( B != zero_zero_int )
% 8.68/4.86       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.68/4.86          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2336_div__add__self1,axiom,
% 8.68/4.86      ! [B: nat,A: nat] :
% 8.68/4.86        ( ( B != zero_zero_nat )
% 8.68/4.86       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.68/4.86          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2337_div__add__self1,axiom,
% 8.68/4.86      ! [B: int,A: int] :
% 8.68/4.86        ( ( B != zero_zero_int )
% 8.68/4.86       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.68/4.86          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2338_bounded__Max__nat,axiom,
% 8.68/4.86      ! [P: nat > $o,X: nat,M5: nat] :
% 8.68/4.86        ( ( P @ X )
% 8.68/4.86       => ( ! [X6: nat] :
% 8.68/4.86              ( ( P @ X6 )
% 8.68/4.86             => ( ord_less_eq_nat @ X6 @ M5 ) )
% 8.68/4.86         => ~ ! [M4: nat] :
% 8.68/4.86                ( ( P @ M4 )
% 8.68/4.86               => ~ ! [X4: nat] :
% 8.68/4.86                      ( ( P @ X4 )
% 8.68/4.86                     => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2339_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: complex,Xs: list_complex] :
% 8.68/4.86        ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2340_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: real,Xs: list_real] :
% 8.68/4.86        ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2341_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: set_nat,Xs: list_set_nat] :
% 8.68/4.86        ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2342_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 8.68/4.86        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2343_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: $o,Xs: list_o] :
% 8.68/4.86        ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2344_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: nat,Xs: list_nat] :
% 8.68/4.86        ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2345_length__pos__if__in__set,axiom,
% 8.68/4.86      ! [X: int,Xs: list_int] :
% 8.68/4.86        ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 8.68/4.86       => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2346_nat__mult__le__cancel1,axiom,
% 8.68/4.86      ! [K: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86       => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.86          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2347_div__greater__zero__iff,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 8.68/4.86        = ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.86          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2348_div__le__mono2,axiom,
% 8.68/4.86      ! [M: nat,N: nat,K: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.86       => ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.86         => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2349_nat__mult__div__cancel1,axiom,
% 8.68/4.86      ! [K: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.68/4.86       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.68/4.86          = ( divide_divide_nat @ M @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2350_div__less__iff__less__mult,axiom,
% 8.68/4.86      ! [Q2: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.68/4.86       => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 8.68/4.86          = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2351_div__less__dividend,axiom,
% 8.68/4.86      ! [N: nat,M: nat] :
% 8.68/4.86        ( ( ord_less_nat @ one_one_nat @ N )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.86         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2352_div__eq__dividend__iff,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.86       => ( ( ( divide_divide_nat @ M @ N )
% 8.68/4.86            = M )
% 8.68/4.86          = ( N = one_one_nat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2353_divmod__digit__1_I1_J,axiom,
% 8.68/4.86      ! [A: code_integer,B: code_integer] :
% 8.68/4.86        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.68/4.86       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.68/4.86         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 8.68/4.86              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2354_divmod__digit__1_I1_J,axiom,
% 8.68/4.86      ! [A: nat,B: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.68/4.86         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86           => ( ( 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 )
% 8.68/4.86              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2355_divmod__digit__1_I1_J,axiom,
% 8.68/4.86      ! [A: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.86         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.68/4.86           => ( ( 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 )
% 8.68/4.86              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2356_power2__commute,axiom,
% 8.68/4.86      ! [X: complex,Y: complex] :
% 8.68/4.86        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2357_power2__commute,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2358_power2__commute,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2359_power2__commute,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2360_nat__less__add__iff2,axiom,
% 8.68/4.86      ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.86       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2361_nat__less__add__iff1,axiom,
% 8.68/4.86      ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ J @ I )
% 8.68/4.86       => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 8.68/4.86          = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2362_field__le__mult__one__interval,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ! [Z5: real] :
% 8.68/4.86            ( ( ord_less_real @ zero_zero_real @ Z5 )
% 8.68/4.86           => ( ( ord_less_real @ Z5 @ one_one_real )
% 8.68/4.86             => ( ord_less_eq_real @ ( times_times_real @ Z5 @ X ) @ Y ) ) )
% 8.68/4.86       => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2363_field__le__mult__one__interval,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ! [Z5: rat] :
% 8.68/4.86            ( ( ord_less_rat @ zero_zero_rat @ Z5 )
% 8.68/4.86           => ( ( ord_less_rat @ Z5 @ one_one_rat )
% 8.68/4.86             => ( ord_less_eq_rat @ ( times_times_rat @ Z5 @ X ) @ Y ) ) )
% 8.68/4.86       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2364_mult__less__cancel__right2,axiom,
% 8.68/4.86      ! [A: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ A @ one_one_real ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2365_mult__less__cancel__right2,axiom,
% 8.68/4.86      ! [A: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ A @ one_one_rat ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2366_mult__less__cancel__right2,axiom,
% 8.68/4.86      ! [A: int,C: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ A @ one_one_int ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2367_mult__less__cancel__right1,axiom,
% 8.68/4.86      ! [C: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ one_one_real @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2368_mult__less__cancel__right1,axiom,
% 8.68/4.86      ! [C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ one_one_rat @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2369_mult__less__cancel__right1,axiom,
% 8.68/4.86      ! [C: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ one_one_int @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2370_mult__less__cancel__left2,axiom,
% 8.68/4.86      ! [C: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ A @ one_one_real ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2371_mult__less__cancel__left2,axiom,
% 8.68/4.86      ! [C: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ A @ one_one_rat ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2372_mult__less__cancel__left2,axiom,
% 8.68/4.86      ! [C: int,A: int] :
% 8.68/4.86        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ A @ one_one_int ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2373_mult__less__cancel__left1,axiom,
% 8.68/4.86      ! [C: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ one_one_real @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2374_mult__less__cancel__left1,axiom,
% 8.68/4.86      ! [C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ one_one_rat @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2375_mult__less__cancel__left1,axiom,
% 8.68/4.86      ! [C: int,B: int] :
% 8.68/4.86        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_int @ one_one_int @ B ) )
% 8.68/4.86          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2376_mult__le__cancel__right2,axiom,
% 8.68/4.86      ! [A: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ A @ one_one_real ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2377_mult__le__cancel__right2,axiom,
% 8.68/4.86      ! [A: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2378_mult__le__cancel__right2,axiom,
% 8.68/4.86      ! [A: int,C: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2379_mult__le__cancel__right1,axiom,
% 8.68/4.86      ! [C: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ one_one_real @ B ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2380_mult__le__cancel__right1,axiom,
% 8.68/4.86      ! [C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2381_mult__le__cancel__right1,axiom,
% 8.68/4.86      ! [C: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2382_mult__le__cancel__left2,axiom,
% 8.68/4.86      ! [C: real,A: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ A @ one_one_real ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2383_mult__le__cancel__left2,axiom,
% 8.68/4.86      ! [C: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2384_mult__le__cancel__left2,axiom,
% 8.68/4.86      ! [C: int,A: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2385_mult__le__cancel__left1,axiom,
% 8.68/4.86      ! [C: real,B: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ one_one_real @ B ) )
% 8.68/4.86          & ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86           => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2386_mult__le__cancel__left1,axiom,
% 8.68/4.86      ! [C: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.68/4.86          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2387_mult__le__cancel__left1,axiom,
% 8.68/4.86      ! [C: int,B: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 8.68/4.86        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 8.68/4.86           => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.68/4.86          & ( ( ord_less_int @ C @ zero_zero_int )
% 8.68/4.86           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2388_divide__left__mono__neg,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.86           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2389_divide__left__mono__neg,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.86       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.86           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2390_mult__imp__le__div__pos,axiom,
% 8.68/4.86      ! [Y: real,Z: real,X: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 8.68/4.86         => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2391_mult__imp__le__div__pos,axiom,
% 8.68/4.86      ! [Y: rat,Z: rat,X: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 8.68/4.86         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2392_mult__imp__div__pos__le,axiom,
% 8.68/4.86      ! [Y: real,X: real,Z: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.68/4.86       => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 8.68/4.86         => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2393_mult__imp__div__pos__le,axiom,
% 8.68/4.86      ! [Y: rat,X: rat,Z: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.68/4.86       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 8.68/4.86         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2394_pos__le__divide__eq,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2395_pos__le__divide__eq,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2396_pos__divide__le__eq,axiom,
% 8.68/4.86      ! [C: real,B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2397_pos__divide__le__eq,axiom,
% 8.68/4.86      ! [C: rat,B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2398_neg__le__divide__eq,axiom,
% 8.68/4.86      ! [C: real,A: real,B: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86          = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2399_neg__le__divide__eq,axiom,
% 8.68/4.86      ! [C: rat,A: rat,B: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2400_neg__divide__le__eq,axiom,
% 8.68/4.86      ! [C: real,B: real,A: real] :
% 8.68/4.86        ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86       => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2401_neg__divide__le__eq,axiom,
% 8.68/4.86      ! [C: rat,B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2402_divide__left__mono,axiom,
% 8.68/4.86      ! [B: real,A: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ B @ A )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.68/4.86         => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.68/4.86           => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2403_divide__left__mono,axiom,
% 8.68/4.86      ! [B: rat,A: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 8.68/4.86         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.68/4.86           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2404_le__divide__eq,axiom,
% 8.68/4.86      ! [A: real,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2405_le__divide__eq,axiom,
% 8.68/4.86      ! [A: rat,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2406_divide__le__eq,axiom,
% 8.68/4.86      ! [B: real,C: real,A: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2407_divide__le__eq,axiom,
% 8.68/4.86      ! [B: rat,C: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2408_le__divide__eq__1,axiom,
% 8.68/4.86      ! [B: real,A: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86            & ( ord_less_eq_real @ A @ B ) )
% 8.68/4.86          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.86            & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2409_le__divide__eq__1,axiom,
% 8.68/4.86      ! [B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86            & ( ord_less_eq_rat @ A @ B ) )
% 8.68/4.86          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.86            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2410_divide__le__eq__1,axiom,
% 8.68/4.86      ! [B: real,A: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86            & ( ord_less_eq_real @ B @ A ) )
% 8.68/4.86          | ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.86            & ( ord_less_eq_real @ A @ B ) )
% 8.68/4.86          | ( A = zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2411_divide__le__eq__1,axiom,
% 8.68/4.86      ! [B: rat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86            & ( ord_less_eq_rat @ B @ A ) )
% 8.68/4.86          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.86            & ( ord_less_eq_rat @ A @ B ) )
% 8.68/4.86          | ( A = zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2412_convex__bound__le,axiom,
% 8.68/4.86      ! [X: real,A: real,Y: real,U: real,V: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ X @ A )
% 8.68/4.86       => ( ( ord_less_eq_real @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 8.68/4.86           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 8.68/4.86             => ( ( ( plus_plus_real @ U @ V )
% 8.68/4.86                  = one_one_real )
% 8.68/4.86               => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2413_convex__bound__le,axiom,
% 8.68/4.86      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ X @ A )
% 8.68/4.86       => ( ( ord_less_eq_rat @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.68/4.86           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 8.68/4.86             => ( ( ( plus_plus_rat @ U @ V )
% 8.68/4.86                  = one_one_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2414_convex__bound__le,axiom,
% 8.68/4.86      ! [X: int,A: int,Y: int,U: int,V: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ X @ A )
% 8.68/4.86       => ( ( ord_less_eq_int @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.68/4.86           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 8.68/4.86             => ( ( ( plus_plus_int @ U @ V )
% 8.68/4.86                  = one_one_int )
% 8.68/4.86               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2415_divide__less__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: real,C: real,W: num] :
% 8.68/4.86        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2416_divide__less__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: rat,C: rat,W: num] :
% 8.68/4.86        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2417_less__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2418_less__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2419_power__Suc__less,axiom,
% 8.68/4.86      ! [A: real,N: nat] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ( ord_less_real @ A @ one_one_real )
% 8.68/4.86         => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2420_power__Suc__less,axiom,
% 8.68/4.86      ! [A: rat,N: nat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ( ord_less_rat @ A @ one_one_rat )
% 8.68/4.86         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2421_power__Suc__less,axiom,
% 8.68/4.86      ! [A: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ A @ one_one_nat )
% 8.68/4.86         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2422_power__Suc__less,axiom,
% 8.68/4.86      ! [A: int,N: nat] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.86       => ( ( ord_less_int @ A @ one_one_int )
% 8.68/4.86         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2423_power__strict__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: real] :
% 8.68/4.86        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86         => ( ( ord_less_real @ A @ one_one_real )
% 8.68/4.86           => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2424_power__strict__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: rat] :
% 8.68/4.86        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86         => ( ( ord_less_rat @ A @ one_one_rat )
% 8.68/4.86           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2425_power__strict__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: nat] :
% 8.68/4.86        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.86         => ( ( ord_less_nat @ A @ one_one_nat )
% 8.68/4.86           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2426_power__strict__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: int] :
% 8.68/4.86        ( ( ord_less_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.86         => ( ( ord_less_int @ A @ one_one_int )
% 8.68/4.86           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2427_power__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: real] :
% 8.68/4.86        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.86         => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.68/4.86           => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2428_power__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: rat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.86         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.68/4.86           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2429_power__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.86         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.68/4.86           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2430_power__decreasing,axiom,
% 8.68/4.86      ! [N: nat,N4: nat,A: int] :
% 8.68/4.86        ( ( ord_less_eq_nat @ N @ N4 )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.86         => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.68/4.86           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2431_zero__power2,axiom,
% 8.68/4.86      ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86      = zero_zero_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2432_zero__power2,axiom,
% 8.68/4.86      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86      = zero_zero_nat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2433_zero__power2,axiom,
% 8.68/4.86      ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86      = zero_zero_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2434_zero__power2,axiom,
% 8.68/4.86      ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86      = zero_zero_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2435_zero__power2,axiom,
% 8.68/4.86      ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86      = zero_zero_complex ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2436_self__le__power,axiom,
% 8.68/4.86      ! [A: real,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_real @ one_one_real @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2437_self__le__power,axiom,
% 8.68/4.86      ! [A: rat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2438_self__le__power,axiom,
% 8.68/4.86      ! [A: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2439_self__le__power,axiom,
% 8.68/4.86      ! [A: int,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_int @ one_one_int @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2440_one__less__power,axiom,
% 8.68/4.86      ! [A: real,N: nat] :
% 8.68/4.86        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2441_one__less__power,axiom,
% 8.68/4.86      ! [A: rat,N: nat] :
% 8.68/4.86        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2442_one__less__power,axiom,
% 8.68/4.86      ! [A: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2443_one__less__power,axiom,
% 8.68/4.86      ! [A: int,N: nat] :
% 8.68/4.86        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.86       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2444_pos2,axiom,
% 8.68/4.86      ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2445_less__eq__div__iff__mult__less__eq,axiom,
% 8.68/4.86      ! [Q2: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.68/4.86       => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 8.68/4.86          = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2446_dividend__less__times__div,axiom,
% 8.68/4.86      ! [N: nat,M: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2447_dividend__less__div__times,axiom,
% 8.68/4.86      ! [N: nat,M: nat] :
% 8.68/4.86        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.86       => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2448_split__div,axiom,
% 8.68/4.86      ! [P: nat > $o,M: nat,N: nat] :
% 8.68/4.86        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 8.68/4.86        = ( ( ( N = zero_zero_nat )
% 8.68/4.86           => ( P @ zero_zero_nat ) )
% 8.68/4.86          & ( ( N != zero_zero_nat )
% 8.68/4.86           => ! [I5: nat,J3: nat] :
% 8.68/4.86                ( ( ord_less_nat @ J3 @ N )
% 8.68/4.86               => ( ( M
% 8.68/4.86                    = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 8.68/4.86                 => ( P @ I5 ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2449_diff__le__diff__pow,axiom,
% 8.68/4.86      ! [K: nat,M: nat,N: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.68/4.86       => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2450_le__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: real,C: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2451_le__divide__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [W: num,B: rat,C: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2452_divide__le__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: real,C: real,W: num] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 8.68/4.86        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.68/4.86           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.68/4.86               => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2453_divide__le__eq__numeral_I1_J,axiom,
% 8.68/4.86      ! [B: rat,C: rat,W: num] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 8.68/4.86        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 8.68/4.86          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.68/4.86           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 8.68/4.86              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.68/4.86               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2454_convex__bound__lt,axiom,
% 8.68/4.86      ! [X: real,A: real,Y: real,U: real,V: real] :
% 8.68/4.86        ( ( ord_less_real @ X @ A )
% 8.68/4.86       => ( ( ord_less_real @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 8.68/4.86           => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 8.68/4.86             => ( ( ( plus_plus_real @ U @ V )
% 8.68/4.86                  = one_one_real )
% 8.68/4.86               => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2455_convex__bound__lt,axiom,
% 8.68/4.86      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 8.68/4.86        ( ( ord_less_rat @ X @ A )
% 8.68/4.86       => ( ( ord_less_rat @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.68/4.86           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 8.68/4.86             => ( ( ( plus_plus_rat @ U @ V )
% 8.68/4.86                  = one_one_rat )
% 8.68/4.86               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2456_convex__bound__lt,axiom,
% 8.68/4.86      ! [X: int,A: int,Y: int,U: int,V: int] :
% 8.68/4.86        ( ( ord_less_int @ X @ A )
% 8.68/4.86       => ( ( ord_less_int @ Y @ A )
% 8.68/4.86         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.68/4.86           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 8.68/4.86             => ( ( ( plus_plus_int @ U @ V )
% 8.68/4.86                  = one_one_int )
% 8.68/4.86               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2457_half__gt__zero,axiom,
% 8.68/4.86      ! [A: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.86       => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2458_half__gt__zero,axiom,
% 8.68/4.86      ! [A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.86       => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2459_half__gt__zero__iff,axiom,
% 8.68/4.86      ! [A: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.68/4.86        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2460_half__gt__zero__iff,axiom,
% 8.68/4.86      ! [A: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 8.68/4.86        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2461_zero__le__power2,axiom,
% 8.68/4.86      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2462_zero__le__power2,axiom,
% 8.68/4.86      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2463_zero__le__power2,axiom,
% 8.68/4.86      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2464_power2__eq__imp__eq,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.68/4.86         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86           => ( X = Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2465_power2__eq__imp__eq,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.68/4.86         => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86           => ( X = Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2466_power2__eq__imp__eq,axiom,
% 8.68/4.86      ! [X: nat,Y: nat] :
% 8.68/4.86        ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86          = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.68/4.86         => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.68/4.86           => ( X = Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2467_power2__eq__imp__eq,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.86         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.86           => ( X = Y ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2468_power2__le__imp__le,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2469_power2__le__imp__le,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2470_power2__le__imp__le,axiom,
% 8.68/4.86      ! [X: nat,Y: nat] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.68/4.86         => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2471_power2__le__imp__le,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.86         => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2472_power2__less__0,axiom,
% 8.68/4.86      ! [A: real] :
% 8.68/4.86        ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2473_power2__less__0,axiom,
% 8.68/4.86      ! [A: rat] :
% 8.68/4.86        ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2474_power2__less__0,axiom,
% 8.68/4.86      ! [A: int] :
% 8.68/4.86        ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2475_exp__add__not__zero__imp__left,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.86         != zero_zero_nat )
% 8.68/4.86       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 8.68/4.86         != zero_zero_nat ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2476_exp__add__not__zero__imp__left,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.86         != zero_zero_int )
% 8.68/4.86       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 8.68/4.86         != zero_zero_int ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2477_exp__add__not__zero__imp__right,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.86         != zero_zero_nat )
% 8.68/4.86       => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.68/4.86         != zero_zero_nat ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2478_exp__add__not__zero__imp__right,axiom,
% 8.68/4.86      ! [M: nat,N: nat] :
% 8.68/4.86        ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 8.68/4.86         != zero_zero_int )
% 8.68/4.86       => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.68/4.86         != zero_zero_int ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2479_div__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [A: nat,N: nat,M: nat] :
% 8.68/4.86        ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86        = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2480_div__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [A: int,N: nat,M: nat] :
% 8.68/4.86        ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86        = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2481_div__exp__mod__exp__eq,axiom,
% 8.68/4.86      ! [A: code_integer,N: nat,M: nat] :
% 8.68/4.86        ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86        = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2482_power2__less__imp__less,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.68/4.86         => ( ord_less_real @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2483_power2__less__imp__less,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.68/4.86         => ( ord_less_rat @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2484_power2__less__imp__less,axiom,
% 8.68/4.86      ! [X: nat,Y: nat] :
% 8.68/4.86        ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.68/4.86         => ( ord_less_nat @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2485_power2__less__imp__less,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.86       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.68/4.86         => ( ord_less_int @ X @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2486_sum__power2__ge__zero,axiom,
% 8.68/4.86      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2487_sum__power2__ge__zero,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2488_sum__power2__ge__zero,axiom,
% 8.68/4.86      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2489_sum__power2__le__zero__iff,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 8.68/4.86        = ( ( X = zero_zero_real )
% 8.68/4.86          & ( Y = zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2490_sum__power2__le__zero__iff,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 8.68/4.86        = ( ( X = zero_zero_rat )
% 8.68/4.86          & ( Y = zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2491_sum__power2__le__zero__iff,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 8.68/4.86        = ( ( X = zero_zero_int )
% 8.68/4.86          & ( Y = zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2492_not__sum__power2__lt__zero,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2493_not__sum__power2__lt__zero,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2494_not__sum__power2__lt__zero,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2495_sum__power2__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.86        = ( ( X != zero_zero_real )
% 8.68/4.86          | ( Y != zero_zero_real ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2496_sum__power2__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.86        = ( ( X != zero_zero_rat )
% 8.68/4.86          | ( Y != zero_zero_rat ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2497_sum__power2__gt__zero__iff,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.86        = ( ( X != zero_zero_int )
% 8.68/4.86          | ( Y != zero_zero_int ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2498_zero__le__even__power_H,axiom,
% 8.68/4.86      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2499_zero__le__even__power_H,axiom,
% 8.68/4.86      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2500_zero__le__even__power_H,axiom,
% 8.68/4.86      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2501_power2__diff,axiom,
% 8.68/4.86      ! [X: complex,Y: complex] :
% 8.68/4.86        ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2502_power2__diff,axiom,
% 8.68/4.86      ! [X: real,Y: real] :
% 8.68/4.86        ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2503_power2__diff,axiom,
% 8.68/4.86      ! [X: rat,Y: rat] :
% 8.68/4.86        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2504_power2__diff,axiom,
% 8.68/4.86      ! [X: int,Y: int] :
% 8.68/4.86        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.86        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( 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 ) ) @ X ) @ Y ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2505_invar__vebt_Ointros_I4_J,axiom,
% 8.68/4.86      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 8.68/4.86        ( ! [X6: vEBT_VEBT] :
% 8.68/4.86            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.86           => ( vEBT_invar_vebt @ X6 @ N ) )
% 8.68/4.86       => ( ( vEBT_invar_vebt @ Summary @ M )
% 8.68/4.86         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.68/4.86              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86           => ( ( M = N )
% 8.68/4.86             => ( ( Deg
% 8.68/4.86                  = ( plus_plus_nat @ N @ M ) )
% 8.68/4.86               => ( ! [I4: nat] :
% 8.68/4.86                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 8.68/4.86                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 8.68/4.86                 => ( ( ( Mi = Ma )
% 8.68/4.86                     => ! [X6: vEBT_VEBT] :
% 8.68/4.86                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.86                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 8.68/4.86                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.68/4.86                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.68/4.86                       => ( ( ( Mi != Ma )
% 8.68/4.86                           => ! [I4: nat] :
% 8.68/4.86                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.86                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 8.68/4.86                                      = I4 )
% 8.68/4.86                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 8.68/4.86                                  & ! [X6: nat] :
% 8.68/4.86                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 8.68/4.86                                          = I4 )
% 8.68/4.86                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 8.68/4.86                                     => ( ( ord_less_nat @ Mi @ X6 )
% 8.68/4.86                                        & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 8.68/4.86                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2506_pred__list__to__short,axiom,
% 8.68/4.86      ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.86       => ( ( ord_less_eq_nat @ X @ Ma )
% 8.68/4.86         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.86           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.86              = none_nat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2507_succ__list__to__short,axiom,
% 8.68/4.86      ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 8.68/4.86        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.86       => ( ( ord_less_eq_nat @ Mi @ X )
% 8.68/4.86         => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.86           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.86              = none_nat ) ) ) ) ).
% 8.68/4.86  
% 8.68/4.86  thf(fact_2508_not__mod__2__eq__0__eq__1,axiom,
% 8.68/4.86      ! [A: nat] :
% 8.68/4.86        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87         != zero_zero_nat )
% 8.68/4.87        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87          = one_one_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2509_not__mod__2__eq__0__eq__1,axiom,
% 8.68/4.87      ! [A: int] :
% 8.68/4.87        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.87         != zero_zero_int )
% 8.68/4.87        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.87          = one_one_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2510_not__mod__2__eq__0__eq__1,axiom,
% 8.68/4.87      ! [A: code_integer] :
% 8.68/4.87        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.87         != zero_z3403309356797280102nteger )
% 8.68/4.87        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.87          = one_one_Code_integer ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2511_not__mod__2__eq__1__eq__0,axiom,
% 8.68/4.87      ! [A: nat] :
% 8.68/4.87        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87         != one_one_nat )
% 8.68/4.87        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87          = zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2512_not__mod__2__eq__1__eq__0,axiom,
% 8.68/4.87      ! [A: int] :
% 8.68/4.87        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.87         != one_one_int )
% 8.68/4.87        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.68/4.87          = zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2513_not__mod__2__eq__1__eq__0,axiom,
% 8.68/4.87      ! [A: code_integer] :
% 8.68/4.87        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.87         != one_one_Code_integer )
% 8.68/4.87        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.68/4.87          = zero_z3403309356797280102nteger ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2514_pred__max,axiom,
% 8.68/4.87      ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_nat @ Ma @ X )
% 8.68/4.87         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = ( some_nat @ Ma ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2515_succ__min,axiom,
% 8.68/4.87      ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_nat @ X @ Mi )
% 8.68/4.87         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = ( some_nat @ Mi ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2516_del__x__not__mi__newnode__not__nil,axiom,
% 8.68/4.87      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( ord_less_nat @ Mi @ X )
% 8.68/4.87          & ( ord_less_eq_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                  = L2 )
% 8.68/4.87               => ( ( Newnode
% 8.68/4.87                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                   => ( ( Newlist
% 8.68/4.87                        = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                     => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                       => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2517_greater__shift,axiom,
% 8.68/4.87      ( ord_less_nat
% 8.68/4.87      = ( ^ [Y3: nat,X3: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2518_less__shift,axiom,
% 8.68/4.87      ( ord_less_nat
% 8.68/4.87      = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_less @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2519_helpyd,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.68/4.87            = ( some_nat @ Y ) )
% 8.68/4.87         => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2520_VEBT_Oinject_I1_J,axiom,
% 8.68/4.87      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 8.68/4.87        ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 8.68/4.87          = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 8.68/4.87        = ( ( X11 = Y11 )
% 8.68/4.87          & ( X12 = Y12 )
% 8.68/4.87          & ( X13 = Y13 )
% 8.68/4.87          & ( X14 = Y14 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2521_idiff__0__right,axiom,
% 8.68/4.87      ! [N: extended_enat] :
% 8.68/4.87        ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 8.68/4.87        = N ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2522_idiff__0,axiom,
% 8.68/4.87      ! [N: extended_enat] :
% 8.68/4.87        ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 8.68/4.87        = zero_z5237406670263579293d_enat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2523_succ__corr,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.68/4.87            = ( some_nat @ Sx ) )
% 8.68/4.87          = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2524_pred__corr,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.68/4.87            = ( some_nat @ Px ) )
% 8.68/4.87          = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2525_succ__correct,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.68/4.87            = ( some_nat @ Sx ) )
% 8.68/4.87          = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2526_pred__correct,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.68/4.87            = ( some_nat @ Sx ) )
% 8.68/4.87          = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2527_geqmaxNone,axiom,
% 8.68/4.87      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.87       => ( ( ord_less_eq_nat @ Ma @ X )
% 8.68/4.87         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = none_nat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2528_helpypredd,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.68/4.87            = ( some_nat @ Y ) )
% 8.68/4.87         => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2529_summaxma,axiom,
% 8.68/4.87      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 8.68/4.87            = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2530_mod__neg__neg__trivial,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ L2 @ K )
% 8.68/4.87         => ( ( modulo_modulo_int @ K @ L2 )
% 8.68/4.87            = K ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2531_mod__pos__pos__trivial,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.68/4.87       => ( ( ord_less_int @ K @ L2 )
% 8.68/4.87         => ( ( modulo_modulo_int @ K @ L2 )
% 8.68/4.87            = K ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2532_zmod__numeral__Bit0,axiom,
% 8.68/4.87      ! [V: num,W: num] :
% 8.68/4.87        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 8.68/4.87        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2533_div__neg__neg__trivial,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ L2 @ K )
% 8.68/4.87         => ( ( divide_divide_int @ K @ L2 )
% 8.68/4.87            = zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2534_div__pos__pos__trivial,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.68/4.87       => ( ( ord_less_int @ K @ L2 )
% 8.68/4.87         => ( ( divide_divide_int @ K @ L2 )
% 8.68/4.87            = zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2535_local_Opower__def,axiom,
% 8.68/4.87      ( vEBT_VEBT_power
% 8.68/4.87      = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2536_split__zdiv,axiom,
% 8.68/4.87      ! [P: int > $o,N: int,K: int] :
% 8.68/4.87        ( ( P @ ( divide_divide_int @ N @ K ) )
% 8.68/4.87        = ( ( ( K = zero_zero_int )
% 8.68/4.87           => ( P @ zero_zero_int ) )
% 8.68/4.87          & ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87           => ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.68/4.87                  & ( ord_less_int @ J3 @ K )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ I5 ) ) )
% 8.68/4.87          & ( ( ord_less_int @ K @ zero_zero_int )
% 8.68/4.87           => ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_int @ K @ J3 )
% 8.68/4.87                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ I5 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2537_split__zmod,axiom,
% 8.68/4.87      ! [P: int > $o,N: int,K: int] :
% 8.68/4.87        ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 8.68/4.87        = ( ( ( K = zero_zero_int )
% 8.68/4.87           => ( P @ N ) )
% 8.68/4.87          & ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87           => ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.68/4.87                  & ( ord_less_int @ J3 @ K )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ J3 ) ) )
% 8.68/4.87          & ( ( ord_less_int @ K @ zero_zero_int )
% 8.68/4.87           => ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_int @ K @ J3 )
% 8.68/4.87                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ J3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2538_zdiv__mono1,axiom,
% 8.68/4.87      ! [A: int,A4: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ A @ A4 )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2539_zdiv__mono2,axiom,
% 8.68/4.87      ! [A: int,B4: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 8.68/4.87         => ( ( ord_less_eq_int @ B4 @ B )
% 8.68/4.87           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2540_div__pos__geq,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.68/4.87       => ( ( ord_less_eq_int @ L2 @ K )
% 8.68/4.87         => ( ( divide_divide_int @ K @ L2 )
% 8.68/4.87            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2541_mod__pos__geq,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.68/4.87       => ( ( ord_less_eq_int @ L2 @ K )
% 8.68/4.87         => ( ( modulo_modulo_int @ K @ L2 )
% 8.68/4.87            = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2542_q__pos__lemma,axiom,
% 8.68/4.87      ! [B4: int,Q4: int,R3: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 8.68/4.87       => ( ( ord_less_int @ R3 @ B4 )
% 8.68/4.87         => ( ( ord_less_int @ zero_zero_int @ B4 )
% 8.68/4.87           => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2543_neg__mod__conj,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 8.68/4.87          & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2544_pos__mod__conj,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 8.68/4.87          & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2545_zdiv__eq__0__iff,axiom,
% 8.68/4.87      ! [I: int,K: int] :
% 8.68/4.87        ( ( ( divide_divide_int @ I @ K )
% 8.68/4.87          = zero_zero_int )
% 8.68/4.87        = ( ( K = zero_zero_int )
% 8.68/4.87          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 8.68/4.87            & ( ord_less_int @ I @ K ) )
% 8.68/4.87          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 8.68/4.87            & ( ord_less_int @ K @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2546_int__div__neg__eq,axiom,
% 8.68/4.87      ! [A: int,B: int,Q2: int,R: int] :
% 8.68/4.87        ( ( A
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.68/4.87         => ( ( ord_less_int @ B @ R )
% 8.68/4.87           => ( ( divide_divide_int @ A @ B )
% 8.68/4.87              = Q2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2547_int__div__pos__eq,axiom,
% 8.68/4.87      ! [A: int,B: int,Q2: int,R: int] :
% 8.68/4.87        ( ( A
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.68/4.87         => ( ( ord_less_int @ R @ B )
% 8.68/4.87           => ( ( divide_divide_int @ A @ B )
% 8.68/4.87              = Q2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2548_int__mod__neg__eq,axiom,
% 8.68/4.87      ! [A: int,B: int,Q2: int,R: int] :
% 8.68/4.87        ( ( A
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.68/4.87         => ( ( ord_less_int @ B @ R )
% 8.68/4.87           => ( ( modulo_modulo_int @ A @ B )
% 8.68/4.87              = R ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2549_int__mod__pos__eq,axiom,
% 8.68/4.87      ! [A: int,B: int,Q2: int,R: int] :
% 8.68/4.87        ( ( A
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.68/4.87         => ( ( ord_less_int @ R @ B )
% 8.68/4.87           => ( ( modulo_modulo_int @ A @ B )
% 8.68/4.87              = R ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2550_zdiv__mono1__neg,axiom,
% 8.68/4.87      ! [A: int,A4: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ A @ A4 )
% 8.68/4.87       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.87         => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2551_zdiv__mono2__neg,axiom,
% 8.68/4.87      ! [A: int,B4: int,B: int] :
% 8.68/4.87        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ B4 )
% 8.68/4.87         => ( ( ord_less_eq_int @ B4 @ B )
% 8.68/4.87           => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2552_div__int__pos__iff,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 8.68/4.87        = ( ( K = zero_zero_int )
% 8.68/4.87          | ( L2 = zero_zero_int )
% 8.68/4.87          | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.68/4.87            & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 8.68/4.87          | ( ( ord_less_int @ K @ zero_zero_int )
% 8.68/4.87            & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2553_split__neg__lemma,axiom,
% 8.68/4.87      ! [K: int,P: int > int > $o,N: int] :
% 8.68/4.87        ( ( ord_less_int @ K @ zero_zero_int )
% 8.68/4.87       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 8.68/4.87          = ( ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_int @ K @ J3 )
% 8.68/4.87                  & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2554_split__pos__lemma,axiom,
% 8.68/4.87      ! [K: int,P: int > int > $o,N: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87       => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 8.68/4.87          = ( ! [I5: int,J3: int] :
% 8.68/4.87                ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 8.68/4.87                  & ( ord_less_int @ J3 @ K )
% 8.68/4.87                  & ( N
% 8.68/4.87                    = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 8.68/4.87               => ( P @ I5 @ J3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2555_div__positive__int,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ L2 @ K )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.68/4.87         => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2556_zdiv__mono2__lemma,axiom,
% 8.68/4.87      ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 8.68/4.87        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 8.68/4.87         => ( ( ord_less_int @ R3 @ B4 )
% 8.68/4.87           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.68/4.87             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 8.68/4.87               => ( ( ord_less_eq_int @ B4 @ B )
% 8.68/4.87                 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2557_zmod__trivial__iff,axiom,
% 8.68/4.87      ! [I: int,K: int] :
% 8.68/4.87        ( ( ( modulo_modulo_int @ I @ K )
% 8.68/4.87          = I )
% 8.68/4.87        = ( ( K = zero_zero_int )
% 8.68/4.87          | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 8.68/4.87            & ( ord_less_int @ I @ K ) )
% 8.68/4.87          | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 8.68/4.87            & ( ord_less_int @ K @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2558_div__neg__pos__less0,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87         => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2559_int__div__less__self,axiom,
% 8.68/4.87      ! [X: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ X )
% 8.68/4.87       => ( ( ord_less_int @ one_one_int @ K )
% 8.68/4.87         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2560_div__nonneg__neg__le0,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.87       => ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.87         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2561_div__nonpos__pos__le0,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87         => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2562_neg__imp__zdiv__neg__iff,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.68/4.87          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2563_pos__imp__zdiv__neg__iff,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87       => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.68/4.87          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2564_pos__imp__zdiv__pos__iff,axiom,
% 8.68/4.87      ! [K: int,I: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 8.68/4.87          = ( ord_less_eq_int @ K @ I ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2565_zdiv__mono2__neg__lemma,axiom,
% 8.68/4.87      ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 8.68/4.87        ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 8.68/4.87       => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) @ zero_zero_int )
% 8.68/4.87         => ( ( ord_less_int @ R @ B )
% 8.68/4.87           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.68/4.87             => ( ( ord_less_int @ zero_zero_int @ B4 )
% 8.68/4.87               => ( ( ord_less_eq_int @ B4 @ B )
% 8.68/4.87                 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2566_unique__quotient__lemma,axiom,
% 8.68/4.87      ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.68/4.87         => ( ( ord_less_int @ R3 @ B )
% 8.68/4.87           => ( ( ord_less_int @ R @ B )
% 8.68/4.87             => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2567_neg__imp__zdiv__nonneg__iff,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ B @ zero_zero_int )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.68/4.87          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2568_pos__imp__zdiv__nonneg__iff,axiom,
% 8.68/4.87      ! [B: int,A: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ B )
% 8.68/4.87       => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.68/4.87          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2569_neg__mod__sign,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ L2 @ zero_zero_int )
% 8.68/4.87       => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2570_Euclidean__Division_Opos__mod__sign,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.68/4.87       => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2571_nonneg1__imp__zdiv__pos__iff,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.68/4.87          = ( ( ord_less_eq_int @ B @ A )
% 8.68/4.87            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2572_neg__mod__bound,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ L2 @ zero_zero_int )
% 8.68/4.87       => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2573_Euclidean__Division_Opos__mod__bound,axiom,
% 8.68/4.87      ! [L2: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.68/4.87       => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2574_unique__quotient__lemma__neg,axiom,
% 8.68/4.87      ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 8.68/4.87       => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 8.68/4.87         => ( ( ord_less_int @ B @ R )
% 8.68/4.87           => ( ( ord_less_int @ B @ R3 )
% 8.68/4.87             => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2575_mod__pos__neg__trivial,axiom,
% 8.68/4.87      ! [K: int,L2: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 8.68/4.87         => ( ( modulo_modulo_int @ K @ L2 )
% 8.68/4.87            = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2576_zmod__zmult2__eq,axiom,
% 8.68/4.87      ! [C: int,A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.87       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 8.68/4.87          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2577_zdiv__zmult2__eq,axiom,
% 8.68/4.87      ! [C: int,A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 8.68/4.87       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.68/4.87          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2578_zmod__le__nonneg__dividend,axiom,
% 8.68/4.87      ! [M: int,K: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 8.68/4.87       => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2579_zero__one__enat__neq_I1_J,axiom,
% 8.68/4.87      zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2580_zmod__eq__0D,axiom,
% 8.68/4.87      ! [M: int,D: int] :
% 8.68/4.87        ( ( ( modulo_modulo_int @ M @ D )
% 8.68/4.87          = zero_zero_int )
% 8.68/4.87       => ? [Q3: int] :
% 8.68/4.87            ( M
% 8.68/4.87            = ( times_times_int @ D @ Q3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2581_zmod__eq__0__iff,axiom,
% 8.68/4.87      ! [M: int,D: int] :
% 8.68/4.87        ( ( ( modulo_modulo_int @ M @ D )
% 8.68/4.87          = zero_zero_int )
% 8.68/4.87        = ( ? [Q5: int] :
% 8.68/4.87              ( M
% 8.68/4.87              = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2582_imult__is__0,axiom,
% 8.68/4.87      ! [M: extended_enat,N: extended_enat] :
% 8.68/4.87        ( ( ( times_7803423173614009249d_enat @ M @ N )
% 8.68/4.87          = zero_z5237406670263579293d_enat )
% 8.68/4.87        = ( ( M = zero_z5237406670263579293d_enat )
% 8.68/4.87          | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2583_iadd__is__0,axiom,
% 8.68/4.87      ! [M: extended_enat,N: extended_enat] :
% 8.68/4.87        ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 8.68/4.87          = zero_z5237406670263579293d_enat )
% 8.68/4.87        = ( ( M = zero_z5237406670263579293d_enat )
% 8.68/4.87          & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2584_neg__zmod__mult__2,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.68/4.87       => ( ( 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 ) )
% 8.68/4.87          = ( 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 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2585_add__diff__assoc__enat,axiom,
% 8.68/4.87      ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 8.68/4.87        ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 8.68/4.87       => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 8.68/4.87          = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2586_pos__zmod__mult__2,axiom,
% 8.68/4.87      ! [A: int,B: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.87       => ( ( 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 ) )
% 8.68/4.87          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2587_nat__induct2,axiom,
% 8.68/4.87      ! [P: nat > $o,N: nat] :
% 8.68/4.87        ( ( P @ zero_zero_nat )
% 8.68/4.87       => ( ( P @ one_one_nat )
% 8.68/4.87         => ( ! [N3: nat] :
% 8.68/4.87                ( ( P @ N3 )
% 8.68/4.87               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.87           => ( P @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2588_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 8.68/4.87      ! [X: nat,N: nat,M: nat] :
% 8.68/4.87        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 8.68/4.87       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.87           => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2589_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 8.68/4.87      ! [X: nat,N: nat,M: nat] :
% 8.68/4.87        ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 8.68/4.87       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.87           => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2590_del__x__mi__lets__in__not__minNull,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( ord_less_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( Xn
% 8.68/4.87                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.68/4.87               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                    = L2 )
% 8.68/4.87                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                   => ( ( Newnode
% 8.68/4.87                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                     => ( ( Newlist
% 8.68/4.87                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                       => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2591_real__average__minus__first,axiom,
% 8.68/4.87      ! [A: real,B: real] :
% 8.68/4.87        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 8.68/4.87        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2592_real__average__minus__second,axiom,
% 8.68/4.87      ! [B: real,A: real] :
% 8.68/4.87        ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 8.68/4.87        = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2593_insert__simp__norm,axiom,
% 8.68/4.87      ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87       => ( ( ord_less_nat @ Mi @ X )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( X != Ma )
% 8.68/4.87             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2594_insert__simp__excp,axiom,
% 8.68/4.87      ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87       => ( ( ord_less_nat @ X @ Mi )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( X != Ma )
% 8.68/4.87             => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2595_zle__add1__eq__le,axiom,
% 8.68/4.87      ! [W: int,Z: int] :
% 8.68/4.87        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 8.68/4.87        = ( ord_less_eq_int @ W @ Z ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2596_divmod__step__eq,axiom,
% 8.68/4.87      ! [L2: num,R: nat,Q2: nat] :
% 8.68/4.87        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 8.68/4.87         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 8.68/4.87            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 8.68/4.87         => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 8.68/4.87            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2597_divmod__step__eq,axiom,
% 8.68/4.87      ! [L2: num,R: int,Q2: int] :
% 8.68/4.87        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 8.68/4.87         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.68/4.87            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 8.68/4.87         => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.68/4.87            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2598_divmod__step__eq,axiom,
% 8.68/4.87      ! [L2: num,R: code_integer,Q2: code_integer] :
% 8.68/4.87        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 8.68/4.87         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 8.68/4.87            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 8.68/4.87        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 8.68/4.87         => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 8.68/4.87            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2599_mintlistlength,axiom,
% 8.68/4.87      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_nat @ Mi @ Ma )
% 8.68/4.87            & ? [M4: nat] :
% 8.68/4.87                ( ( ( some_nat @ M4 )
% 8.68/4.87                  = ( vEBT_vebt_mint @ Summary ) )
% 8.68/4.87                & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2600_option_Ocollapse,axiom,
% 8.68/4.87      ! [Option: option_nat] :
% 8.68/4.87        ( ( Option != none_nat )
% 8.68/4.87       => ( ( some_nat @ ( the_nat @ Option ) )
% 8.68/4.87          = Option ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2601_option_Ocollapse,axiom,
% 8.68/4.87      ! [Option: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( Option != none_P5556105721700978146at_nat )
% 8.68/4.87       => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 8.68/4.87          = Option ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2602_option_Ocollapse,axiom,
% 8.68/4.87      ! [Option: option_num] :
% 8.68/4.87        ( ( Option != none_num )
% 8.68/4.87       => ( ( some_num @ ( the_num @ Option ) )
% 8.68/4.87          = Option ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2603_minNullmin,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT] :
% 8.68/4.87        ( ( vEBT_VEBT_minNull @ T )
% 8.68/4.87       => ( ( vEBT_vebt_mint @ T )
% 8.68/4.87          = none_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2604_minminNull,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT] :
% 8.68/4.87        ( ( ( vEBT_vebt_mint @ T )
% 8.68/4.87          = none_nat )
% 8.68/4.87       => ( vEBT_VEBT_minNull @ T ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2605_mint__member,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_mint @ T )
% 8.68/4.87            = ( some_nat @ Maxi ) )
% 8.68/4.87         => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2606_option_Oinject,axiom,
% 8.68/4.87      ! [X22: nat,Y22: nat] :
% 8.68/4.87        ( ( ( some_nat @ X22 )
% 8.68/4.87          = ( some_nat @ Y22 ) )
% 8.68/4.87        = ( X22 = Y22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2607_option_Oinject,axiom,
% 8.68/4.87      ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 8.68/4.87        ( ( ( some_P7363390416028606310at_nat @ X22 )
% 8.68/4.87          = ( some_P7363390416028606310at_nat @ Y22 ) )
% 8.68/4.87        = ( X22 = Y22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2608_option_Oinject,axiom,
% 8.68/4.87      ! [X22: num,Y22: num] :
% 8.68/4.87        ( ( ( some_num @ X22 )
% 8.68/4.87          = ( some_num @ Y22 ) )
% 8.68/4.87        = ( X22 = Y22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2609_mint__corr__help,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_mint @ T )
% 8.68/4.87            = ( some_nat @ Mini ) )
% 8.68/4.87         => ( ( vEBT_vebt_member @ T @ X )
% 8.68/4.87           => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2610_mint__corr,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( vEBT_vebt_mint @ T )
% 8.68/4.87            = ( some_nat @ X ) )
% 8.68/4.87         => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2611_mint__sound,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 8.68/4.87         => ( ( vEBT_vebt_mint @ T )
% 8.68/4.87            = ( some_nat @ X ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2612_double__eq__0__iff,axiom,
% 8.68/4.87      ! [A: real] :
% 8.68/4.87        ( ( ( plus_plus_real @ A @ A )
% 8.68/4.87          = zero_zero_real )
% 8.68/4.87        = ( A = zero_zero_real ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2613_double__eq__0__iff,axiom,
% 8.68/4.87      ! [A: rat] :
% 8.68/4.87        ( ( ( plus_plus_rat @ A @ A )
% 8.68/4.87          = zero_zero_rat )
% 8.68/4.87        = ( A = zero_zero_rat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2614_double__eq__0__iff,axiom,
% 8.68/4.87      ! [A: int] :
% 8.68/4.87        ( ( ( plus_plus_int @ A @ A )
% 8.68/4.87          = zero_zero_int )
% 8.68/4.87        = ( A = zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2615_del__single__cont,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( X = Ma ) )
% 8.68/4.87       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2616_misiz,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat,M: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ( ( some_nat @ M )
% 8.68/4.87            = ( vEBT_vebt_mint @ T ) )
% 8.68/4.87         => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2617_not__None__eq,axiom,
% 8.68/4.87      ! [X: option_nat] :
% 8.68/4.87        ( ( X != none_nat )
% 8.68/4.87        = ( ? [Y3: nat] :
% 8.68/4.87              ( X
% 8.68/4.87              = ( some_nat @ Y3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2618_not__None__eq,axiom,
% 8.68/4.87      ! [X: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( X != none_P5556105721700978146at_nat )
% 8.68/4.87        = ( ? [Y3: product_prod_nat_nat] :
% 8.68/4.87              ( X
% 8.68/4.87              = ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2619_not__None__eq,axiom,
% 8.68/4.87      ! [X: option_num] :
% 8.68/4.87        ( ( X != none_num )
% 8.68/4.87        = ( ? [Y3: num] :
% 8.68/4.87              ( X
% 8.68/4.87              = ( some_num @ Y3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2620_not__Some__eq,axiom,
% 8.68/4.87      ! [X: option_nat] :
% 8.68/4.87        ( ( ! [Y3: nat] :
% 8.68/4.87              ( X
% 8.68/4.87             != ( some_nat @ Y3 ) ) )
% 8.68/4.87        = ( X = none_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2621_not__Some__eq,axiom,
% 8.68/4.87      ! [X: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( ! [Y3: product_prod_nat_nat] :
% 8.68/4.87              ( X
% 8.68/4.87             != ( some_P7363390416028606310at_nat @ Y3 ) ) )
% 8.68/4.87        = ( X = none_P5556105721700978146at_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2622_not__Some__eq,axiom,
% 8.68/4.87      ! [X: option_num] :
% 8.68/4.87        ( ( ! [Y3: num] :
% 8.68/4.87              ( X
% 8.68/4.87             != ( some_num @ Y3 ) ) )
% 8.68/4.87        = ( X = none_num ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2623_max__nat_Oeq__neutr__iff,axiom,
% 8.68/4.87      ! [A: nat,B: nat] :
% 8.68/4.87        ( ( ( ord_max_nat @ A @ B )
% 8.68/4.87          = zero_zero_nat )
% 8.68/4.87        = ( ( A = zero_zero_nat )
% 8.68/4.87          & ( B = zero_zero_nat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2624_max__nat_Oleft__neutral,axiom,
% 8.68/4.87      ! [A: nat] :
% 8.68/4.87        ( ( ord_max_nat @ zero_zero_nat @ A )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2625_max__nat_Oneutr__eq__iff,axiom,
% 8.68/4.87      ! [A: nat,B: nat] :
% 8.68/4.87        ( ( zero_zero_nat
% 8.68/4.87          = ( ord_max_nat @ A @ B ) )
% 8.68/4.87        = ( ( A = zero_zero_nat )
% 8.68/4.87          & ( B = zero_zero_nat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2626_max__nat_Oright__neutral,axiom,
% 8.68/4.87      ! [A: nat] :
% 8.68/4.87        ( ( ord_max_nat @ A @ zero_zero_nat )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2627_max__0L,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_max_nat @ zero_zero_nat @ N )
% 8.68/4.87        = N ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2628_max__0R,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_max_nat @ N @ zero_zero_nat )
% 8.68/4.87        = N ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2629_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 8.68/4.87         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 8.68/4.87            = ( numera1916890842035813515d_enat @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 8.68/4.87         => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 8.68/4.87            = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2630_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 8.68/4.87         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 8.68/4.87            = ( numera6620942414471956472nteger @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 8.68/4.87         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 8.68/4.87            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2631_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.87         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.87            = ( numeral_numeral_real @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.87         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 8.68/4.87            = ( numeral_numeral_real @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2632_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.87         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.87            = ( numeral_numeral_rat @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.87         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 8.68/4.87            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2633_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 8.68/4.87         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 8.68/4.87            = ( numeral_numeral_nat @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 8.68/4.87         => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 8.68/4.87            = ( numeral_numeral_nat @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2634_max__number__of_I1_J,axiom,
% 8.68/4.87      ! [U: num,V: num] :
% 8.68/4.87        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.87         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.87            = ( numeral_numeral_int @ V ) ) )
% 8.68/4.87        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.87         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 8.68/4.87            = ( numeral_numeral_int @ U ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2635_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 8.68/4.87        = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2636_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 8.68/4.87        = ( numera6620942414471956472nteger @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2637_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 8.68/4.87        = ( numeral_numeral_real @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2638_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 8.68/4.87        = ( numeral_numeral_rat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2639_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 8.68/4.87        = ( numeral_numeral_nat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2640_max__0__1_I3_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 8.68/4.87        = ( numeral_numeral_int @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2641_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 8.68/4.87        = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2642_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 8.68/4.87        = ( numera6620942414471956472nteger @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2643_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 8.68/4.87        = ( numeral_numeral_real @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2644_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 8.68/4.87        = ( numeral_numeral_rat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2645_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 8.68/4.87        = ( numeral_numeral_nat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2646_max__0__1_I4_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 8.68/4.87        = ( numeral_numeral_int @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2647_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 8.68/4.87      = one_one_real ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2648_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 8.68/4.87      = one_one_rat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2649_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 8.68/4.87      = one_one_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2650_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 8.68/4.87      = one_on7984719198319812577d_enat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2651_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 8.68/4.87      = one_one_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2652_max__0__1_I1_J,axiom,
% 8.68/4.87      ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 8.68/4.87      = one_one_Code_integer ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2653_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 8.68/4.87      = one_one_real ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2654_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 8.68/4.87      = one_one_rat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2655_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 8.68/4.87      = one_one_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2656_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 8.68/4.87      = one_on7984719198319812577d_enat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2657_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 8.68/4.87      = one_one_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2658_max__0__1_I2_J,axiom,
% 8.68/4.87      ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 8.68/4.87      = one_one_Code_integer ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2659_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 8.68/4.87        = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2660_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 8.68/4.87        = ( numera6620942414471956472nteger @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2661_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 8.68/4.87        = ( numeral_numeral_real @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2662_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 8.68/4.87        = ( numeral_numeral_rat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2663_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 8.68/4.87        = ( numeral_numeral_nat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2664_max__0__1_I5_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 8.68/4.87        = ( numeral_numeral_int @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2665_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 8.68/4.87        = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2666_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 8.68/4.87        = ( numera6620942414471956472nteger @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2667_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 8.68/4.87        = ( numeral_numeral_real @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2668_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 8.68/4.87        = ( numeral_numeral_rat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2669_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 8.68/4.87        = ( numeral_numeral_nat @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2670_max__0__1_I6_J,axiom,
% 8.68/4.87      ! [X: num] :
% 8.68/4.87        ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 8.68/4.87        = ( numeral_numeral_int @ X ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2671_zle__diff1__eq,axiom,
% 8.68/4.87      ! [W: int,Z: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 8.68/4.87        = ( ord_less_int @ W @ Z ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2672_max__add__distrib__left,axiom,
% 8.68/4.87      ! [X: real,Y: real,Z: real] :
% 8.68/4.87        ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2673_max__add__distrib__left,axiom,
% 8.68/4.87      ! [X: rat,Y: rat,Z: rat] :
% 8.68/4.87        ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2674_max__add__distrib__left,axiom,
% 8.68/4.87      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2675_max__add__distrib__left,axiom,
% 8.68/4.87      ! [X: int,Y: int,Z: int] :
% 8.68/4.87        ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2676_max__add__distrib__left,axiom,
% 8.68/4.87      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 8.68/4.87        ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2677_max__add__distrib__right,axiom,
% 8.68/4.87      ! [X: real,Y: real,Z: real] :
% 8.68/4.87        ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 8.68/4.87        = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2678_max__add__distrib__right,axiom,
% 8.68/4.87      ! [X: rat,Y: rat,Z: rat] :
% 8.68/4.87        ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 8.68/4.87        = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2679_max__add__distrib__right,axiom,
% 8.68/4.87      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 8.68/4.87        = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2680_max__add__distrib__right,axiom,
% 8.68/4.87      ! [X: int,Y: int,Z: int] :
% 8.68/4.87        ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 8.68/4.87        = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2681_max__add__distrib__right,axiom,
% 8.68/4.87      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 8.68/4.87        ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 8.68/4.87        = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2682_max__diff__distrib__left,axiom,
% 8.68/4.87      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 8.68/4.87        ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2683_max__diff__distrib__left,axiom,
% 8.68/4.87      ! [X: real,Y: real,Z: real] :
% 8.68/4.87        ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2684_max__diff__distrib__left,axiom,
% 8.68/4.87      ! [X: rat,Y: rat,Z: rat] :
% 8.68/4.87        ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2685_max__diff__distrib__left,axiom,
% 8.68/4.87      ! [X: int,Y: int,Z: int] :
% 8.68/4.87        ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 8.68/4.87        = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2686_nat__add__max__left,axiom,
% 8.68/4.87      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 8.68/4.87        = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2687_nat__add__max__right,axiom,
% 8.68/4.87      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 8.68/4.87        = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2688_nat__mult__max__left,axiom,
% 8.68/4.87      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.87        ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 8.68/4.87        = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2689_nat__mult__max__right,axiom,
% 8.68/4.87      ! [M: nat,N: nat,Q2: nat] :
% 8.68/4.87        ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 8.68/4.87        = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2690_nat__minus__add__max,axiom,
% 8.68/4.87      ! [N: nat,M: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 8.68/4.87        = ( ord_max_nat @ N @ M ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2691_minus__int__code_I1_J,axiom,
% 8.68/4.87      ! [K: int] :
% 8.68/4.87        ( ( minus_minus_int @ K @ zero_zero_int )
% 8.68/4.87        = K ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2692_int__distrib_I3_J,axiom,
% 8.68/4.87      ! [Z1: int,Z22: int,W: int] :
% 8.68/4.87        ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 8.68/4.87        = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2693_int__distrib_I4_J,axiom,
% 8.68/4.87      ! [W: int,Z1: int,Z22: int] :
% 8.68/4.87        ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 8.68/4.87        = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2694_option_Odistinct_I1_J,axiom,
% 8.68/4.87      ! [X22: nat] :
% 8.68/4.87        ( none_nat
% 8.68/4.87       != ( some_nat @ X22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2695_option_Odistinct_I1_J,axiom,
% 8.68/4.87      ! [X22: product_prod_nat_nat] :
% 8.68/4.87        ( none_P5556105721700978146at_nat
% 8.68/4.87       != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2696_option_Odistinct_I1_J,axiom,
% 8.68/4.87      ! [X22: num] :
% 8.68/4.87        ( none_num
% 8.68/4.87       != ( some_num @ X22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2697_option_OdiscI,axiom,
% 8.68/4.87      ! [Option: option_nat,X22: nat] :
% 8.68/4.87        ( ( Option
% 8.68/4.87          = ( some_nat @ X22 ) )
% 8.68/4.87       => ( Option != none_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2698_option_OdiscI,axiom,
% 8.68/4.87      ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 8.68/4.87        ( ( Option
% 8.68/4.87          = ( some_P7363390416028606310at_nat @ X22 ) )
% 8.68/4.87       => ( Option != none_P5556105721700978146at_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2699_option_OdiscI,axiom,
% 8.68/4.87      ! [Option: option_num,X22: num] :
% 8.68/4.87        ( ( Option
% 8.68/4.87          = ( some_num @ X22 ) )
% 8.68/4.87       => ( Option != none_num ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2700_option_Oexhaust,axiom,
% 8.68/4.87      ! [Y: option_nat] :
% 8.68/4.87        ( ( Y != none_nat )
% 8.68/4.87       => ~ ! [X23: nat] :
% 8.68/4.87              ( Y
% 8.68/4.87             != ( some_nat @ X23 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2701_option_Oexhaust,axiom,
% 8.68/4.87      ! [Y: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( Y != none_P5556105721700978146at_nat )
% 8.68/4.87       => ~ ! [X23: product_prod_nat_nat] :
% 8.68/4.87              ( Y
% 8.68/4.87             != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2702_option_Oexhaust,axiom,
% 8.68/4.87      ! [Y: option_num] :
% 8.68/4.87        ( ( Y != none_num )
% 8.68/4.87       => ~ ! [X23: num] :
% 8.68/4.87              ( Y
% 8.68/4.87             != ( some_num @ X23 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2703_split__option__ex,axiom,
% 8.68/4.87      ( ( ^ [P3: option_nat > $o] :
% 8.68/4.87          ? [X7: option_nat] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option_nat > $o] :
% 8.68/4.87            ( ( P4 @ none_nat )
% 8.68/4.87            | ? [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2704_split__option__ex,axiom,
% 8.68/4.87      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 8.68/4.87          ? [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 8.68/4.87            ( ( P4 @ none_P5556105721700978146at_nat )
% 8.68/4.87            | ? [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2705_split__option__ex,axiom,
% 8.68/4.87      ( ( ^ [P3: option_num > $o] :
% 8.68/4.87          ? [X7: option_num] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option_num > $o] :
% 8.68/4.87            ( ( P4 @ none_num )
% 8.68/4.87            | ? [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2706_split__option__all,axiom,
% 8.68/4.87      ( ( ^ [P3: option_nat > $o] :
% 8.68/4.87          ! [X7: option_nat] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option_nat > $o] :
% 8.68/4.87            ( ( P4 @ none_nat )
% 8.68/4.87            & ! [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2707_split__option__all,axiom,
% 8.68/4.87      ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 8.68/4.87          ! [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 8.68/4.87            ( ( P4 @ none_P5556105721700978146at_nat )
% 8.68/4.87            & ! [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2708_split__option__all,axiom,
% 8.68/4.87      ( ( ^ [P3: option_num > $o] :
% 8.68/4.87          ! [X7: option_num] : ( P3 @ X7 ) )
% 8.68/4.87      = ( ^ [P4: option_num > $o] :
% 8.68/4.87            ( ( P4 @ none_num )
% 8.68/4.87            & ! [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2709_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 8.68/4.87        ( ( ( X = none_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: nat,B5: nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2710_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( ( X = none_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: nat,B5: product_prod_nat_nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2711_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 8.68/4.87        ( ( ( X = none_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_num )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: nat,B5: num] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_num @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2712_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 8.68/4.87        ( ( ( X = none_P5556105721700978146at_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: product_prod_nat_nat,B5: nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2713_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( ( X = none_P5556105721700978146at_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2714_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 8.68/4.87        ( ( ( X = none_P5556105721700978146at_nat )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_num )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: product_prod_nat_nat,B5: num] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_P7363390416028606310at_nat @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_num @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2715_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 8.68/4.87        ( ( ( X = none_num )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: num,B5: nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_num @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2716_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( ( X = none_num )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: num,B5: product_prod_nat_nat] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_num @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_P7363390416028606310at_nat @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2717_combine__options__cases,axiom,
% 8.68/4.87      ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 8.68/4.87        ( ( ( X = none_num )
% 8.68/4.87         => ( P @ X @ Y ) )
% 8.68/4.87       => ( ( ( Y = none_num )
% 8.68/4.87           => ( P @ X @ Y ) )
% 8.68/4.87         => ( ! [A5: num,B5: num] :
% 8.68/4.87                ( ( X
% 8.68/4.87                  = ( some_num @ A5 ) )
% 8.68/4.87               => ( ( Y
% 8.68/4.87                    = ( some_num @ B5 ) )
% 8.68/4.87                 => ( P @ X @ Y ) ) )
% 8.68/4.87           => ( P @ X @ Y ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2718_less__eq__int__code_I1_J,axiom,
% 8.68/4.87      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2719_less__int__code_I1_J,axiom,
% 8.68/4.87      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2720_times__int__code_I1_J,axiom,
% 8.68/4.87      ! [K: int] :
% 8.68/4.87        ( ( times_times_int @ K @ zero_zero_int )
% 8.68/4.87        = zero_zero_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2721_times__int__code_I2_J,axiom,
% 8.68/4.87      ! [L2: int] :
% 8.68/4.87        ( ( times_times_int @ zero_zero_int @ L2 )
% 8.68/4.87        = zero_zero_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2722_plus__int__code_I1_J,axiom,
% 8.68/4.87      ! [K: int] :
% 8.68/4.87        ( ( plus_plus_int @ K @ zero_zero_int )
% 8.68/4.87        = K ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2723_plus__int__code_I2_J,axiom,
% 8.68/4.87      ! [L2: int] :
% 8.68/4.87        ( ( plus_plus_int @ zero_zero_int @ L2 )
% 8.68/4.87        = L2 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2724_int__le__induct,axiom,
% 8.68/4.87      ! [I: int,K: int,P: int > $o] :
% 8.68/4.87        ( ( ord_less_eq_int @ I @ K )
% 8.68/4.87       => ( ( P @ K )
% 8.68/4.87         => ( ! [I4: int] :
% 8.68/4.87                ( ( ord_less_eq_int @ I4 @ K )
% 8.68/4.87               => ( ( P @ I4 )
% 8.68/4.87                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2725_int__less__induct,axiom,
% 8.68/4.87      ! [I: int,K: int,P: int > $o] :
% 8.68/4.87        ( ( ord_less_int @ I @ K )
% 8.68/4.87       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 8.68/4.87         => ( ! [I4: int] :
% 8.68/4.87                ( ( ord_less_int @ I4 @ K )
% 8.68/4.87               => ( ( P @ I4 )
% 8.68/4.87                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2726_int__distrib_I2_J,axiom,
% 8.68/4.87      ! [W: int,Z1: int,Z22: int] :
% 8.68/4.87        ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 8.68/4.87        = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2727_int__distrib_I1_J,axiom,
% 8.68/4.87      ! [Z1: int,Z22: int,W: int] :
% 8.68/4.87        ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 8.68/4.87        = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2728_option_Osel,axiom,
% 8.68/4.87      ! [X22: nat] :
% 8.68/4.87        ( ( the_nat @ ( some_nat @ X22 ) )
% 8.68/4.87        = X22 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2729_option_Osel,axiom,
% 8.68/4.87      ! [X22: product_prod_nat_nat] :
% 8.68/4.87        ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 8.68/4.87        = X22 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2730_option_Osel,axiom,
% 8.68/4.87      ! [X22: num] :
% 8.68/4.87        ( ( the_num @ ( some_num @ X22 ) )
% 8.68/4.87        = X22 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2731_option_Oexpand,axiom,
% 8.68/4.87      ! [Option: option_nat,Option2: option_nat] :
% 8.68/4.87        ( ( ( Option = none_nat )
% 8.68/4.87          = ( Option2 = none_nat ) )
% 8.68/4.87       => ( ( ( Option != none_nat )
% 8.68/4.87           => ( ( Option2 != none_nat )
% 8.68/4.87             => ( ( the_nat @ Option )
% 8.68/4.87                = ( the_nat @ Option2 ) ) ) )
% 8.68/4.87         => ( Option = Option2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2732_option_Oexpand,axiom,
% 8.68/4.87      ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( ( Option = none_P5556105721700978146at_nat )
% 8.68/4.87          = ( Option2 = none_P5556105721700978146at_nat ) )
% 8.68/4.87       => ( ( ( Option != none_P5556105721700978146at_nat )
% 8.68/4.87           => ( ( Option2 != none_P5556105721700978146at_nat )
% 8.68/4.87             => ( ( the_Pr8591224930841456533at_nat @ Option )
% 8.68/4.87                = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 8.68/4.87         => ( Option = Option2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2733_option_Oexpand,axiom,
% 8.68/4.87      ! [Option: option_num,Option2: option_num] :
% 8.68/4.87        ( ( ( Option = none_num )
% 8.68/4.87          = ( Option2 = none_num ) )
% 8.68/4.87       => ( ( ( Option != none_num )
% 8.68/4.87           => ( ( Option2 != none_num )
% 8.68/4.87             => ( ( the_num @ Option )
% 8.68/4.87                = ( the_num @ Option2 ) ) ) )
% 8.68/4.87         => ( Option = Option2 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2734_invar__vebt_Ointros_I2_J,axiom,
% 8.68/4.87      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 8.68/4.87        ( ! [X6: vEBT_VEBT] :
% 8.68/4.87            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.87           => ( vEBT_invar_vebt @ X6 @ N ) )
% 8.68/4.87       => ( ( vEBT_invar_vebt @ Summary @ M )
% 8.68/4.87         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.68/4.87              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.87           => ( ( M = N )
% 8.68/4.87             => ( ( Deg
% 8.68/4.87                  = ( plus_plus_nat @ N @ M ) )
% 8.68/4.87               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 8.68/4.87                 => ( ! [X6: vEBT_VEBT] :
% 8.68/4.87                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.87                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 8.68/4.87                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2735_zmult__zless__mono2,axiom,
% 8.68/4.87      ! [I: int,J: int,K: int] :
% 8.68/4.87        ( ( ord_less_int @ I @ J )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.87         => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2736_odd__nonzero,axiom,
% 8.68/4.87      ! [Z: int] :
% 8.68/4.87        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 8.68/4.87       != zero_zero_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2737_int__induct,axiom,
% 8.68/4.87      ! [P: int > $o,K: int,I: int] :
% 8.68/4.87        ( ( P @ K )
% 8.68/4.87       => ( ! [I4: int] :
% 8.68/4.87              ( ( ord_less_eq_int @ K @ I4 )
% 8.68/4.87             => ( ( P @ I4 )
% 8.68/4.87               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87         => ( ! [I4: int] :
% 8.68/4.87                ( ( ord_less_eq_int @ I4 @ K )
% 8.68/4.87               => ( ( P @ I4 )
% 8.68/4.87                 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2738_int__ge__induct,axiom,
% 8.68/4.87      ! [K: int,I: int,P: int > $o] :
% 8.68/4.87        ( ( ord_less_eq_int @ K @ I )
% 8.68/4.87       => ( ( P @ K )
% 8.68/4.87         => ( ! [I4: int] :
% 8.68/4.87                ( ( ord_less_eq_int @ K @ I4 )
% 8.68/4.87               => ( ( P @ I4 )
% 8.68/4.87                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2739_zless__add1__eq,axiom,
% 8.68/4.87      ! [W: int,Z: int] :
% 8.68/4.87        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 8.68/4.87        = ( ( ord_less_int @ W @ Z )
% 8.68/4.87          | ( W = Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2740_int__gr__induct,axiom,
% 8.68/4.87      ! [K: int,I: int,P: int > $o] :
% 8.68/4.87        ( ( ord_less_int @ K @ I )
% 8.68/4.87       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 8.68/4.87         => ( ! [I4: int] :
% 8.68/4.87                ( ( ord_less_int @ K @ I4 )
% 8.68/4.87               => ( ( P @ I4 )
% 8.68/4.87                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2741_option_Oexhaust__sel,axiom,
% 8.68/4.87      ! [Option: option_nat] :
% 8.68/4.87        ( ( Option != none_nat )
% 8.68/4.87       => ( Option
% 8.68/4.87          = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2742_option_Oexhaust__sel,axiom,
% 8.68/4.87      ! [Option: option4927543243414619207at_nat] :
% 8.68/4.87        ( ( Option != none_P5556105721700978146at_nat )
% 8.68/4.87       => ( Option
% 8.68/4.87          = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2743_option_Oexhaust__sel,axiom,
% 8.68/4.87      ! [Option: option_num] :
% 8.68/4.87        ( ( Option != none_num )
% 8.68/4.87       => ( Option
% 8.68/4.87          = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2744_int__one__le__iff__zero__less,axiom,
% 8.68/4.87      ! [Z: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ one_one_int @ Z )
% 8.68/4.87        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2745_pos__zmult__eq__1__iff,axiom,
% 8.68/4.87      ! [M: int,N: int] :
% 8.68/4.87        ( ( ord_less_int @ zero_zero_int @ M )
% 8.68/4.87       => ( ( ( times_times_int @ M @ N )
% 8.68/4.87            = one_one_int )
% 8.68/4.87          = ( ( M = one_one_int )
% 8.68/4.87            & ( N = one_one_int ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2746_odd__less__0__iff,axiom,
% 8.68/4.87      ! [Z: int] :
% 8.68/4.87        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 8.68/4.87        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2747_zless__imp__add1__zle,axiom,
% 8.68/4.87      ! [W: int,Z: int] :
% 8.68/4.87        ( ( ord_less_int @ W @ Z )
% 8.68/4.87       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2748_add1__zle__eq,axiom,
% 8.68/4.87      ! [W: int,Z: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 8.68/4.87        = ( ord_less_int @ W @ Z ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2749_le__imp__0__less,axiom,
% 8.68/4.87      ! [Z: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.68/4.87       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2750_nested__mint,axiom,
% 8.68/4.87      ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.68/4.87       => ( ( N
% 8.68/4.87            = ( suc @ ( suc @ Va ) ) )
% 8.68/4.87         => ( ~ ( ord_less_nat @ Ma @ Mi )
% 8.68/4.87           => ( ( Ma != Mi )
% 8.68/4.87             => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2751_aampt,axiom,
% 8.68/4.87      ( ( ( xa = ma )
% 8.68/4.87       => ( mi
% 8.68/4.87          = ( if_nat
% 8.68/4.87            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 8.68/4.87              = none_nat )
% 8.68/4.87            @ mi
% 8.68/4.87            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.87      & ( ( xa != ma )
% 8.68/4.87       => ( mi = ma ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2752_verit__le__mono__div__int,axiom,
% 8.68/4.87      ! [A2: int,B3: int,N: int] :
% 8.68/4.87        ( ( ord_less_int @ A2 @ B3 )
% 8.68/4.87       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.68/4.87         => ( ord_less_eq_int
% 8.68/4.87            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 8.68/4.87              @ ( if_int
% 8.68/4.87                @ ( ( modulo_modulo_int @ B3 @ N )
% 8.68/4.87                  = zero_zero_int )
% 8.68/4.87                @ one_one_int
% 8.68/4.87                @ zero_zero_int ) )
% 8.68/4.87            @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2753_buildup__gives__valid,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87       => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2754_verit__le__mono__div,axiom,
% 8.68/4.87      ! [A2: nat,B3: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ A2 @ B3 )
% 8.68/4.87       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87         => ( ord_less_eq_nat
% 8.68/4.87            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 8.68/4.87              @ ( if_nat
% 8.68/4.87                @ ( ( modulo_modulo_nat @ B3 @ N )
% 8.68/4.87                  = zero_zero_nat )
% 8.68/4.87                @ one_one_nat
% 8.68/4.87                @ zero_zero_nat ) )
% 8.68/4.87            @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2755_inrange,axiom,
% 8.68/4.87      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.87       => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2756_mul__def,axiom,
% 8.68/4.87      ( vEBT_VEBT_mul
% 8.68/4.87      = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2757_add__def,axiom,
% 8.68/4.87      ( vEBT_VEBT_add
% 8.68/4.87      = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2758_set__bit__0,axiom,
% 8.68/4.87      ! [A: int] :
% 8.68/4.87        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 8.68/4.87        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2759_set__bit__0,axiom,
% 8.68/4.87      ! [A: nat] :
% 8.68/4.87        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 8.68/4.87        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2760_even__odd__cases,axiom,
% 8.68/4.87      ! [X: nat] :
% 8.68/4.87        ( ! [N3: nat] :
% 8.68/4.87            ( X
% 8.68/4.87           != ( plus_plus_nat @ N3 @ N3 ) )
% 8.68/4.87       => ~ ! [N3: nat] :
% 8.68/4.87              ( X
% 8.68/4.87             != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2761_set__vebt_H__def,axiom,
% 8.68/4.87      ( vEBT_VEBT_set_vebt
% 8.68/4.87      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2762_deg__SUcn__Node,axiom,
% 8.68/4.87      ! [Tree: vEBT_VEBT,N: nat] :
% 8.68/4.87        ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 8.68/4.87       => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.68/4.87            ( Tree
% 8.68/4.87            = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2763_add__shift,axiom,
% 8.68/4.87      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.87        ( ( ( plus_plus_nat @ X @ Y )
% 8.68/4.87          = Z )
% 8.68/4.87        = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.68/4.87          = ( some_nat @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2764_mul__shift,axiom,
% 8.68/4.87      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.87        ( ( ( times_times_nat @ X @ Y )
% 8.68/4.87          = Z )
% 8.68/4.87        = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.68/4.87          = ( some_nat @ Z ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2765_verit__eq__simplify_I8_J,axiom,
% 8.68/4.87      ! [X22: num,Y22: num] :
% 8.68/4.87        ( ( ( bit0 @ X22 )
% 8.68/4.87          = ( bit0 @ Y22 ) )
% 8.68/4.87        = ( X22 = Y22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2766_nat_Oinject,axiom,
% 8.68/4.87      ! [X22: nat,Y22: nat] :
% 8.68/4.87        ( ( ( suc @ X22 )
% 8.68/4.87          = ( suc @ Y22 ) )
% 8.68/4.87        = ( X22 = Y22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2767_old_Onat_Oinject,axiom,
% 8.68/4.87      ! [Nat: nat,Nat2: nat] :
% 8.68/4.87        ( ( ( suc @ Nat )
% 8.68/4.87          = ( suc @ Nat2 ) )
% 8.68/4.87        = ( Nat = Nat2 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2768_max__enat__simps_I2_J,axiom,
% 8.68/4.87      ! [Q2: extended_enat] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 8.68/4.87        = Q2 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2769_max__enat__simps_I3_J,axiom,
% 8.68/4.87      ! [Q2: extended_enat] :
% 8.68/4.87        ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 8.68/4.87        = Q2 ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2770_Suc__less__eq,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.68/4.87        = ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2771_Suc__mono,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ M @ N )
% 8.68/4.87       => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2772_lessI,axiom,
% 8.68/4.87      ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2773_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: set_nat,L2: set_nat,U: set_nat] :
% 8.68/4.87        ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_set_nat @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2774_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: set_int,L2: set_int,U: set_int] :
% 8.68/4.87        ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_set_int @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2775_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: rat,L2: rat,U: rat] :
% 8.68/4.87        ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_rat @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2776_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: num,L2: num,U: num] :
% 8.68/4.87        ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_num @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_num @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2777_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: nat,L2: nat,U: nat] :
% 8.68/4.87        ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_nat @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2778_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: int,L2: int,U: int] :
% 8.68/4.87        ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_int @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_int @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2779_atLeastAtMost__iff,axiom,
% 8.68/4.87      ! [I: real,L2: real,U: real] :
% 8.68/4.87        ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 8.68/4.87        = ( ( ord_less_eq_real @ L2 @ I )
% 8.68/4.87          & ( ord_less_eq_real @ I @ U ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2780_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 8.68/4.87        ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 8.68/4.87          = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2781_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 8.68/4.87        ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 8.68/4.87          = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2782_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: num,H2: num,L3: num,H3: num] :
% 8.68/4.87        ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 8.68/4.87          = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2783_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 8.68/4.87        ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 8.68/4.87          = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2784_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: int,H2: int,L3: int,H3: int] :
% 8.68/4.87        ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 8.68/4.87          = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2785_Icc__eq__Icc,axiom,
% 8.68/4.87      ! [L2: real,H2: real,L3: real,H3: real] :
% 8.68/4.87        ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 8.68/4.87          = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 8.68/4.87        = ( ( ( L2 = L3 )
% 8.68/4.87            & ( H2 = H3 ) )
% 8.68/4.87          | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 8.68/4.87            & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2786_Suc__le__mono,axiom,
% 8.68/4.87      ! [N: nat,M: nat] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 8.68/4.87        = ( ord_less_eq_nat @ N @ M ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2787_add__Suc__right,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 8.68/4.87        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2788_diff__Suc__Suc,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.68/4.87        = ( minus_minus_nat @ M @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2789_Suc__diff__diff,axiom,
% 8.68/4.87      ! [M: nat,N: nat,K: nat] :
% 8.68/4.87        ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 8.68/4.87        = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2790_set__bit__nonnegative__int__iff,axiom,
% 8.68/4.87      ! [N: nat,K: int] :
% 8.68/4.87        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 8.68/4.87        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2791_set__bit__negative__int__iff,axiom,
% 8.68/4.87      ! [N: nat,K: int] :
% 8.68/4.87        ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 8.68/4.87        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2792_max__Suc__Suc,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.68/4.87        = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2793_power__0__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 8.68/4.87        = zero_zero_rat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2794_power__0__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.68/4.87        = zero_zero_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2795_power__0__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 8.68/4.87        = zero_zero_real ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2796_power__0__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 8.68/4.87        = zero_zero_int ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2797_power__0__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 8.68/4.87        = zero_zero_complex ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2798_power__Suc0__right,axiom,
% 8.68/4.87      ! [A: nat] :
% 8.68/4.87        ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2799_power__Suc0__right,axiom,
% 8.68/4.87      ! [A: real] :
% 8.68/4.87        ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2800_power__Suc0__right,axiom,
% 8.68/4.87      ! [A: int] :
% 8.68/4.87        ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2801_power__Suc0__right,axiom,
% 8.68/4.87      ! [A: complex] :
% 8.68/4.87        ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = A ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2802_zero__less__Suc,axiom,
% 8.68/4.87      ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2803_less__Suc0,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = ( N = zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2804_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 8.68/4.87        ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_set_int @ C @ A )
% 8.68/4.87            & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2805_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.87        ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_rat @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_rat @ C @ A )
% 8.68/4.87            & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2806_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: num,B: num,C: num,D: num] :
% 8.68/4.87        ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_num @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_num @ C @ A )
% 8.68/4.87            & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2807_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.87        ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_nat @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.87            & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2808_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.87        ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_int @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_int @ C @ A )
% 8.68/4.87            & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2809_atLeastatMost__subset__iff,axiom,
% 8.68/4.87      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.87        ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 8.68/4.87        = ( ~ ( ord_less_eq_real @ A @ B )
% 8.68/4.87          | ( ( ord_less_eq_real @ C @ A )
% 8.68/4.87            & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2810_one__eq__mult__iff,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ( suc @ zero_zero_nat )
% 8.68/4.87          = ( times_times_nat @ M @ N ) )
% 8.68/4.87        = ( ( M
% 8.68/4.87            = ( suc @ zero_zero_nat ) )
% 8.68/4.87          & ( N
% 8.68/4.87            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2811_mult__eq__1__iff,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ( times_times_nat @ M @ N )
% 8.68/4.87          = ( suc @ zero_zero_nat ) )
% 8.68/4.87        = ( ( M
% 8.68/4.87            = ( suc @ zero_zero_nat ) )
% 8.68/4.87          & ( N
% 8.68/4.87            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2812_div__by__Suc__0,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = M ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2813_power__Suc__0,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.68/4.87        = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2814_nat__power__eq__Suc__0__iff,axiom,
% 8.68/4.87      ! [X: nat,M: nat] :
% 8.68/4.87        ( ( ( power_power_nat @ X @ M )
% 8.68/4.87          = ( suc @ zero_zero_nat ) )
% 8.68/4.87        = ( ( M = zero_zero_nat )
% 8.68/4.87          | ( X
% 8.68/4.87            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2815_mult__Suc__right,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( times_times_nat @ M @ ( suc @ N ) )
% 8.68/4.87        = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2816_diff__Suc__1,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 8.68/4.87        = N ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2817_mod__by__Suc__0,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.68/4.87        = zero_zero_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2818_Suc__pred,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.68/4.87          = N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2819_one__le__mult__iff,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 8.68/4.87        = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.68/4.87          & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2820_diff__Suc__diff__eq2,axiom,
% 8.68/4.87      ! [K: nat,J: nat,I: nat] :
% 8.68/4.87        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.87       => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 8.68/4.87          = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2821_diff__Suc__diff__eq1,axiom,
% 8.68/4.87      ! [K: nat,J: nat,I: nat] :
% 8.68/4.87        ( ( ord_less_eq_nat @ K @ J )
% 8.68/4.87       => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 8.68/4.87          = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2822_Suc__numeral,axiom,
% 8.68/4.87      ! [N: num] :
% 8.68/4.87        ( ( suc @ ( numeral_numeral_nat @ N ) )
% 8.68/4.87        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2823_Suc__mod__mult__self1,axiom,
% 8.68/4.87      ! [M: nat,K: nat,N: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 8.68/4.87        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2824_Suc__mod__mult__self2,axiom,
% 8.68/4.87      ! [M: nat,N: nat,K: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 8.68/4.87        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2825_Suc__mod__mult__self3,axiom,
% 8.68/4.87      ! [K: nat,N: nat,M: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 8.68/4.87        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2826_Suc__mod__mult__self4,axiom,
% 8.68/4.87      ! [N: nat,K: nat,M: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 8.68/4.87        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2827_add__2__eq__Suc_H,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87        = ( suc @ ( suc @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2828_add__2__eq__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.68/4.87        = ( suc @ ( suc @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2829_div2__Suc__Suc,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87        = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2830_Suc__1,axiom,
% 8.68/4.87      ( ( suc @ one_one_nat )
% 8.68/4.87      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2831_mod2__Suc__Suc,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87        = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2832_Suc__diff__1,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.87       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.68/4.87          = N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2833_Suc__times__numeral__mod__eq,axiom,
% 8.68/4.87      ! [K: num,N: nat] :
% 8.68/4.87        ( ( ( numeral_numeral_nat @ K )
% 8.68/4.87         != one_one_nat )
% 8.68/4.87       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 8.68/4.87          = one_one_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2834_not__mod2__eq__Suc__0__eq__0,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87         != ( suc @ zero_zero_nat ) )
% 8.68/4.87        = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.87          = zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2835_del__x__not__mia,axiom,
% 8.68/4.87      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( ord_less_nat @ Mi @ X )
% 8.68/4.87          & ( ord_less_eq_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                  = L2 )
% 8.68/4.87               => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                    = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                      @ ( vEBT_Node
% 8.68/4.87                        @ ( some_P7363390416028606310at_nat
% 8.68/4.87                          @ ( product_Pair_nat_nat @ Mi
% 8.68/4.87                            @ ( if_nat @ ( X = Ma )
% 8.68/4.87                              @ ( if_nat
% 8.68/4.87                                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                                  = none_nat )
% 8.68/4.87                                @ Mi
% 8.68/4.87                                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 8.68/4.87                              @ Ma ) ) )
% 8.68/4.87                        @ Deg
% 8.68/4.87                        @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                        @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                      @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2836_del__x__not__mi__new__node__nil,axiom,
% 8.68/4.87      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.68/4.87        ( ( ( ord_less_nat @ Mi @ X )
% 8.68/4.87          & ( ord_less_eq_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                  = L2 )
% 8.68/4.87               => ( ( Newnode
% 8.68/4.87                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                 => ( ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                   => ( ( Sn
% 8.68/4.87                        = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                     => ( ( Newlist
% 8.68/4.87                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                       => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                            = ( vEBT_Node
% 8.68/4.87                              @ ( some_P7363390416028606310at_nat
% 8.68/4.87                                @ ( product_Pair_nat_nat @ Mi
% 8.68/4.87                                  @ ( if_nat @ ( X = Ma )
% 8.68/4.87                                    @ ( if_nat
% 8.68/4.87                                      @ ( ( vEBT_vebt_maxt @ Sn )
% 8.68/4.87                                        = none_nat )
% 8.68/4.87                                      @ Mi
% 8.68/4.87                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 8.68/4.87                                    @ Ma ) ) )
% 8.68/4.87                              @ Deg
% 8.68/4.87                              @ Newlist
% 8.68/4.87                              @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2837_del__x__not__mi,axiom,
% 8.68/4.87      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( ord_less_nat @ Mi @ X )
% 8.68/4.87          & ( ord_less_eq_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                  = L2 )
% 8.68/4.87               => ( ( Newnode
% 8.68/4.87                    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                 => ( ( Newlist
% 8.68/4.87                      = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                   => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                     => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                            = ( vEBT_Node
% 8.68/4.87                              @ ( some_P7363390416028606310at_nat
% 8.68/4.87                                @ ( product_Pair_nat_nat @ Mi
% 8.68/4.87                                  @ ( if_nat @ ( X = Ma )
% 8.68/4.87                                    @ ( if_nat
% 8.68/4.87                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                                        = none_nat )
% 8.68/4.87                                      @ Mi
% 8.68/4.87                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 8.68/4.87                                    @ Ma ) ) )
% 8.68/4.87                              @ Deg
% 8.68/4.87                              @ Newlist
% 8.68/4.87                              @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 8.68/4.87                        & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2838_del__x__mia,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( ord_less_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                  @ ( vEBT_Node
% 8.68/4.87                    @ ( some_P7363390416028606310at_nat
% 8.68/4.87                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                        @ ( if_nat
% 8.68/4.87                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                            = Ma )
% 8.68/4.87                          @ ( if_nat
% 8.68/4.87                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                              = none_nat )
% 8.68/4.87                            @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.87                          @ Ma ) ) )
% 8.68/4.87                    @ Deg
% 8.68/4.87                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                  @ ( vEBT_Node
% 8.68/4.87                    @ ( some_P7363390416028606310at_nat
% 8.68/4.87                      @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                        @ ( if_nat
% 8.68/4.87                          @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                            = Ma )
% 8.68/4.87                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                          @ Ma ) ) )
% 8.68/4.87                    @ Deg
% 8.68/4.87                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                    @ Summary ) )
% 8.68/4.87                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2839_del__x__mi__lets__in__minNull,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( ord_less_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( Xn
% 8.68/4.87                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.68/4.87               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                    = L2 )
% 8.68/4.87                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                   => ( ( Newnode
% 8.68/4.87                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                     => ( ( Newlist
% 8.68/4.87                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                       => ( ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                         => ( ( Sn
% 8.68/4.87                              = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                              = ( vEBT_Node
% 8.68/4.87                                @ ( some_P7363390416028606310at_nat
% 8.68/4.87                                  @ ( product_Pair_nat_nat @ Xn
% 8.68/4.87                                    @ ( if_nat @ ( Xn = Ma )
% 8.68/4.87                                      @ ( if_nat
% 8.68/4.87                                        @ ( ( vEBT_vebt_maxt @ Sn )
% 8.68/4.87                                          = none_nat )
% 8.68/4.87                                        @ Xn
% 8.68/4.87                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 8.68/4.87                                      @ Ma ) ) )
% 8.68/4.87                                @ Deg
% 8.68/4.87                                @ Newlist
% 8.68/4.87                                @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2840_del__x__mi__lets__in,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( ord_less_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( Xn
% 8.68/4.87                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.68/4.87               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                    = L2 )
% 8.68/4.87                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                   => ( ( Newnode
% 8.68/4.87                        = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                     => ( ( Newlist
% 8.68/4.87                          = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 8.68/4.87                       => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                              = ( vEBT_Node
% 8.68/4.87                                @ ( some_P7363390416028606310at_nat
% 8.68/4.87                                  @ ( product_Pair_nat_nat @ Xn
% 8.68/4.87                                    @ ( if_nat @ ( Xn = Ma )
% 8.68/4.87                                      @ ( if_nat
% 8.68/4.87                                        @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                                          = none_nat )
% 8.68/4.87                                        @ Xn
% 8.68/4.87                                        @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 8.68/4.87                                      @ Ma ) ) )
% 8.68/4.87                                @ Deg
% 8.68/4.87                                @ Newlist
% 8.68/4.87                                @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 8.68/4.87                          & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.68/4.87                           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2841_del__x__mi,axiom,
% 8.68/4.87      ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat] :
% 8.68/4.87        ( ( ( X = Mi )
% 8.68/4.87          & ( ord_less_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                = H2 )
% 8.68/4.87             => ( ( Xn
% 8.68/4.87                  = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.68/4.87               => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.68/4.87                    = L2 )
% 8.68/4.87                 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                   => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87                      = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                        @ ( vEBT_Node
% 8.68/4.87                          @ ( some_P7363390416028606310at_nat
% 8.68/4.87                            @ ( product_Pair_nat_nat @ Xn
% 8.68/4.87                              @ ( if_nat @ ( Xn = Ma )
% 8.68/4.87                                @ ( if_nat
% 8.68/4.87                                  @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                                    = none_nat )
% 8.68/4.87                                  @ Xn
% 8.68/4.87                                  @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 8.68/4.87                                @ Ma ) ) )
% 8.68/4.87                          @ Deg
% 8.68/4.87                          @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 8.68/4.87                          @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 8.68/4.87                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2842_del__in__range,axiom,
% 8.68/4.87      ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ( ord_less_eq_nat @ Mi @ X )
% 8.68/4.87          & ( ord_less_eq_nat @ X @ Ma ) )
% 8.68/4.87       => ( ( Mi != Ma )
% 8.68/4.87         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87           => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87              = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87                @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                  @ ( vEBT_Node
% 8.68/4.87                    @ ( some_P7363390416028606310at_nat
% 8.68/4.87                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.87                        @ ( if_nat
% 8.68/4.87                          @ ( ( ( X = Mi )
% 8.68/4.87                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                                = Ma ) )
% 8.68/4.87                            & ( ( X != Mi )
% 8.68/4.87                             => ( X = Ma ) ) )
% 8.68/4.87                          @ ( if_nat
% 8.68/4.87                            @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                              = none_nat )
% 8.68/4.87                            @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.87                            @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.87                          @ Ma ) ) )
% 8.68/4.87                    @ Deg
% 8.68/4.87                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                    @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                  @ ( vEBT_Node
% 8.68/4.87                    @ ( some_P7363390416028606310at_nat
% 8.68/4.87                      @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.87                        @ ( if_nat
% 8.68/4.87                          @ ( ( ( X = Mi )
% 8.68/4.87                             => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.87                                = Ma ) )
% 8.68/4.87                            & ( ( X != Mi )
% 8.68/4.87                             => ( X = Ma ) ) )
% 8.68/4.87                          @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                          @ Ma ) ) )
% 8.68/4.87                    @ Deg
% 8.68/4.87                    @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                    @ Summary ) )
% 8.68/4.87                @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2843_pred__less__length__list,axiom,
% 8.68/4.87      ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_eq_nat @ X @ Ma )
% 8.68/4.87         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87           => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87              = ( if_option_nat
% 8.68/4.87                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                   != none_nat )
% 8.68/4.87                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 8.68/4.87                @ ( if_option_nat
% 8.68/4.87                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.87                    = none_nat )
% 8.68/4.87                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.68/4.87                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2844_pred__lesseq__max,axiom,
% 8.68/4.87      ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_eq_nat @ X @ Ma )
% 8.68/4.87         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87              @ ( if_option_nat
% 8.68/4.87                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                   != none_nat )
% 8.68/4.87                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 8.68/4.87                @ ( if_option_nat
% 8.68/4.87                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.87                    = none_nat )
% 8.68/4.87                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.68/4.87                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.87              @ none_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2845_succ__greatereq__min,axiom,
% 8.68/4.87      ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_eq_nat @ Mi @ X )
% 8.68/4.87         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87              @ ( if_option_nat
% 8.68/4.87                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                   != none_nat )
% 8.68/4.87                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 8.68/4.87                @ ( if_option_nat
% 8.68/4.87                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.87                    = none_nat )
% 8.68/4.87                  @ none_nat
% 8.68/4.87                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.87              @ none_nat ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2846_succ__less__length__list,axiom,
% 8.68/4.87      ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 8.68/4.87        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.68/4.87       => ( ( ord_less_eq_nat @ Mi @ X )
% 8.68/4.87         => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.87           => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.68/4.87              = ( if_option_nat
% 8.68/4.87                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.87                   != none_nat )
% 8.68/4.87                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.87                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 8.68/4.87                @ ( if_option_nat
% 8.68/4.87                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.87                    = none_nat )
% 8.68/4.87                  @ none_nat
% 8.68/4.87                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2847_dsimp,axiom,
% 8.68/4.87      ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 8.68/4.87      = ( vEBT_Node
% 8.68/4.87        @ ( some_P7363390416028606310at_nat
% 8.68/4.87          @ ( product_Pair_nat_nat @ mi
% 8.68/4.87            @ ( if_nat @ ( xa = ma )
% 8.68/4.87              @ ( if_nat
% 8.68/4.87                @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 8.68/4.87                  = none_nat )
% 8.68/4.87                @ mi
% 8.68/4.87                @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) )
% 8.68/4.87              @ ma ) ) )
% 8.68/4.87        @ deg
% 8.68/4.87        @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) )
% 8.68/4.87        @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2848_mult__commute__abs,axiom,
% 8.68/4.87      ! [C: real] :
% 8.68/4.87        ( ( ^ [X3: real] : ( times_times_real @ X3 @ C ) )
% 8.68/4.87        = ( times_times_real @ C ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2849_mult__commute__abs,axiom,
% 8.68/4.87      ! [C: rat] :
% 8.68/4.87        ( ( ^ [X3: rat] : ( times_times_rat @ X3 @ C ) )
% 8.68/4.87        = ( times_times_rat @ C ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2850_mult__commute__abs,axiom,
% 8.68/4.87      ! [C: nat] :
% 8.68/4.87        ( ( ^ [X3: nat] : ( times_times_nat @ X3 @ C ) )
% 8.68/4.87        = ( times_times_nat @ C ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2851_mult__commute__abs,axiom,
% 8.68/4.87      ! [C: int] :
% 8.68/4.87        ( ( ^ [X3: int] : ( times_times_int @ X3 @ C ) )
% 8.68/4.87        = ( times_times_int @ C ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2852_Suc__inject,axiom,
% 8.68/4.87      ! [X: nat,Y: nat] :
% 8.68/4.87        ( ( ( suc @ X )
% 8.68/4.87          = ( suc @ Y ) )
% 8.68/4.87       => ( X = Y ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2853_n__not__Suc__n,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( N
% 8.68/4.87       != ( suc @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2854_max__def__raw,axiom,
% 8.68/4.87      ( ord_ma741700101516333627d_enat
% 8.68/4.87      = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2855_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_Code_integer
% 8.68/4.87      = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2856_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_set_int
% 8.68/4.87      = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2857_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_rat
% 8.68/4.87      = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2858_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_num
% 8.68/4.87      = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2859_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_nat
% 8.68/4.87      = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2860_max__def__raw,axiom,
% 8.68/4.87      ( ord_max_int
% 8.68/4.87      = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2861_lambda__zero,axiom,
% 8.68/4.87      ( ( ^ [H: complex] : zero_zero_complex )
% 8.68/4.87      = ( times_times_complex @ zero_zero_complex ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2862_lambda__zero,axiom,
% 8.68/4.87      ( ( ^ [H: real] : zero_zero_real )
% 8.68/4.87      = ( times_times_real @ zero_zero_real ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2863_lambda__zero,axiom,
% 8.68/4.87      ( ( ^ [H: rat] : zero_zero_rat )
% 8.68/4.87      = ( times_times_rat @ zero_zero_rat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2864_lambda__zero,axiom,
% 8.68/4.87      ( ( ^ [H: nat] : zero_zero_nat )
% 8.68/4.87      = ( times_times_nat @ zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2865_lambda__zero,axiom,
% 8.68/4.87      ( ( ^ [H: int] : zero_zero_int )
% 8.68/4.87      = ( times_times_int @ zero_zero_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2866_lambda__one,axiom,
% 8.68/4.87      ( ( ^ [X3: complex] : X3 )
% 8.68/4.87      = ( times_times_complex @ one_one_complex ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2867_lambda__one,axiom,
% 8.68/4.87      ( ( ^ [X3: real] : X3 )
% 8.68/4.87      = ( times_times_real @ one_one_real ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2868_lambda__one,axiom,
% 8.68/4.87      ( ( ^ [X3: rat] : X3 )
% 8.68/4.87      = ( times_times_rat @ one_one_rat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2869_lambda__one,axiom,
% 8.68/4.87      ( ( ^ [X3: nat] : X3 )
% 8.68/4.87      = ( times_times_nat @ one_one_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2870_lambda__one,axiom,
% 8.68/4.87      ( ( ^ [X3: int] : X3 )
% 8.68/4.87      = ( times_times_int @ one_one_int ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2871_vebt__buildup_Ocases,axiom,
% 8.68/4.87      ! [X: nat] :
% 8.68/4.87        ( ( X != zero_zero_nat )
% 8.68/4.87       => ( ( X
% 8.68/4.87           != ( suc @ zero_zero_nat ) )
% 8.68/4.87         => ~ ! [Va2: nat] :
% 8.68/4.87                ( X
% 8.68/4.87               != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2872_not0__implies__Suc,axiom,
% 8.68/4.87      ! [N: nat] :
% 8.68/4.87        ( ( N != zero_zero_nat )
% 8.68/4.87       => ? [M4: nat] :
% 8.68/4.87            ( N
% 8.68/4.87            = ( suc @ M4 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2873_Zero__not__Suc,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( zero_zero_nat
% 8.68/4.87       != ( suc @ M ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2874_Zero__neq__Suc,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( zero_zero_nat
% 8.68/4.87       != ( suc @ M ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2875_Suc__neq__Zero,axiom,
% 8.68/4.87      ! [M: nat] :
% 8.68/4.87        ( ( suc @ M )
% 8.68/4.87       != zero_zero_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2876_zero__induct,axiom,
% 8.68/4.87      ! [P: nat > $o,K: nat] :
% 8.68/4.87        ( ( P @ K )
% 8.68/4.87       => ( ! [N3: nat] :
% 8.68/4.87              ( ( P @ ( suc @ N3 ) )
% 8.68/4.87             => ( P @ N3 ) )
% 8.68/4.87         => ( P @ zero_zero_nat ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2877_diff__induct,axiom,
% 8.68/4.87      ! [P: nat > nat > $o,M: nat,N: nat] :
% 8.68/4.87        ( ! [X6: nat] : ( P @ X6 @ zero_zero_nat )
% 8.68/4.87       => ( ! [Y5: nat] : ( P @ zero_zero_nat @ ( suc @ Y5 ) )
% 8.68/4.87         => ( ! [X6: nat,Y5: nat] :
% 8.68/4.87                ( ( P @ X6 @ Y5 )
% 8.68/4.87               => ( P @ ( suc @ X6 ) @ ( suc @ Y5 ) ) )
% 8.68/4.87           => ( P @ M @ N ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2878_nat__induct,axiom,
% 8.68/4.87      ! [P: nat > $o,N: nat] :
% 8.68/4.87        ( ( P @ zero_zero_nat )
% 8.68/4.87       => ( ! [N3: nat] :
% 8.68/4.87              ( ( P @ N3 )
% 8.68/4.87             => ( P @ ( suc @ N3 ) ) )
% 8.68/4.87         => ( P @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2879_old_Onat_Oexhaust,axiom,
% 8.68/4.87      ! [Y: nat] :
% 8.68/4.87        ( ( Y != zero_zero_nat )
% 8.68/4.87       => ~ ! [Nat3: nat] :
% 8.68/4.87              ( Y
% 8.68/4.87             != ( suc @ Nat3 ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2880_nat_OdiscI,axiom,
% 8.68/4.87      ! [Nat: nat,X22: nat] :
% 8.68/4.87        ( ( Nat
% 8.68/4.87          = ( suc @ X22 ) )
% 8.68/4.87       => ( Nat != zero_zero_nat ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2881_old_Onat_Odistinct_I1_J,axiom,
% 8.68/4.87      ! [Nat2: nat] :
% 8.68/4.87        ( zero_zero_nat
% 8.68/4.87       != ( suc @ Nat2 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2882_old_Onat_Odistinct_I2_J,axiom,
% 8.68/4.87      ! [Nat2: nat] :
% 8.68/4.87        ( ( suc @ Nat2 )
% 8.68/4.87       != zero_zero_nat ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2883_nat_Odistinct_I1_J,axiom,
% 8.68/4.87      ! [X22: nat] :
% 8.68/4.87        ( zero_zero_nat
% 8.68/4.87       != ( suc @ X22 ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2884_not__less__less__Suc__eq,axiom,
% 8.68/4.87      ! [N: nat,M: nat] :
% 8.68/4.87        ( ~ ( ord_less_nat @ N @ M )
% 8.68/4.87       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.68/4.87          = ( N = M ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2885_strict__inc__induct,axiom,
% 8.68/4.87      ! [I: nat,J: nat,P: nat > $o] :
% 8.68/4.87        ( ( ord_less_nat @ I @ J )
% 8.68/4.87       => ( ! [I4: nat] :
% 8.68/4.87              ( ( J
% 8.68/4.87                = ( suc @ I4 ) )
% 8.68/4.87             => ( P @ I4 ) )
% 8.68/4.87         => ( ! [I4: nat] :
% 8.68/4.87                ( ( ord_less_nat @ I4 @ J )
% 8.68/4.87               => ( ( P @ ( suc @ I4 ) )
% 8.68/4.87                 => ( P @ I4 ) ) )
% 8.68/4.87           => ( P @ I ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2886_less__Suc__induct,axiom,
% 8.68/4.87      ! [I: nat,J: nat,P: nat > nat > $o] :
% 8.68/4.87        ( ( ord_less_nat @ I @ J )
% 8.68/4.87       => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 8.68/4.87         => ( ! [I4: nat,J2: nat,K3: nat] :
% 8.68/4.87                ( ( ord_less_nat @ I4 @ J2 )
% 8.68/4.87               => ( ( ord_less_nat @ J2 @ K3 )
% 8.68/4.87                 => ( ( P @ I4 @ J2 )
% 8.68/4.87                   => ( ( P @ J2 @ K3 )
% 8.68/4.87                     => ( P @ I4 @ K3 ) ) ) ) )
% 8.68/4.87           => ( P @ I @ J ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2887_less__trans__Suc,axiom,
% 8.68/4.87      ! [I: nat,J: nat,K: nat] :
% 8.68/4.87        ( ( ord_less_nat @ I @ J )
% 8.68/4.87       => ( ( ord_less_nat @ J @ K )
% 8.68/4.87         => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2888_Suc__less__SucD,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.68/4.87       => ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2889_less__antisym,axiom,
% 8.68/4.87      ! [N: nat,M: nat] :
% 8.68/4.87        ( ~ ( ord_less_nat @ N @ M )
% 8.68/4.87       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.68/4.87         => ( M = N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2890_Suc__less__eq2,axiom,
% 8.68/4.87      ! [N: nat,M: nat] :
% 8.68/4.87        ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.68/4.87        = ( ? [M6: nat] :
% 8.68/4.87              ( ( M
% 8.68/4.87                = ( suc @ M6 ) )
% 8.68/4.87              & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2891_All__less__Suc,axiom,
% 8.68/4.87      ! [N: nat,P: nat > $o] :
% 8.68/4.87        ( ( ! [I5: nat] :
% 8.68/4.87              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 8.68/4.87             => ( P @ I5 ) ) )
% 8.68/4.87        = ( ( P @ N )
% 8.68/4.87          & ! [I5: nat] :
% 8.68/4.87              ( ( ord_less_nat @ I5 @ N )
% 8.68/4.87             => ( P @ I5 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2892_not__less__eq,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ~ ( ord_less_nat @ M @ N ) )
% 8.68/4.87        = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2893_less__Suc__eq,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.68/4.87        = ( ( ord_less_nat @ M @ N )
% 8.68/4.87          | ( M = N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2894_Ex__less__Suc,axiom,
% 8.68/4.87      ! [N: nat,P: nat > $o] :
% 8.68/4.87        ( ( ? [I5: nat] :
% 8.68/4.87              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 8.68/4.87              & ( P @ I5 ) ) )
% 8.68/4.87        = ( ( P @ N )
% 8.68/4.87          | ? [I5: nat] :
% 8.68/4.87              ( ( ord_less_nat @ I5 @ N )
% 8.68/4.87              & ( P @ I5 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2895_less__SucI,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ M @ N )
% 8.68/4.87       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2896_less__SucE,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.68/4.87       => ( ~ ( ord_less_nat @ M @ N )
% 8.68/4.87         => ( M = N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2897_Suc__lessI,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ M @ N )
% 8.68/4.87       => ( ( ( suc @ M )
% 8.68/4.87           != N )
% 8.68/4.87         => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2898_Suc__lessE,axiom,
% 8.68/4.87      ! [I: nat,K: nat] :
% 8.68/4.87        ( ( ord_less_nat @ ( suc @ I ) @ K )
% 8.68/4.87       => ~ ! [J2: nat] :
% 8.68/4.87              ( ( ord_less_nat @ I @ J2 )
% 8.68/4.87             => ( K
% 8.68/4.87               != ( suc @ J2 ) ) ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2899_Suc__lessD,axiom,
% 8.68/4.87      ! [M: nat,N: nat] :
% 8.68/4.87        ( ( ord_less_nat @ ( suc @ M ) @ N )
% 8.68/4.87       => ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.87  
% 8.68/4.87  thf(fact_2900_Nat_OlessE,axiom,
% 8.68/4.87      ! [I: nat,K: nat] :
% 8.68/4.88        ( ( ord_less_nat @ I @ K )
% 8.68/4.88       => ( ( K
% 8.68/4.88           != ( suc @ I ) )
% 8.68/4.88         => ~ ! [J2: nat] :
% 8.68/4.88                ( ( ord_less_nat @ I @ J2 )
% 8.68/4.88               => ( K
% 8.68/4.88                 != ( suc @ J2 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2901_set__vebt__def,axiom,
% 8.68/4.88      ( vEBT_set_vebt
% 8.68/4.88      = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2902_transitive__stepwise__le,axiom,
% 8.68/4.88      ! [M: nat,N: nat,R4: nat > nat > $o] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88       => ( ! [X6: nat] : ( R4 @ X6 @ X6 )
% 8.68/4.88         => ( ! [X6: nat,Y5: nat,Z5: nat] :
% 8.68/4.88                ( ( R4 @ X6 @ Y5 )
% 8.68/4.88               => ( ( R4 @ Y5 @ Z5 )
% 8.68/4.88                 => ( R4 @ X6 @ Z5 ) ) )
% 8.68/4.88           => ( ! [N3: nat] : ( R4 @ N3 @ ( suc @ N3 ) )
% 8.68/4.88             => ( R4 @ M @ N ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2903_nat__induct__at__least,axiom,
% 8.68/4.88      ! [M: nat,N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88       => ( ( P @ M )
% 8.68/4.88         => ( ! [N3: nat] :
% 8.68/4.88                ( ( ord_less_eq_nat @ M @ N3 )
% 8.68/4.88               => ( ( P @ N3 )
% 8.68/4.88                 => ( P @ ( suc @ N3 ) ) ) )
% 8.68/4.88           => ( P @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2904_full__nat__induct,axiom,
% 8.68/4.88      ! [P: nat > $o,N: nat] :
% 8.68/4.88        ( ! [N3: nat] :
% 8.68/4.88            ( ! [M2: nat] :
% 8.68/4.88                ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 8.68/4.88               => ( P @ M2 ) )
% 8.68/4.88           => ( P @ N3 ) )
% 8.68/4.88       => ( P @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2905_not__less__eq__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 8.68/4.88        = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2906_Suc__n__not__le__n,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2907_le__Suc__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.68/4.88        = ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88          | ( M
% 8.68/4.88            = ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2908_Suc__le__D,axiom,
% 8.68/4.88      ! [N: nat,M7: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
% 8.68/4.88       => ? [M4: nat] :
% 8.68/4.88            ( M7
% 8.68/4.88            = ( suc @ M4 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2909_le__SucI,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88       => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2910_le__SucE,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.68/4.88       => ( ~ ( ord_less_eq_nat @ M @ N )
% 8.68/4.88         => ( M
% 8.68/4.88            = ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2911_Suc__leD,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.68/4.88       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2912_add__Suc__shift,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 8.68/4.88        = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2913_add__Suc,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 8.68/4.88        = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2914_nat__arith_Osuc1,axiom,
% 8.68/4.88      ! [A2: nat,K: nat,A: nat] :
% 8.68/4.88        ( ( A2
% 8.68/4.88          = ( plus_plus_nat @ K @ A ) )
% 8.68/4.88       => ( ( suc @ A2 )
% 8.68/4.88          = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2915_zero__induct__lemma,axiom,
% 8.68/4.88      ! [P: nat > $o,K: nat,I: nat] :
% 8.68/4.88        ( ( P @ K )
% 8.68/4.88       => ( ! [N3: nat] :
% 8.68/4.88              ( ( P @ ( suc @ N3 ) )
% 8.68/4.88             => ( P @ N3 ) )
% 8.68/4.88         => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2916_Suc__mult__cancel1,axiom,
% 8.68/4.88      ! [K: nat,M: nat,N: nat] :
% 8.68/4.88        ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 8.68/4.88          = ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.68/4.88        = ( M = N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2917_numeral__code_I2_J,axiom,
% 8.68/4.88      ! [N: num] :
% 8.68/4.88        ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 8.68/4.88        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2918_numeral__code_I2_J,axiom,
% 8.68/4.88      ! [N: num] :
% 8.68/4.88        ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 8.68/4.88        = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2919_numeral__code_I2_J,axiom,
% 8.68/4.88      ! [N: num] :
% 8.68/4.88        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 8.68/4.88        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2920_numeral__code_I2_J,axiom,
% 8.68/4.88      ! [N: num] :
% 8.68/4.88        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.68/4.88        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2921_numeral__code_I2_J,axiom,
% 8.68/4.88      ! [N: num] :
% 8.68/4.88        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 8.68/4.88        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2922_mod__Suc__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 8.68/4.88        = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2923_mod__Suc__Suc__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 8.68/4.88        = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2924_set__bit__greater__eq,axiom,
% 8.68/4.88      ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2925_power__numeral__even,axiom,
% 8.68/4.88      ! [Z: complex,W: num] :
% 8.68/4.88        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 8.68/4.88        = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2926_power__numeral__even,axiom,
% 8.68/4.88      ! [Z: real,W: num] :
% 8.68/4.88        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 8.68/4.88        = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2927_power__numeral__even,axiom,
% 8.68/4.88      ! [Z: rat,W: num] :
% 8.68/4.88        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 8.68/4.88        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2928_power__numeral__even,axiom,
% 8.68/4.88      ! [Z: nat,W: num] :
% 8.68/4.88        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 8.68/4.88        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2929_power__numeral__even,axiom,
% 8.68/4.88      ! [Z: int,W: num] :
% 8.68/4.88        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 8.68/4.88        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2930_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 8.68/4.88        ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_set_int @ C @ A )
% 8.68/4.88              & ( ord_less_eq_set_int @ B @ D )
% 8.68/4.88              & ( ( ord_less_set_int @ C @ A )
% 8.68/4.88                | ( ord_less_set_int @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2931_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.68/4.88        ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_rat @ C @ A )
% 8.68/4.88              & ( ord_less_eq_rat @ B @ D )
% 8.68/4.88              & ( ( ord_less_rat @ C @ A )
% 8.68/4.88                | ( ord_less_rat @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2932_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: num,B: num,C: num,D: num] :
% 8.68/4.88        ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_num @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_num @ C @ A )
% 8.68/4.88              & ( ord_less_eq_num @ B @ D )
% 8.68/4.88              & ( ( ord_less_num @ C @ A )
% 8.68/4.88                | ( ord_less_num @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_num @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2933_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.68/4.88        ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.88              & ( ord_less_eq_nat @ B @ D )
% 8.68/4.88              & ( ( ord_less_nat @ C @ A )
% 8.68/4.88                | ( ord_less_nat @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2934_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: int,B: int,C: int,D: int] :
% 8.68/4.88        ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_int @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_int @ C @ A )
% 8.68/4.88              & ( ord_less_eq_int @ B @ D )
% 8.68/4.88              & ( ( ord_less_int @ C @ A )
% 8.68/4.88                | ( ord_less_int @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_int @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2935_atLeastatMost__psubset__iff,axiom,
% 8.68/4.88      ! [A: real,B: real,C: real,D: real] :
% 8.68/4.88        ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 8.68/4.88        = ( ( ~ ( ord_less_eq_real @ A @ B )
% 8.68/4.88            | ( ( ord_less_eq_real @ C @ A )
% 8.68/4.88              & ( ord_less_eq_real @ B @ D )
% 8.68/4.88              & ( ( ord_less_real @ C @ A )
% 8.68/4.88                | ( ord_less_real @ B @ D ) ) ) )
% 8.68/4.88          & ( ord_less_eq_real @ C @ D ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2936_ex__nat__less,axiom,
% 8.68/4.88      ! [N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ? [M3: nat] :
% 8.68/4.88              ( ( ord_less_eq_nat @ M3 @ N )
% 8.68/4.88              & ( P @ M3 ) ) )
% 8.68/4.88        = ( ? [X3: nat] :
% 8.68/4.88              ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.68/4.88              & ( P @ X3 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2937_all__nat__less,axiom,
% 8.68/4.88      ! [N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ! [M3: nat] :
% 8.68/4.88              ( ( ord_less_eq_nat @ M3 @ N )
% 8.68/4.88             => ( P @ M3 ) ) )
% 8.68/4.88        = ( ! [X3: nat] :
% 8.68/4.88              ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.68/4.88             => ( P @ X3 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2938_lift__Suc__mono__less__iff,axiom,
% 8.68/4.88      ! [F: nat > real,N: nat,M: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 8.68/4.88          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2939_lift__Suc__mono__less__iff,axiom,
% 8.68/4.88      ! [F: nat > rat,N: nat,M: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 8.68/4.88          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2940_lift__Suc__mono__less__iff,axiom,
% 8.68/4.88      ! [F: nat > num,N: nat,M: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 8.68/4.88          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2941_lift__Suc__mono__less__iff,axiom,
% 8.68/4.88      ! [F: nat > nat,N: nat,M: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 8.68/4.88          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2942_lift__Suc__mono__less__iff,axiom,
% 8.68/4.88      ! [F: nat > int,N: nat,M: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 8.68/4.88          = ( ord_less_nat @ N @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2943_lift__Suc__mono__less,axiom,
% 8.68/4.88      ! [F: nat > real,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2944_lift__Suc__mono__less,axiom,
% 8.68/4.88      ! [F: nat > rat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2945_lift__Suc__mono__less,axiom,
% 8.68/4.88      ! [F: nat > num,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2946_lift__Suc__mono__less,axiom,
% 8.68/4.88      ! [F: nat > nat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2947_lift__Suc__mono__less,axiom,
% 8.68/4.88      ! [F: nat > int,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2948_power__Suc,axiom,
% 8.68/4.88      ! [A: complex,N: nat] :
% 8.68/4.88        ( ( power_power_complex @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2949_power__Suc,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( power_power_real @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2950_power__Suc,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2951_power__Suc,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2952_power__Suc,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( power_power_int @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2953_power__Suc2,axiom,
% 8.68/4.88      ! [A: complex,N: nat] :
% 8.68/4.88        ( ( power_power_complex @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2954_power__Suc2,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( power_power_real @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2955_power__Suc2,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2956_power__Suc2,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2957_power__Suc2,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( power_power_int @ A @ ( suc @ N ) )
% 8.68/4.88        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2958_lift__Suc__antimono__le,axiom,
% 8.68/4.88      ! [F: nat > set_int,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2959_lift__Suc__antimono__le,axiom,
% 8.68/4.88      ! [F: nat > rat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2960_lift__Suc__antimono__le,axiom,
% 8.68/4.88      ! [F: nat > num,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2961_lift__Suc__antimono__le,axiom,
% 8.68/4.88      ! [F: nat > nat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2962_lift__Suc__antimono__le,axiom,
% 8.68/4.88      ! [F: nat > int,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2963_lift__Suc__mono__le,axiom,
% 8.68/4.88      ! [F: nat > set_int,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2964_lift__Suc__mono__le,axiom,
% 8.68/4.88      ! [F: nat > rat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2965_lift__Suc__mono__le,axiom,
% 8.68/4.88      ! [F: nat > num,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2966_lift__Suc__mono__le,axiom,
% 8.68/4.88      ! [F: nat > nat,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2967_lift__Suc__mono__le,axiom,
% 8.68/4.88      ! [F: nat > int,N: nat,N5: nat] :
% 8.68/4.88        ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ N5 )
% 8.68/4.88         => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2968_less__Suc__eq__0__disj,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.68/4.88        = ( ( M = zero_zero_nat )
% 8.68/4.88          | ? [J3: nat] :
% 8.68/4.88              ( ( M
% 8.68/4.88                = ( suc @ J3 ) )
% 8.68/4.88              & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2969_gr0__implies__Suc,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ? [M4: nat] :
% 8.68/4.88            ( N
% 8.68/4.88            = ( suc @ M4 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2970_All__less__Suc2,axiom,
% 8.68/4.88      ! [N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ! [I5: nat] :
% 8.68/4.88              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 8.68/4.88             => ( P @ I5 ) ) )
% 8.68/4.88        = ( ( P @ zero_zero_nat )
% 8.68/4.88          & ! [I5: nat] :
% 8.68/4.88              ( ( ord_less_nat @ I5 @ N )
% 8.68/4.88             => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2971_gr0__conv__Suc,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88        = ( ? [M3: nat] :
% 8.68/4.88              ( N
% 8.68/4.88              = ( suc @ M3 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2972_Ex__less__Suc2,axiom,
% 8.68/4.88      ! [N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ? [I5: nat] :
% 8.68/4.88              ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 8.68/4.88              & ( P @ I5 ) ) )
% 8.68/4.88        = ( ( P @ zero_zero_nat )
% 8.68/4.88          | ? [I5: nat] :
% 8.68/4.88              ( ( ord_less_nat @ I5 @ N )
% 8.68/4.88              & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2973_Suc__leI,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ M @ N )
% 8.68/4.88       => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2974_Suc__le__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.68/4.88        = ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2975_dec__induct,axiom,
% 8.68/4.88      ! [I: nat,J: nat,P: nat > $o] :
% 8.68/4.88        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.88       => ( ( P @ I )
% 8.68/4.88         => ( ! [N3: nat] :
% 8.68/4.88                ( ( ord_less_eq_nat @ I @ N3 )
% 8.68/4.88               => ( ( ord_less_nat @ N3 @ J )
% 8.68/4.88                 => ( ( P @ N3 )
% 8.68/4.88                   => ( P @ ( suc @ N3 ) ) ) ) )
% 8.68/4.88           => ( P @ J ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2976_inc__induct,axiom,
% 8.68/4.88      ! [I: nat,J: nat,P: nat > $o] :
% 8.68/4.88        ( ( ord_less_eq_nat @ I @ J )
% 8.68/4.88       => ( ( P @ J )
% 8.68/4.88         => ( ! [N3: nat] :
% 8.68/4.88                ( ( ord_less_eq_nat @ I @ N3 )
% 8.68/4.88               => ( ( ord_less_nat @ N3 @ J )
% 8.68/4.88                 => ( ( P @ ( suc @ N3 ) )
% 8.68/4.88                   => ( P @ N3 ) ) ) )
% 8.68/4.88           => ( P @ I ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2977_Suc__le__lessD,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.68/4.88       => ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2978_le__less__Suc__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88       => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.68/4.88          = ( N = M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2979_less__Suc__eq__le,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ M @ ( suc @ N ) )
% 8.68/4.88        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2980_less__eq__Suc__le,axiom,
% 8.68/4.88      ( ord_less_nat
% 8.68/4.88      = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2981_le__imp__less__Suc,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ M @ N )
% 8.68/4.88       => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2982_add__is__1,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ( plus_plus_nat @ M @ N )
% 8.68/4.88          = ( suc @ zero_zero_nat ) )
% 8.68/4.88        = ( ( ( M
% 8.68/4.88              = ( suc @ zero_zero_nat ) )
% 8.68/4.88            & ( N = zero_zero_nat ) )
% 8.68/4.88          | ( ( M = zero_zero_nat )
% 8.68/4.88            & ( N
% 8.68/4.88              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2983_one__is__add,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ( suc @ zero_zero_nat )
% 8.68/4.88          = ( plus_plus_nat @ M @ N ) )
% 8.68/4.88        = ( ( ( M
% 8.68/4.88              = ( suc @ zero_zero_nat ) )
% 8.68/4.88            & ( N = zero_zero_nat ) )
% 8.68/4.88          | ( ( M = zero_zero_nat )
% 8.68/4.88            & ( N
% 8.68/4.88              = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2984_option_Osize_I4_J,axiom,
% 8.68/4.88      ! [X22: nat] :
% 8.68/4.88        ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 8.68/4.88        = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2985_option_Osize_I4_J,axiom,
% 8.68/4.88      ! [X22: product_prod_nat_nat] :
% 8.68/4.88        ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 8.68/4.88        = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2986_option_Osize_I4_J,axiom,
% 8.68/4.88      ! [X22: num] :
% 8.68/4.88        ( ( size_size_option_num @ ( some_num @ X22 ) )
% 8.68/4.88        = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2987_less__natE,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ M @ N )
% 8.68/4.88       => ~ ! [Q3: nat] :
% 8.68/4.88              ( N
% 8.68/4.88             != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2988_less__add__Suc1,axiom,
% 8.68/4.88      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2989_less__add__Suc2,axiom,
% 8.68/4.88      ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2990_less__iff__Suc__add,axiom,
% 8.68/4.88      ( ord_less_nat
% 8.68/4.88      = ( ^ [M3: nat,N2: nat] :
% 8.68/4.88          ? [K2: nat] :
% 8.68/4.88            ( N2
% 8.68/4.88            = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2991_less__imp__Suc__add,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ M @ N )
% 8.68/4.88       => ? [K3: nat] :
% 8.68/4.88            ( N
% 8.68/4.88            = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2992_option_Osize_I3_J,axiom,
% 8.68/4.88      ( ( size_size_option_nat @ none_nat )
% 8.68/4.88      = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2993_option_Osize_I3_J,axiom,
% 8.68/4.88      ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 8.68/4.88      = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2994_option_Osize_I3_J,axiom,
% 8.68/4.88      ( ( size_size_option_num @ none_num )
% 8.68/4.88      = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2995_diff__less__Suc,axiom,
% 8.68/4.88      ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2996_Suc__diff__Suc,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ N @ M )
% 8.68/4.88       => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 8.68/4.88          = ( minus_minus_nat @ M @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2997_Suc__mult__less__cancel1,axiom,
% 8.68/4.88      ! [K: nat,M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.68/4.88        = ( ord_less_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2998_Suc__diff__le,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.88       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 8.68/4.88          = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_2999_Suc__mult__le__cancel1,axiom,
% 8.68/4.88      ! [K: nat,M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 8.68/4.88        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3000_One__nat__def,axiom,
% 8.68/4.88      ( one_one_nat
% 8.68/4.88      = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3001_Suc__div__le__mono,axiom,
% 8.68/4.88      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3002_mult__Suc,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( times_times_nat @ ( suc @ M ) @ N )
% 8.68/4.88        = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3003_Suc__eq__plus1,axiom,
% 8.68/4.88      ( suc
% 8.68/4.88      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3004_plus__1__eq__Suc,axiom,
% 8.68/4.88      ( ( plus_plus_nat @ one_one_nat )
% 8.68/4.88      = suc ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3005_Suc__eq__plus1__left,axiom,
% 8.68/4.88      ( suc
% 8.68/4.88      = ( plus_plus_nat @ one_one_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3006_diff__Suc__eq__diff__pred,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 8.68/4.88        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3007_mod__Suc,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 8.68/4.88            = N )
% 8.68/4.88         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 8.68/4.88            = zero_zero_nat ) )
% 8.68/4.88        & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 8.68/4.88           != N )
% 8.68/4.88         => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 8.68/4.88            = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3008_mod__induct,axiom,
% 8.68/4.88      ! [P: nat > $o,N: nat,P5: nat,M: nat] :
% 8.68/4.88        ( ( P @ N )
% 8.68/4.88       => ( ( ord_less_nat @ N @ P5 )
% 8.68/4.88         => ( ( ord_less_nat @ M @ P5 )
% 8.68/4.88           => ( ! [N3: nat] :
% 8.68/4.88                  ( ( ord_less_nat @ N3 @ P5 )
% 8.68/4.88                 => ( ( P @ N3 )
% 8.68/4.88                   => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 8.68/4.88             => ( P @ M ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3009_mod__Suc__le__divisor,axiom,
% 8.68/4.88      ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3010_power__inject__base,axiom,
% 8.68/4.88      ! [A: real,N: nat,B: real] :
% 8.68/4.88        ( ( ( power_power_real @ A @ ( suc @ N ) )
% 8.68/4.88          = ( power_power_real @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.88         => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.88           => ( A = B ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3011_power__inject__base,axiom,
% 8.68/4.88      ! [A: rat,N: nat,B: rat] :
% 8.68/4.88        ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.68/4.88          = ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.88         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.88           => ( A = B ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3012_power__inject__base,axiom,
% 8.68/4.88      ! [A: nat,N: nat,B: nat] :
% 8.68/4.88        ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.68/4.88          = ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.88         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.88           => ( A = B ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3013_power__inject__base,axiom,
% 8.68/4.88      ! [A: int,N: nat,B: int] :
% 8.68/4.88        ( ( ( power_power_int @ A @ ( suc @ N ) )
% 8.68/4.88          = ( power_power_int @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.88         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.88           => ( A = B ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3014_power__le__imp__le__base,axiom,
% 8.68/4.88      ! [A: real,N: nat,B: real] :
% 8.68/4.88        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.68/4.88         => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3015_power__le__imp__le__base,axiom,
% 8.68/4.88      ! [A: rat,N: nat,B: rat] :
% 8.68/4.88        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.68/4.88         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3016_power__le__imp__le__base,axiom,
% 8.68/4.88      ! [A: nat,N: nat,B: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.68/4.88         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3017_power__le__imp__le__base,axiom,
% 8.68/4.88      ! [A: int,N: nat,B: int] :
% 8.68/4.88        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 8.68/4.88       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.68/4.88         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3018_power__gt1,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_real @ one_one_real @ A )
% 8.68/4.88       => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3019_power__gt1,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( ord_less_rat @ one_one_rat @ A )
% 8.68/4.88       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3020_power__gt1,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ one_one_nat @ A )
% 8.68/4.88       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3021_power__gt1,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( ord_less_int @ one_one_int @ A )
% 8.68/4.88       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3022_numeral__1__eq__Suc__0,axiom,
% 8.68/4.88      ( ( numeral_numeral_nat @ one )
% 8.68/4.88      = ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3023_ex__least__nat__less,axiom,
% 8.68/4.88      ! [P: nat > $o,N: nat] :
% 8.68/4.88        ( ( P @ N )
% 8.68/4.88       => ( ~ ( P @ zero_zero_nat )
% 8.68/4.88         => ? [K3: nat] :
% 8.68/4.88              ( ( ord_less_nat @ K3 @ N )
% 8.68/4.88              & ! [I2: nat] :
% 8.68/4.88                  ( ( ord_less_eq_nat @ I2 @ K3 )
% 8.68/4.88                 => ~ ( P @ I2 ) )
% 8.68/4.88              & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3024_verit__la__disequality,axiom,
% 8.68/4.88      ! [A: rat,B: rat] :
% 8.68/4.88        ( ( A = B )
% 8.68/4.88        | ~ ( ord_less_eq_rat @ A @ B )
% 8.68/4.88        | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3025_verit__la__disequality,axiom,
% 8.68/4.88      ! [A: num,B: num] :
% 8.68/4.88        ( ( A = B )
% 8.68/4.88        | ~ ( ord_less_eq_num @ A @ B )
% 8.68/4.88        | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3026_verit__la__disequality,axiom,
% 8.68/4.88      ! [A: nat,B: nat] :
% 8.68/4.88        ( ( A = B )
% 8.68/4.88        | ~ ( ord_less_eq_nat @ A @ B )
% 8.68/4.88        | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3027_verit__la__disequality,axiom,
% 8.68/4.88      ! [A: int,B: int] :
% 8.68/4.88        ( ( A = B )
% 8.68/4.88        | ~ ( ord_less_eq_int @ A @ B )
% 8.68/4.88        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3028_verit__comp__simplify1_I2_J,axiom,
% 8.68/4.88      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3029_verit__comp__simplify1_I2_J,axiom,
% 8.68/4.88      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3030_verit__comp__simplify1_I2_J,axiom,
% 8.68/4.88      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3031_verit__comp__simplify1_I2_J,axiom,
% 8.68/4.88      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3032_verit__comp__simplify1_I2_J,axiom,
% 8.68/4.88      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3033_verit__comp__simplify1_I1_J,axiom,
% 8.68/4.88      ! [A: real] :
% 8.68/4.88        ~ ( ord_less_real @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3034_verit__comp__simplify1_I1_J,axiom,
% 8.68/4.88      ! [A: rat] :
% 8.68/4.88        ~ ( ord_less_rat @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3035_verit__comp__simplify1_I1_J,axiom,
% 8.68/4.88      ! [A: num] :
% 8.68/4.88        ~ ( ord_less_num @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3036_verit__comp__simplify1_I1_J,axiom,
% 8.68/4.88      ! [A: nat] :
% 8.68/4.88        ~ ( ord_less_nat @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3037_verit__comp__simplify1_I1_J,axiom,
% 8.68/4.88      ! [A: int] :
% 8.68/4.88        ~ ( ord_less_int @ A @ A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3038_diff__Suc__less,axiom,
% 8.68/4.88      ! [N: nat,I: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3039_n__less__n__mult__m,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.68/4.88         => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3040_n__less__m__mult__n,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.68/4.88         => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3041_one__less__mult,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.68/4.88       => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.68/4.88         => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3042_nat__induct__non__zero,axiom,
% 8.68/4.88      ! [N: nat,P: nat > $o] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ( P @ one_one_nat )
% 8.68/4.88         => ( ! [N3: nat] :
% 8.68/4.88                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.68/4.88               => ( ( P @ N3 )
% 8.68/4.88                 => ( P @ ( suc @ N3 ) ) ) )
% 8.68/4.88           => ( P @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3043_power__gt__expt,axiom,
% 8.68/4.88      ! [N: nat,K: nat] :
% 8.68/4.88        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.68/4.88       => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3044_realpow__pos__nth2,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.88       => ? [R2: real] :
% 8.68/4.88            ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.68/4.88            & ( ( power_power_real @ R2 @ ( suc @ N ) )
% 8.68/4.88              = A ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3045_nat__one__le__power,axiom,
% 8.68/4.88      ! [I: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 8.68/4.88       => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3046_verit__la__generic,axiom,
% 8.68/4.88      ! [A: int,X: int] :
% 8.68/4.88        ( ( ord_less_eq_int @ A @ X )
% 8.68/4.88        | ( A = X )
% 8.68/4.88        | ( ord_less_eq_int @ X @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3047_power__Suc__le__self,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.68/4.88       => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.68/4.88         => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3048_power__Suc__le__self,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.68/4.88       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.68/4.88         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3049_power__Suc__le__self,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.68/4.88       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.68/4.88         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3050_power__Suc__le__self,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.68/4.88       => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.68/4.88         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3051_power__Suc__less__one,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_real @ zero_zero_real @ A )
% 8.68/4.88       => ( ( ord_less_real @ A @ one_one_real )
% 8.68/4.88         => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3052_power__Suc__less__one,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.68/4.88       => ( ( ord_less_rat @ A @ one_one_rat )
% 8.68/4.88         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3053_power__Suc__less__one,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.68/4.88       => ( ( ord_less_nat @ A @ one_one_nat )
% 8.68/4.88         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3054_power__Suc__less__one,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( ord_less_int @ zero_zero_int @ A )
% 8.68/4.88       => ( ( ord_less_int @ A @ one_one_int )
% 8.68/4.88         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3055_numeral__2__eq__2,axiom,
% 8.68/4.88      ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 8.68/4.88      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3056_double__not__eq__Suc__double,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 8.68/4.88       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3057_Suc__double__not__eq__double,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.88       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3058_div__if,axiom,
% 8.68/4.88      ( divide_divide_nat
% 8.68/4.88      = ( ^ [M3: nat,N2: nat] :
% 8.68/4.88            ( if_nat
% 8.68/4.88            @ ( ( ord_less_nat @ M3 @ N2 )
% 8.68/4.88              | ( N2 = zero_zero_nat ) )
% 8.68/4.88            @ zero_zero_nat
% 8.68/4.88            @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3059_div__geq,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ~ ( ord_less_nat @ M @ N )
% 8.68/4.88         => ( ( divide_divide_nat @ M @ N )
% 8.68/4.88            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3060_Suc__diff__eq__diff__pred,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 8.68/4.88          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3061_Suc__pred_H,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( N
% 8.68/4.88          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3062_div__nat__eqI,axiom,
% 8.68/4.88      ! [N: nat,Q2: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 8.68/4.88       => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 8.68/4.88         => ( ( divide_divide_nat @ M @ N )
% 8.68/4.88            = Q2 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3063_add__eq__if,axiom,
% 8.68/4.88      ( plus_plus_nat
% 8.68/4.88      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3064_Suc__nat__number__of__add,axiom,
% 8.68/4.88      ! [V: num,N: nat] :
% 8.68/4.88        ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 8.68/4.88        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3065_set__bit__Suc,axiom,
% 8.68/4.88      ! [N: nat,A: code_integer] :
% 8.68/4.88        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 8.68/4.88        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3066_set__bit__Suc,axiom,
% 8.68/4.88      ! [N: nat,A: int] :
% 8.68/4.88        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 8.68/4.88        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3067_set__bit__Suc,axiom,
% 8.68/4.88      ! [N: nat,A: nat] :
% 8.68/4.88        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 8.68/4.88        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3068_num_Osize_I5_J,axiom,
% 8.68/4.88      ! [X22: num] :
% 8.68/4.88        ( ( size_size_num @ ( bit0 @ X22 ) )
% 8.68/4.88        = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3069_less__2__cases__iff,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.88        = ( ( N = zero_zero_nat )
% 8.68/4.88          | ( N
% 8.68/4.88            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3070_less__2__cases,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.68/4.88       => ( ( N = zero_zero_nat )
% 8.68/4.88          | ( N
% 8.68/4.88            = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3071_le__div__geq,axiom,
% 8.68/4.88      ! [N: nat,M: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ( ord_less_eq_nat @ N @ M )
% 8.68/4.88         => ( ( divide_divide_nat @ M @ N )
% 8.68/4.88            = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3072_split__div_H,axiom,
% 8.68/4.88      ! [P: nat > $o,M: nat,N: nat] :
% 8.68/4.88        ( ( P @ ( divide_divide_nat @ M @ N ) )
% 8.68/4.88        = ( ( ( N = zero_zero_nat )
% 8.68/4.88            & ( P @ zero_zero_nat ) )
% 8.68/4.88          | ? [Q5: nat] :
% 8.68/4.88              ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 8.68/4.88              & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 8.68/4.88              & ( P @ Q5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3073_Suc__times__mod__eq,axiom,
% 8.68/4.88      ! [M: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 8.68/4.88       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 8.68/4.88          = one_one_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3074_power__odd__eq,axiom,
% 8.68/4.88      ! [A: complex,N: nat] :
% 8.68/4.88        ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.68/4.88        = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3075_power__odd__eq,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.68/4.88        = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3076_power__odd__eq,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.68/4.88        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3077_power__odd__eq,axiom,
% 8.68/4.88      ! [A: nat,N: nat] :
% 8.68/4.88        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.68/4.88        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3078_power__odd__eq,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.68/4.88        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3079_nat__bit__induct,axiom,
% 8.68/4.88      ! [P: nat > $o,N: nat] :
% 8.68/4.88        ( ( P @ zero_zero_nat )
% 8.68/4.88       => ( ! [N3: nat] :
% 8.68/4.88              ( ( P @ N3 )
% 8.68/4.88             => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.68/4.88               => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 8.68/4.88         => ( ! [N3: nat] :
% 8.68/4.88                ( ( P @ N3 )
% 8.68/4.88               => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 8.68/4.88           => ( P @ N ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3080_Suc__n__div__2__gt__zero,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3081_div__2__gt__zero,axiom,
% 8.68/4.88      ! [N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.68/4.88       => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3082_verit__comp__simplify1_I3_J,axiom,
% 8.68/4.88      ! [B4: real,A4: real] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 8.68/4.88        = ( ord_less_real @ A4 @ B4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3083_verit__comp__simplify1_I3_J,axiom,
% 8.68/4.88      ! [B4: rat,A4: rat] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 8.68/4.88        = ( ord_less_rat @ A4 @ B4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3084_verit__comp__simplify1_I3_J,axiom,
% 8.68/4.88      ! [B4: num,A4: num] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 8.68/4.88        = ( ord_less_num @ A4 @ B4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3085_verit__comp__simplify1_I3_J,axiom,
% 8.68/4.88      ! [B4: nat,A4: nat] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 8.68/4.88        = ( ord_less_nat @ A4 @ B4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3086_verit__comp__simplify1_I3_J,axiom,
% 8.68/4.88      ! [B4: int,A4: int] :
% 8.68/4.88        ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 8.68/4.88        = ( ord_less_int @ A4 @ B4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3087_verit__sum__simplify,axiom,
% 8.68/4.88      ! [A: complex] :
% 8.68/4.88        ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.68/4.88        = A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3088_verit__sum__simplify,axiom,
% 8.68/4.88      ! [A: real] :
% 8.68/4.88        ( ( plus_plus_real @ A @ zero_zero_real )
% 8.68/4.88        = A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3089_verit__sum__simplify,axiom,
% 8.68/4.88      ! [A: rat] :
% 8.68/4.88        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.68/4.88        = A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3090_verit__sum__simplify,axiom,
% 8.68/4.88      ! [A: nat] :
% 8.68/4.88        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.68/4.88        = A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3091_verit__sum__simplify,axiom,
% 8.68/4.88      ! [A: int] :
% 8.68/4.88        ( ( plus_plus_int @ A @ zero_zero_int )
% 8.68/4.88        = A ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3092_verit__eq__simplify_I10_J,axiom,
% 8.68/4.88      ! [X22: num] :
% 8.68/4.88        ( one
% 8.68/4.88       != ( bit0 @ X22 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3093_odd__0__le__power__imp__0__le,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.68/4.88       => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3094_odd__0__le__power__imp__0__le,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.68/4.88       => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3095_odd__0__le__power__imp__0__le,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.68/4.88       => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3096_odd__power__less__zero,axiom,
% 8.68/4.88      ! [A: real,N: nat] :
% 8.68/4.88        ( ( ord_less_real @ A @ zero_zero_real )
% 8.68/4.88       => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3097_odd__power__less__zero,axiom,
% 8.68/4.88      ! [A: rat,N: nat] :
% 8.68/4.88        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.68/4.88       => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3098_odd__power__less__zero,axiom,
% 8.68/4.88      ! [A: int,N: nat] :
% 8.68/4.88        ( ( ord_less_int @ A @ zero_zero_int )
% 8.68/4.88       => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3099_int__power__div__base,axiom,
% 8.68/4.88      ! [M: nat,K: int] :
% 8.68/4.88        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.68/4.88       => ( ( ord_less_int @ zero_zero_int @ K )
% 8.68/4.88         => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 8.68/4.88            = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3100_invar__vebt_Ointros_I3_J,axiom,
% 8.68/4.88      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 8.68/4.88        ( ! [X6: vEBT_VEBT] :
% 8.68/4.88            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.88           => ( vEBT_invar_vebt @ X6 @ N ) )
% 8.68/4.88       => ( ( vEBT_invar_vebt @ Summary @ M )
% 8.68/4.88         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.68/4.88              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.88           => ( ( M
% 8.68/4.88                = ( suc @ N ) )
% 8.68/4.88             => ( ( Deg
% 8.68/4.88                  = ( plus_plus_nat @ N @ M ) )
% 8.68/4.88               => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 8.68/4.88                 => ( ! [X6: vEBT_VEBT] :
% 8.68/4.88                        ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.88                       => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 8.68/4.88                   => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3101_div__less__mono,axiom,
% 8.68/4.88      ! [A2: nat,B3: nat,N: nat] :
% 8.68/4.88        ( ( ord_less_nat @ A2 @ B3 )
% 8.68/4.88       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.68/4.88         => ( ( ( modulo_modulo_nat @ A2 @ N )
% 8.68/4.88              = zero_zero_nat )
% 8.68/4.88           => ( ( ( modulo_modulo_nat @ B3 @ N )
% 8.68/4.88                = zero_zero_nat )
% 8.68/4.88             => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3102_div__mod__decomp,axiom,
% 8.68/4.88      ! [A2: nat,N: nat] :
% 8.68/4.88        ( A2
% 8.68/4.88        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3103_zdiv__mono__strict,axiom,
% 8.68/4.88      ! [A2: int,B3: int,N: int] :
% 8.68/4.88        ( ( ord_less_int @ A2 @ B3 )
% 8.68/4.88       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.68/4.88         => ( ( ( modulo_modulo_int @ A2 @ N )
% 8.68/4.88              = zero_zero_int )
% 8.68/4.88           => ( ( ( modulo_modulo_int @ B3 @ N )
% 8.68/4.88                = zero_zero_int )
% 8.68/4.88             => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3104_div__mod__decomp__int,axiom,
% 8.68/4.88      ! [A2: int,N: int] :
% 8.68/4.88        ( A2
% 8.68/4.88        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3105_invar__vebt_Ointros_I5_J,axiom,
% 8.68/4.88      ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 8.68/4.88        ( ! [X6: vEBT_VEBT] :
% 8.68/4.88            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.88           => ( vEBT_invar_vebt @ X6 @ N ) )
% 8.68/4.88       => ( ( vEBT_invar_vebt @ Summary @ M )
% 8.68/4.88         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.68/4.88              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.88           => ( ( M
% 8.68/4.88                = ( suc @ N ) )
% 8.68/4.88             => ( ( Deg
% 8.68/4.88                  = ( plus_plus_nat @ N @ M ) )
% 8.68/4.88               => ( ! [I4: nat] :
% 8.68/4.88                      ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.88                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 8.68/4.88                        = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 8.68/4.88                 => ( ( ( Mi = Ma )
% 8.68/4.88                     => ! [X6: vEBT_VEBT] :
% 8.68/4.88                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.68/4.88                         => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 8.68/4.88                   => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.68/4.88                     => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.68/4.88                       => ( ( ( Mi != Ma )
% 8.68/4.88                           => ! [I4: nat] :
% 8.68/4.88                                ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.68/4.88                               => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 8.68/4.88                                      = I4 )
% 8.68/4.88                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 8.68/4.88                                  & ! [X6: nat] :
% 8.68/4.88                                      ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 8.68/4.88                                          = I4 )
% 8.68/4.88                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 8.68/4.88                                     => ( ( ord_less_nat @ Mi @ X6 )
% 8.68/4.88                                        & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 8.68/4.88                         => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3106_vebt__delete_Osimps_I7_J,axiom,
% 8.68/4.88      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.88        ( ( ( ( ord_less_nat @ X @ Mi )
% 8.68/4.88            | ( ord_less_nat @ Ma @ X ) )
% 8.68/4.88         => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 8.68/4.88        & ( ~ ( ( ord_less_nat @ X @ Mi )
% 8.68/4.88              | ( ord_less_nat @ Ma @ X ) )
% 8.68/4.88         => ( ( ( ( X = Mi )
% 8.68/4.88                & ( X = Ma ) )
% 8.68/4.88             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88                = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 8.68/4.88            & ( ~ ( ( X = Mi )
% 8.68/4.88                  & ( X = Ma ) )
% 8.68/4.88             => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88                = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.88                  @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                    @ ( vEBT_Node
% 8.68/4.88                      @ ( some_P7363390416028606310at_nat
% 8.68/4.88                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.88                          @ ( if_nat
% 8.68/4.88                            @ ( ( ( X = Mi )
% 8.68/4.88                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.88                                  = Ma ) )
% 8.68/4.88                              & ( ( X != Mi )
% 8.68/4.88                               => ( X = Ma ) ) )
% 8.68/4.88                            @ ( if_nat
% 8.68/4.88                              @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                = none_nat )
% 8.68/4.88                              @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.88                              @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88                            @ Ma ) ) )
% 8.68/4.88                      @ ( suc @ ( suc @ Va ) )
% 8.68/4.88                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                      @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                    @ ( vEBT_Node
% 8.68/4.88                      @ ( some_P7363390416028606310at_nat
% 8.68/4.88                        @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.68/4.88                          @ ( if_nat
% 8.68/4.88                            @ ( ( ( X = Mi )
% 8.68/4.88                               => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.68/4.88                                  = Ma ) )
% 8.68/4.88                              & ( ( X != Mi )
% 8.68/4.88                               => ( X = Ma ) ) )
% 8.68/4.88                            @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                            @ Ma ) ) )
% 8.68/4.88                      @ ( suc @ ( suc @ Va ) )
% 8.68/4.88                      @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                      @ Summary ) )
% 8.68/4.88                  @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3107_vebt__pred_Osimps_I7_J,axiom,
% 8.68/4.88      ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.88        ( ( ( ord_less_nat @ Ma @ X )
% 8.68/4.88         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88            = ( some_nat @ Ma ) ) )
% 8.68/4.88        & ( ~ ( ord_less_nat @ Ma @ X )
% 8.68/4.88         => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.88              @ ( if_option_nat
% 8.68/4.88                @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                   != none_nat )
% 8.68/4.88                  & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                @ ( if_option_nat
% 8.68/4.88                  @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.88                    = none_nat )
% 8.68/4.88                  @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.68/4.88                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88              @ none_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3108_vebt__succ_Osimps_I6_J,axiom,
% 8.68/4.88      ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.68/4.88        ( ( ( ord_less_nat @ X @ Mi )
% 8.68/4.88         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88            = ( some_nat @ Mi ) ) )
% 8.68/4.88        & ( ~ ( ord_less_nat @ X @ Mi )
% 8.68/4.88         => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88            = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.88              @ ( if_option_nat
% 8.68/4.88                @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                   != none_nat )
% 8.68/4.88                  & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                @ ( if_option_nat
% 8.68/4.88                  @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.88                    = none_nat )
% 8.68/4.88                  @ none_nat
% 8.68/4.88                  @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88              @ none_nat ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3109_vebt__insert_Osimps_I5_J,axiom,
% 8.68/4.88      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88        = ( if_VEBT_VEBT
% 8.68/4.88          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.88            & ~ ( ( X = Mi )
% 8.68/4.88                | ( X = Ma ) ) )
% 8.68/4.88          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 8.68/4.88          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3110_vebt__member_Osimps_I5_J,axiom,
% 8.68/4.88      ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88        = ( ( X != Mi )
% 8.68/4.88         => ( ( X != Ma )
% 8.68/4.88           => ( ~ ( ord_less_nat @ X @ Mi )
% 8.68/4.88              & ( ~ ( ord_less_nat @ X @ Mi )
% 8.68/4.88               => ( ~ ( ord_less_nat @ Ma @ X )
% 8.68/4.88                  & ( ~ ( ord_less_nat @ Ma @ X )
% 8.68/4.88                   => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.88                       => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                      & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3111_vebt__insert_Osimps_I4_J,axiom,
% 8.68/4.88      ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 8.68/4.88        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3112_vebt__pred_Osimps_I6_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 8.68/4.88        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3113_vebt__succ_Osimps_I5_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 8.68/4.88        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3114_vebt__delete_Osimps_I6_J,axiom,
% 8.68/4.88      ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 8.68/4.88        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3115_vebt__insert_Osimps_I2_J,axiom,
% 8.68/4.88      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 8.68/4.88        = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3116_vebt__delete_Osimps_I4_J,axiom,
% 8.68/4.88      ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu )
% 8.68/4.88        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3117_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 8.68/4.88      ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 8.68/4.88        ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3118_vebt__member_Osimps_I2_J,axiom,
% 8.68/4.88      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 8.68/4.88        ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3119_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 8.68/4.88      ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3120_is__pred__in__set__def,axiom,
% 8.68/4.88      ( vEBT_is_pred_in_set
% 8.68/4.88      = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 8.68/4.88            ( ( member_nat @ Y3 @ Xs2 )
% 8.68/4.88            & ( ord_less_nat @ Y3 @ X3 )
% 8.68/4.88            & ! [Z3: nat] :
% 8.68/4.88                ( ( member_nat @ Z3 @ Xs2 )
% 8.68/4.88               => ( ( ord_less_nat @ Z3 @ X3 )
% 8.68/4.88                 => ( ord_less_eq_nat @ Z3 @ Y3 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3121_is__succ__in__set__def,axiom,
% 8.68/4.88      ( vEBT_is_succ_in_set
% 8.68/4.88      = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 8.68/4.88            ( ( member_nat @ Y3 @ Xs2 )
% 8.68/4.88            & ( ord_less_nat @ X3 @ Y3 )
% 8.68/4.88            & ! [Z3: nat] :
% 8.68/4.88                ( ( member_nat @ Z3 @ Xs2 )
% 8.68/4.88               => ( ( ord_less_nat @ X3 @ Z3 )
% 8.68/4.88                 => ( ord_less_eq_nat @ Y3 @ Z3 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3122_vebt__insert_Osimps_I3_J,axiom,
% 8.68/4.88      ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 8.68/4.88        = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3123_vebt__member_Osimps_I3_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 8.68/4.88        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3124_vebt__succ_Osimps_I3_J,axiom,
% 8.68/4.88      ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 8.68/4.88        ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3125_vebt__pred_Osimps_I4_J,axiom,
% 8.68/4.88      ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 8.68/4.88        ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3126_vebt__member_Osimps_I4_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 8.68/4.88        ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3127_vebt__delete_Osimps_I5_J,axiom,
% 8.68/4.88      ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 8.68/4.88        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3128_vebt__succ_Osimps_I4_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 8.68/4.88        ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3129_vebt__pred_Osimps_I5_J,axiom,
% 8.68/4.88      ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 8.68/4.88        ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3130_vebt__pred_Oelims,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.68/4.88        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 8.68/4.88          = Y )
% 8.68/4.88       => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.68/4.88                ( X
% 8.68/4.88                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.68/4.88           => ( ( Xa2 = zero_zero_nat )
% 8.68/4.88             => ( Y != none_nat ) ) )
% 8.68/4.88         => ( ! [A5: $o] :
% 8.68/4.88                ( ? [Uw2: $o] :
% 8.68/4.88                    ( X
% 8.68/4.88                    = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 8.68/4.88               => ( ( Xa2
% 8.68/4.88                    = ( suc @ zero_zero_nat ) )
% 8.68/4.88                 => ~ ( ( A5
% 8.68/4.88                       => ( Y
% 8.68/4.88                          = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.88                      & ( ~ A5
% 8.68/4.88                       => ( Y = none_nat ) ) ) ) )
% 8.68/4.88           => ( ! [A5: $o,B5: $o] :
% 8.68/4.88                  ( ( X
% 8.68/4.88                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.88                 => ( ? [Va2: nat] :
% 8.68/4.88                        ( Xa2
% 8.68/4.88                        = ( suc @ ( suc @ Va2 ) ) )
% 8.68/4.88                   => ~ ( ( B5
% 8.68/4.88                         => ( Y
% 8.68/4.88                            = ( some_nat @ one_one_nat ) ) )
% 8.68/4.88                        & ( ~ B5
% 8.68/4.88                         => ( ( A5
% 8.68/4.88                             => ( Y
% 8.68/4.88                                = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.88                            & ( ~ A5
% 8.68/4.88                             => ( Y = none_nat ) ) ) ) ) ) )
% 8.68/4.88             => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 8.68/4.88                      ( X
% 8.68/4.88                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 8.68/4.88                 => ( Y != none_nat ) )
% 8.68/4.88               => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 8.68/4.88                        ( X
% 8.68/4.88                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 8.68/4.88                   => ( Y != none_nat ) )
% 8.68/4.88                 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 8.68/4.88                          ( X
% 8.68/4.88                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 8.68/4.88                     => ( Y != none_nat ) )
% 8.68/4.88                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.88                          ( ( X
% 8.68/4.88                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.88                         => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.88                               => ( Y
% 8.68/4.88                                  = ( some_nat @ Ma2 ) ) )
% 8.68/4.88                              & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.88                               => ( Y
% 8.68/4.88                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.88                                    @ ( if_option_nat
% 8.68/4.88                                      @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                         != none_nat )
% 8.68/4.88                                        & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                      @ ( if_option_nat
% 8.68/4.88                                        @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.88                                          = none_nat )
% 8.68/4.88                                        @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 8.68/4.88                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88                                    @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3131_vebt__succ_Oelims,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.68/4.88        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 8.68/4.88          = Y )
% 8.68/4.88       => ( ! [Uu2: $o,B5: $o] :
% 8.68/4.88              ( ( X
% 8.68/4.88                = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 8.68/4.88             => ( ( Xa2 = zero_zero_nat )
% 8.68/4.88               => ~ ( ( B5
% 8.68/4.88                     => ( Y
% 8.68/4.88                        = ( some_nat @ one_one_nat ) ) )
% 8.68/4.88                    & ( ~ B5
% 8.68/4.88                     => ( Y = none_nat ) ) ) ) )
% 8.68/4.88         => ( ( ? [Uv2: $o,Uw2: $o] :
% 8.68/4.88                  ( X
% 8.68/4.88                  = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 8.68/4.88             => ( ? [N3: nat] :
% 8.68/4.88                    ( Xa2
% 8.68/4.88                    = ( suc @ N3 ) )
% 8.68/4.88               => ( Y != none_nat ) ) )
% 8.68/4.88           => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.88                    ( X
% 8.68/4.88                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 8.68/4.88               => ( Y != none_nat ) )
% 8.68/4.88             => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 8.68/4.88                      ( X
% 8.68/4.88                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 8.68/4.88                 => ( Y != none_nat ) )
% 8.68/4.88               => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 8.68/4.88                        ( X
% 8.68/4.88                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 8.68/4.88                   => ( Y != none_nat ) )
% 8.68/4.88                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.88                        ( ( X
% 8.68/4.88                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.88                       => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.88                             => ( Y
% 8.68/4.88                                = ( some_nat @ Mi2 ) ) )
% 8.68/4.88                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.88                             => ( Y
% 8.68/4.88                                = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.88                                  @ ( if_option_nat
% 8.68/4.88                                    @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                       != none_nat )
% 8.68/4.88                                      & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                                    @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                    @ ( if_option_nat
% 8.68/4.88                                      @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.88                                        = none_nat )
% 8.68/4.88                                      @ none_nat
% 8.68/4.88                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88                                  @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3132_vebt__delete_Oelims,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.68/4.88        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 8.68/4.88          = Y )
% 8.68/4.88       => ( ! [A5: $o,B5: $o] :
% 8.68/4.88              ( ( X
% 8.68/4.88                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.88             => ( ( Xa2 = zero_zero_nat )
% 8.68/4.88               => ( Y
% 8.68/4.88                 != ( vEBT_Leaf @ $false @ B5 ) ) ) )
% 8.68/4.88         => ( ! [A5: $o] :
% 8.68/4.88                ( ? [B5: $o] :
% 8.68/4.88                    ( X
% 8.68/4.88                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.88               => ( ( Xa2
% 8.68/4.88                    = ( suc @ zero_zero_nat ) )
% 8.68/4.88                 => ( Y
% 8.68/4.88                   != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 8.68/4.88           => ( ! [A5: $o,B5: $o] :
% 8.68/4.88                  ( ( X
% 8.68/4.88                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.88                 => ( ? [N3: nat] :
% 8.68/4.88                        ( Xa2
% 8.68/4.88                        = ( suc @ ( suc @ N3 ) ) )
% 8.68/4.88                   => ( Y
% 8.68/4.88                     != ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 8.68/4.88             => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.88                    ( ( X
% 8.68/4.88                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.88                   => ( Y
% 8.68/4.88                     != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 8.68/4.88               => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 8.68/4.88                      ( ( X
% 8.68/4.88                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 8.68/4.88                     => ( Y
% 8.68/4.88                       != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 8.68/4.88                 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 8.68/4.88                        ( ( X
% 8.68/4.88                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 8.68/4.88                       => ( Y
% 8.68/4.88                         != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 8.68/4.88                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.88                          ( ( X
% 8.68/4.88                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.88                         => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.88                                  | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.68/4.88                               => ( Y
% 8.68/4.88                                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.68/4.88                              & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.88                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.68/4.88                               => ( ( ( ( Xa2 = Mi2 )
% 8.68/4.88                                      & ( Xa2 = Ma2 ) )
% 8.68/4.88                                   => ( Y
% 8.68/4.88                                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.68/4.88                                  & ( ~ ( ( Xa2 = Mi2 )
% 8.68/4.88                                        & ( Xa2 = Ma2 ) )
% 8.68/4.88                                   => ( Y
% 8.68/4.88                                      = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.88                                        @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                          @ ( vEBT_Node
% 8.68/4.88                                            @ ( some_P7363390416028606310at_nat
% 8.68/4.88                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.68/4.88                                                @ ( if_nat
% 8.68/4.88                                                  @ ( ( ( Xa2 = Mi2 )
% 8.68/4.88                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.68/4.88                                                        = Ma2 ) )
% 8.68/4.88                                                    & ( ( Xa2 != Mi2 )
% 8.68/4.88                                                     => ( Xa2 = Ma2 ) ) )
% 8.68/4.88                                                  @ ( if_nat
% 8.68/4.88                                                    @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                                      = none_nat )
% 8.68/4.88                                                    @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.68/4.88                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.88                                                  @ Ma2 ) ) )
% 8.68/4.88                                            @ ( suc @ ( suc @ Va2 ) )
% 8.68/4.88                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                            @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                          @ ( vEBT_Node
% 8.68/4.88                                            @ ( some_P7363390416028606310at_nat
% 8.68/4.88                                              @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.68/4.88                                                @ ( if_nat
% 8.68/4.88                                                  @ ( ( ( Xa2 = Mi2 )
% 8.68/4.88                                                     => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.68/4.88                                                        = Ma2 ) )
% 8.68/4.88                                                    & ( ( Xa2 != Mi2 )
% 8.68/4.88                                                     => ( Xa2 = Ma2 ) ) )
% 8.68/4.88                                                  @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.88                                                  @ Ma2 ) ) )
% 8.68/4.88                                            @ ( suc @ ( suc @ Va2 ) )
% 8.68/4.88                                            @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.88                                            @ Summary2 ) )
% 8.68/4.88                                        @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3133_cppi,axiom,
% 8.68/4.88      ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 8.68/4.88        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.88             => ( ( P @ X6 )
% 8.68/4.88                = ( P6 @ X6 ) ) )
% 8.68/4.88         => ( ! [X6: int] :
% 8.68/4.88                ( ! [Xa: int] :
% 8.68/4.88                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                   => ! [Xb: int] :
% 8.68/4.88                        ( ( member_int @ Xb @ A2 )
% 8.68/4.88                       => ( X6
% 8.68/4.88                         != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 8.68/4.88               => ( ( P @ X6 )
% 8.68/4.88                 => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 8.68/4.88           => ( ! [X6: int,K3: int] :
% 8.68/4.88                  ( ( P6 @ X6 )
% 8.68/4.88                  = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.88             => ( ( ? [X2: int] : ( P @ X2 ) )
% 8.68/4.88                = ( ? [X3: int] :
% 8.68/4.88                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                      & ( P6 @ X3 ) )
% 8.68/4.88                  | ? [X3: int] :
% 8.68/4.88                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                      & ? [Y3: int] :
% 8.68/4.88                          ( ( member_int @ Y3 @ A2 )
% 8.68/4.88                          & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3134_cpmi,axiom,
% 8.68/4.88      ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 8.68/4.88        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.88             => ( ( P @ X6 )
% 8.68/4.88                = ( P6 @ X6 ) ) )
% 8.68/4.88         => ( ! [X6: int] :
% 8.68/4.88                ( ! [Xa: int] :
% 8.68/4.88                    ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                   => ! [Xb: int] :
% 8.68/4.88                        ( ( member_int @ Xb @ B3 )
% 8.68/4.88                       => ( X6
% 8.68/4.88                         != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 8.68/4.88               => ( ( P @ X6 )
% 8.68/4.88                 => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 8.68/4.88           => ( ! [X6: int,K3: int] :
% 8.68/4.88                  ( ( P6 @ X6 )
% 8.68/4.88                  = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.88             => ( ( ? [X2: int] : ( P @ X2 ) )
% 8.68/4.88                = ( ? [X3: int] :
% 8.68/4.88                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                      & ( P6 @ X3 ) )
% 8.68/4.88                  | ? [X3: int] :
% 8.68/4.88                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                      & ? [Y3: int] :
% 8.68/4.88                          ( ( member_int @ Y3 @ B3 )
% 8.68/4.88                          & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3135_bset_I6_J,axiom,
% 8.68/4.88      ! [D4: int,B3: set_int,T: int] :
% 8.68/4.88        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.88       => ! [X4: int] :
% 8.68/4.88            ( ! [Xa3: int] :
% 8.68/4.88                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88               => ! [Xb2: int] :
% 8.68/4.88                    ( ( member_int @ Xb2 @ B3 )
% 8.68/4.88                   => ( X4
% 8.68/4.88                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.88           => ( ( ord_less_eq_int @ X4 @ T )
% 8.68/4.88             => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3136_bset_I8_J,axiom,
% 8.68/4.88      ! [D4: int,T: int,B3: set_int] :
% 8.68/4.88        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.88       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 8.68/4.88         => ! [X4: int] :
% 8.68/4.88              ( ! [Xa3: int] :
% 8.68/4.88                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.88                 => ! [Xb2: int] :
% 8.68/4.88                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.88                     => ( X4
% 8.68/4.88                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.88             => ( ( ord_less_eq_int @ T @ X4 )
% 8.68/4.88               => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3137_Leaf__0__not,axiom,
% 8.68/4.88      ! [A: $o,B: $o] :
% 8.68/4.88        ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3138_deg__1__Leafy,axiom,
% 8.68/4.88      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.88        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.88       => ( ( N = one_one_nat )
% 8.68/4.88         => ? [A5: $o,B5: $o] :
% 8.68/4.88              ( T
% 8.68/4.88              = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3139_deg__1__Leaf,axiom,
% 8.68/4.88      ! [T: vEBT_VEBT] :
% 8.68/4.88        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 8.68/4.88       => ? [A5: $o,B5: $o] :
% 8.68/4.88            ( T
% 8.68/4.88            = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3140_deg1Leaf,axiom,
% 8.68/4.88      ! [T: vEBT_VEBT] :
% 8.68/4.88        ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 8.68/4.88        = ( ? [A3: $o,B2: $o] :
% 8.68/4.88              ( T
% 8.68/4.88              = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3141_VEBT_Osize_I4_J,axiom,
% 8.68/4.88      ! [X21: $o,X222: $o] :
% 8.68/4.88        ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 8.68/4.88        = zero_zero_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3142_VEBT_Oexhaust,axiom,
% 8.68/4.88      ! [Y: vEBT_VEBT] :
% 8.68/4.88        ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 8.68/4.88            ( Y
% 8.68/4.88           != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 8.68/4.88       => ~ ! [X212: $o,X223: $o] :
% 8.68/4.88              ( Y
% 8.68/4.88             != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3143_VEBT_Odistinct_I1_J,axiom,
% 8.68/4.88      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 8.68/4.88        ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 8.68/4.88       != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3144_VEBT__internal_Ovalid_H_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 8.68/4.88       => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3145_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 8.68/4.88      vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3146_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 8.68/4.88      ! [Uv: $o] :
% 8.68/4.88        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3147_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 8.68/4.88      ! [Uu: $o] :
% 8.68/4.88        ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3148_vebt__delete_Osimps_I3_J,axiom,
% 8.68/4.88      ! [A: $o,B: $o,N: nat] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 8.68/4.88        = ( vEBT_Leaf @ A @ B ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3149_vebt__delete_Osimps_I1_J,axiom,
% 8.68/4.88      ! [A: $o,B: $o] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 8.68/4.88        = ( vEBT_Leaf @ $false @ B ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3150_vebt__buildup_Osimps_I1_J,axiom,
% 8.68/4.88      ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 8.68/4.88      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3151_VEBT__internal_Onaive__member_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [A5: $o,B5: $o,X6: nat] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 8.68/4.88       => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 8.68/4.88         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X6 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3152_invar__vebt_Ointros_I1_J,axiom,
% 8.68/4.88      ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3153_vebt__delete_Osimps_I2_J,axiom,
% 8.68/4.88      ! [A: $o,B: $o] :
% 8.68/4.88        ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 8.68/4.88        = ( vEBT_Leaf @ A @ $false ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3154_VEBT__internal_OminNull_Ocases,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT] :
% 8.68/4.88        ( ( X
% 8.68/4.88         != ( vEBT_Leaf @ $false @ $false ) )
% 8.68/4.88       => ( ! [Uv2: $o] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.68/4.88         => ( ! [Uu2: $o] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.68/4.88           => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 8.68/4.88             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3155_vebt__member_Osimps_I1_J,axiom,
% 8.68/4.88      ! [A: $o,B: $o,X: nat] :
% 8.68/4.88        ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.68/4.88        = ( ( ( X = zero_zero_nat )
% 8.68/4.88           => A )
% 8.68/4.88          & ( ( X != zero_zero_nat )
% 8.68/4.88           => ( ( ( X = one_one_nat )
% 8.68/4.88               => B )
% 8.68/4.88              & ( X = one_one_nat ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3156_vebt__buildup_Osimps_I2_J,axiom,
% 8.68/4.88      ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 8.68/4.88      = ( vEBT_Leaf @ $false @ $false ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3157_vebt__insert_Osimps_I1_J,axiom,
% 8.68/4.88      ! [X: nat,A: $o,B: $o] :
% 8.68/4.88        ( ( ( X = zero_zero_nat )
% 8.68/4.88         => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.68/4.88            = ( vEBT_Leaf @ $true @ B ) ) )
% 8.68/4.88        & ( ( X != zero_zero_nat )
% 8.68/4.88         => ( ( ( X = one_one_nat )
% 8.68/4.88             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.68/4.88                = ( vEBT_Leaf @ A @ $true ) ) )
% 8.68/4.88            & ( ( X != one_one_nat )
% 8.68/4.88             => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.68/4.88                = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3158_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT] :
% 8.68/4.88        ( ~ ( vEBT_VEBT_minNull @ X )
% 8.68/4.88       => ( ! [Uv2: $o] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.68/4.88         => ( ! [Uu2: $o] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.68/4.88           => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3159_pinf_I1_J,axiom,
% 8.68/4.88      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 8.68/4.88        ( ? [Z4: real] :
% 8.68/4.88          ! [X6: real] :
% 8.68/4.88            ( ( ord_less_real @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: real] :
% 8.68/4.88            ! [X6: real] :
% 8.68/4.88              ( ( ord_less_real @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: real] :
% 8.68/4.88            ! [X4: real] :
% 8.68/4.88              ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3160_pinf_I1_J,axiom,
% 8.68/4.88      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 8.68/4.88        ( ? [Z4: rat] :
% 8.68/4.88          ! [X6: rat] :
% 8.68/4.88            ( ( ord_less_rat @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: rat] :
% 8.68/4.88            ! [X6: rat] :
% 8.68/4.88              ( ( ord_less_rat @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: rat] :
% 8.68/4.88            ! [X4: rat] :
% 8.68/4.88              ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3161_pinf_I1_J,axiom,
% 8.68/4.88      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 8.68/4.88        ( ? [Z4: num] :
% 8.68/4.88          ! [X6: num] :
% 8.68/4.88            ( ( ord_less_num @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: num] :
% 8.68/4.88            ! [X6: num] :
% 8.68/4.88              ( ( ord_less_num @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: num] :
% 8.68/4.88            ! [X4: num] :
% 8.68/4.88              ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3162_pinf_I1_J,axiom,
% 8.68/4.88      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 8.68/4.88        ( ? [Z4: nat] :
% 8.68/4.88          ! [X6: nat] :
% 8.68/4.88            ( ( ord_less_nat @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: nat] :
% 8.68/4.88            ! [X6: nat] :
% 8.68/4.88              ( ( ord_less_nat @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: nat] :
% 8.68/4.88            ! [X4: nat] :
% 8.68/4.88              ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3163_pinf_I1_J,axiom,
% 8.68/4.88      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 8.68/4.88        ( ? [Z4: int] :
% 8.68/4.88          ! [X6: int] :
% 8.68/4.88            ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: int] :
% 8.68/4.88            ! [X4: int] :
% 8.68/4.88              ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3164_pinf_I2_J,axiom,
% 8.68/4.88      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 8.68/4.88        ( ? [Z4: real] :
% 8.68/4.88          ! [X6: real] :
% 8.68/4.88            ( ( ord_less_real @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: real] :
% 8.68/4.88            ! [X6: real] :
% 8.68/4.88              ( ( ord_less_real @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: real] :
% 8.68/4.88            ! [X4: real] :
% 8.68/4.88              ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3165_pinf_I2_J,axiom,
% 8.68/4.88      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 8.68/4.88        ( ? [Z4: rat] :
% 8.68/4.88          ! [X6: rat] :
% 8.68/4.88            ( ( ord_less_rat @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: rat] :
% 8.68/4.88            ! [X6: rat] :
% 8.68/4.88              ( ( ord_less_rat @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: rat] :
% 8.68/4.88            ! [X4: rat] :
% 8.68/4.88              ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3166_pinf_I2_J,axiom,
% 8.68/4.88      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 8.68/4.88        ( ? [Z4: num] :
% 8.68/4.88          ! [X6: num] :
% 8.68/4.88            ( ( ord_less_num @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: num] :
% 8.68/4.88            ! [X6: num] :
% 8.68/4.88              ( ( ord_less_num @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: num] :
% 8.68/4.88            ! [X4: num] :
% 8.68/4.88              ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3167_pinf_I2_J,axiom,
% 8.68/4.88      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 8.68/4.88        ( ? [Z4: nat] :
% 8.68/4.88          ! [X6: nat] :
% 8.68/4.88            ( ( ord_less_nat @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: nat] :
% 8.68/4.88            ! [X6: nat] :
% 8.68/4.88              ( ( ord_less_nat @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: nat] :
% 8.68/4.88            ! [X4: nat] :
% 8.68/4.88              ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3168_pinf_I2_J,axiom,
% 8.68/4.88      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 8.68/4.88        ( ? [Z4: int] :
% 8.68/4.88          ! [X6: int] :
% 8.68/4.88            ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: int] :
% 8.68/4.88            ! [X4: int] :
% 8.68/4.88              ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3169_pinf_I3_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3170_pinf_I3_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3171_pinf_I3_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3172_pinf_I3_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3173_pinf_I3_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3174_pinf_I4_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3175_pinf_I4_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3176_pinf_I4_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3177_pinf_I4_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3178_pinf_I4_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3179_pinf_I5_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_real @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3180_pinf_I5_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3181_pinf_I5_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_num @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3182_pinf_I5_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3183_pinf_I5_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_int @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3184_pinf_I7_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88       => ( ord_less_real @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3185_pinf_I7_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88       => ( ord_less_rat @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3186_pinf_I7_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.88       => ( ord_less_num @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3187_pinf_I7_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.88       => ( ord_less_nat @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3188_pinf_I7_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.88       => ( ord_less_int @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3189_minf_I1_J,axiom,
% 8.68/4.88      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 8.68/4.88        ( ? [Z4: real] :
% 8.68/4.88          ! [X6: real] :
% 8.68/4.88            ( ( ord_less_real @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: real] :
% 8.68/4.88            ! [X6: real] :
% 8.68/4.88              ( ( ord_less_real @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: real] :
% 8.68/4.88            ! [X4: real] :
% 8.68/4.88              ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3190_minf_I1_J,axiom,
% 8.68/4.88      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 8.68/4.88        ( ? [Z4: rat] :
% 8.68/4.88          ! [X6: rat] :
% 8.68/4.88            ( ( ord_less_rat @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: rat] :
% 8.68/4.88            ! [X6: rat] :
% 8.68/4.88              ( ( ord_less_rat @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: rat] :
% 8.68/4.88            ! [X4: rat] :
% 8.68/4.88              ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3191_minf_I1_J,axiom,
% 8.68/4.88      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 8.68/4.88        ( ? [Z4: num] :
% 8.68/4.88          ! [X6: num] :
% 8.68/4.88            ( ( ord_less_num @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: num] :
% 8.68/4.88            ! [X6: num] :
% 8.68/4.88              ( ( ord_less_num @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: num] :
% 8.68/4.88            ! [X4: num] :
% 8.68/4.88              ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3192_minf_I1_J,axiom,
% 8.68/4.88      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 8.68/4.88        ( ? [Z4: nat] :
% 8.68/4.88          ! [X6: nat] :
% 8.68/4.88            ( ( ord_less_nat @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: nat] :
% 8.68/4.88            ! [X6: nat] :
% 8.68/4.88              ( ( ord_less_nat @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: nat] :
% 8.68/4.88            ! [X4: nat] :
% 8.68/4.88              ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3193_minf_I1_J,axiom,
% 8.68/4.88      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 8.68/4.88        ( ? [Z4: int] :
% 8.68/4.88          ! [X6: int] :
% 8.68/4.88            ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: int] :
% 8.68/4.88            ! [X4: int] :
% 8.68/4.88              ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  & ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  & ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3194_minf_I2_J,axiom,
% 8.68/4.88      ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 8.68/4.88        ( ? [Z4: real] :
% 8.68/4.88          ! [X6: real] :
% 8.68/4.88            ( ( ord_less_real @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: real] :
% 8.68/4.88            ! [X6: real] :
% 8.68/4.88              ( ( ord_less_real @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: real] :
% 8.68/4.88            ! [X4: real] :
% 8.68/4.88              ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3195_minf_I2_J,axiom,
% 8.68/4.88      ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 8.68/4.88        ( ? [Z4: rat] :
% 8.68/4.88          ! [X6: rat] :
% 8.68/4.88            ( ( ord_less_rat @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: rat] :
% 8.68/4.88            ! [X6: rat] :
% 8.68/4.88              ( ( ord_less_rat @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: rat] :
% 8.68/4.88            ! [X4: rat] :
% 8.68/4.88              ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3196_minf_I2_J,axiom,
% 8.68/4.88      ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 8.68/4.88        ( ? [Z4: num] :
% 8.68/4.88          ! [X6: num] :
% 8.68/4.88            ( ( ord_less_num @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: num] :
% 8.68/4.88            ! [X6: num] :
% 8.68/4.88              ( ( ord_less_num @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: num] :
% 8.68/4.88            ! [X4: num] :
% 8.68/4.88              ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3197_minf_I2_J,axiom,
% 8.68/4.88      ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 8.68/4.88        ( ? [Z4: nat] :
% 8.68/4.88          ! [X6: nat] :
% 8.68/4.88            ( ( ord_less_nat @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: nat] :
% 8.68/4.88            ! [X6: nat] :
% 8.68/4.88              ( ( ord_less_nat @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: nat] :
% 8.68/4.88            ! [X4: nat] :
% 8.68/4.88              ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3198_minf_I2_J,axiom,
% 8.68/4.88      ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 8.68/4.88        ( ? [Z4: int] :
% 8.68/4.88          ! [X6: int] :
% 8.68/4.88            ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.88           => ( ( P @ X6 )
% 8.68/4.88              = ( P6 @ X6 ) ) )
% 8.68/4.88       => ( ? [Z4: int] :
% 8.68/4.88            ! [X6: int] :
% 8.68/4.88              ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.88             => ( ( Q @ X6 )
% 8.68/4.88                = ( Q6 @ X6 ) ) )
% 8.68/4.88         => ? [Z5: int] :
% 8.68/4.88            ! [X4: int] :
% 8.68/4.88              ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88             => ( ( ( P @ X4 )
% 8.68/4.88                  | ( Q @ X4 ) )
% 8.68/4.88                = ( ( P6 @ X4 )
% 8.68/4.88                  | ( Q6 @ X4 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3199_minf_I3_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3200_minf_I3_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3201_minf_I3_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3202_minf_I3_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3203_minf_I3_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3204_minf_I4_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3205_minf_I4_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3206_minf_I4_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3207_minf_I4_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3208_minf_I4_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88       => ( X4 != T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3209_minf_I5_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88       => ( ord_less_real @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3210_minf_I5_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88       => ( ord_less_rat @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3211_minf_I5_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88       => ( ord_less_num @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3212_minf_I5_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88       => ( ord_less_nat @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3213_minf_I5_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88       => ( ord_less_int @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3214_minf_I7_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.88       => ~ ( ord_less_real @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3215_minf_I7_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.88       => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3216_minf_I7_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.88       => ~ ( ord_less_num @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3217_minf_I7_J,axiom,
% 8.68/4.88      ! [T: nat] :
% 8.68/4.88      ? [Z5: nat] :
% 8.68/4.88      ! [X4: nat] :
% 8.68/4.88        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.88       => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3218_minf_I7_J,axiom,
% 8.68/4.88      ! [T: int] :
% 8.68/4.88      ? [Z5: int] :
% 8.68/4.88      ! [X4: int] :
% 8.68/4.88        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.88       => ~ ( ord_less_int @ T @ X4 ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3219_vebt__succ_Osimps_I2_J,axiom,
% 8.68/4.88      ! [Uv: $o,Uw: $o,N: nat] :
% 8.68/4.88        ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3220_vebt__pred_Osimps_I1_J,axiom,
% 8.68/4.88      ! [Uu: $o,Uv: $o] :
% 8.68/4.88        ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 8.68/4.88        = none_nat ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3221_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT] :
% 8.68/4.88        ( ( vEBT_VEBT_minNull @ X )
% 8.68/4.88       => ( ( X
% 8.68/4.88           != ( vEBT_Leaf @ $false @ $false ) )
% 8.68/4.88         => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3222_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 8.68/4.88      ! [X: vEBT_VEBT,Y: $o] :
% 8.68/4.88        ( ( ( vEBT_VEBT_minNull @ X )
% 8.68/4.88          = Y )
% 8.68/4.88       => ( ( ( X
% 8.68/4.88              = ( vEBT_Leaf @ $false @ $false ) )
% 8.68/4.88           => ~ Y )
% 8.68/4.88         => ( ( ? [Uv2: $o] :
% 8.68/4.88                  ( X
% 8.68/4.88                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.68/4.88             => Y )
% 8.68/4.88           => ( ( ? [Uu2: $o] :
% 8.68/4.88                    ( X
% 8.68/4.88                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.68/4.88               => Y )
% 8.68/4.88             => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.68/4.88                      ( X
% 8.68/4.88                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 8.68/4.88                 => ~ Y )
% 8.68/4.88               => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.68/4.88                        ( X
% 8.68/4.88                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 8.68/4.88                   => Y ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3223_vebt__pred_Osimps_I2_J,axiom,
% 8.68/4.88      ! [A: $o,Uw: $o] :
% 8.68/4.88        ( ( A
% 8.68/4.88         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 8.68/4.88            = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.88        & ( ~ A
% 8.68/4.88         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 8.68/4.88            = none_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3224_vebt__succ_Osimps_I1_J,axiom,
% 8.68/4.88      ! [B: $o,Uu: $o] :
% 8.68/4.88        ( ( B
% 8.68/4.88         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 8.68/4.88            = ( some_nat @ one_one_nat ) ) )
% 8.68/4.88        & ( ~ B
% 8.68/4.88         => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 8.68/4.88            = none_nat ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3225_VEBT__internal_Omembermima_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 8.68/4.88       => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 8.68/4.88         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X6 ) )
% 8.68/4.88           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X6 ) )
% 8.68/4.88             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X6 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3226_vebt__pred_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [Uu2: $o,Uv2: $o] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 8.68/4.88       => ( ! [A5: $o,Uw2: $o] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 8.68/4.88         => ( ! [A5: $o,B5: $o,Va2: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 8.68/4.88           => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 8.68/4.88             => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 8.68/4.88               => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 8.68/4.88                      ( X
% 8.68/4.88                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 8.68/4.88                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                        ( X
% 8.68/4.88                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3227_vebt__succ_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [Uu2: $o,B5: $o] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 8.68/4.88       => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 8.68/4.88         => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 8.68/4.88           => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 8.68/4.88             => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 8.68/4.88               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                      ( X
% 8.68/4.88                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3228_vebt__delete_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [A5: $o,B5: $o] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) )
% 8.68/4.88       => ( ! [A5: $o,B5: $o] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) )
% 8.68/4.88         => ( ! [A5: $o,B5: $o,N3: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 8.68/4.88           => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu2 ) )
% 8.68/4.88             => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X6 ) )
% 8.68/4.88               => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                      ( X
% 8.68/4.88                     != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X6 ) )
% 8.68/4.88                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                        ( X
% 8.68/4.88                       != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3229_vebt__insert_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [A5: $o,B5: $o,X6: nat] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 8.68/4.88       => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X6 ) )
% 8.68/4.88         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X6 ) )
% 8.68/4.88           => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) )
% 8.68/4.88             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3230_vebt__member_Ocases,axiom,
% 8.68/4.88      ! [X: produc9072475918466114483BT_nat] :
% 8.68/4.88        ( ! [A5: $o,B5: $o,X6: nat] :
% 8.68/4.88            ( X
% 8.68/4.88           != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 8.68/4.88       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X6: nat] :
% 8.68/4.88              ( X
% 8.68/4.88             != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X6 ) )
% 8.68/4.88         => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                ( X
% 8.68/4.88               != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X6 ) )
% 8.68/4.88           => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                  ( X
% 8.68/4.88                 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X6 ) )
% 8.68/4.88             => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 8.68/4.88                    ( X
% 8.68/4.88                   != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3231_vebt__pred_Osimps_I3_J,axiom,
% 8.68/4.88      ! [B: $o,A: $o,Va: nat] :
% 8.68/4.88        ( ( B
% 8.68/4.88         => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 8.68/4.88            = ( some_nat @ one_one_nat ) ) )
% 8.68/4.88        & ( ~ B
% 8.68/4.88         => ( ( A
% 8.68/4.88             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 8.68/4.88                = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.88            & ( ~ A
% 8.68/4.88             => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 8.68/4.88                = none_nat ) ) ) ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3232_pinf_I6_J,axiom,
% 8.68/4.88      ! [T: real] :
% 8.68/4.88      ? [Z5: real] :
% 8.68/4.88      ! [X4: real] :
% 8.68/4.88        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3233_pinf_I6_J,axiom,
% 8.68/4.88      ! [T: rat] :
% 8.68/4.88      ? [Z5: rat] :
% 8.68/4.88      ! [X4: rat] :
% 8.68/4.88        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.88       => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 8.68/4.88  
% 8.68/4.88  thf(fact_3234_pinf_I6_J,axiom,
% 8.68/4.88      ! [T: num] :
% 8.68/4.88      ? [Z5: num] :
% 8.68/4.88      ! [X4: num] :
% 8.68/4.88        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.89       => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3235_pinf_I6_J,axiom,
% 8.68/4.89      ! [T: nat] :
% 8.68/4.89      ? [Z5: nat] :
% 8.68/4.89      ! [X4: nat] :
% 8.68/4.89        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.89       => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3236_pinf_I6_J,axiom,
% 8.68/4.89      ! [T: int] :
% 8.68/4.89      ? [Z5: int] :
% 8.68/4.89      ! [X4: int] :
% 8.68/4.89        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.89       => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3237_pinf_I8_J,axiom,
% 8.68/4.89      ! [T: real] :
% 8.68/4.89      ? [Z5: real] :
% 8.68/4.89      ! [X4: real] :
% 8.68/4.89        ( ( ord_less_real @ Z5 @ X4 )
% 8.68/4.89       => ( ord_less_eq_real @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3238_pinf_I8_J,axiom,
% 8.68/4.89      ! [T: rat] :
% 8.68/4.89      ? [Z5: rat] :
% 8.68/4.89      ! [X4: rat] :
% 8.68/4.89        ( ( ord_less_rat @ Z5 @ X4 )
% 8.68/4.89       => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3239_pinf_I8_J,axiom,
% 8.68/4.89      ! [T: num] :
% 8.68/4.89      ? [Z5: num] :
% 8.68/4.89      ! [X4: num] :
% 8.68/4.89        ( ( ord_less_num @ Z5 @ X4 )
% 8.68/4.89       => ( ord_less_eq_num @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3240_pinf_I8_J,axiom,
% 8.68/4.89      ! [T: nat] :
% 8.68/4.89      ? [Z5: nat] :
% 8.68/4.89      ! [X4: nat] :
% 8.68/4.89        ( ( ord_less_nat @ Z5 @ X4 )
% 8.68/4.89       => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3241_pinf_I8_J,axiom,
% 8.68/4.89      ! [T: int] :
% 8.68/4.89      ? [Z5: int] :
% 8.68/4.89      ! [X4: int] :
% 8.68/4.89        ( ( ord_less_int @ Z5 @ X4 )
% 8.68/4.89       => ( ord_less_eq_int @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3242_minf_I6_J,axiom,
% 8.68/4.89      ! [T: real] :
% 8.68/4.89      ? [Z5: real] :
% 8.68/4.89      ! [X4: real] :
% 8.68/4.89        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.89       => ( ord_less_eq_real @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3243_minf_I6_J,axiom,
% 8.68/4.89      ! [T: rat] :
% 8.68/4.89      ? [Z5: rat] :
% 8.68/4.89      ! [X4: rat] :
% 8.68/4.89        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.89       => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3244_minf_I6_J,axiom,
% 8.68/4.89      ! [T: num] :
% 8.68/4.89      ? [Z5: num] :
% 8.68/4.89      ! [X4: num] :
% 8.68/4.89        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.89       => ( ord_less_eq_num @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3245_minf_I6_J,axiom,
% 8.68/4.89      ! [T: nat] :
% 8.68/4.89      ? [Z5: nat] :
% 8.68/4.89      ! [X4: nat] :
% 8.68/4.89        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.89       => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3246_minf_I6_J,axiom,
% 8.68/4.89      ! [T: int] :
% 8.68/4.89      ? [Z5: int] :
% 8.68/4.89      ! [X4: int] :
% 8.68/4.89        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.89       => ( ord_less_eq_int @ X4 @ T ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3247_minf_I8_J,axiom,
% 8.68/4.89      ! [T: real] :
% 8.68/4.89      ? [Z5: real] :
% 8.68/4.89      ! [X4: real] :
% 8.68/4.89        ( ( ord_less_real @ X4 @ Z5 )
% 8.68/4.89       => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3248_minf_I8_J,axiom,
% 8.68/4.89      ! [T: rat] :
% 8.68/4.89      ? [Z5: rat] :
% 8.68/4.89      ! [X4: rat] :
% 8.68/4.89        ( ( ord_less_rat @ X4 @ Z5 )
% 8.68/4.89       => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3249_minf_I8_J,axiom,
% 8.68/4.89      ! [T: num] :
% 8.68/4.89      ? [Z5: num] :
% 8.68/4.89      ! [X4: num] :
% 8.68/4.89        ( ( ord_less_num @ X4 @ Z5 )
% 8.68/4.89       => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3250_minf_I8_J,axiom,
% 8.68/4.89      ! [T: nat] :
% 8.68/4.89      ? [Z5: nat] :
% 8.68/4.89      ! [X4: nat] :
% 8.68/4.89        ( ( ord_less_nat @ X4 @ Z5 )
% 8.68/4.89       => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3251_minf_I8_J,axiom,
% 8.68/4.89      ! [T: int] :
% 8.68/4.89      ? [Z5: int] :
% 8.68/4.89      ! [X4: int] :
% 8.68/4.89        ( ( ord_less_int @ X4 @ Z5 )
% 8.68/4.89       => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3252_inf__period_I1_J,axiom,
% 8.68/4.89      ! [P: real > $o,D4: real,Q: real > $o] :
% 8.68/4.89        ( ! [X6: real,K3: real] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: real,K3: real] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: real,K4: real] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                & ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 8.68/4.89                & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3253_inf__period_I1_J,axiom,
% 8.68/4.89      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 8.68/4.89        ( ! [X6: rat,K3: rat] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: rat,K3: rat] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: rat,K4: rat] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                & ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 8.68/4.89                & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3254_inf__period_I1_J,axiom,
% 8.68/4.89      ! [P: int > $o,D4: int,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int,K3: int] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int,K3: int] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int,K4: int] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                & ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 8.68/4.89                & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3255_inf__period_I2_J,axiom,
% 8.68/4.89      ! [P: real > $o,D4: real,Q: real > $o] :
% 8.68/4.89        ( ! [X6: real,K3: real] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: real,K3: real] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: real,K4: real] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                | ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 8.68/4.89                | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3256_inf__period_I2_J,axiom,
% 8.68/4.89      ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 8.68/4.89        ( ! [X6: rat,K3: rat] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: rat,K3: rat] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: rat,K4: rat] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                | ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 8.68/4.89                | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3257_inf__period_I2_J,axiom,
% 8.68/4.89      ! [P: int > $o,D4: int,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int,K3: int] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89            = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int,K3: int] :
% 8.68/4.89              ( ( Q @ X6 )
% 8.68/4.89              = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int,K4: int] :
% 8.68/4.89              ( ( ( P @ X4 )
% 8.68/4.89                | ( Q @ X4 ) )
% 8.68/4.89              = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 8.68/4.89                | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3258_conj__le__cong,axiom,
% 8.68/4.89      ! [X: int,X5: int,P: $o,P6: $o] :
% 8.68/4.89        ( ( X = X5 )
% 8.68/4.89       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 8.68/4.89           => ( P = P6 ) )
% 8.68/4.89         => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.89              & P )
% 8.68/4.89            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 8.68/4.89              & P6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3259_imp__le__cong,axiom,
% 8.68/4.89      ! [X: int,X5: int,P: $o,P6: $o] :
% 8.68/4.89        ( ( X = X5 )
% 8.68/4.89       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 8.68/4.89           => ( P = P6 ) )
% 8.68/4.89         => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.68/4.89             => P )
% 8.68/4.89            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 8.68/4.89             => P6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3260_bset_I1_J,axiom,
% 8.68/4.89      ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ! [Xa: int] :
% 8.68/4.89                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb: int] :
% 8.68/4.89                    ( ( member_int @ Xb @ B3 )
% 8.68/4.89                   => ( X6
% 8.68/4.89                     != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89           => ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ! [Xa: int] :
% 8.68/4.89                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb: int] :
% 8.68/4.89                      ( ( member_int @ Xb @ B3 )
% 8.68/4.89                     => ( X6
% 8.68/4.89                       != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89             => ( ( Q @ X6 )
% 8.68/4.89               => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ( P @ X4 )
% 8.68/4.89                  & ( Q @ X4 ) )
% 8.68/4.89               => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 8.68/4.89                  & ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3261_bset_I2_J,axiom,
% 8.68/4.89      ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ! [Xa: int] :
% 8.68/4.89                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb: int] :
% 8.68/4.89                    ( ( member_int @ Xb @ B3 )
% 8.68/4.89                   => ( X6
% 8.68/4.89                     != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89           => ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ! [Xa: int] :
% 8.68/4.89                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb: int] :
% 8.68/4.89                      ( ( member_int @ Xb @ B3 )
% 8.68/4.89                     => ( X6
% 8.68/4.89                       != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89             => ( ( Q @ X6 )
% 8.68/4.89               => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ( P @ X4 )
% 8.68/4.89                  | ( Q @ X4 ) )
% 8.68/4.89               => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 8.68/4.89                  | ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3262_aset_I1_J,axiom,
% 8.68/4.89      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ! [Xa: int] :
% 8.68/4.89                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb: int] :
% 8.68/4.89                    ( ( member_int @ Xb @ A2 )
% 8.68/4.89                   => ( X6
% 8.68/4.89                     != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89           => ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ! [Xa: int] :
% 8.68/4.89                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb: int] :
% 8.68/4.89                      ( ( member_int @ Xb @ A2 )
% 8.68/4.89                     => ( X6
% 8.68/4.89                       != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89             => ( ( Q @ X6 )
% 8.68/4.89               => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ( P @ X4 )
% 8.68/4.89                  & ( Q @ X4 ) )
% 8.68/4.89               => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 8.68/4.89                  & ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3263_aset_I2_J,axiom,
% 8.68/4.89      ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ! [Xa: int] :
% 8.68/4.89                ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb: int] :
% 8.68/4.89                    ( ( member_int @ Xb @ A2 )
% 8.68/4.89                   => ( X6
% 8.68/4.89                     != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89           => ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ! [Xa: int] :
% 8.68/4.89                  ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb: int] :
% 8.68/4.89                      ( ( member_int @ Xb @ A2 )
% 8.68/4.89                     => ( X6
% 8.68/4.89                       != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 8.68/4.89             => ( ( Q @ X6 )
% 8.68/4.89               => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ( P @ X4 )
% 8.68/4.89                  | ( Q @ X4 ) )
% 8.68/4.89               => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 8.68/4.89                  | ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3264_plusinfinity,axiom,
% 8.68/4.89      ! [D: int,P6: int > $o,P: int > $o] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D )
% 8.68/4.89       => ( ! [X6: int,K3: int] :
% 8.68/4.89              ( ( P6 @ X6 )
% 8.68/4.89              = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.68/4.89         => ( ? [Z4: int] :
% 8.68/4.89              ! [X6: int] :
% 8.68/4.89                ( ( ord_less_int @ Z4 @ X6 )
% 8.68/4.89               => ( ( P @ X6 )
% 8.68/4.89                  = ( P6 @ X6 ) ) )
% 8.68/4.89           => ( ? [X_12: int] : ( P6 @ X_12 )
% 8.68/4.89             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3265_minusinfinity,axiom,
% 8.68/4.89      ! [D: int,P1: int > $o,P: int > $o] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D )
% 8.68/4.89       => ( ! [X6: int,K3: int] :
% 8.68/4.89              ( ( P1 @ X6 )
% 8.68/4.89              = ( P1 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.68/4.89         => ( ? [Z4: int] :
% 8.68/4.89              ! [X6: int] :
% 8.68/4.89                ( ( ord_less_int @ X6 @ Z4 )
% 8.68/4.89               => ( ( P @ X6 )
% 8.68/4.89                  = ( P1 @ X6 ) ) )
% 8.68/4.89           => ( ? [X_12: int] : ( P1 @ X_12 )
% 8.68/4.89             => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3266_vebt__member_Oelims_I2_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                   => A5 )
% 8.68/4.89                  & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                   => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                       => B5 )
% 8.68/4.89                      & ( Xa2 = one_one_nat ) ) ) ) )
% 8.68/4.89         => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                ( ? [Summary2: vEBT_VEBT] :
% 8.68/4.89                    ( X
% 8.68/4.89                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89               => ~ ( ( Xa2 != Mi2 )
% 8.68/4.89                   => ( ( Xa2 != Ma2 )
% 8.68/4.89                     => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                        & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                         => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                            & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                             => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                                 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3267_vebt__member_Oelims_I3_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                 => A5 )
% 8.68/4.89                & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                 => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                     => B5 )
% 8.68/4.89                    & ( Xa2 = one_one_nat ) ) ) ) )
% 8.68/4.89         => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.68/4.89           => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 8.68/4.89             => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.68/4.89                    ( X
% 8.68/4.89                   != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.68/4.89               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                      ( ? [Summary2: vEBT_VEBT] :
% 8.68/4.89                          ( X
% 8.68/4.89                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                     => ( ( Xa2 != Mi2 )
% 8.68/4.89                       => ( ( Xa2 != Ma2 )
% 8.68/4.89                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3268_vebt__member_Oelims_I1_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.68/4.89        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ( Y
% 8.68/4.89                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                       => A5 )
% 8.68/4.89                      & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                       => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                           => B5 )
% 8.68/4.89                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 8.68/4.89         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.68/4.89             => Y )
% 8.68/4.89           => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                    ( X
% 8.68/4.89                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 8.68/4.89               => Y )
% 8.68/4.89             => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.68/4.89                 => Y )
% 8.68/4.89               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                      ( ? [Summary2: vEBT_VEBT] :
% 8.68/4.89                          ( X
% 8.68/4.89                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                        = ( ~ ( ( Xa2 != Mi2 )
% 8.68/4.89                             => ( ( Xa2 != Ma2 )
% 8.68/4.89                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3269_incr__mult__lemma,axiom,
% 8.68/4.89      ! [D: int,P: int > $o,K: int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( plus_plus_int @ X6 @ D ) ) )
% 8.68/4.89         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.68/4.89           => ! [X4: int] :
% 8.68/4.89                ( ( P @ X4 )
% 8.68/4.89               => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3270_decr__mult__lemma,axiom,
% 8.68/4.89      ! [D: int,P: int > $o,K: int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D )
% 8.68/4.89       => ( ! [X6: int] :
% 8.68/4.89              ( ( P @ X6 )
% 8.68/4.89             => ( P @ ( minus_minus_int @ X6 @ D ) ) )
% 8.68/4.89         => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.68/4.89           => ! [X4: int] :
% 8.68/4.89                ( ( P @ X4 )
% 8.68/4.89               => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3271_periodic__finite__ex,axiom,
% 8.68/4.89      ! [D: int,P: int > $o] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D )
% 8.68/4.89       => ( ! [X6: int,K3: int] :
% 8.68/4.89              ( ( P @ X6 )
% 8.68/4.89              = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 8.68/4.89         => ( ( ? [X2: int] : ( P @ X2 ) )
% 8.68/4.89            = ( ? [X3: int] :
% 8.68/4.89                  ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 8.68/4.89                  & ( P @ X3 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3272_aset_I7_J,axiom,
% 8.68/4.89      ! [D4: int,A2: set_int,T: int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ! [X4: int] :
% 8.68/4.89            ( ! [Xa3: int] :
% 8.68/4.89                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb2: int] :
% 8.68/4.89                    ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                   => ( X4
% 8.68/4.89                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89           => ( ( ord_less_int @ T @ X4 )
% 8.68/4.89             => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3273_aset_I5_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,A2: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ T @ A2 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ord_less_int @ X4 @ T )
% 8.68/4.89               => ( ord_less_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3274_aset_I4_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,A2: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ T @ A2 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( X4 != T )
% 8.68/4.89               => ( ( plus_plus_int @ X4 @ D4 )
% 8.68/4.89                 != T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3275_aset_I3_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,A2: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( X4 = T )
% 8.68/4.89               => ( ( plus_plus_int @ X4 @ D4 )
% 8.68/4.89                  = T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3276_bset_I7_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ T @ B3 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ord_less_int @ T @ X4 )
% 8.68/4.89               => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3277_bset_I5_J,axiom,
% 8.68/4.89      ! [D4: int,B3: set_int,T: int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ! [X4: int] :
% 8.68/4.89            ( ! [Xa3: int] :
% 8.68/4.89                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb2: int] :
% 8.68/4.89                    ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                   => ( X4
% 8.68/4.89                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89           => ( ( ord_less_int @ X4 @ T )
% 8.68/4.89             => ( ord_less_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3278_bset_I4_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ T @ B3 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( X4 != T )
% 8.68/4.89               => ( ( minus_minus_int @ X4 @ D4 )
% 8.68/4.89                 != T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3279_bset_I3_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ B3 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( X4 = T )
% 8.68/4.89               => ( ( minus_minus_int @ X4 @ D4 )
% 8.68/4.89                  = T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3280_invar__vebt_Osimps,axiom,
% 8.68/4.89      ( vEBT_invar_vebt
% 8.68/4.89      = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 8.68/4.89            ( ( ? [A3: $o,B2: $o] :
% 8.68/4.89                  ( A1
% 8.68/4.89                  = ( vEBT_Leaf @ A3 @ B2 ) )
% 8.68/4.89              & ( A22
% 8.68/4.89                = ( suc @ zero_zero_nat ) ) )
% 8.68/4.89            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 8.68/4.89                ( ( A1
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 8.68/4.89                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 8.68/4.89                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.68/4.89                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 8.68/4.89                & ( A22
% 8.68/4.89                  = ( plus_plus_nat @ N2 @ N2 ) )
% 8.68/4.89                & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.68/4.89            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 8.68/4.89                ( ( A1
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 8.68/4.89                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 8.68/4.89                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.68/4.89                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 8.68/4.89                & ( A22
% 8.68/4.89                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 8.68/4.89                & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.68/4.89            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 8.68/4.89                ( ( A1
% 8.68/4.89                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 8.68/4.89                & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 8.68/4.89                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.68/4.89                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 8.68/4.89                & ( A22
% 8.68/4.89                  = ( plus_plus_nat @ N2 @ N2 ) )
% 8.68/4.89                & ! [I5: nat] :
% 8.68/4.89                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 8.68/4.89                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 8.68/4.89                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 8.68/4.89                & ( ( Mi3 = Ma3 )
% 8.68/4.89                 => ! [X3: vEBT_VEBT] :
% 8.68/4.89                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.68/4.89                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.68/4.89                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 8.68/4.89                & ( ( Mi3 != Ma3 )
% 8.68/4.89                 => ! [I5: nat] :
% 8.68/4.89                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 8.68/4.89                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 8.68/4.89                            = I5 )
% 8.68/4.89                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 8.68/4.89                        & ! [X3: nat] :
% 8.68/4.89                            ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 8.68/4.89                                = I5 )
% 8.68/4.89                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 8.68/4.89                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.68/4.89                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 8.68/4.89            | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 8.68/4.89                ( ( A1
% 8.68/4.89                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 8.68/4.89                & ! [X3: vEBT_VEBT] :
% 8.68/4.89                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                   => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 8.68/4.89                & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 8.68/4.89                & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.68/4.89                  = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 8.68/4.89                & ( A22
% 8.68/4.89                  = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 8.68/4.89                & ! [I5: nat] :
% 8.68/4.89                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 8.68/4.89                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 8.68/4.89                      = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 8.68/4.89                & ( ( Mi3 = Ma3 )
% 8.68/4.89                 => ! [X3: vEBT_VEBT] :
% 8.68/4.89                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.68/4.89                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.68/4.89                & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.68/4.89                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 8.68/4.89                & ( ( Mi3 != Ma3 )
% 8.68/4.89                 => ! [I5: nat] :
% 8.68/4.89                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 8.68/4.89                     => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 8.68/4.89                            = I5 )
% 8.68/4.89                         => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 8.68/4.89                        & ! [X3: nat] :
% 8.68/4.89                            ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 8.68/4.89                                = I5 )
% 8.68/4.89                              & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 8.68/4.89                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.68/4.89                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3281_invar__vebt_Ocases,axiom,
% 8.68/4.89      ! [A12: vEBT_VEBT,A23: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ A12 @ A23 )
% 8.68/4.89       => ( ( ? [A5: $o,B5: $o] :
% 8.68/4.89                ( A12
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89           => ( A23
% 8.68/4.89             != ( suc @ zero_zero_nat ) ) )
% 8.68/4.89         => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 8.68/4.89                ( ( A12
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.89               => ( ( A23 = Deg2 )
% 8.68/4.89                 => ( ! [X4: vEBT_VEBT] :
% 8.68/4.89                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                       => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 8.68/4.89                   => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 8.68/4.89                     => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.68/4.89                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                       => ( ( M4 = N3 )
% 8.68/4.89                         => ( ( Deg2
% 8.68/4.89                              = ( plus_plus_nat @ N3 @ M4 ) )
% 8.68/4.89                           => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 8.68/4.89                             => ~ ! [X4: vEBT_VEBT] :
% 8.68/4.89                                    ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                                   => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 8.68/4.89           => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 8.68/4.89                  ( ( A12
% 8.68/4.89                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.89                 => ( ( A23 = Deg2 )
% 8.68/4.89                   => ( ! [X4: vEBT_VEBT] :
% 8.68/4.89                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                         => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 8.68/4.89                     => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 8.68/4.89                       => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.68/4.89                            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                         => ( ( M4
% 8.68/4.89                              = ( suc @ N3 ) )
% 8.68/4.89                           => ( ( Deg2
% 8.68/4.89                                = ( plus_plus_nat @ N3 @ M4 ) )
% 8.68/4.89                             => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 8.68/4.89                               => ~ ! [X4: vEBT_VEBT] :
% 8.68/4.89                                      ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                                     => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 8.68/4.89             => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 8.68/4.89                    ( ( A12
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.89                   => ( ( A23 = Deg2 )
% 8.68/4.89                     => ( ! [X4: vEBT_VEBT] :
% 8.68/4.89                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                           => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 8.68/4.89                       => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 8.68/4.89                         => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.68/4.89                              = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                           => ( ( M4 = N3 )
% 8.68/4.89                             => ( ( Deg2
% 8.68/4.89                                  = ( plus_plus_nat @ N3 @ M4 ) )
% 8.68/4.89                               => ( ! [I2: nat] :
% 8.68/4.89                                      ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 8.68/4.89                                        = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.68/4.89                                 => ( ( ( Mi2 = Ma2 )
% 8.68/4.89                                     => ! [X4: vEBT_VEBT] :
% 8.68/4.89                                          ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                                         => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 8.68/4.89                                   => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 8.68/4.89                                     => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.68/4.89                                       => ~ ( ( Mi2 != Ma2 )
% 8.68/4.89                                           => ! [I2: nat] :
% 8.68/4.89                                                ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                                               => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 8.68/4.89                                                      = I2 )
% 8.68/4.89                                                   => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 8.68/4.89                                                  & ! [X4: nat] :
% 8.68/4.89                                                      ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 8.68/4.89                                                          = I2 )
% 8.68/4.89                                                        & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 8.68/4.89                                                     => ( ( ord_less_nat @ Mi2 @ X4 )
% 8.68/4.89                                                        & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.89               => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 8.68/4.89                      ( ( A12
% 8.68/4.89                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.89                     => ( ( A23 = Deg2 )
% 8.68/4.89                       => ( ! [X4: vEBT_VEBT] :
% 8.68/4.89                              ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                             => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 8.68/4.89                         => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 8.68/4.89                           => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.68/4.89                                = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                             => ( ( M4
% 8.68/4.89                                  = ( suc @ N3 ) )
% 8.68/4.89                               => ( ( Deg2
% 8.68/4.89                                    = ( plus_plus_nat @ N3 @ M4 ) )
% 8.68/4.89                                 => ( ! [I2: nat] :
% 8.68/4.89                                        ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                                       => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 8.68/4.89                                          = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.68/4.89                                   => ( ( ( Mi2 = Ma2 )
% 8.68/4.89                                       => ! [X4: vEBT_VEBT] :
% 8.68/4.89                                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.68/4.89                                           => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 8.68/4.89                                     => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 8.68/4.89                                       => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.68/4.89                                         => ~ ( ( Mi2 != Ma2 )
% 8.68/4.89                                             => ! [I2: nat] :
% 8.68/4.89                                                  ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 8.68/4.89                                                 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 8.68/4.89                                                        = I2 )
% 8.68/4.89                                                     => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 8.68/4.89                                                    & ! [X4: nat] :
% 8.68/4.89                                                        ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 8.68/4.89                                                            = I2 )
% 8.68/4.89                                                          & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 8.68/4.89                                                       => ( ( ord_less_nat @ Mi2 @ X4 )
% 8.68/4.89                                                          & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3282_vebt__insert_Oelims,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.68/4.89        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                   => ( Y
% 8.68/4.89                      = ( vEBT_Leaf @ $true @ B5 ) ) )
% 8.68/4.89                  & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                   => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                       => ( Y
% 8.68/4.89                          = ( vEBT_Leaf @ A5 @ $true ) ) )
% 8.68/4.89                      & ( ( Xa2 != one_one_nat )
% 8.68/4.89                       => ( Y
% 8.68/4.89                          = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 8.68/4.89         => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.68/4.89                ( ( X
% 8.68/4.89                  = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 8.68/4.89               => ( Y
% 8.68/4.89                 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 8.68/4.89           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.68/4.89                  ( ( X
% 8.68/4.89                    = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 8.68/4.89                 => ( Y
% 8.68/4.89                   != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 8.68/4.89             => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.89                    ( ( X
% 8.68/4.89                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                   => ( Y
% 8.68/4.89                     != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.68/4.89               => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.89                      ( ( X
% 8.68/4.89                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                       != ( if_VEBT_VEBT
% 8.68/4.89                          @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                            & ~ ( ( Xa2 = Mi2 )
% 8.68/4.89                                | ( Xa2 = Ma2 ) ) )
% 8.68/4.89                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 8.68/4.89                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3283_aset_I8_J,axiom,
% 8.68/4.89      ! [D4: int,A2: set_int,T: int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ! [X4: int] :
% 8.68/4.89            ( ! [Xa3: int] :
% 8.68/4.89                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89               => ! [Xb2: int] :
% 8.68/4.89                    ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                   => ( X4
% 8.68/4.89                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89           => ( ( ord_less_eq_int @ T @ X4 )
% 8.68/4.89             => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3284_aset_I6_J,axiom,
% 8.68/4.89      ! [D4: int,T: int,A2: set_int] :
% 8.68/4.89        ( ( ord_less_int @ zero_zero_int @ D4 )
% 8.68/4.89       => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 8.68/4.89         => ! [X4: int] :
% 8.68/4.89              ( ! [Xa3: int] :
% 8.68/4.89                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.68/4.89                 => ! [Xb2: int] :
% 8.68/4.89                      ( ( member_int @ Xb2 @ A2 )
% 8.68/4.89                     => ( X4
% 8.68/4.89                       != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.68/4.89             => ( ( ord_less_eq_int @ X4 @ T )
% 8.68/4.89               => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3285_vebt__mint_Oelims,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Y: option_nat] :
% 8.68/4.89        ( ( ( vEBT_vebt_mint @ X )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ~ ( ( A5
% 8.68/4.89                   => ( Y
% 8.68/4.89                      = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89                  & ( ~ A5
% 8.68/4.89                   => ( ( B5
% 8.68/4.89                       => ( Y
% 8.68/4.89                          = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89                      & ( ~ B5
% 8.68/4.89                       => ( Y = none_nat ) ) ) ) ) )
% 8.68/4.89         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.68/4.89             => ( Y != none_nat ) )
% 8.68/4.89           => ~ ! [Mi2: nat] :
% 8.68/4.89                  ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 8.68/4.89                 => ( Y
% 8.68/4.89                   != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3286_vebt__maxt_Oelims,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Y: option_nat] :
% 8.68/4.89        ( ( ( vEBT_vebt_maxt @ X )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ~ ( ( B5
% 8.68/4.89                   => ( Y
% 8.68/4.89                      = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89                  & ( ~ B5
% 8.68/4.89                   => ( ( A5
% 8.68/4.89                       => ( Y
% 8.68/4.89                          = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89                      & ( ~ A5
% 8.68/4.89                       => ( Y = none_nat ) ) ) ) ) )
% 8.68/4.89         => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.68/4.89             => ( Y != none_nat ) )
% 8.68/4.89           => ~ ! [Mi2: nat,Ma2: nat] :
% 8.68/4.89                  ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 8.68/4.89                 => ( Y
% 8.68/4.89                   != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3287_vebt__mint_Osimps_I1_J,axiom,
% 8.68/4.89      ! [A: $o,B: $o] :
% 8.68/4.89        ( ( A
% 8.68/4.89         => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89            = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89        & ( ~ A
% 8.68/4.89         => ( ( B
% 8.68/4.89             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89                = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89            & ( ~ B
% 8.68/4.89             => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89                = none_nat ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3288_vebt__maxt_Osimps_I1_J,axiom,
% 8.68/4.89      ! [B: $o,A: $o] :
% 8.68/4.89        ( ( B
% 8.68/4.89         => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89            = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89        & ( ~ B
% 8.68/4.89         => ( ( A
% 8.68/4.89             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89                = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89            & ( ~ A
% 8.68/4.89             => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.68/4.89                = none_nat ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3289_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.68/4.89        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.68/4.89                ( X
% 8.68/4.89                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.68/4.89           => Y )
% 8.68/4.89         => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 8.68/4.89             => Y )
% 8.68/4.89           => ( ! [Mi2: nat,Ma2: nat] :
% 8.68/4.89                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.68/4.89                 => ( Y
% 8.68/4.89                    = ( ~ ( ( Xa2 = Mi2 )
% 8.68/4.89                          | ( Xa2 = Ma2 ) ) ) ) )
% 8.68/4.89             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                    ( ? [Vc2: vEBT_VEBT] :
% 8.68/4.89                        ( X
% 8.68/4.89                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.68/4.89                   => ( Y
% 8.68/4.89                      = ( ~ ( ( Xa2 = Mi2 )
% 8.68/4.89                            | ( Xa2 = Ma2 )
% 8.68/4.89                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 8.68/4.89               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                      ( ? [Vd2: vEBT_VEBT] :
% 8.68/4.89                          ( X
% 8.68/4.89                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                        = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3290_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.68/4.89       => ( ! [Uu2: $o,Uv2: $o] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.68/4.89         => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 8.68/4.89           => ( ! [Mi2: nat,Ma2: nat] :
% 8.68/4.89                  ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.68/4.89                 => ( ( Xa2 = Mi2 )
% 8.68/4.89                    | ( Xa2 = Ma2 ) ) )
% 8.68/4.89             => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                    ( ? [Vc2: vEBT_VEBT] :
% 8.68/4.89                        ( X
% 8.68/4.89                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.68/4.89                   => ( ( Xa2 = Mi2 )
% 8.68/4.89                      | ( Xa2 = Ma2 )
% 8.68/4.89                      | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 8.68/4.89               => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                      ( ? [Vd2: vEBT_VEBT] :
% 8.68/4.89                          ( X
% 8.68/4.89                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.68/4.89                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                         => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3291_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.68/4.89        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ( Y
% 8.68/4.89                = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                       => A5 )
% 8.68/4.89                      & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                       => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                           => B5 )
% 8.68/4.89                          & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 8.68/4.89         => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 8.68/4.89             => Y )
% 8.68/4.89           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                  ( ? [S3: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.68/4.89                 => ( Y
% 8.68/4.89                    = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3292_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                   => A5 )
% 8.68/4.89                  & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                   => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                       => B5 )
% 8.68/4.89                      & ( Xa2 = one_one_nat ) ) ) ) )
% 8.68/4.89         => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                ( ? [S3: vEBT_VEBT] :
% 8.68/4.89                    ( X
% 8.68/4.89                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.68/4.89               => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3293_buildup__nothing__in__min__max,axiom,
% 8.68/4.89      ! [N: nat,X: nat] :
% 8.68/4.89        ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3294_buildup__nothing__in__leaf,axiom,
% 8.68/4.89      ! [N: nat,X: nat] :
% 8.68/4.89        ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3295_both__member__options__def,axiom,
% 8.68/4.89      ( vEBT_V8194947554948674370ptions
% 8.68/4.89      = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 8.68/4.89            ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 8.68/4.89            | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3296_member__valid__both__member__options,axiom,
% 8.68/4.89      ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ Tree @ N )
% 8.68/4.89       => ( ( vEBT_vebt_member @ Tree @ X )
% 8.68/4.89         => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 8.68/4.89            | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3297_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 8.68/4.89        ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3298_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 8.68/4.89        ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3299_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 8.68/4.89      ! [A: $o,B: $o,X: nat] :
% 8.68/4.89        ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.68/4.89        = ( ( ( X = zero_zero_nat )
% 8.68/4.89           => A )
% 8.68/4.89          & ( ( X != zero_zero_nat )
% 8.68/4.89           => ( ( ( X = one_one_nat )
% 8.68/4.89               => B )
% 8.68/4.89              & ( X = one_one_nat ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3300_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 8.68/4.89      ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 8.68/4.89        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 8.68/4.89        = ( ( X = Mi )
% 8.68/4.89          | ( X = Ma ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3301_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc8306885398267862888on_nat] :
% 8.68/4.89        ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 8.68/4.89         => ~ ! [F2: nat > nat > nat,A5: nat,B5: nat] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3302_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc5542196010084753463at_nat] :
% 8.68/4.89        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 8.68/4.89         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3303_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc1193250871479095198on_num] :
% 8.68/4.89        ( ! [Uu2: num > num > num,Uv2: option_num] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: num > num > num,V2: num] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 8.68/4.89         => ~ ! [F2: num > num > num,A5: num,B5: num] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3304_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc2233624965454879586on_nat] :
% 8.68/4.89        ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 8.68/4.89         => ~ ! [F2: nat > nat > $o,X6: nat,Y5: nat] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X6 ) @ ( some_nat @ Y5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3305_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc5491161045314408544at_nat] :
% 8.68/4.89        ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 8.68/4.89         => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X6: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X6 ) @ ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3306_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.68/4.89      ! [X: produc7036089656553540234on_num] :
% 8.68/4.89        ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 8.68/4.89       => ( ! [Uw2: num > num > $o,V2: num] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 8.68/4.89         => ~ ! [F2: num > num > $o,X6: num,Y5: num] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X6 ) @ ( some_num @ Y5 ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3307_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.68/4.89      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 8.68/4.89        ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 8.68/4.89        = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3308_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.68/4.89      ! [F: num > num > num,A: num,B: num] :
% 8.68/4.89        ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 8.68/4.89        = ( some_num @ ( F @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3309_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.68/4.89      ! [F: nat > nat > nat,A: nat,B: nat] :
% 8.68/4.89        ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 8.68/4.89        = ( some_nat @ ( F @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3310_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 8.68/4.89      ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 8.68/4.89        ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 8.68/4.89        = none_P5556105721700978146at_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3311_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 8.68/4.89      ! [Uu: num > num > num,Uv: option_num] :
% 8.68/4.89        ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 8.68/4.89        = none_num ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3312_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 8.68/4.89      ! [Uu: nat > nat > nat,Uv: option_nat] :
% 8.68/4.89        ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 8.68/4.89        = none_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3313_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 8.68/4.89        ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 8.68/4.89        = none_P5556105721700978146at_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3314_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uw: num > num > num,V: num] :
% 8.68/4.89        ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 8.68/4.89        = none_num ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3315_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uw: nat > nat > nat,V: nat] :
% 8.68/4.89        ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 8.68/4.89        = none_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3316_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.68/4.89      ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb3: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 8.68/4.89        ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb3 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 8.68/4.89           => ( Y != none_P5556105721700978146at_nat ) )
% 8.68/4.89         => ( ( ? [V2: product_prod_nat_nat] :
% 8.68/4.89                  ( Xa2
% 8.68/4.89                  = ( some_P7363390416028606310at_nat @ V2 ) )
% 8.68/4.89             => ( ( Xb3 = none_P5556105721700978146at_nat )
% 8.68/4.89               => ( Y != none_P5556105721700978146at_nat ) ) )
% 8.68/4.89           => ~ ! [A5: product_prod_nat_nat] :
% 8.68/4.89                  ( ( Xa2
% 8.68/4.89                    = ( some_P7363390416028606310at_nat @ A5 ) )
% 8.68/4.89                 => ! [B5: product_prod_nat_nat] :
% 8.68/4.89                      ( ( Xb3
% 8.68/4.89                        = ( some_P7363390416028606310at_nat @ B5 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                       != ( some_P7363390416028606310at_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3317_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.68/4.89      ! [X: num > num > num,Xa2: option_num,Xb3: option_num,Y: option_num] :
% 8.68/4.89        ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb3 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( ( Xa2 = none_num )
% 8.68/4.89           => ( Y != none_num ) )
% 8.68/4.89         => ( ( ? [V2: num] :
% 8.68/4.89                  ( Xa2
% 8.68/4.89                  = ( some_num @ V2 ) )
% 8.68/4.89             => ( ( Xb3 = none_num )
% 8.68/4.89               => ( Y != none_num ) ) )
% 8.68/4.89           => ~ ! [A5: num] :
% 8.68/4.89                  ( ( Xa2
% 8.68/4.89                    = ( some_num @ A5 ) )
% 8.68/4.89                 => ! [B5: num] :
% 8.68/4.89                      ( ( Xb3
% 8.68/4.89                        = ( some_num @ B5 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                       != ( some_num @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3318_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.68/4.89      ! [X: nat > nat > nat,Xa2: option_nat,Xb3: option_nat,Y: option_nat] :
% 8.68/4.89        ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb3 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( ( Xa2 = none_nat )
% 8.68/4.89           => ( Y != none_nat ) )
% 8.68/4.89         => ( ( ? [V2: nat] :
% 8.68/4.89                  ( Xa2
% 8.68/4.89                  = ( some_nat @ V2 ) )
% 8.68/4.89             => ( ( Xb3 = none_nat )
% 8.68/4.89               => ( Y != none_nat ) ) )
% 8.68/4.89           => ~ ! [A5: nat] :
% 8.68/4.89                  ( ( Xa2
% 8.68/4.89                    = ( some_nat @ A5 ) )
% 8.68/4.89                 => ! [B5: nat] :
% 8.68/4.89                      ( ( Xb3
% 8.68/4.89                        = ( some_nat @ B5 ) )
% 8.68/4.89                     => ( Y
% 8.68/4.89                       != ( some_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3319_vebt__maxt_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.68/4.89        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 8.68/4.89        = none_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3320_vebt__mint_Osimps_I2_J,axiom,
% 8.68/4.89      ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.68/4.89        ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 8.68/4.89        = none_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3321_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 8.68/4.89      ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 8.68/4.89        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 8.68/4.89        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.89           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3322_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 8.68/4.89      ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 8.68/4.89        ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X )
% 8.68/4.89        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.89           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89          & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3323_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 8.68/4.89      ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 8.68/4.89        ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 8.68/4.89        = ( ( X = Mi )
% 8.68/4.89          | ( X = Ma )
% 8.68/4.89          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.68/4.89             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89            & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3324_vebt__mint_Ocases,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT] :
% 8.68/4.89        ( ! [A5: $o,B5: $o] :
% 8.68/4.89            ( X
% 8.68/4.89           != ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89       => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89              ( X
% 8.68/4.89             != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.68/4.89         => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3325_vebt__maxt_Osimps_I3_J,axiom,
% 8.68/4.89      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 8.68/4.89        ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 8.68/4.89        = ( some_nat @ Ma ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3326_vebt__mint_Osimps_I3_J,axiom,
% 8.68/4.89      ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 8.68/4.89        ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 8.68/4.89        = ( some_nat @ Mi ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3327_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.68/4.89       => ( ! [Mi2: nat,Ma2: nat] :
% 8.68/4.89              ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.68/4.89                  ( X
% 8.68/4.89                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.68/4.89             => ~ ( ( Xa2 = Mi2 )
% 8.68/4.89                  | ( Xa2 = Ma2 ) ) )
% 8.68/4.89         => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                ( ? [Vc2: vEBT_VEBT] :
% 8.68/4.89                    ( X
% 8.68/4.89                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.68/4.89               => ~ ( ( Xa2 = Mi2 )
% 8.68/4.89                    | ( Xa2 = Ma2 )
% 8.68/4.89                    | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 8.68/4.89           => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                  ( ? [Vd2: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.68/4.89                 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                       => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                      & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3328_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.68/4.89        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.68/4.89       => ( ! [A5: $o,B5: $o] :
% 8.68/4.89              ( ( X
% 8.68/4.89                = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89             => ( ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                 => A5 )
% 8.68/4.89                & ( ( Xa2 != zero_zero_nat )
% 8.68/4.89                 => ( ( ( Xa2 = one_one_nat )
% 8.68/4.89                     => B5 )
% 8.68/4.89                    & ( Xa2 = one_one_nat ) ) ) ) )
% 8.68/4.89         => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.68/4.89                ( X
% 8.68/4.89               != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 8.68/4.89           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 8.68/4.89                  ( ? [S3: vEBT_VEBT] :
% 8.68/4.89                      ( X
% 8.68/4.89                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.68/4.89                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                     => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3329_succ__empty,axiom,
% 8.68/4.89      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.89       => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.68/4.89            = none_nat )
% 8.68/4.89          = ( ( collect_nat
% 8.68/4.89              @ ^ [Y3: nat] :
% 8.68/4.89                  ( ( vEBT_vebt_member @ T @ Y3 )
% 8.68/4.89                  & ( ord_less_nat @ X @ Y3 ) ) )
% 8.68/4.89            = bot_bot_set_nat ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3330_pred__empty,axiom,
% 8.68/4.89      ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.89       => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.68/4.89            = none_nat )
% 8.68/4.89          = ( ( collect_nat
% 8.68/4.89              @ ^ [Y3: nat] :
% 8.68/4.89                  ( ( vEBT_vebt_member @ T @ Y3 )
% 8.68/4.89                  & ( ord_less_nat @ Y3 @ X ) ) )
% 8.68/4.89            = bot_bot_set_nat ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3331_vebt__succ_Opelims,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.68/4.89        ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.68/4.89         => ( ! [Uu2: $o,B5: $o] :
% 8.68/4.89                ( ( X
% 8.68/4.89                  = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 8.68/4.89               => ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                 => ( ( ( B5
% 8.68/4.89                       => ( Y
% 8.68/4.89                          = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89                      & ( ~ B5
% 8.68/4.89                       => ( Y = none_nat ) ) )
% 8.68/4.89                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 8.68/4.89           => ( ! [Uv2: $o,Uw2: $o] :
% 8.68/4.89                  ( ( X
% 8.68/4.89                    = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 8.68/4.89                 => ! [N3: nat] :
% 8.68/4.89                      ( ( Xa2
% 8.68/4.89                        = ( suc @ N3 ) )
% 8.68/4.89                     => ( ( Y = none_nat )
% 8.68/4.89                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 8.68/4.89             => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.68/4.89                    ( ( X
% 8.68/4.89                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 8.68/4.89                   => ( ( Y = none_nat )
% 8.68/4.89                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 8.68/4.89               => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 8.68/4.89                      ( ( X
% 8.68/4.89                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 8.68/4.89                     => ( ( Y = none_nat )
% 8.68/4.89                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 8.68/4.89                 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 8.68/4.89                        ( ( X
% 8.68/4.89                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 8.68/4.89                       => ( ( Y = none_nat )
% 8.68/4.89                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 8.68/4.89                   => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.89                          ( ( X
% 8.68/4.89                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                         => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                               => ( Y
% 8.68/4.89                                  = ( some_nat @ Mi2 ) ) )
% 8.68/4.89                              & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.68/4.89                               => ( Y
% 8.68/4.89                                  = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                                    @ ( if_option_nat
% 8.68/4.89                                      @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                         != none_nat )
% 8.68/4.89                                        & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.89                                      @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                      @ ( if_option_nat
% 8.68/4.89                                        @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.89                                          = none_nat )
% 8.68/4.89                                        @ none_nat
% 8.68/4.89                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.89                                    @ none_nat ) ) ) )
% 8.68/4.89                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3332_psubsetI,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( A2 != B3 )
% 8.68/4.89         => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3333_vebt__pred_Opelims,axiom,
% 8.68/4.89      ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.68/4.89        ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 8.68/4.89          = Y )
% 8.68/4.89       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.68/4.89         => ( ! [Uu2: $o,Uv2: $o] :
% 8.68/4.89                ( ( X
% 8.68/4.89                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.68/4.89               => ( ( Xa2 = zero_zero_nat )
% 8.68/4.89                 => ( ( Y = none_nat )
% 8.68/4.89                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 8.68/4.89           => ( ! [A5: $o,Uw2: $o] :
% 8.68/4.89                  ( ( X
% 8.68/4.89                    = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 8.68/4.89                 => ( ( Xa2
% 8.68/4.89                      = ( suc @ zero_zero_nat ) )
% 8.68/4.89                   => ( ( ( A5
% 8.68/4.89                         => ( Y
% 8.68/4.89                            = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89                        & ( ~ A5
% 8.68/4.89                         => ( Y = none_nat ) ) )
% 8.68/4.89                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 8.68/4.89             => ( ! [A5: $o,B5: $o] :
% 8.68/4.89                    ( ( X
% 8.68/4.89                      = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.89                   => ! [Va2: nat] :
% 8.68/4.89                        ( ( Xa2
% 8.68/4.89                          = ( suc @ ( suc @ Va2 ) ) )
% 8.68/4.89                       => ( ( ( B5
% 8.68/4.89                             => ( Y
% 8.68/4.89                                = ( some_nat @ one_one_nat ) ) )
% 8.68/4.89                            & ( ~ B5
% 8.68/4.89                             => ( ( A5
% 8.68/4.89                                 => ( Y
% 8.68/4.89                                    = ( some_nat @ zero_zero_nat ) ) )
% 8.68/4.89                                & ( ~ A5
% 8.68/4.89                                 => ( Y = none_nat ) ) ) ) )
% 8.68/4.89                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 8.68/4.89               => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 8.68/4.89                      ( ( X
% 8.68/4.89                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 8.68/4.89                     => ( ( Y = none_nat )
% 8.68/4.89                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 8.68/4.89                 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 8.68/4.89                        ( ( X
% 8.68/4.89                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 8.68/4.89                       => ( ( Y = none_nat )
% 8.68/4.89                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 8.68/4.89                   => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 8.68/4.89                          ( ( X
% 8.68/4.89                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 8.68/4.89                         => ( ( Y = none_nat )
% 8.68/4.89                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 8.68/4.89                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.89                            ( ( X
% 8.68/4.89                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.68/4.89                           => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                 => ( Y
% 8.68/4.89                                    = ( some_nat @ Ma2 ) ) )
% 8.68/4.89                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.68/4.89                                 => ( Y
% 8.68/4.89                                    = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.68/4.89                                      @ ( if_option_nat
% 8.68/4.89                                        @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                           != none_nat )
% 8.68/4.89                                          & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.68/4.89                                        @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.68/4.89                                        @ ( if_option_nat
% 8.68/4.89                                          @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.68/4.89                                            = none_nat )
% 8.68/4.89                                          @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 8.68/4.89                                          @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.68/4.89                                      @ none_nat ) ) ) )
% 8.68/4.89                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3334_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le72135733267957522d_enat @ B @ A )
% 8.68/4.89       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3335_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: code_integer,A: code_integer] :
% 8.68/4.89        ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.68/4.89       => ( ( ord_max_Code_integer @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3336_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: real,A: real] :
% 8.68/4.89        ( ( ord_less_real @ B @ A )
% 8.68/4.89       => ( ( ord_max_real @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3337_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_rat @ B @ A )
% 8.68/4.89       => ( ( ord_max_rat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3338_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: num,A: num] :
% 8.68/4.89        ( ( ord_less_num @ B @ A )
% 8.68/4.89       => ( ( ord_max_num @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3339_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_nat @ B @ A )
% 8.68/4.89       => ( ( ord_max_nat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3340_max_Oabsorb3,axiom,
% 8.68/4.89      ! [B: int,A: int] :
% 8.68/4.89        ( ( ord_less_int @ B @ A )
% 8.68/4.89       => ( ( ord_max_int @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3341_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: extended_enat,B: extended_enat] :
% 8.68/4.89        ( ( ord_le72135733267957522d_enat @ A @ B )
% 8.68/4.89       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3342_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: code_integer,B: code_integer] :
% 8.68/4.89        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.68/4.89       => ( ( ord_max_Code_integer @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3343_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: real,B: real] :
% 8.68/4.89        ( ( ord_less_real @ A @ B )
% 8.68/4.89       => ( ( ord_max_real @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3344_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: rat,B: rat] :
% 8.68/4.89        ( ( ord_less_rat @ A @ B )
% 8.68/4.89       => ( ( ord_max_rat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3345_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: num,B: num] :
% 8.68/4.89        ( ( ord_less_num @ A @ B )
% 8.68/4.89       => ( ( ord_max_num @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3346_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: nat,B: nat] :
% 8.68/4.89        ( ( ord_less_nat @ A @ B )
% 8.68/4.89       => ( ( ord_max_nat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3347_max_Oabsorb4,axiom,
% 8.68/4.89      ! [A: int,B: int] :
% 8.68/4.89        ( ( ord_less_int @ A @ B )
% 8.68/4.89       => ( ( ord_max_int @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3348_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 8.68/4.89        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 8.68/4.89          & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3349_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 8.68/4.89        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 8.68/4.89          & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3350_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: real,Y: real,Z: real] :
% 8.68/4.89        ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_less_real @ X @ Z )
% 8.68/4.89          & ( ord_less_real @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3351_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: rat,Y: rat,Z: rat] :
% 8.68/4.89        ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_less_rat @ X @ Z )
% 8.68/4.89          & ( ord_less_rat @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3352_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: num,Y: num,Z: num] :
% 8.68/4.89        ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_less_num @ X @ Z )
% 8.68/4.89          & ( ord_less_num @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3353_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: nat,Y: nat,Z: nat] :
% 8.68/4.89        ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_less_nat @ X @ Z )
% 8.68/4.89          & ( ord_less_nat @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3354_max__less__iff__conj,axiom,
% 8.68/4.89      ! [X: int,Y: int,Z: int] :
% 8.68/4.89        ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 8.68/4.89        = ( ( ord_less_int @ X @ Z )
% 8.68/4.89          & ( ord_less_int @ Y @ Z ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3355_buildup__gives__empty,axiom,
% 8.68/4.89      ! [N: nat] :
% 8.68/4.89        ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 8.68/4.89        = bot_bot_set_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3356_Diff__empty,axiom,
% 8.68/4.89      ! [A2: set_int] :
% 8.68/4.89        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 8.68/4.89        = A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3357_Diff__empty,axiom,
% 8.68/4.89      ! [A2: set_real] :
% 8.68/4.89        ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 8.68/4.89        = A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3358_Diff__empty,axiom,
% 8.68/4.89      ! [A2: set_nat] :
% 8.68/4.89        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 8.68/4.89        = A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3359_empty__Diff,axiom,
% 8.68/4.89      ! [A2: set_int] :
% 8.68/4.89        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 8.68/4.89        = bot_bot_set_int ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3360_empty__Diff,axiom,
% 8.68/4.89      ! [A2: set_real] :
% 8.68/4.89        ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 8.68/4.89        = bot_bot_set_real ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3361_empty__Diff,axiom,
% 8.68/4.89      ! [A2: set_nat] :
% 8.68/4.89        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 8.68/4.89        = bot_bot_set_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3362_Diff__cancel,axiom,
% 8.68/4.89      ! [A2: set_int] :
% 8.68/4.89        ( ( minus_minus_set_int @ A2 @ A2 )
% 8.68/4.89        = bot_bot_set_int ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3363_Diff__cancel,axiom,
% 8.68/4.89      ! [A2: set_real] :
% 8.68/4.89        ( ( minus_minus_set_real @ A2 @ A2 )
% 8.68/4.89        = bot_bot_set_real ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3364_Diff__cancel,axiom,
% 8.68/4.89      ! [A2: set_nat] :
% 8.68/4.89        ( ( minus_minus_set_nat @ A2 @ A2 )
% 8.68/4.89        = bot_bot_set_nat ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3365_subset__antisym,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.68/4.89         => ( A2 = B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3366_subsetI,axiom,
% 8.68/4.89      ! [A2: set_complex,B3: set_complex] :
% 8.68/4.89        ( ! [X6: complex] :
% 8.68/4.89            ( ( member_complex @ X6 @ A2 )
% 8.68/4.89           => ( member_complex @ X6 @ B3 ) )
% 8.68/4.89       => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3367_subsetI,axiom,
% 8.68/4.89      ! [A2: set_real,B3: set_real] :
% 8.68/4.89        ( ! [X6: real] :
% 8.68/4.89            ( ( member_real @ X6 @ A2 )
% 8.68/4.89           => ( member_real @ X6 @ B3 ) )
% 8.68/4.89       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3368_subsetI,axiom,
% 8.68/4.89      ! [A2: set_set_nat,B3: set_set_nat] :
% 8.68/4.89        ( ! [X6: set_nat] :
% 8.68/4.89            ( ( member_set_nat @ X6 @ A2 )
% 8.68/4.89           => ( member_set_nat @ X6 @ B3 ) )
% 8.68/4.89       => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3369_subsetI,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat] :
% 8.68/4.89        ( ! [X6: nat] :
% 8.68/4.89            ( ( member_nat @ X6 @ A2 )
% 8.68/4.89           => ( member_nat @ X6 @ B3 ) )
% 8.68/4.89       => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3370_subsetI,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ( member_int @ X6 @ A2 )
% 8.68/4.89           => ( member_int @ X6 @ B3 ) )
% 8.68/4.89       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3371_maxt__corr__help__empty,axiom,
% 8.68/4.89      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.89       => ( ( ( vEBT_vebt_maxt @ T )
% 8.68/4.89            = none_nat )
% 8.68/4.89         => ( ( vEBT_VEBT_set_vebt @ T )
% 8.68/4.89            = bot_bot_set_nat ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3372_mint__corr__help__empty,axiom,
% 8.68/4.89      ! [T: vEBT_VEBT,N: nat] :
% 8.68/4.89        ( ( vEBT_invar_vebt @ T @ N )
% 8.68/4.89       => ( ( ( vEBT_vebt_mint @ T )
% 8.68/4.89            = none_nat )
% 8.68/4.89         => ( ( vEBT_VEBT_set_vebt @ T )
% 8.68/4.89            = bot_bot_set_nat ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3373_Diff__eq__empty__iff,axiom,
% 8.68/4.89      ! [A2: set_real,B3: set_real] :
% 8.68/4.89        ( ( ( minus_minus_set_real @ A2 @ B3 )
% 8.68/4.89          = bot_bot_set_real )
% 8.68/4.89        = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3374_Diff__eq__empty__iff,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat] :
% 8.68/4.89        ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 8.68/4.89          = bot_bot_set_nat )
% 8.68/4.89        = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3375_Diff__eq__empty__iff,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( ( minus_minus_set_int @ A2 @ B3 )
% 8.68/4.89          = bot_bot_set_int )
% 8.68/4.89        = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3376_empty__subsetI,axiom,
% 8.68/4.89      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3377_empty__subsetI,axiom,
% 8.68/4.89      ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3378_empty__subsetI,axiom,
% 8.68/4.89      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3379_subset__empty,axiom,
% 8.68/4.89      ! [A2: set_nat] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 8.68/4.89        = ( A2 = bot_bot_set_nat ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3380_subset__empty,axiom,
% 8.68/4.89      ! [A2: set_real] :
% 8.68/4.89        ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 8.68/4.89        = ( A2 = bot_bot_set_real ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3381_subset__empty,axiom,
% 8.68/4.89      ! [A2: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 8.68/4.89        = ( A2 = bot_bot_set_int ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3382_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 8.68/4.89          & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3383_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.68/4.89          & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3384_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: rat,C: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.89          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3385_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: num,C: num,A: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_less_eq_num @ B @ A )
% 8.68/4.89          & ( ord_less_eq_num @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3386_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: nat,C: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.89          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3387_max_Obounded__iff,axiom,
% 8.68/4.89      ! [B: int,C: int,A: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 8.68/4.89        = ( ( ord_less_eq_int @ B @ A )
% 8.68/4.89          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3388_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: extended_enat,B: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ A @ B )
% 8.68/4.89       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3389_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: code_integer,B: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.68/4.89       => ( ( ord_max_Code_integer @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3390_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: rat,B: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ A @ B )
% 8.68/4.89       => ( ( ord_max_rat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3391_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: num,B: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ A @ B )
% 8.68/4.89       => ( ( ord_max_num @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3392_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: nat,B: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ A @ B )
% 8.68/4.89       => ( ( ord_max_nat @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3393_max_Oabsorb2,axiom,
% 8.68/4.89      ! [A: int,B: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ A @ B )
% 8.68/4.89       => ( ( ord_max_int @ A @ B )
% 8.68/4.89          = B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3394_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 8.68/4.89       => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3395_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: code_integer,A: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.68/4.89       => ( ( ord_max_Code_integer @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3396_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.89       => ( ( ord_max_rat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3397_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: num,A: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ B @ A )
% 8.68/4.89       => ( ( ord_max_num @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3398_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.89       => ( ( ord_max_nat @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3399_max_Oabsorb1,axiom,
% 8.68/4.89      ! [B: int,A: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.89       => ( ( ord_max_int @ A @ B )
% 8.68/4.89          = A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3400_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: set_int,B: set_int] :
% 8.68/4.89        ( ( bot_bot_set_set_int
% 8.68/4.89          = ( set_or370866239135849197et_int @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3401_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: rat,B: rat] :
% 8.68/4.89        ( ( bot_bot_set_rat
% 8.68/4.89          = ( set_or633870826150836451st_rat @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3402_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: num,B: num] :
% 8.68/4.89        ( ( bot_bot_set_num
% 8.68/4.89          = ( set_or7049704709247886629st_num @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3403_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: nat,B: nat] :
% 8.68/4.89        ( ( bot_bot_set_nat
% 8.68/4.89          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3404_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: int,B: int] :
% 8.68/4.89        ( ( bot_bot_set_int
% 8.68/4.89          = ( set_or1266510415728281911st_int @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3405_atLeastatMost__empty__iff2,axiom,
% 8.68/4.89      ! [A: real,B: real] :
% 8.68/4.89        ( ( bot_bot_set_real
% 8.68/4.89          = ( set_or1222579329274155063t_real @ A @ B ) )
% 8.68/4.89        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3406_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: set_int,B: set_int] :
% 8.68/4.89        ( ( ( set_or370866239135849197et_int @ A @ B )
% 8.68/4.89          = bot_bot_set_set_int )
% 8.68/4.89        = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3407_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: rat,B: rat] :
% 8.68/4.89        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 8.68/4.89          = bot_bot_set_rat )
% 8.68/4.89        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3408_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: num,B: num] :
% 8.68/4.89        ( ( ( set_or7049704709247886629st_num @ A @ B )
% 8.68/4.89          = bot_bot_set_num )
% 8.68/4.89        = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3409_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: nat,B: nat] :
% 8.68/4.89        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.68/4.89          = bot_bot_set_nat )
% 8.68/4.89        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3410_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: int,B: int] :
% 8.68/4.89        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 8.68/4.89          = bot_bot_set_int )
% 8.68/4.89        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3411_atLeastatMost__empty__iff,axiom,
% 8.68/4.89      ! [A: real,B: real] :
% 8.68/4.89        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 8.68/4.89          = bot_bot_set_real )
% 8.68/4.89        = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3412_atLeastatMost__empty,axiom,
% 8.68/4.89      ! [B: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_rat @ B @ A )
% 8.68/4.89       => ( ( set_or633870826150836451st_rat @ A @ B )
% 8.68/4.89          = bot_bot_set_rat ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3413_atLeastatMost__empty,axiom,
% 8.68/4.89      ! [B: num,A: num] :
% 8.68/4.89        ( ( ord_less_num @ B @ A )
% 8.68/4.89       => ( ( set_or7049704709247886629st_num @ A @ B )
% 8.68/4.89          = bot_bot_set_num ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3414_atLeastatMost__empty,axiom,
% 8.68/4.89      ! [B: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_nat @ B @ A )
% 8.68/4.89       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.68/4.89          = bot_bot_set_nat ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3415_atLeastatMost__empty,axiom,
% 8.68/4.89      ! [B: int,A: int] :
% 8.68/4.89        ( ( ord_less_int @ B @ A )
% 8.68/4.89       => ( ( set_or1266510415728281911st_int @ A @ B )
% 8.68/4.89          = bot_bot_set_int ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3416_atLeastatMost__empty,axiom,
% 8.68/4.89      ! [B: real,A: real] :
% 8.68/4.89        ( ( ord_less_real @ B @ A )
% 8.68/4.89       => ( ( set_or1222579329274155063t_real @ A @ B )
% 8.68/4.89          = bot_bot_set_real ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3417_double__diff,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.68/4.89       => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 8.68/4.89         => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 8.68/4.89            = A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3418_double__diff,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int,C4: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 8.68/4.89         => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 8.68/4.89            = A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3419_Diff__subset,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3420_Diff__subset,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3421_Diff__mono,axiom,
% 8.68/4.89      ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 8.68/4.89       => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 8.68/4.89         => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3422_Diff__mono,axiom,
% 8.68/4.89      ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ C4 )
% 8.68/4.89       => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 8.68/4.89         => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3423_Collect__mono__iff,axiom,
% 8.68/4.89      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 8.68/4.89        ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 8.68/4.89        = ( ! [X3: product_prod_int_int] :
% 8.68/4.89              ( ( P @ X3 )
% 8.68/4.89             => ( Q @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3424_Collect__mono__iff,axiom,
% 8.68/4.89      ! [P: complex > $o,Q: complex > $o] :
% 8.68/4.89        ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 8.68/4.89        = ( ! [X3: complex] :
% 8.68/4.89              ( ( P @ X3 )
% 8.68/4.89             => ( Q @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3425_Collect__mono__iff,axiom,
% 8.68/4.89      ! [P: set_nat > $o,Q: set_nat > $o] :
% 8.68/4.89        ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 8.68/4.89        = ( ! [X3: set_nat] :
% 8.68/4.89              ( ( P @ X3 )
% 8.68/4.89             => ( Q @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3426_Collect__mono__iff,axiom,
% 8.68/4.89      ! [P: nat > $o,Q: nat > $o] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 8.68/4.89        = ( ! [X3: nat] :
% 8.68/4.89              ( ( P @ X3 )
% 8.68/4.89             => ( Q @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3427_Collect__mono__iff,axiom,
% 8.68/4.89      ! [P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 8.68/4.89        = ( ! [X3: int] :
% 8.68/4.89              ( ( P @ X3 )
% 8.68/4.89             => ( Q @ X3 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3428_set__eq__subset,axiom,
% 8.68/4.89      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 8.68/4.89      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.89            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 8.68/4.89            & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3429_subset__trans,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int,C4: set_int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 8.68/4.89         => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3430_Collect__mono,axiom,
% 8.68/4.89      ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 8.68/4.89        ( ! [X6: product_prod_int_int] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89           => ( Q @ X6 ) )
% 8.68/4.89       => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3431_Collect__mono,axiom,
% 8.68/4.89      ! [P: complex > $o,Q: complex > $o] :
% 8.68/4.89        ( ! [X6: complex] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89           => ( Q @ X6 ) )
% 8.68/4.89       => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3432_Collect__mono,axiom,
% 8.68/4.89      ! [P: set_nat > $o,Q: set_nat > $o] :
% 8.68/4.89        ( ! [X6: set_nat] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89           => ( Q @ X6 ) )
% 8.68/4.89       => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3433_Collect__mono,axiom,
% 8.68/4.89      ! [P: nat > $o,Q: nat > $o] :
% 8.68/4.89        ( ! [X6: nat] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89           => ( Q @ X6 ) )
% 8.68/4.89       => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3434_Collect__mono,axiom,
% 8.68/4.89      ! [P: int > $o,Q: int > $o] :
% 8.68/4.89        ( ! [X6: int] :
% 8.68/4.89            ( ( P @ X6 )
% 8.68/4.89           => ( Q @ X6 ) )
% 8.68/4.89       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3435_subset__refl,axiom,
% 8.68/4.89      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3436_subset__iff,axiom,
% 8.68/4.89      ( ord_le211207098394363844omplex
% 8.68/4.89      = ( ^ [A6: set_complex,B6: set_complex] :
% 8.68/4.89          ! [T2: complex] :
% 8.68/4.89            ( ( member_complex @ T2 @ A6 )
% 8.68/4.89           => ( member_complex @ T2 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3437_subset__iff,axiom,
% 8.68/4.89      ( ord_less_eq_set_real
% 8.68/4.89      = ( ^ [A6: set_real,B6: set_real] :
% 8.68/4.89          ! [T2: real] :
% 8.68/4.89            ( ( member_real @ T2 @ A6 )
% 8.68/4.89           => ( member_real @ T2 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3438_subset__iff,axiom,
% 8.68/4.89      ( ord_le6893508408891458716et_nat
% 8.68/4.89      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 8.68/4.89          ! [T2: set_nat] :
% 8.68/4.89            ( ( member_set_nat @ T2 @ A6 )
% 8.68/4.89           => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3439_subset__iff,axiom,
% 8.68/4.89      ( ord_less_eq_set_nat
% 8.68/4.89      = ( ^ [A6: set_nat,B6: set_nat] :
% 8.68/4.89          ! [T2: nat] :
% 8.68/4.89            ( ( member_nat @ T2 @ A6 )
% 8.68/4.89           => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3440_subset__iff,axiom,
% 8.68/4.89      ( ord_less_eq_set_int
% 8.68/4.89      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.89          ! [T2: int] :
% 8.68/4.89            ( ( member_int @ T2 @ A6 )
% 8.68/4.89           => ( member_int @ T2 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3441_equalityD2,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( A2 = B3 )
% 8.68/4.89       => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3442_equalityD1,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( A2 = B3 )
% 8.68/4.89       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3443_subset__eq,axiom,
% 8.68/4.89      ( ord_le211207098394363844omplex
% 8.68/4.89      = ( ^ [A6: set_complex,B6: set_complex] :
% 8.68/4.89          ! [X3: complex] :
% 8.68/4.89            ( ( member_complex @ X3 @ A6 )
% 8.68/4.89           => ( member_complex @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3444_subset__eq,axiom,
% 8.68/4.89      ( ord_less_eq_set_real
% 8.68/4.89      = ( ^ [A6: set_real,B6: set_real] :
% 8.68/4.89          ! [X3: real] :
% 8.68/4.89            ( ( member_real @ X3 @ A6 )
% 8.68/4.89           => ( member_real @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3445_subset__eq,axiom,
% 8.68/4.89      ( ord_le6893508408891458716et_nat
% 8.68/4.89      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 8.68/4.89          ! [X3: set_nat] :
% 8.68/4.89            ( ( member_set_nat @ X3 @ A6 )
% 8.68/4.89           => ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3446_subset__eq,axiom,
% 8.68/4.89      ( ord_less_eq_set_nat
% 8.68/4.89      = ( ^ [A6: set_nat,B6: set_nat] :
% 8.68/4.89          ! [X3: nat] :
% 8.68/4.89            ( ( member_nat @ X3 @ A6 )
% 8.68/4.89           => ( member_nat @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3447_subset__eq,axiom,
% 8.68/4.89      ( ord_less_eq_set_int
% 8.68/4.89      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.89          ! [X3: int] :
% 8.68/4.89            ( ( member_int @ X3 @ A6 )
% 8.68/4.89           => ( member_int @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3448_equalityE,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( A2 = B3 )
% 8.68/4.89       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89           => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3449_subsetD,axiom,
% 8.68/4.89      ! [A2: set_complex,B3: set_complex,C: complex] :
% 8.68/4.89        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.68/4.89       => ( ( member_complex @ C @ A2 )
% 8.68/4.89         => ( member_complex @ C @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3450_subsetD,axiom,
% 8.68/4.89      ! [A2: set_real,B3: set_real,C: real] :
% 8.68/4.89        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.68/4.89       => ( ( member_real @ C @ A2 )
% 8.68/4.89         => ( member_real @ C @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3451_subsetD,axiom,
% 8.68/4.89      ! [A2: set_set_nat,B3: set_set_nat,C: set_nat] :
% 8.68/4.89        ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 8.68/4.89       => ( ( member_set_nat @ C @ A2 )
% 8.68/4.89         => ( member_set_nat @ C @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3452_subsetD,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat,C: nat] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.68/4.89       => ( ( member_nat @ C @ A2 )
% 8.68/4.89         => ( member_nat @ C @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3453_subsetD,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int,C: int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( member_int @ C @ A2 )
% 8.68/4.89         => ( member_int @ C @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3454_in__mono,axiom,
% 8.68/4.89      ! [A2: set_complex,B3: set_complex,X: complex] :
% 8.68/4.89        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.68/4.89       => ( ( member_complex @ X @ A2 )
% 8.68/4.89         => ( member_complex @ X @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3455_in__mono,axiom,
% 8.68/4.89      ! [A2: set_real,B3: set_real,X: real] :
% 8.68/4.89        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.68/4.89       => ( ( member_real @ X @ A2 )
% 8.68/4.89         => ( member_real @ X @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3456_in__mono,axiom,
% 8.68/4.89      ! [A2: set_set_nat,B3: set_set_nat,X: set_nat] :
% 8.68/4.89        ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 8.68/4.89       => ( ( member_set_nat @ X @ A2 )
% 8.68/4.89         => ( member_set_nat @ X @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3457_in__mono,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat,X: nat] :
% 8.68/4.89        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.68/4.89       => ( ( member_nat @ X @ A2 )
% 8.68/4.89         => ( member_nat @ X @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3458_in__mono,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int,X: int] :
% 8.68/4.89        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.89       => ( ( member_int @ X @ A2 )
% 8.68/4.89         => ( member_int @ X @ B3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3459_psubset__imp__ex__mem,axiom,
% 8.68/4.89      ! [A2: set_complex,B3: set_complex] :
% 8.68/4.89        ( ( ord_less_set_complex @ A2 @ B3 )
% 8.68/4.89       => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3460_psubset__imp__ex__mem,axiom,
% 8.68/4.89      ! [A2: set_real,B3: set_real] :
% 8.68/4.89        ( ( ord_less_set_real @ A2 @ B3 )
% 8.68/4.89       => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3461_psubset__imp__ex__mem,axiom,
% 8.68/4.89      ! [A2: set_set_nat,B3: set_set_nat] :
% 8.68/4.89        ( ( ord_less_set_set_nat @ A2 @ B3 )
% 8.68/4.89       => ? [B5: set_nat] : ( member_set_nat @ B5 @ ( minus_2163939370556025621et_nat @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3462_psubset__imp__ex__mem,axiom,
% 8.68/4.89      ! [A2: set_int,B3: set_int] :
% 8.68/4.89        ( ( ord_less_set_int @ A2 @ B3 )
% 8.68/4.89       => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3463_psubset__imp__ex__mem,axiom,
% 8.68/4.89      ! [A2: set_nat,B3: set_nat] :
% 8.68/4.89        ( ( ord_less_set_nat @ A2 @ B3 )
% 8.68/4.89       => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3464_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_real,P: real > $o] :
% 8.68/4.89        ( ord_less_eq_set_real
% 8.68/4.89        @ ( collect_real
% 8.68/4.89          @ ^ [X3: real] :
% 8.68/4.89              ( ( member_real @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3465_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 8.68/4.89        ( ord_le2843351958646193337nt_int
% 8.68/4.89        @ ( collec213857154873943460nt_int
% 8.68/4.89          @ ^ [X3: product_prod_int_int] :
% 8.68/4.89              ( ( member5262025264175285858nt_int @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3466_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_complex,P: complex > $o] :
% 8.68/4.89        ( ord_le211207098394363844omplex
% 8.68/4.89        @ ( collect_complex
% 8.68/4.89          @ ^ [X3: complex] :
% 8.68/4.89              ( ( member_complex @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3467_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_set_nat,P: set_nat > $o] :
% 8.68/4.89        ( ord_le6893508408891458716et_nat
% 8.68/4.89        @ ( collect_set_nat
% 8.68/4.89          @ ^ [X3: set_nat] :
% 8.68/4.89              ( ( member_set_nat @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3468_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_nat,P: nat > $o] :
% 8.68/4.89        ( ord_less_eq_set_nat
% 8.68/4.89        @ ( collect_nat
% 8.68/4.89          @ ^ [X3: nat] :
% 8.68/4.89              ( ( member_nat @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3469_Collect__subset,axiom,
% 8.68/4.89      ! [A2: set_int,P: int > $o] :
% 8.68/4.89        ( ord_less_eq_set_int
% 8.68/4.89        @ ( collect_int
% 8.68/4.89          @ ^ [X3: int] :
% 8.68/4.89              ( ( member_int @ X3 @ A2 )
% 8.68/4.89              & ( P @ X3 ) ) )
% 8.68/4.89        @ A2 ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3470_less__eq__set__def,axiom,
% 8.68/4.89      ( ord_le211207098394363844omplex
% 8.68/4.89      = ( ^ [A6: set_complex,B6: set_complex] :
% 8.68/4.89            ( ord_le4573692005234683329plex_o
% 8.68/4.89            @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 8.68/4.89            @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3471_less__eq__set__def,axiom,
% 8.68/4.89      ( ord_less_eq_set_real
% 8.68/4.89      = ( ^ [A6: set_real,B6: set_real] :
% 8.68/4.89            ( ord_less_eq_real_o
% 8.68/4.89            @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 8.68/4.89            @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3472_less__eq__set__def,axiom,
% 8.68/4.89      ( ord_le6893508408891458716et_nat
% 8.68/4.89      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 8.68/4.89            ( ord_le3964352015994296041_nat_o
% 8.68/4.89            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 8.68/4.89            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3473_less__eq__set__def,axiom,
% 8.68/4.89      ( ord_less_eq_set_nat
% 8.68/4.89      = ( ^ [A6: set_nat,B6: set_nat] :
% 8.68/4.89            ( ord_less_eq_nat_o
% 8.68/4.89            @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 8.68/4.89            @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3474_less__eq__set__def,axiom,
% 8.68/4.89      ( ord_less_eq_set_int
% 8.68/4.89      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.89            ( ord_less_eq_int_o
% 8.68/4.89            @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 8.68/4.89            @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3475_max_Omono,axiom,
% 8.68/4.89      ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 8.68/4.89       => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 8.68/4.89         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3476_max_Omono,axiom,
% 8.68/4.89      ! [C: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ C @ A )
% 8.68/4.89       => ( ( ord_le3102999989581377725nteger @ D @ B )
% 8.68/4.89         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3477_max_Omono,axiom,
% 8.68/4.89      ! [C: rat,A: rat,D: rat,B: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ C @ A )
% 8.68/4.89       => ( ( ord_less_eq_rat @ D @ B )
% 8.68/4.89         => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3478_max_Omono,axiom,
% 8.68/4.89      ! [C: num,A: num,D: num,B: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ C @ A )
% 8.68/4.89       => ( ( ord_less_eq_num @ D @ B )
% 8.68/4.89         => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3479_max_Omono,axiom,
% 8.68/4.89      ! [C: nat,A: nat,D: nat,B: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.89       => ( ( ord_less_eq_nat @ D @ B )
% 8.68/4.89         => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3480_max_Omono,axiom,
% 8.68/4.89      ! [C: int,A: int,D: int,B: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ C @ A )
% 8.68/4.89       => ( ( ord_less_eq_int @ D @ B )
% 8.68/4.89         => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3481_max_OorderE,axiom,
% 8.68/4.89      ! [B: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3482_max_OorderE,axiom,
% 8.68/4.89      ! [B: code_integer,A: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3483_max_OorderE,axiom,
% 8.68/4.89      ! [B: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_max_rat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3484_max_OorderE,axiom,
% 8.68/4.89      ! [B: num,A: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_max_num @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3485_max_OorderE,axiom,
% 8.68/4.89      ! [B: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_max_nat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3486_max_OorderE,axiom,
% 8.68/4.89      ! [B: int,A: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.89       => ( A
% 8.68/4.89          = ( ord_max_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3487_max_OorderI,axiom,
% 8.68/4.89      ! [A: extended_enat,B: extended_enat] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 8.68/4.89       => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3488_max_OorderI,axiom,
% 8.68/4.89      ! [A: code_integer,B: code_integer] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_max_Code_integer @ A @ B ) )
% 8.68/4.89       => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3489_max_OorderI,axiom,
% 8.68/4.89      ! [A: rat,B: rat] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_max_rat @ A @ B ) )
% 8.68/4.89       => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3490_max_OorderI,axiom,
% 8.68/4.89      ! [A: num,B: num] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_max_num @ A @ B ) )
% 8.68/4.89       => ( ord_less_eq_num @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3491_max_OorderI,axiom,
% 8.68/4.89      ! [A: nat,B: nat] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_max_nat @ A @ B ) )
% 8.68/4.89       => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3492_max_OorderI,axiom,
% 8.68/4.89      ! [A: int,B: int] :
% 8.68/4.89        ( ( A
% 8.68/4.89          = ( ord_max_int @ A @ B ) )
% 8.68/4.89       => ( ord_less_eq_int @ B @ A ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3493_max_OboundedE,axiom,
% 8.68/4.89      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 8.68/4.89           => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3494_max_OboundedE,axiom,
% 8.68/4.89      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.68/4.89           => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3495_max_OboundedE,axiom,
% 8.68/4.89      ! [B: rat,C: rat,A: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.89           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3496_max_OboundedE,axiom,
% 8.68/4.89      ! [B: num,C: num,A: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_less_eq_num @ B @ A )
% 8.68/4.89           => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3497_max_OboundedE,axiom,
% 8.68/4.89      ! [B: nat,C: nat,A: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.89           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3498_max_OboundedE,axiom,
% 8.68/4.89      ! [B: int,C: int,A: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 8.68/4.89       => ~ ( ( ord_less_eq_int @ B @ A )
% 8.68/4.89           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3499_max_OboundedI,axiom,
% 8.68/4.89      ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ B @ A )
% 8.68/4.89       => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 8.68/4.89         => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3500_max_OboundedI,axiom,
% 8.68/4.89      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ B @ A )
% 8.68/4.89       => ( ( ord_le3102999989581377725nteger @ C @ A )
% 8.68/4.89         => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3501_max_OboundedI,axiom,
% 8.68/4.89      ! [B: rat,A: rat,C: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ B @ A )
% 8.68/4.89       => ( ( ord_less_eq_rat @ C @ A )
% 8.68/4.89         => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3502_max_OboundedI,axiom,
% 8.68/4.89      ! [B: num,A: num,C: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ B @ A )
% 8.68/4.89       => ( ( ord_less_eq_num @ C @ A )
% 8.68/4.89         => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3503_max_OboundedI,axiom,
% 8.68/4.89      ! [B: nat,A: nat,C: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ B @ A )
% 8.68/4.89       => ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.89         => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3504_max_OboundedI,axiom,
% 8.68/4.89      ! [B: int,A: int,C: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ B @ A )
% 8.68/4.89       => ( ( ord_less_eq_int @ C @ A )
% 8.68/4.89         => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3505_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_le2932123472753598470d_enat
% 8.68/4.89      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3506_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_le3102999989581377725nteger
% 8.68/4.89      = ( ^ [B2: code_integer,A3: code_integer] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_max_Code_integer @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3507_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_less_eq_rat
% 8.68/4.89      = ( ^ [B2: rat,A3: rat] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3508_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_less_eq_num
% 8.68/4.89      = ( ^ [B2: num,A3: num] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3509_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_less_eq_nat
% 8.68/4.89      = ( ^ [B2: nat,A3: nat] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3510_max_Oorder__iff,axiom,
% 8.68/4.89      ( ord_less_eq_int
% 8.68/4.89      = ( ^ [B2: int,A3: int] :
% 8.68/4.89            ( A3
% 8.68/4.89            = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3511_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3512_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3513_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3514_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3515_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3516_max_Ocobounded1,axiom,
% 8.68/4.89      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3517_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3518_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3519_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3520_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3521_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3522_max_Ocobounded2,axiom,
% 8.68/4.89      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3523_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 8.68/4.89        = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 8.68/4.89          | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3524_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 8.68/4.89        = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 8.68/4.89          | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3525_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 8.68/4.89        = ( ( ord_less_eq_rat @ Z @ X )
% 8.68/4.89          | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3526_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: num,X: num,Y: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 8.68/4.89        = ( ( ord_less_eq_num @ Z @ X )
% 8.68/4.89          | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3527_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: nat,X: nat,Y: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 8.68/4.89        = ( ( ord_less_eq_nat @ Z @ X )
% 8.68/4.89          | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3528_le__max__iff__disj,axiom,
% 8.68/4.89      ! [Z: int,X: int,Y: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 8.68/4.89        = ( ( ord_less_eq_int @ Z @ X )
% 8.68/4.89          | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3529_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_le2932123472753598470d_enat
% 8.68/4.89      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 8.68/4.89            ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3530_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_le3102999989581377725nteger
% 8.68/4.89      = ( ^ [B2: code_integer,A3: code_integer] :
% 8.68/4.89            ( ( ord_max_Code_integer @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3531_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_less_eq_rat
% 8.68/4.89      = ( ^ [B2: rat,A3: rat] :
% 8.68/4.89            ( ( ord_max_rat @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3532_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_less_eq_num
% 8.68/4.89      = ( ^ [B2: num,A3: num] :
% 8.68/4.89            ( ( ord_max_num @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3533_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_less_eq_nat
% 8.68/4.89      = ( ^ [B2: nat,A3: nat] :
% 8.68/4.89            ( ( ord_max_nat @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3534_max_Oabsorb__iff1,axiom,
% 8.68/4.89      ( ord_less_eq_int
% 8.68/4.89      = ( ^ [B2: int,A3: int] :
% 8.68/4.89            ( ( ord_max_int @ A3 @ B2 )
% 8.68/4.89            = A3 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3535_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_le2932123472753598470d_enat
% 8.68/4.89      = ( ^ [A3: extended_enat,B2: extended_enat] :
% 8.68/4.89            ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3536_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_le3102999989581377725nteger
% 8.68/4.89      = ( ^ [A3: code_integer,B2: code_integer] :
% 8.68/4.89            ( ( ord_max_Code_integer @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3537_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_less_eq_rat
% 8.68/4.89      = ( ^ [A3: rat,B2: rat] :
% 8.68/4.89            ( ( ord_max_rat @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3538_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_less_eq_num
% 8.68/4.89      = ( ^ [A3: num,B2: num] :
% 8.68/4.89            ( ( ord_max_num @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3539_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_less_eq_nat
% 8.68/4.89      = ( ^ [A3: nat,B2: nat] :
% 8.68/4.89            ( ( ord_max_nat @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3540_max_Oabsorb__iff2,axiom,
% 8.68/4.89      ( ord_less_eq_int
% 8.68/4.89      = ( ^ [A3: int,B2: int] :
% 8.68/4.89            ( ( ord_max_int @ A3 @ B2 )
% 8.68/4.89            = B2 ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3541_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ C @ A )
% 8.68/4.89       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3542_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.68/4.89        ( ( ord_le3102999989581377725nteger @ C @ A )
% 8.68/4.89       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3543_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: rat,A: rat,B: rat] :
% 8.68/4.89        ( ( ord_less_eq_rat @ C @ A )
% 8.68/4.89       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3544_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: num,A: num,B: num] :
% 8.68/4.89        ( ( ord_less_eq_num @ C @ A )
% 8.68/4.89       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3545_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: nat,A: nat,B: nat] :
% 8.68/4.89        ( ( ord_less_eq_nat @ C @ A )
% 8.68/4.89       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3546_max_OcoboundedI1,axiom,
% 8.68/4.89      ! [C: int,A: int,B: int] :
% 8.68/4.89        ( ( ord_less_eq_int @ C @ A )
% 8.68/4.89       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3547_max_OcoboundedI2,axiom,
% 8.68/4.89      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 8.68/4.89        ( ( ord_le2932123472753598470d_enat @ C @ B )
% 8.68/4.89       => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 8.68/4.89  
% 8.68/4.89  thf(fact_3548_max_OcoboundedI2,axiom,
% 8.68/4.89      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.68/4.90        ( ( ord_le3102999989581377725nteger @ C @ B )
% 8.68/4.90       => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3549_max_OcoboundedI2,axiom,
% 8.68/4.90      ! [C: rat,B: rat,A: rat] :
% 8.68/4.90        ( ( ord_less_eq_rat @ C @ B )
% 8.68/4.90       => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3550_max_OcoboundedI2,axiom,
% 8.68/4.90      ! [C: num,B: num,A: num] :
% 8.68/4.90        ( ( ord_less_eq_num @ C @ B )
% 8.68/4.90       => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3551_max_OcoboundedI2,axiom,
% 8.68/4.90      ! [C: nat,B: nat,A: nat] :
% 8.68/4.90        ( ( ord_less_eq_nat @ C @ B )
% 8.68/4.90       => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3552_max_OcoboundedI2,axiom,
% 8.68/4.90      ! [C: int,B: int,A: int] :
% 8.68/4.90        ( ( ord_less_eq_int @ C @ B )
% 8.68/4.90       => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3553_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 8.68/4.90        ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 8.68/4.90        = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 8.68/4.90          | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3554_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 8.68/4.90        ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 8.68/4.90        = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 8.68/4.90          | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3555_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: real,X: real,Y: real] :
% 8.68/4.90        ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 8.68/4.90        = ( ( ord_less_real @ Z @ X )
% 8.68/4.90          | ( ord_less_real @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3556_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: rat,X: rat,Y: rat] :
% 8.68/4.90        ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 8.68/4.90        = ( ( ord_less_rat @ Z @ X )
% 8.68/4.90          | ( ord_less_rat @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3557_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: num,X: num,Y: num] :
% 8.68/4.90        ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 8.68/4.90        = ( ( ord_less_num @ Z @ X )
% 8.68/4.90          | ( ord_less_num @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3558_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: nat,X: nat,Y: nat] :
% 8.68/4.90        ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 8.68/4.90        = ( ( ord_less_nat @ Z @ X )
% 8.68/4.90          | ( ord_less_nat @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3559_less__max__iff__disj,axiom,
% 8.68/4.90      ! [Z: int,X: int,Y: int] :
% 8.68/4.90        ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 8.68/4.90        = ( ( ord_less_int @ Z @ X )
% 8.68/4.90          | ( ord_less_int @ Z @ Y ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3560_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 8.68/4.90        ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 8.68/4.90           => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3561_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.68/4.90        ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 8.68/4.90           => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3562_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: real,C: real,A: real] :
% 8.68/4.90        ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_less_real @ B @ A )
% 8.68/4.90           => ~ ( ord_less_real @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3563_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: rat,C: rat,A: rat] :
% 8.68/4.90        ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_less_rat @ B @ A )
% 8.68/4.90           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3564_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: num,C: num,A: num] :
% 8.68/4.90        ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_less_num @ B @ A )
% 8.68/4.90           => ~ ( ord_less_num @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3565_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: nat,C: nat,A: nat] :
% 8.68/4.90        ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_less_nat @ B @ A )
% 8.68/4.90           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3566_max_Ostrict__boundedE,axiom,
% 8.68/4.90      ! [B: int,C: int,A: int] :
% 8.68/4.90        ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 8.68/4.90       => ~ ( ( ord_less_int @ B @ A )
% 8.68/4.90           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3567_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_le72135733267957522d_enat
% 8.68/4.90      = ( ^ [B2: extended_enat,A3: extended_enat] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3568_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_le6747313008572928689nteger
% 8.68/4.90      = ( ^ [B2: code_integer,A3: code_integer] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_Code_integer @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3569_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_less_real
% 8.68/4.90      = ( ^ [B2: real,A3: real] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_real @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3570_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_less_rat
% 8.68/4.90      = ( ^ [B2: rat,A3: rat] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_rat @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3571_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_less_num
% 8.68/4.90      = ( ^ [B2: num,A3: num] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_num @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3572_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_less_nat
% 8.68/4.90      = ( ^ [B2: nat,A3: nat] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_nat @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3573_max_Ostrict__order__iff,axiom,
% 8.68/4.90      ( ord_less_int
% 8.68/4.90      = ( ^ [B2: int,A3: int] :
% 8.68/4.90            ( ( A3
% 8.68/4.90              = ( ord_max_int @ A3 @ B2 ) )
% 8.68/4.90            & ( A3 != B2 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3574_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 8.68/4.90        ( ( ord_le72135733267957522d_enat @ C @ A )
% 8.68/4.90       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3575_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.68/4.90        ( ( ord_le6747313008572928689nteger @ C @ A )
% 8.68/4.90       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3576_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: real,A: real,B: real] :
% 8.68/4.90        ( ( ord_less_real @ C @ A )
% 8.68/4.90       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3577_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: rat,A: rat,B: rat] :
% 8.68/4.90        ( ( ord_less_rat @ C @ A )
% 8.68/4.90       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3578_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: num,A: num,B: num] :
% 8.68/4.90        ( ( ord_less_num @ C @ A )
% 8.68/4.90       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3579_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: nat,A: nat,B: nat] :
% 8.68/4.90        ( ( ord_less_nat @ C @ A )
% 8.68/4.90       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3580_max_Ostrict__coboundedI1,axiom,
% 8.68/4.90      ! [C: int,A: int,B: int] :
% 8.68/4.90        ( ( ord_less_int @ C @ A )
% 8.68/4.90       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3581_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 8.68/4.90        ( ( ord_le72135733267957522d_enat @ C @ B )
% 8.68/4.90       => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3582_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.68/4.90        ( ( ord_le6747313008572928689nteger @ C @ B )
% 8.68/4.90       => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3583_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: real,B: real,A: real] :
% 8.68/4.90        ( ( ord_less_real @ C @ B )
% 8.68/4.90       => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3584_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: rat,B: rat,A: rat] :
% 8.68/4.90        ( ( ord_less_rat @ C @ B )
% 8.68/4.90       => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3585_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: num,B: num,A: num] :
% 8.68/4.90        ( ( ord_less_num @ C @ B )
% 8.68/4.90       => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3586_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: nat,B: nat,A: nat] :
% 8.68/4.90        ( ( ord_less_nat @ C @ B )
% 8.68/4.90       => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3587_max_Ostrict__coboundedI2,axiom,
% 8.68/4.90      ! [C: int,B: int,A: int] :
% 8.68/4.90        ( ( ord_less_int @ C @ B )
% 8.68/4.90       => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3588_psubsetE,axiom,
% 8.68/4.90      ! [A2: set_int,B3: set_int] :
% 8.68/4.90        ( ( ord_less_set_int @ A2 @ B3 )
% 8.68/4.90       => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.90           => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3589_psubset__eq,axiom,
% 8.68/4.90      ( ord_less_set_int
% 8.68/4.90      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.90            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 8.68/4.90            & ( A6 != B6 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3590_psubset__imp__subset,axiom,
% 8.68/4.90      ! [A2: set_int,B3: set_int] :
% 8.68/4.90        ( ( ord_less_set_int @ A2 @ B3 )
% 8.68/4.90       => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3591_psubset__subset__trans,axiom,
% 8.68/4.90      ! [A2: set_int,B3: set_int,C4: set_int] :
% 8.68/4.90        ( ( ord_less_set_int @ A2 @ B3 )
% 8.68/4.90       => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 8.68/4.90         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3592_subset__not__subset__eq,axiom,
% 8.68/4.90      ( ord_less_set_int
% 8.68/4.90      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.90            ( ( ord_less_eq_set_int @ A6 @ B6 )
% 8.68/4.90            & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3593_subset__psubset__trans,axiom,
% 8.68/4.90      ! [A2: set_int,B3: set_int,C4: set_int] :
% 8.68/4.90        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.68/4.90       => ( ( ord_less_set_int @ B3 @ C4 )
% 8.68/4.90         => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3594_subset__iff__psubset__eq,axiom,
% 8.68/4.90      ( ord_less_eq_set_int
% 8.68/4.90      = ( ^ [A6: set_int,B6: set_int] :
% 8.68/4.90            ( ( ord_less_set_int @ A6 @ B6 )
% 8.68/4.90            | ( A6 = B6 ) ) ) ) ).
% 8.68/4.90  
% 8.68/4.90  thf(fact_3595_vebt__delete_Opelims,axiom,
% 8.68/4.90      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.68/4.90        ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 8.68/4.90          = Y )
% 8.68/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.68/4.90         => ( ! [A5: $o,B5: $o] :
% 8.68/4.90                ( ( X
% 8.68/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.90               => ( ( Xa2 = zero_zero_nat )
% 8.68/4.90                 => ( ( Y
% 8.68/4.90                      = ( vEBT_Leaf @ $false @ B5 ) )
% 8.68/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 8.68/4.90           => ( ! [A5: $o,B5: $o] :
% 8.68/4.90                  ( ( X
% 8.68/4.90                    = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.90                 => ( ( Xa2
% 8.68/4.90                      = ( suc @ zero_zero_nat ) )
% 8.68/4.90                   => ( ( Y
% 8.68/4.90                        = ( vEBT_Leaf @ A5 @ $false ) )
% 8.68/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 8.68/4.90             => ( ! [A5: $o,B5: $o] :
% 8.68/4.90                    ( ( X
% 8.68/4.90                      = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.90                   => ! [N3: nat] :
% 8.68/4.90                        ( ( Xa2
% 8.68/4.90                          = ( suc @ ( suc @ N3 ) ) )
% 8.68/4.90                       => ( ( Y
% 8.68/4.90                            = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.68/4.90                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 8.68/4.90               => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.68/4.90                      ( ( X
% 8.68/4.90                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.90                     => ( ( Y
% 8.68/4.90                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.68/4.90                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 8.68/4.90                 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 8.68/4.90                        ( ( X
% 8.68/4.90                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 8.68/4.90                       => ( ( Y
% 8.68/4.90                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 8.68/4.90                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 8.69/4.90                   => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 8.69/4.90                          ( ( X
% 8.69/4.90                            = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 8.69/4.90                         => ( ( Y
% 8.69/4.90                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 8.69/4.90                           => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 8.69/4.90                     => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                            ( ( X
% 8.69/4.90                              = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                           => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                    | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.69/4.90                                 => ( Y
% 8.69/4.90                                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.69/4.90                                & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                      | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.69/4.90                                 => ( ( ( ( Xa2 = Mi2 )
% 8.69/4.90                                        & ( Xa2 = Ma2 ) )
% 8.69/4.90                                     => ( Y
% 8.69/4.90                                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.69/4.90                                    & ( ~ ( ( Xa2 = Mi2 )
% 8.69/4.90                                          & ( Xa2 = Ma2 ) )
% 8.69/4.90                                     => ( Y
% 8.69/4.90                                        = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                                          @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                            @ ( vEBT_Node
% 8.69/4.90                                              @ ( some_P7363390416028606310at_nat
% 8.69/4.90                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.69/4.90                                                  @ ( if_nat
% 8.69/4.90                                                    @ ( ( ( Xa2 = Mi2 )
% 8.69/4.90                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.69/4.90                                                          = Ma2 ) )
% 8.69/4.90                                                      & ( ( Xa2 != Mi2 )
% 8.69/4.90                                                       => ( Xa2 = Ma2 ) ) )
% 8.69/4.90                                                    @ ( if_nat
% 8.69/4.90                                                      @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                                        = none_nat )
% 8.69/4.90                                                      @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.69/4.90                                                      @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.69/4.90                                                    @ Ma2 ) ) )
% 8.69/4.90                                              @ ( suc @ ( suc @ Va2 ) )
% 8.69/4.90                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                              @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                            @ ( vEBT_Node
% 8.69/4.90                                              @ ( some_P7363390416028606310at_nat
% 8.69/4.90                                                @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.69/4.90                                                  @ ( if_nat
% 8.69/4.90                                                    @ ( ( ( Xa2 = Mi2 )
% 8.69/4.90                                                       => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.69/4.90                                                          = Ma2 ) )
% 8.69/4.90                                                      & ( ( Xa2 != Mi2 )
% 8.69/4.90                                                       => ( Xa2 = Ma2 ) ) )
% 8.69/4.90                                                    @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.69/4.90                                                    @ Ma2 ) ) )
% 8.69/4.90                                              @ ( suc @ ( suc @ Va2 ) )
% 8.69/4.90                                              @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                              @ Summary2 ) )
% 8.69/4.90                                          @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 8.69/4.90                             => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3596_vebt__insert_Opelims,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.69/4.90        ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 8.69/4.90          = Y )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                     => ( Y
% 8.69/4.90                        = ( vEBT_Leaf @ $true @ B5 ) ) )
% 8.69/4.90                    & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                     => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                         => ( Y
% 8.69/4.90                            = ( vEBT_Leaf @ A5 @ $true ) ) )
% 8.69/4.90                        & ( ( Xa2 != one_one_nat )
% 8.69/4.90                         => ( Y
% 8.69/4.90                            = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 8.69/4.90           => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 8.69/4.90                 => ( ( Y
% 8.69/4.90                      = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 8.69/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 8.69/4.90             => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 8.69/4.90                   => ( ( Y
% 8.69/4.90                        = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 8.69/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 8.69/4.90               => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                      ( ( X
% 8.69/4.90                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                     => ( ( Y
% 8.69/4.90                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 8.69/4.90                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                        ( ( X
% 8.69/4.90                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                       => ( ( Y
% 8.69/4.90                            = ( if_VEBT_VEBT
% 8.69/4.90                              @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                                & ~ ( ( Xa2 = Mi2 )
% 8.69/4.90                                    | ( Xa2 = Ma2 ) ) )
% 8.69/4.90                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 8.69/4.90                              @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 8.69/4.90                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3597_vebt__member_Opelims_I3_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 8.69/4.90                 => ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                     => A5 )
% 8.69/4.90                    & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                     => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                         => B5 )
% 8.69/4.90                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.69/4.90           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 8.69/4.90             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 8.69/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 8.69/4.90               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.90                      ( ( X
% 8.69/4.90                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.69/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 8.69/4.90                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                        ( ( X
% 8.69/4.90                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 8.69/4.90                         => ( ( Xa2 != Mi2 )
% 8.69/4.90                           => ( ( Xa2 != Ma2 )
% 8.69/4.90                             => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                    & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                                         => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3598_vebt__member_Opelims_I1_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.69/4.90        ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.69/4.90          = Y )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( Y
% 8.69/4.90                    = ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                       => A5 )
% 8.69/4.90                      & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                       => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                           => B5 )
% 8.69/4.90                          & ( Xa2 = one_one_nat ) ) ) ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 8.69/4.90           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.69/4.90                 => ( ~ Y
% 8.69/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 8.69/4.90             => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 8.69/4.90                   => ( ~ Y
% 8.69/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 8.69/4.90               => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.90                      ( ( X
% 8.69/4.90                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.69/4.90                     => ( ~ Y
% 8.69/4.90                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 8.69/4.90                 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                        ( ( X
% 8.69/4.90                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                       => ( ( Y
% 8.69/4.90                            = ( ( Xa2 != Mi2 )
% 8.69/4.90                             => ( ( Xa2 != Ma2 )
% 8.69/4.90                               => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                  & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                                   => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                      & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                       => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                                           => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 8.69/4.90                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3599_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 8.69/4.90                 => ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                     => A5 )
% 8.69/4.90                    & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                     => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                         => B5 )
% 8.69/4.90                        & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.69/4.90           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 8.69/4.90             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.69/4.90                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 8.69/4.90                     => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3600_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 8.69/4.90                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                       => A5 )
% 8.69/4.90                      & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                       => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                           => B5 )
% 8.69/4.90                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.69/4.90           => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.69/4.90                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 8.69/4.90                   => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                         => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                        & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3601_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.69/4.90        ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.69/4.90          = Y )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( Y
% 8.69/4.90                    = ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                       => A5 )
% 8.69/4.90                      & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                       => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                           => B5 )
% 8.69/4.90                          & ( Xa2 = one_one_nat ) ) ) ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 8.69/4.90           => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 8.69/4.90                 => ( ~ Y
% 8.69/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 8.69/4.90             => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 8.69/4.90                   => ( ( Y
% 8.69/4.90                        = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                           => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 8.69/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3602_vebt__member_Opelims_I2_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [A5: $o,B5: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.90               => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 8.69/4.90                 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.69/4.90                       => A5 )
% 8.69/4.90                      & ( ( Xa2 != zero_zero_nat )
% 8.69/4.90                       => ( ( ( Xa2 = one_one_nat )
% 8.69/4.90                           => B5 )
% 8.69/4.90                          & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.69/4.90           => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 8.69/4.90                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 8.69/4.90                   => ~ ( ( Xa2 != Mi2 )
% 8.69/4.90                       => ( ( Xa2 != Ma2 )
% 8.69/4.90                         => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                            & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.69/4.90                             => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.69/4.90                                 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                                     => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                                    & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3603_DiffI,axiom,
% 8.69/4.90      ! [C: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( member_complex @ C @ A2 )
% 8.69/4.90       => ( ~ ( member_complex @ C @ B3 )
% 8.69/4.90         => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3604_DiffI,axiom,
% 8.69/4.90      ! [C: real,A2: set_real,B3: set_real] :
% 8.69/4.90        ( ( member_real @ C @ A2 )
% 8.69/4.90       => ( ~ ( member_real @ C @ B3 )
% 8.69/4.90         => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3605_DiffI,axiom,
% 8.69/4.90      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.90        ( ( member_set_nat @ C @ A2 )
% 8.69/4.90       => ( ~ ( member_set_nat @ C @ B3 )
% 8.69/4.90         => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3606_DiffI,axiom,
% 8.69/4.90      ! [C: int,A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( member_int @ C @ A2 )
% 8.69/4.90       => ( ~ ( member_int @ C @ B3 )
% 8.69/4.90         => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3607_DiffI,axiom,
% 8.69/4.90      ! [C: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( member_nat @ C @ A2 )
% 8.69/4.90       => ( ~ ( member_nat @ C @ B3 )
% 8.69/4.90         => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3608_Diff__iff,axiom,
% 8.69/4.90      ! [C: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.90        = ( ( member_complex @ C @ A2 )
% 8.69/4.90          & ~ ( member_complex @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3609_Diff__iff,axiom,
% 8.69/4.90      ! [C: real,A2: set_real,B3: set_real] :
% 8.69/4.90        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 8.69/4.90        = ( ( member_real @ C @ A2 )
% 8.69/4.90          & ~ ( member_real @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3610_Diff__iff,axiom,
% 8.69/4.90      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.90        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 8.69/4.90        = ( ( member_set_nat @ C @ A2 )
% 8.69/4.90          & ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3611_Diff__iff,axiom,
% 8.69/4.90      ! [C: int,A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.90        = ( ( member_int @ C @ A2 )
% 8.69/4.90          & ~ ( member_int @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3612_Diff__iff,axiom,
% 8.69/4.90      ! [C: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.90        = ( ( member_nat @ C @ A2 )
% 8.69/4.90          & ~ ( member_nat @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3613_Diff__idemp,axiom,
% 8.69/4.90      ! [A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ B3 )
% 8.69/4.90        = ( minus_minus_set_nat @ A2 @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3614_DiffE,axiom,
% 8.69/4.90      ! [C: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( ( member_complex @ C @ A2 )
% 8.69/4.90           => ( member_complex @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3615_DiffE,axiom,
% 8.69/4.90      ! [C: real,A2: set_real,B3: set_real] :
% 8.69/4.90        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( ( member_real @ C @ A2 )
% 8.69/4.90           => ( member_real @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3616_DiffE,axiom,
% 8.69/4.90      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.90        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( ( member_set_nat @ C @ A2 )
% 8.69/4.90           => ( member_set_nat @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3617_DiffE,axiom,
% 8.69/4.90      ! [C: int,A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( ( member_int @ C @ A2 )
% 8.69/4.90           => ( member_int @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3618_DiffE,axiom,
% 8.69/4.90      ! [C: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( ( member_nat @ C @ A2 )
% 8.69/4.90           => ( member_nat @ C @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3619_DiffD1,axiom,
% 8.69/4.90      ! [C: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.90       => ( member_complex @ C @ A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3620_DiffD1,axiom,
% 8.69/4.90      ! [C: real,A2: set_real,B3: set_real] :
% 8.69/4.90        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 8.69/4.90       => ( member_real @ C @ A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3621_DiffD1,axiom,
% 8.69/4.90      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.90        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 8.69/4.90       => ( member_set_nat @ C @ A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3622_DiffD1,axiom,
% 8.69/4.90      ! [C: int,A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.90       => ( member_int @ C @ A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3623_DiffD1,axiom,
% 8.69/4.90      ! [C: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.90       => ( member_nat @ C @ A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3624_DiffD2,axiom,
% 8.69/4.90      ! [C: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( member_complex @ C @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3625_DiffD2,axiom,
% 8.69/4.90      ! [C: real,A2: set_real,B3: set_real] :
% 8.69/4.90        ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( member_real @ C @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3626_DiffD2,axiom,
% 8.69/4.90      ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.90        ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( member_set_nat @ C @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3627_DiffD2,axiom,
% 8.69/4.90      ! [C: int,A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( member_int @ C @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3628_DiffD2,axiom,
% 8.69/4.90      ! [C: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.90       => ~ ( member_nat @ C @ B3 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3629_minus__set__def,axiom,
% 8.69/4.90      ( minus_minus_set_real
% 8.69/4.90      = ( ^ [A6: set_real,B6: set_real] :
% 8.69/4.90            ( collect_real
% 8.69/4.90            @ ( minus_minus_real_o
% 8.69/4.90              @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3630_minus__set__def,axiom,
% 8.69/4.90      ( minus_1052850069191792384nt_int
% 8.69/4.90      = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 8.69/4.90            ( collec213857154873943460nt_int
% 8.69/4.90            @ ( minus_711738161318947805_int_o
% 8.69/4.90              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3631_minus__set__def,axiom,
% 8.69/4.90      ( minus_811609699411566653omplex
% 8.69/4.90      = ( ^ [A6: set_complex,B6: set_complex] :
% 8.69/4.90            ( collect_complex
% 8.69/4.90            @ ( minus_8727706125548526216plex_o
% 8.69/4.90              @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3632_minus__set__def,axiom,
% 8.69/4.90      ( minus_2163939370556025621et_nat
% 8.69/4.90      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 8.69/4.90            ( collect_set_nat
% 8.69/4.90            @ ( minus_6910147592129066416_nat_o
% 8.69/4.90              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3633_minus__set__def,axiom,
% 8.69/4.90      ( minus_minus_set_int
% 8.69/4.90      = ( ^ [A6: set_int,B6: set_int] :
% 8.69/4.90            ( collect_int
% 8.69/4.90            @ ( minus_minus_int_o
% 8.69/4.90              @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3634_minus__set__def,axiom,
% 8.69/4.90      ( minus_minus_set_nat
% 8.69/4.90      = ( ^ [A6: set_nat,B6: set_nat] :
% 8.69/4.90            ( collect_nat
% 8.69/4.90            @ ( minus_minus_nat_o
% 8.69/4.90              @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 8.69/4.90              @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3635_set__diff__eq,axiom,
% 8.69/4.90      ( minus_minus_set_real
% 8.69/4.90      = ( ^ [A6: set_real,B6: set_real] :
% 8.69/4.90            ( collect_real
% 8.69/4.90            @ ^ [X3: real] :
% 8.69/4.90                ( ( member_real @ X3 @ A6 )
% 8.69/4.90                & ~ ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3636_set__diff__eq,axiom,
% 8.69/4.90      ( minus_1052850069191792384nt_int
% 8.69/4.90      = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 8.69/4.90            ( collec213857154873943460nt_int
% 8.69/4.90            @ ^ [X3: product_prod_int_int] :
% 8.69/4.90                ( ( member5262025264175285858nt_int @ X3 @ A6 )
% 8.69/4.90                & ~ ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3637_set__diff__eq,axiom,
% 8.69/4.90      ( minus_811609699411566653omplex
% 8.69/4.90      = ( ^ [A6: set_complex,B6: set_complex] :
% 8.69/4.90            ( collect_complex
% 8.69/4.90            @ ^ [X3: complex] :
% 8.69/4.90                ( ( member_complex @ X3 @ A6 )
% 8.69/4.90                & ~ ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3638_set__diff__eq,axiom,
% 8.69/4.90      ( minus_2163939370556025621et_nat
% 8.69/4.90      = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 8.69/4.90            ( collect_set_nat
% 8.69/4.90            @ ^ [X3: set_nat] :
% 8.69/4.90                ( ( member_set_nat @ X3 @ A6 )
% 8.69/4.90                & ~ ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3639_set__diff__eq,axiom,
% 8.69/4.90      ( minus_minus_set_int
% 8.69/4.90      = ( ^ [A6: set_int,B6: set_int] :
% 8.69/4.90            ( collect_int
% 8.69/4.90            @ ^ [X3: int] :
% 8.69/4.90                ( ( member_int @ X3 @ A6 )
% 8.69/4.90                & ~ ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3640_set__diff__eq,axiom,
% 8.69/4.90      ( minus_minus_set_nat
% 8.69/4.90      = ( ^ [A6: set_nat,B6: set_nat] :
% 8.69/4.90            ( collect_nat
% 8.69/4.90            @ ^ [X3: nat] :
% 8.69/4.90                ( ( member_nat @ X3 @ A6 )
% 8.69/4.90                & ~ ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3641_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.69/4.90        ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.69/4.90          = Y )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [Uu2: $o,Uv2: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/4.90               => ( ~ Y
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 8.69/4.90           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 8.69/4.90                 => ( ~ Y
% 8.69/4.90                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 8.69/4.90             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.69/4.90                   => ( ( Y
% 8.69/4.90                        = ( ( Xa2 = Mi2 )
% 8.69/4.90                          | ( Xa2 = Ma2 ) ) )
% 8.69/4.90                     => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 8.69/4.90               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.90                      ( ( X
% 8.69/4.90                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.69/4.90                     => ( ( Y
% 8.69/4.90                          = ( ( Xa2 = Mi2 )
% 8.69/4.90                            | ( Xa2 = Ma2 )
% 8.69/4.90                            | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 8.69/4.90                       => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 8.69/4.90                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 8.69/4.90                        ( ( X
% 8.69/4.90                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.69/4.90                       => ( ( Y
% 8.69/4.90                            = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                               => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                              & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 8.69/4.90                         => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3642_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [Uu2: $o,Uv2: $o] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/4.90               => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 8.69/4.90           => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 8.69/4.90                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 8.69/4.90             => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.69/4.90                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 8.69/4.90                     => ( ( Xa2 = Mi2 )
% 8.69/4.90                        | ( Xa2 = Ma2 ) ) ) )
% 8.69/4.90               => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.90                      ( ( X
% 8.69/4.90                        = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.69/4.90                     => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 8.69/4.90                       => ( ( Xa2 = Mi2 )
% 8.69/4.90                          | ( Xa2 = Ma2 )
% 8.69/4.90                          | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 8.69/4.90                 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 8.69/4.90                        ( ( X
% 8.69/4.90                          = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.69/4.90                       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 8.69/4.90                         => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                             => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                            & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3643_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 8.69/4.90      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/4.90        ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.69/4.90       => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/4.90         => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.69/4.90                ( ( X
% 8.69/4.90                  = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 8.69/4.90               => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 8.69/4.90                 => ~ ( ( Xa2 = Mi2 )
% 8.69/4.90                      | ( Xa2 = Ma2 ) ) ) )
% 8.69/4.90           => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.90                  ( ( X
% 8.69/4.90                    = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 8.69/4.90                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 8.69/4.90                   => ~ ( ( Xa2 = Mi2 )
% 8.69/4.90                        | ( Xa2 = Ma2 )
% 8.69/4.90                        | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 8.69/4.90             => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 8.69/4.90                    ( ( X
% 8.69/4.90                      = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 8.69/4.90                   => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 8.69/4.90                     => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 8.69/4.90                           => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.90                          & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3644_unset__bit__0,axiom,
% 8.69/4.90      ! [A: int] :
% 8.69/4.90        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 8.69/4.90        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3645_unset__bit__0,axiom,
% 8.69/4.90      ! [A: nat] :
% 8.69/4.90        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 8.69/4.90        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3646_unset__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: code_integer] :
% 8.69/4.90        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3647_unset__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: int] :
% 8.69/4.90        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3648_unset__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: nat] :
% 8.69/4.90        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3649_flip__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: code_integer] :
% 8.69/4.90        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3650_flip__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: int] :
% 8.69/4.90        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3651_flip__bit__Suc,axiom,
% 8.69/4.90      ! [N: nat,A: nat] :
% 8.69/4.90        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 8.69/4.90        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3652_Bolzano,axiom,
% 8.69/4.90      ! [A: real,B: real,P: real > real > $o] :
% 8.69/4.90        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.90       => ( ! [A5: real,B5: real,C2: real] :
% 8.69/4.90              ( ( P @ A5 @ B5 )
% 8.69/4.90             => ( ( P @ B5 @ C2 )
% 8.69/4.90               => ( ( ord_less_eq_real @ A5 @ B5 )
% 8.69/4.90                 => ( ( ord_less_eq_real @ B5 @ C2 )
% 8.69/4.90                   => ( P @ A5 @ C2 ) ) ) ) )
% 8.69/4.90         => ( ! [X6: real] :
% 8.69/4.90                ( ( ord_less_eq_real @ A @ X6 )
% 8.69/4.90               => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/4.90                 => ? [D5: real] :
% 8.69/4.90                      ( ( ord_less_real @ zero_zero_real @ D5 )
% 8.69/4.90                      & ! [A5: real,B5: real] :
% 8.69/4.90                          ( ( ( ord_less_eq_real @ A5 @ X6 )
% 8.69/4.90                            & ( ord_less_eq_real @ X6 @ B5 )
% 8.69/4.90                            & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 8.69/4.90                         => ( P @ A5 @ B5 ) ) ) ) )
% 8.69/4.90           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3653_unset__bit__nonnegative__int__iff,axiom,
% 8.69/4.90      ! [N: nat,K: int] :
% 8.69/4.90        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 8.69/4.90        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3654_flip__bit__nonnegative__int__iff,axiom,
% 8.69/4.90      ! [N: nat,K: int] :
% 8.69/4.90        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 8.69/4.90        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3655_unset__bit__negative__int__iff,axiom,
% 8.69/4.90      ! [N: nat,K: int] :
% 8.69/4.90        ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 8.69/4.90        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3656_flip__bit__negative__int__iff,axiom,
% 8.69/4.90      ! [N: nat,K: int] :
% 8.69/4.90        ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 8.69/4.90        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3657_unset__bit__less__eq,axiom,
% 8.69/4.90      ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3658_mult__le__cancel__iff1,axiom,
% 8.69/4.90      ! [Z: real,X: real,Y: real] :
% 8.69/4.90        ( ( ord_less_real @ zero_zero_real @ Z )
% 8.69/4.90       => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3659_mult__le__cancel__iff1,axiom,
% 8.69/4.90      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.90        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 8.69/4.90       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3660_mult__le__cancel__iff1,axiom,
% 8.69/4.90      ! [Z: int,X: int,Y: int] :
% 8.69/4.90        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.90       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3661_mult__le__cancel__iff2,axiom,
% 8.69/4.90      ! [Z: real,X: real,Y: real] :
% 8.69/4.90        ( ( ord_less_real @ zero_zero_real @ Z )
% 8.69/4.90       => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 8.69/4.90          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3662_mult__le__cancel__iff2,axiom,
% 8.69/4.90      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.90        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 8.69/4.90       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 8.69/4.90          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3663_mult__le__cancel__iff2,axiom,
% 8.69/4.90      ! [Z: int,X: int,Y: int] :
% 8.69/4.90        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.90       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 8.69/4.90          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3664_divides__aux__eq,axiom,
% 8.69/4.90      ! [Q2: nat,R: nat] :
% 8.69/4.90        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 8.69/4.90        = ( R = zero_zero_nat ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3665_divides__aux__eq,axiom,
% 8.69/4.90      ! [Q2: int,R: int] :
% 8.69/4.90        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90        = ( R = zero_zero_int ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3666_neg__eucl__rel__int__mult__2,axiom,
% 8.69/4.90      ! [B: int,A: int,Q2: int,R: int] :
% 8.69/4.90        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.69/4.90       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3667_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3668_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3669_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3670_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3671_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3672_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_o,Ys: list_o] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3673_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_o,Ys: list_nat] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3674_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_o,Ys: list_int] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3675_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3676_product__nth,axiom,
% 8.69/4.90      ! [N: nat,Xs: list_nat,Ys: list_o] :
% 8.69/4.90        ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 8.69/4.90       => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys ) @ N )
% 8.69/4.90          = ( product_Pair_nat_o @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3677_obtain__set__succ,axiom,
% 8.69/4.90      ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( ord_less_nat @ X @ Z )
% 8.69/4.90       => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 8.69/4.90         => ( ( finite_finite_nat @ B3 )
% 8.69/4.90           => ( ( A2 = B3 )
% 8.69/4.90             => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3678_obtain__set__pred,axiom,
% 8.69/4.90      ! [Z: nat,X: nat,A2: set_nat] :
% 8.69/4.90        ( ( ord_less_nat @ Z @ X )
% 8.69/4.90       => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 8.69/4.90         => ( ( finite_finite_nat @ A2 )
% 8.69/4.90           => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3679_set__vebt__finite,axiom,
% 8.69/4.90      ! [T: vEBT_VEBT,N: nat] :
% 8.69/4.90        ( ( vEBT_invar_vebt @ T @ N )
% 8.69/4.90       => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3680_pred__none__empty,axiom,
% 8.69/4.90      ! [Xs: set_nat,A: nat] :
% 8.69/4.90        ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 8.69/4.90       => ( ( finite_finite_nat @ Xs )
% 8.69/4.90         => ~ ? [X4: nat] :
% 8.69/4.90                ( ( member_nat @ X4 @ Xs )
% 8.69/4.90                & ( ord_less_nat @ X4 @ A ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3681_succ__none__empty,axiom,
% 8.69/4.90      ! [Xs: set_nat,A: nat] :
% 8.69/4.90        ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 8.69/4.90       => ( ( finite_finite_nat @ Xs )
% 8.69/4.90         => ~ ? [X4: nat] :
% 8.69/4.90                ( ( member_nat @ X4 @ Xs )
% 8.69/4.90                & ( ord_less_nat @ A @ X4 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3682_List_Ofinite__set,axiom,
% 8.69/4.90      ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3683_List_Ofinite__set,axiom,
% 8.69/4.90      ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3684_List_Ofinite__set,axiom,
% 8.69/4.90      ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3685_List_Ofinite__set,axiom,
% 8.69/4.90      ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3686_finite__atLeastAtMost,axiom,
% 8.69/4.90      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3687_infinite__Icc__iff,axiom,
% 8.69/4.90      ! [A: rat,B: rat] :
% 8.69/4.90        ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 8.69/4.90        = ( ord_less_rat @ A @ B ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3688_infinite__Icc__iff,axiom,
% 8.69/4.90      ! [A: real,B: real] :
% 8.69/4.90        ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 8.69/4.90        = ( ord_less_real @ A @ B ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3689_length__product,axiom,
% 8.69/4.90      ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3690_length__product,axiom,
% 8.69/4.90      ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 8.69/4.90        ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3691_length__product,axiom,
% 8.69/4.90      ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 8.69/4.90        ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3692_length__product,axiom,
% 8.69/4.90      ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 8.69/4.90        ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3693_length__product,axiom,
% 8.69/4.90      ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3694_length__product,axiom,
% 8.69/4.90      ! [Xs: list_o,Ys: list_o] :
% 8.69/4.90        ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3695_length__product,axiom,
% 8.69/4.90      ! [Xs: list_o,Ys: list_nat] :
% 8.69/4.90        ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3696_length__product,axiom,
% 8.69/4.90      ! [Xs: list_o,Ys: list_int] :
% 8.69/4.90        ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3697_length__product,axiom,
% 8.69/4.90      ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 8.69/4.90        ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3698_length__product,axiom,
% 8.69/4.90      ! [Xs: list_nat,Ys: list_o] :
% 8.69/4.90        ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 8.69/4.90        = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3699_unique__remainder,axiom,
% 8.69/4.90      ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 8.69/4.90        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 8.69/4.90         => ( R = R3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3700_unique__quotient,axiom,
% 8.69/4.90      ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 8.69/4.90        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 8.69/4.90         => ( Q2 = Q4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3701_bounded__nat__set__is__finite,axiom,
% 8.69/4.90      ! [N4: set_nat,N: nat] :
% 8.69/4.90        ( ! [X6: nat] :
% 8.69/4.90            ( ( member_nat @ X6 @ N4 )
% 8.69/4.90           => ( ord_less_nat @ X6 @ N ) )
% 8.69/4.90       => ( finite_finite_nat @ N4 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3702_finite__nat__set__iff__bounded,axiom,
% 8.69/4.90      ( finite_finite_nat
% 8.69/4.90      = ( ^ [N6: set_nat] :
% 8.69/4.90          ? [M3: nat] :
% 8.69/4.90          ! [X3: nat] :
% 8.69/4.90            ( ( member_nat @ X3 @ N6 )
% 8.69/4.90           => ( ord_less_nat @ X3 @ M3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3703_finite__nat__set__iff__bounded__le,axiom,
% 8.69/4.90      ( finite_finite_nat
% 8.69/4.90      = ( ^ [N6: set_nat] :
% 8.69/4.90          ? [M3: nat] :
% 8.69/4.90          ! [X3: nat] :
% 8.69/4.90            ( ( member_nat @ X3 @ N6 )
% 8.69/4.90           => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3704_finite__list,axiom,
% 8.69/4.90      ! [A2: set_VEBT_VEBT] :
% 8.69/4.90        ( ( finite5795047828879050333T_VEBT @ A2 )
% 8.69/4.90       => ? [Xs3: list_VEBT_VEBT] :
% 8.69/4.90            ( ( set_VEBT_VEBT2 @ Xs3 )
% 8.69/4.90            = A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3705_finite__list,axiom,
% 8.69/4.90      ! [A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ? [Xs3: list_nat] :
% 8.69/4.90            ( ( set_nat2 @ Xs3 )
% 8.69/4.90            = A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3706_finite__list,axiom,
% 8.69/4.90      ! [A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ? [Xs3: list_int] :
% 8.69/4.90            ( ( set_int2 @ Xs3 )
% 8.69/4.90            = A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3707_finite__list,axiom,
% 8.69/4.90      ! [A2: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.90       => ? [Xs3: list_complex] :
% 8.69/4.90            ( ( set_complex2 @ Xs3 )
% 8.69/4.90            = A2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3708_finite__M__bounded__by__nat,axiom,
% 8.69/4.90      ! [P: nat > $o,I: nat] :
% 8.69/4.90        ( finite_finite_nat
% 8.69/4.90        @ ( collect_nat
% 8.69/4.90          @ ^ [K2: nat] :
% 8.69/4.90              ( ( P @ K2 )
% 8.69/4.90              & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3709_finite__less__ub,axiom,
% 8.69/4.90      ! [F: nat > nat,U: nat] :
% 8.69/4.90        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 8.69/4.90       => ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3710_finite__lists__length__eq,axiom,
% 8.69/4.90      ! [A2: set_complex,N: nat] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.90       => ( finite8712137658972009173omplex
% 8.69/4.90          @ ( collect_list_complex
% 8.69/4.90            @ ^ [Xs2: list_complex] :
% 8.69/4.90                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.69/4.90                  = N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3711_finite__lists__length__eq,axiom,
% 8.69/4.90      ! [A2: set_VEBT_VEBT,N: nat] :
% 8.69/4.90        ( ( finite5795047828879050333T_VEBT @ A2 )
% 8.69/4.90       => ( finite3004134309566078307T_VEBT
% 8.69/4.90          @ ( collec5608196760682091941T_VEBT
% 8.69/4.90            @ ^ [Xs2: list_VEBT_VEBT] :
% 8.69/4.90                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.69/4.90                  = N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3712_finite__lists__length__eq,axiom,
% 8.69/4.90      ! [A2: set_o,N: nat] :
% 8.69/4.90        ( ( finite_finite_o @ A2 )
% 8.69/4.90       => ( finite_finite_list_o
% 8.69/4.90          @ ( collect_list_o
% 8.69/4.90            @ ^ [Xs2: list_o] :
% 8.69/4.90                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ( size_size_list_o @ Xs2 )
% 8.69/4.90                  = N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3713_finite__lists__length__eq,axiom,
% 8.69/4.90      ! [A2: set_nat,N: nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( finite8100373058378681591st_nat
% 8.69/4.90          @ ( collect_list_nat
% 8.69/4.90            @ ^ [Xs2: list_nat] :
% 8.69/4.90                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ( size_size_list_nat @ Xs2 )
% 8.69/4.90                  = N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3714_finite__lists__length__eq,axiom,
% 8.69/4.90      ! [A2: set_int,N: nat] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( finite3922522038869484883st_int
% 8.69/4.90          @ ( collect_list_int
% 8.69/4.90            @ ^ [Xs2: list_int] :
% 8.69/4.90                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ( size_size_list_int @ Xs2 )
% 8.69/4.90                  = N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3715_eucl__rel__int__by0,axiom,
% 8.69/4.90      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3716_div__int__unique,axiom,
% 8.69/4.90      ! [K: int,L2: int,Q2: int,R: int] :
% 8.69/4.90        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90       => ( ( divide_divide_int @ K @ L2 )
% 8.69/4.90          = Q2 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3717_mod__int__unique,axiom,
% 8.69/4.90      ! [K: int,L2: int,Q2: int,R: int] :
% 8.69/4.90        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90       => ( ( modulo_modulo_int @ K @ L2 )
% 8.69/4.90          = R ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3718_ex__min__if__finite,axiom,
% 8.69/4.90      ! [S2: set_real] :
% 8.69/4.90        ( ( finite_finite_real @ S2 )
% 8.69/4.90       => ( ( S2 != bot_bot_set_real )
% 8.69/4.90         => ? [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ S2 )
% 8.69/4.90              & ~ ? [Xa: real] :
% 8.69/4.90                    ( ( member_real @ Xa @ S2 )
% 8.69/4.90                    & ( ord_less_real @ Xa @ X6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3719_ex__min__if__finite,axiom,
% 8.69/4.90      ! [S2: set_rat] :
% 8.69/4.90        ( ( finite_finite_rat @ S2 )
% 8.69/4.90       => ( ( S2 != bot_bot_set_rat )
% 8.69/4.90         => ? [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ S2 )
% 8.69/4.90              & ~ ? [Xa: rat] :
% 8.69/4.90                    ( ( member_rat @ Xa @ S2 )
% 8.69/4.90                    & ( ord_less_rat @ Xa @ X6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3720_ex__min__if__finite,axiom,
% 8.69/4.90      ! [S2: set_num] :
% 8.69/4.90        ( ( finite_finite_num @ S2 )
% 8.69/4.90       => ( ( S2 != bot_bot_set_num )
% 8.69/4.90         => ? [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ S2 )
% 8.69/4.90              & ~ ? [Xa: num] :
% 8.69/4.90                    ( ( member_num @ Xa @ S2 )
% 8.69/4.90                    & ( ord_less_num @ Xa @ X6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3721_ex__min__if__finite,axiom,
% 8.69/4.90      ! [S2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ S2 )
% 8.69/4.90       => ( ( S2 != bot_bot_set_nat )
% 8.69/4.90         => ? [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ S2 )
% 8.69/4.90              & ~ ? [Xa: nat] :
% 8.69/4.90                    ( ( member_nat @ Xa @ S2 )
% 8.69/4.90                    & ( ord_less_nat @ Xa @ X6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3722_ex__min__if__finite,axiom,
% 8.69/4.90      ! [S2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ S2 )
% 8.69/4.90       => ( ( S2 != bot_bot_set_int )
% 8.69/4.90         => ? [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ S2 )
% 8.69/4.90              & ~ ? [Xa: int] :
% 8.69/4.90                    ( ( member_int @ Xa @ S2 )
% 8.69/4.90                    & ( ord_less_int @ Xa @ X6 ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3723_infinite__growing,axiom,
% 8.69/4.90      ! [X8: set_real] :
% 8.69/4.90        ( ( X8 != bot_bot_set_real )
% 8.69/4.90       => ( ! [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ X8 )
% 8.69/4.90             => ? [Xa: real] :
% 8.69/4.90                  ( ( member_real @ Xa @ X8 )
% 8.69/4.90                  & ( ord_less_real @ X6 @ Xa ) ) )
% 8.69/4.90         => ~ ( finite_finite_real @ X8 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3724_infinite__growing,axiom,
% 8.69/4.90      ! [X8: set_rat] :
% 8.69/4.90        ( ( X8 != bot_bot_set_rat )
% 8.69/4.90       => ( ! [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ X8 )
% 8.69/4.90             => ? [Xa: rat] :
% 8.69/4.90                  ( ( member_rat @ Xa @ X8 )
% 8.69/4.90                  & ( ord_less_rat @ X6 @ Xa ) ) )
% 8.69/4.90         => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3725_infinite__growing,axiom,
% 8.69/4.90      ! [X8: set_num] :
% 8.69/4.90        ( ( X8 != bot_bot_set_num )
% 8.69/4.90       => ( ! [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ X8 )
% 8.69/4.90             => ? [Xa: num] :
% 8.69/4.90                  ( ( member_num @ Xa @ X8 )
% 8.69/4.90                  & ( ord_less_num @ X6 @ Xa ) ) )
% 8.69/4.90         => ~ ( finite_finite_num @ X8 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3726_infinite__growing,axiom,
% 8.69/4.90      ! [X8: set_nat] :
% 8.69/4.90        ( ( X8 != bot_bot_set_nat )
% 8.69/4.90       => ( ! [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ X8 )
% 8.69/4.90             => ? [Xa: nat] :
% 8.69/4.90                  ( ( member_nat @ Xa @ X8 )
% 8.69/4.90                  & ( ord_less_nat @ X6 @ Xa ) ) )
% 8.69/4.90         => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3727_infinite__growing,axiom,
% 8.69/4.90      ! [X8: set_int] :
% 8.69/4.90        ( ( X8 != bot_bot_set_int )
% 8.69/4.90       => ( ! [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ X8 )
% 8.69/4.90             => ? [Xa: int] :
% 8.69/4.90                  ( ( member_int @ Xa @ X8 )
% 8.69/4.90                  & ( ord_less_int @ X6 @ Xa ) ) )
% 8.69/4.90         => ~ ( finite_finite_int @ X8 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3728_infinite__Icc,axiom,
% 8.69/4.90      ! [A: rat,B: rat] :
% 8.69/4.90        ( ( ord_less_rat @ A @ B )
% 8.69/4.90       => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3729_infinite__Icc,axiom,
% 8.69/4.90      ! [A: real,B: real] :
% 8.69/4.90        ( ( ord_less_real @ A @ B )
% 8.69/4.90       => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3730_finite__lists__length__le,axiom,
% 8.69/4.90      ! [A2: set_complex,N: nat] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.90       => ( finite8712137658972009173omplex
% 8.69/4.90          @ ( collect_list_complex
% 8.69/4.90            @ ^ [Xs2: list_complex] :
% 8.69/4.90                ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3731_finite__lists__length__le,axiom,
% 8.69/4.90      ! [A2: set_VEBT_VEBT,N: nat] :
% 8.69/4.90        ( ( finite5795047828879050333T_VEBT @ A2 )
% 8.69/4.90       => ( finite3004134309566078307T_VEBT
% 8.69/4.90          @ ( collec5608196760682091941T_VEBT
% 8.69/4.90            @ ^ [Xs2: list_VEBT_VEBT] :
% 8.69/4.90                ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3732_finite__lists__length__le,axiom,
% 8.69/4.90      ! [A2: set_o,N: nat] :
% 8.69/4.90        ( ( finite_finite_o @ A2 )
% 8.69/4.90       => ( finite_finite_list_o
% 8.69/4.90          @ ( collect_list_o
% 8.69/4.90            @ ^ [Xs2: list_o] :
% 8.69/4.90                ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3733_finite__lists__length__le,axiom,
% 8.69/4.90      ! [A2: set_nat,N: nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( finite8100373058378681591st_nat
% 8.69/4.90          @ ( collect_list_nat
% 8.69/4.90            @ ^ [Xs2: list_nat] :
% 8.69/4.90                ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3734_finite__lists__length__le,axiom,
% 8.69/4.90      ! [A2: set_int,N: nat] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( finite3922522038869484883st_int
% 8.69/4.90          @ ( collect_list_int
% 8.69/4.90            @ ^ [Xs2: list_int] :
% 8.69/4.90                ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 8.69/4.90                & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3735_eucl__rel__int__dividesI,axiom,
% 8.69/4.90      ! [L2: int,K: int,Q2: int] :
% 8.69/4.90        ( ( L2 != zero_zero_int )
% 8.69/4.90       => ( ( K
% 8.69/4.90            = ( times_times_int @ Q2 @ L2 ) )
% 8.69/4.90         => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3736_eucl__rel__int,axiom,
% 8.69/4.90      ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3737_subset__eq__atLeast0__atMost__finite,axiom,
% 8.69/4.90      ! [N4: set_nat,N: nat] :
% 8.69/4.90        ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.90       => ( finite_finite_nat @ N4 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3738_eucl__rel__int__iff,axiom,
% 8.69/4.90      ! [K: int,L2: int,Q2: int,R: int] :
% 8.69/4.90        ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90        = ( ( K
% 8.69/4.90            = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 8.69/4.90          & ( ( ord_less_int @ zero_zero_int @ L2 )
% 8.69/4.90           => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 8.69/4.90              & ( ord_less_int @ R @ L2 ) ) )
% 8.69/4.90          & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 8.69/4.90           => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 8.69/4.90               => ( ( ord_less_int @ L2 @ R )
% 8.69/4.90                  & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 8.69/4.90              & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 8.69/4.90               => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3739_mult__less__iff1,axiom,
% 8.69/4.90      ! [Z: real,X: real,Y: real] :
% 8.69/4.90        ( ( ord_less_real @ zero_zero_real @ Z )
% 8.69/4.90       => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_real @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3740_mult__less__iff1,axiom,
% 8.69/4.90      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.90        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 8.69/4.90       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_rat @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3741_mult__less__iff1,axiom,
% 8.69/4.90      ! [Z: int,X: int,Y: int] :
% 8.69/4.90        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.90       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 8.69/4.90          = ( ord_less_int @ X @ Y ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3742_pos__eucl__rel__int__mult__2,axiom,
% 8.69/4.90      ! [B: int,A: int,Q2: int,R: int] :
% 8.69/4.90        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.69/4.90       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.90         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3743_finite__Collect__le__nat,axiom,
% 8.69/4.90      ! [K: nat] :
% 8.69/4.90        ( finite_finite_nat
% 8.69/4.90        @ ( collect_nat
% 8.69/4.90          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3744_finite__Collect__less__nat,axiom,
% 8.69/4.90      ! [K: nat] :
% 8.69/4.90        ( finite_finite_nat
% 8.69/4.90        @ ( collect_nat
% 8.69/4.90          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3745_finite__Collect__subsets,axiom,
% 8.69/4.90      ! [A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( finite1152437895449049373et_nat
% 8.69/4.90          @ ( collect_set_nat
% 8.69/4.90            @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A2 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3746_finite__Collect__subsets,axiom,
% 8.69/4.90      ! [A2: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.90       => ( finite6551019134538273531omplex
% 8.69/4.90          @ ( collect_set_complex
% 8.69/4.90            @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A2 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3747_finite__Collect__subsets,axiom,
% 8.69/4.90      ! [A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( finite6197958912794628473et_int
% 8.69/4.90          @ ( collect_set_int
% 8.69/4.90            @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A2 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3748_finite__roots__unity,axiom,
% 8.69/4.90      ! [N: nat] :
% 8.69/4.90        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.69/4.90       => ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [Z3: real] :
% 8.69/4.90                ( ( power_power_real @ Z3 @ N )
% 8.69/4.90                = one_one_real ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3749_finite__roots__unity,axiom,
% 8.69/4.90      ! [N: nat] :
% 8.69/4.90        ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.69/4.90       => ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [Z3: complex] :
% 8.69/4.90                ( ( power_power_complex @ Z3 @ N )
% 8.69/4.90                = one_one_complex ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3750_finite__Diff2,axiom,
% 8.69/4.90      ! [B3: set_int,A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ B3 )
% 8.69/4.90       => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.90          = ( finite_finite_int @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3751_finite__Diff2,axiom,
% 8.69/4.90      ! [B3: set_complex,A2: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.90       => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.90          = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3752_finite__Diff2,axiom,
% 8.69/4.90      ! [B3: set_nat,A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ B3 )
% 8.69/4.90       => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.90          = ( finite_finite_nat @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3753_finite__Diff,axiom,
% 8.69/4.90      ! [A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3754_finite__Diff,axiom,
% 8.69/4.90      ! [A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.90       => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3755_finite__Diff,axiom,
% 8.69/4.90      ! [A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3756_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > complex,Y: real > complex] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3757_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3758_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_int,X: int > complex,Y: int > complex] :
% 8.69/4.90        ( ( finite_finite_int
% 8.69/4.90          @ ( collect_int
% 8.69/4.90            @ ^ [I5: int] :
% 8.69/4.90                ( ( member_int @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3759_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [I5: complex] :
% 8.69/4.90                ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_complex ) ) ) )
% 8.69/4.90       => ( ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_complex ) ) ) )
% 8.69/4.90         => ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3760_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > real,Y: real > real] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_real ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3761_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_real ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3762_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_int,X: int > real,Y: int > real] :
% 8.69/4.90        ( ( finite_finite_int
% 8.69/4.90          @ ( collect_int
% 8.69/4.90            @ ^ [I5: int] :
% 8.69/4.90                ( ( member_int @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_real ) ) ) )
% 8.69/4.90         => ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3763_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 8.69/4.90        ( ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [I5: complex] :
% 8.69/4.90                ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_real ) ) ) )
% 8.69/4.90       => ( ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_real ) ) ) )
% 8.69/4.90         => ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3764_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > rat,Y: real > rat] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_rat ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_rat ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_rat ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3765_prod_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != one_one_rat ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != one_one_rat ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != one_one_rat ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3766_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > complex,Y: real > complex] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3767_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3768_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_int,X: int > complex,Y: int > complex] :
% 8.69/4.90        ( ( finite_finite_int
% 8.69/4.90          @ ( collect_int
% 8.69/4.90            @ ^ [I5: int] :
% 8.69/4.90                ( ( member_int @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_complex ) ) ) )
% 8.69/4.90       => ( ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_complex ) ) ) )
% 8.69/4.90         => ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3769_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [I5: complex] :
% 8.69/4.90                ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_complex ) ) ) )
% 8.69/4.90       => ( ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_complex ) ) ) )
% 8.69/4.90         => ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_complex ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3770_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > real,Y: real > real] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_real ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3771_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_real ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3772_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_int,X: int > real,Y: int > real] :
% 8.69/4.90        ( ( finite_finite_int
% 8.69/4.90          @ ( collect_int
% 8.69/4.90            @ ^ [I5: int] :
% 8.69/4.90                ( ( member_int @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_real ) ) ) )
% 8.69/4.90       => ( ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_real ) ) ) )
% 8.69/4.90         => ( finite_finite_int
% 8.69/4.90            @ ( collect_int
% 8.69/4.90              @ ^ [I5: int] :
% 8.69/4.90                  ( ( member_int @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3773_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 8.69/4.90        ( ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [I5: complex] :
% 8.69/4.90                ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_real ) ) ) )
% 8.69/4.90       => ( ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_real ) ) ) )
% 8.69/4.90         => ( finite3207457112153483333omplex
% 8.69/4.90            @ ( collect_complex
% 8.69/4.90              @ ^ [I5: complex] :
% 8.69/4.90                  ( ( member_complex @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3774_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_real,X: real > rat,Y: real > rat] :
% 8.69/4.90        ( ( finite_finite_real
% 8.69/4.90          @ ( collect_real
% 8.69/4.90            @ ^ [I5: real] :
% 8.69/4.90                ( ( member_real @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_rat ) ) ) )
% 8.69/4.90       => ( ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_rat ) ) ) )
% 8.69/4.90         => ( finite_finite_real
% 8.69/4.90            @ ( collect_real
% 8.69/4.90              @ ^ [I5: real] :
% 8.69/4.90                  ( ( member_real @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3775_sum_Ofinite__Collect__op,axiom,
% 8.69/4.90      ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 8.69/4.90        ( ( finite_finite_nat
% 8.69/4.90          @ ( collect_nat
% 8.69/4.90            @ ^ [I5: nat] :
% 8.69/4.90                ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                & ( ( X @ I5 )
% 8.69/4.90                 != zero_zero_rat ) ) ) )
% 8.69/4.90       => ( ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( Y @ I5 )
% 8.69/4.90                   != zero_zero_rat ) ) ) )
% 8.69/4.90         => ( finite_finite_nat
% 8.69/4.90            @ ( collect_nat
% 8.69/4.90              @ ^ [I5: nat] :
% 8.69/4.90                  ( ( member_nat @ I5 @ I6 )
% 8.69/4.90                  & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 8.69/4.90                   != zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3776_finite__atLeastAtMost__int,axiom,
% 8.69/4.90      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3777_finite__interval__int1,axiom,
% 8.69/4.90      ! [A: int,B: int] :
% 8.69/4.90        ( finite_finite_int
% 8.69/4.90        @ ( collect_int
% 8.69/4.90          @ ^ [I5: int] :
% 8.69/4.90              ( ( ord_less_eq_int @ A @ I5 )
% 8.69/4.90              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3778_finite__interval__int3,axiom,
% 8.69/4.90      ! [A: int,B: int] :
% 8.69/4.90        ( finite_finite_int
% 8.69/4.90        @ ( collect_int
% 8.69/4.90          @ ^ [I5: int] :
% 8.69/4.90              ( ( ord_less_int @ A @ I5 )
% 8.69/4.90              & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3779_finite__interval__int2,axiom,
% 8.69/4.90      ! [A: int,B: int] :
% 8.69/4.90        ( finite_finite_int
% 8.69/4.90        @ ( collect_int
% 8.69/4.90          @ ^ [I5: int] :
% 8.69/4.90              ( ( ord_less_eq_int @ A @ I5 )
% 8.69/4.90              & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3780_finite__maxlen,axiom,
% 8.69/4.90      ! [M5: set_list_VEBT_VEBT] :
% 8.69/4.90        ( ( finite3004134309566078307T_VEBT @ M5 )
% 8.69/4.90       => ? [N3: nat] :
% 8.69/4.90          ! [X4: list_VEBT_VEBT] :
% 8.69/4.90            ( ( member2936631157270082147T_VEBT @ X4 @ M5 )
% 8.69/4.90           => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X4 ) @ N3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3781_finite__maxlen,axiom,
% 8.69/4.90      ! [M5: set_list_o] :
% 8.69/4.90        ( ( finite_finite_list_o @ M5 )
% 8.69/4.90       => ? [N3: nat] :
% 8.69/4.90          ! [X4: list_o] :
% 8.69/4.90            ( ( member_list_o @ X4 @ M5 )
% 8.69/4.90           => ( ord_less_nat @ ( size_size_list_o @ X4 ) @ N3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3782_finite__maxlen,axiom,
% 8.69/4.90      ! [M5: set_list_nat] :
% 8.69/4.90        ( ( finite8100373058378681591st_nat @ M5 )
% 8.69/4.90       => ? [N3: nat] :
% 8.69/4.90          ! [X4: list_nat] :
% 8.69/4.90            ( ( member_list_nat @ X4 @ M5 )
% 8.69/4.90           => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3783_finite__maxlen,axiom,
% 8.69/4.90      ! [M5: set_list_int] :
% 8.69/4.90        ( ( finite3922522038869484883st_int @ M5 )
% 8.69/4.90       => ? [N3: nat] :
% 8.69/4.90          ! [X4: list_int] :
% 8.69/4.90            ( ( member_list_int @ X4 @ M5 )
% 8.69/4.90           => ( ord_less_nat @ ( size_size_list_int @ X4 ) @ N3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3784_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_real,A: real] :
% 8.69/4.90        ( ( finite_finite_real @ A2 )
% 8.69/4.90       => ( ( member_real @ A @ A2 )
% 8.69/4.90         => ? [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_real @ A @ X6 )
% 8.69/4.90              & ! [Xa: real] :
% 8.69/4.90                  ( ( member_real @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_real @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3785_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_set_nat,A: set_nat] :
% 8.69/4.90        ( ( finite1152437895449049373et_nat @ A2 )
% 8.69/4.90       => ( ( member_set_nat @ A @ A2 )
% 8.69/4.90         => ? [X6: set_nat] :
% 8.69/4.90              ( ( member_set_nat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_set_nat @ A @ X6 )
% 8.69/4.90              & ! [Xa: set_nat] :
% 8.69/4.90                  ( ( member_set_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_nat @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3786_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_set_int,A: set_int] :
% 8.69/4.90        ( ( finite6197958912794628473et_int @ A2 )
% 8.69/4.90       => ( ( member_set_int @ A @ A2 )
% 8.69/4.90         => ? [X6: set_int] :
% 8.69/4.90              ( ( member_set_int @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_set_int @ A @ X6 )
% 8.69/4.90              & ! [Xa: set_int] :
% 8.69/4.90                  ( ( member_set_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3787_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_rat,A: rat] :
% 8.69/4.90        ( ( finite_finite_rat @ A2 )
% 8.69/4.90       => ( ( member_rat @ A @ A2 )
% 8.69/4.90         => ? [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_rat @ A @ X6 )
% 8.69/4.90              & ! [Xa: rat] :
% 8.69/4.90                  ( ( member_rat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3788_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_num,A: num] :
% 8.69/4.90        ( ( finite_finite_num @ A2 )
% 8.69/4.90       => ( ( member_num @ A @ A2 )
% 8.69/4.90         => ? [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_num @ A @ X6 )
% 8.69/4.90              & ! [Xa: num] :
% 8.69/4.90                  ( ( member_num @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_num @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3789_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_nat,A: nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( ( member_nat @ A @ A2 )
% 8.69/4.90         => ? [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_nat @ A @ X6 )
% 8.69/4.90              & ! [Xa: nat] :
% 8.69/4.90                  ( ( member_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3790_finite__has__maximal2,axiom,
% 8.69/4.90      ! [A2: set_int,A: int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( ( member_int @ A @ A2 )
% 8.69/4.90         => ? [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_int @ A @ X6 )
% 8.69/4.90              & ! [Xa: int] :
% 8.69/4.90                  ( ( member_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_int @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3791_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_real,A: real] :
% 8.69/4.90        ( ( finite_finite_real @ A2 )
% 8.69/4.90       => ( ( member_real @ A @ A2 )
% 8.69/4.90         => ? [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_real @ X6 @ A )
% 8.69/4.90              & ! [Xa: real] :
% 8.69/4.90                  ( ( member_real @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_real @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3792_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_set_nat,A: set_nat] :
% 8.69/4.90        ( ( finite1152437895449049373et_nat @ A2 )
% 8.69/4.90       => ( ( member_set_nat @ A @ A2 )
% 8.69/4.90         => ? [X6: set_nat] :
% 8.69/4.90              ( ( member_set_nat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_set_nat @ X6 @ A )
% 8.69/4.90              & ! [Xa: set_nat] :
% 8.69/4.90                  ( ( member_set_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_nat @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3793_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_set_int,A: set_int] :
% 8.69/4.90        ( ( finite6197958912794628473et_int @ A2 )
% 8.69/4.90       => ( ( member_set_int @ A @ A2 )
% 8.69/4.90         => ? [X6: set_int] :
% 8.69/4.90              ( ( member_set_int @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_set_int @ X6 @ A )
% 8.69/4.90              & ! [Xa: set_int] :
% 8.69/4.90                  ( ( member_set_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3794_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_rat,A: rat] :
% 8.69/4.90        ( ( finite_finite_rat @ A2 )
% 8.69/4.90       => ( ( member_rat @ A @ A2 )
% 8.69/4.90         => ? [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_rat @ X6 @ A )
% 8.69/4.90              & ! [Xa: rat] :
% 8.69/4.90                  ( ( member_rat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3795_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_num,A: num] :
% 8.69/4.90        ( ( finite_finite_num @ A2 )
% 8.69/4.90       => ( ( member_num @ A @ A2 )
% 8.69/4.90         => ? [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_num @ X6 @ A )
% 8.69/4.90              & ! [Xa: num] :
% 8.69/4.90                  ( ( member_num @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_num @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3796_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_nat,A: nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( ( member_nat @ A @ A2 )
% 8.69/4.90         => ? [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_nat @ X6 @ A )
% 8.69/4.90              & ! [Xa: nat] :
% 8.69/4.90                  ( ( member_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3797_finite__has__minimal2,axiom,
% 8.69/4.90      ! [A2: set_int,A: int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( ( member_int @ A @ A2 )
% 8.69/4.90         => ? [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ A2 )
% 8.69/4.90              & ( ord_less_eq_int @ X6 @ A )
% 8.69/4.90              & ! [Xa: int] :
% 8.69/4.90                  ( ( member_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_int @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3798_finite__subset,axiom,
% 8.69/4.90      ! [A2: set_nat,B3: set_nat] :
% 8.69/4.90        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.90       => ( ( finite_finite_nat @ B3 )
% 8.69/4.90         => ( finite_finite_nat @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3799_finite__subset,axiom,
% 8.69/4.90      ! [A2: set_complex,B3: set_complex] :
% 8.69/4.90        ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.90       => ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.90         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3800_finite__subset,axiom,
% 8.69/4.90      ! [A2: set_int,B3: set_int] :
% 8.69/4.90        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.69/4.90       => ( ( finite_finite_int @ B3 )
% 8.69/4.90         => ( finite_finite_int @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3801_infinite__super,axiom,
% 8.69/4.90      ! [S2: set_nat,T3: set_nat] :
% 8.69/4.90        ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.90       => ( ~ ( finite_finite_nat @ S2 )
% 8.69/4.90         => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3802_infinite__super,axiom,
% 8.69/4.90      ! [S2: set_complex,T3: set_complex] :
% 8.69/4.90        ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.90       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 8.69/4.90         => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3803_infinite__super,axiom,
% 8.69/4.90      ! [S2: set_int,T3: set_int] :
% 8.69/4.90        ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.90       => ( ~ ( finite_finite_int @ S2 )
% 8.69/4.90         => ~ ( finite_finite_int @ T3 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3804_rev__finite__subset,axiom,
% 8.69/4.90      ! [B3: set_nat,A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ B3 )
% 8.69/4.90       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.90         => ( finite_finite_nat @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3805_rev__finite__subset,axiom,
% 8.69/4.90      ! [B3: set_complex,A2: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.90       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.90         => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3806_rev__finite__subset,axiom,
% 8.69/4.90      ! [B3: set_int,A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ B3 )
% 8.69/4.90       => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.69/4.90         => ( finite_finite_int @ A2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3807_Diff__infinite__finite,axiom,
% 8.69/4.90      ! [T3: set_int,S2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ T3 )
% 8.69/4.90       => ( ~ ( finite_finite_int @ S2 )
% 8.69/4.90         => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3808_Diff__infinite__finite,axiom,
% 8.69/4.90      ! [T3: set_complex,S2: set_complex] :
% 8.69/4.90        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.90       => ( ~ ( finite3207457112153483333omplex @ S2 )
% 8.69/4.90         => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3809_Diff__infinite__finite,axiom,
% 8.69/4.90      ! [T3: set_nat,S2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ T3 )
% 8.69/4.90       => ( ~ ( finite_finite_nat @ S2 )
% 8.69/4.90         => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3810_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_real] :
% 8.69/4.90        ( ( finite_finite_real @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_real )
% 8.69/4.90         => ? [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: real] :
% 8.69/4.90                  ( ( member_real @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_real @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3811_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_set_int] :
% 8.69/4.90        ( ( finite6197958912794628473et_int @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_set_int )
% 8.69/4.90         => ? [X6: set_int] :
% 8.69/4.90              ( ( member_set_int @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: set_int] :
% 8.69/4.90                  ( ( member_set_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3812_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_rat] :
% 8.69/4.90        ( ( finite_finite_rat @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_rat )
% 8.69/4.90         => ? [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: rat] :
% 8.69/4.90                  ( ( member_rat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3813_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_num] :
% 8.69/4.90        ( ( finite_finite_num @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_num )
% 8.69/4.90         => ? [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: num] :
% 8.69/4.90                  ( ( member_num @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_num @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3814_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_nat )
% 8.69/4.90         => ? [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: nat] :
% 8.69/4.90                  ( ( member_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3815_finite__has__minimal,axiom,
% 8.69/4.90      ! [A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_int )
% 8.69/4.90         => ? [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: int] :
% 8.69/4.90                  ( ( member_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_int @ Xa @ X6 )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3816_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_real] :
% 8.69/4.90        ( ( finite_finite_real @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_real )
% 8.69/4.90         => ? [X6: real] :
% 8.69/4.90              ( ( member_real @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: real] :
% 8.69/4.90                  ( ( member_real @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_real @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3817_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_set_int] :
% 8.69/4.90        ( ( finite6197958912794628473et_int @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_set_int )
% 8.69/4.90         => ? [X6: set_int] :
% 8.69/4.90              ( ( member_set_int @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: set_int] :
% 8.69/4.90                  ( ( member_set_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3818_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_rat] :
% 8.69/4.90        ( ( finite_finite_rat @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_rat )
% 8.69/4.90         => ? [X6: rat] :
% 8.69/4.90              ( ( member_rat @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: rat] :
% 8.69/4.90                  ( ( member_rat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3819_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_num] :
% 8.69/4.90        ( ( finite_finite_num @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_num )
% 8.69/4.90         => ? [X6: num] :
% 8.69/4.90              ( ( member_num @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: num] :
% 8.69/4.90                  ( ( member_num @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_num @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3820_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_nat] :
% 8.69/4.90        ( ( finite_finite_nat @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_nat )
% 8.69/4.90         => ? [X6: nat] :
% 8.69/4.90              ( ( member_nat @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: nat] :
% 8.69/4.90                  ( ( member_nat @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3821_finite__has__maximal,axiom,
% 8.69/4.90      ! [A2: set_int] :
% 8.69/4.90        ( ( finite_finite_int @ A2 )
% 8.69/4.90       => ( ( A2 != bot_bot_set_int )
% 8.69/4.90         => ? [X6: int] :
% 8.69/4.90              ( ( member_int @ X6 @ A2 )
% 8.69/4.90              & ! [Xa: int] :
% 8.69/4.90                  ( ( member_int @ Xa @ A2 )
% 8.69/4.90                 => ( ( ord_less_eq_int @ X6 @ Xa )
% 8.69/4.90                   => ( X6 = Xa ) ) ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3822_arcosh__1,axiom,
% 8.69/4.90      ( ( arcosh_real @ one_one_real )
% 8.69/4.90      = zero_zero_real ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3823_finite__nth__roots,axiom,
% 8.69/4.90      ! [N: nat,C: complex] :
% 8.69/4.90        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.90       => ( finite3207457112153483333omplex
% 8.69/4.90          @ ( collect_complex
% 8.69/4.90            @ ^ [Z3: complex] :
% 8.69/4.90                ( ( power_power_complex @ Z3 @ N )
% 8.69/4.90                = C ) ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3824_artanh__0,axiom,
% 8.69/4.90      ( ( artanh_real @ zero_zero_real )
% 8.69/4.90      = zero_zero_real ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3825_arsinh__0,axiom,
% 8.69/4.90      ( ( arsinh_real @ zero_zero_real )
% 8.69/4.90      = zero_zero_real ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3826_prod_Oinject,axiom,
% 8.69/4.90      ! [X1: int,X22: int,Y1: int,Y22: int] :
% 8.69/4.90        ( ( ( product_Pair_int_int @ X1 @ X22 )
% 8.69/4.90          = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 8.69/4.90        = ( ( X1 = Y1 )
% 8.69/4.90          & ( X22 = Y22 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3827_prod_Oinject,axiom,
% 8.69/4.90      ! [X1: code_integer > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc6137756002093451184nteger @ X1 @ X22 )
% 8.69/4.90          = ( produc6137756002093451184nteger @ Y1 @ Y22 ) )
% 8.69/4.90        = ( ( X1 = Y1 )
% 8.69/4.90          & ( X22 = Y22 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3828_prod_Oinject,axiom,
% 8.69/4.90      ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 8.69/4.90          = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 8.69/4.90        = ( ( X1 = Y1 )
% 8.69/4.90          & ( X22 = Y22 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3829_prod_Oinject,axiom,
% 8.69/4.90      ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 8.69/4.90          = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 8.69/4.90        = ( ( X1 = Y1 )
% 8.69/4.90          & ( X22 = Y22 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3830_prod_Oinject,axiom,
% 8.69/4.90      ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 8.69/4.90          = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 8.69/4.90        = ( ( X1 = Y1 )
% 8.69/4.90          & ( X22 = Y22 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3831_old_Oprod_Oinject,axiom,
% 8.69/4.90      ! [A: int,B: int,A4: int,B4: int] :
% 8.69/4.90        ( ( ( product_Pair_int_int @ A @ B )
% 8.69/4.90          = ( product_Pair_int_int @ A4 @ B4 ) )
% 8.69/4.90        = ( ( A = A4 )
% 8.69/4.90          & ( B = B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3832_old_Oprod_Oinject,axiom,
% 8.69/4.90      ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc6137756002093451184nteger @ A @ B )
% 8.69/4.90          = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 8.69/4.90        = ( ( A = A4 )
% 8.69/4.90          & ( B = B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3833_old_Oprod_Oinject,axiom,
% 8.69/4.90      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc8603105652947943368nteger @ A @ B )
% 8.69/4.90          = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 8.69/4.90        = ( ( A = A4 )
% 8.69/4.90          & ( B = B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3834_old_Oprod_Oinject,axiom,
% 8.69/4.90      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 8.69/4.90          = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 8.69/4.90        = ( ( A = A4 )
% 8.69/4.90          & ( B = B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3835_old_Oprod_Oinject,axiom,
% 8.69/4.90      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 8.69/4.90          = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 8.69/4.90        = ( ( A = A4 )
% 8.69/4.90          & ( B = B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3836_old_Oprod_Oexhaust,axiom,
% 8.69/4.90      ! [Y: product_prod_int_int] :
% 8.69/4.90        ~ ! [A5: int,B5: int] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( product_Pair_int_int @ A5 @ B5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3837_old_Oprod_Oexhaust,axiom,
% 8.69/4.90      ! [Y: produc8763457246119570046nteger] :
% 8.69/4.90        ~ ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc6137756002093451184nteger @ A5 @ B5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3838_old_Oprod_Oexhaust,axiom,
% 8.69/4.90      ! [Y: produc1908205239877642774nteger] :
% 8.69/4.90        ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc8603105652947943368nteger @ A5 @ B5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3839_old_Oprod_Oexhaust,axiom,
% 8.69/4.90      ! [Y: produc2285326912895808259nt_int] :
% 8.69/4.90        ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc5700946648718959541nt_int @ A5 @ B5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3840_old_Oprod_Oexhaust,axiom,
% 8.69/4.90      ! [Y: produc7773217078559923341nt_int] :
% 8.69/4.90        ~ ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc4305682042979456191nt_int @ A5 @ B5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3841_surj__pair,axiom,
% 8.69/4.90      ! [P5: product_prod_int_int] :
% 8.69/4.90      ? [X6: int,Y5: int] :
% 8.69/4.90        ( P5
% 8.69/4.90        = ( product_Pair_int_int @ X6 @ Y5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3842_surj__pair,axiom,
% 8.69/4.90      ! [P5: produc8763457246119570046nteger] :
% 8.69/4.90      ? [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.90        ( P5
% 8.69/4.90        = ( produc6137756002093451184nteger @ X6 @ Y5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3843_surj__pair,axiom,
% 8.69/4.90      ! [P5: produc1908205239877642774nteger] :
% 8.69/4.90      ? [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.90        ( P5
% 8.69/4.90        = ( produc8603105652947943368nteger @ X6 @ Y5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3844_surj__pair,axiom,
% 8.69/4.90      ! [P5: produc2285326912895808259nt_int] :
% 8.69/4.90      ? [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 8.69/4.90        ( P5
% 8.69/4.90        = ( produc5700946648718959541nt_int @ X6 @ Y5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3845_surj__pair,axiom,
% 8.69/4.90      ! [P5: produc7773217078559923341nt_int] :
% 8.69/4.90      ? [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 8.69/4.90        ( P5
% 8.69/4.90        = ( produc4305682042979456191nt_int @ X6 @ Y5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3846_prod__cases,axiom,
% 8.69/4.90      ! [P: product_prod_int_int > $o,P5: product_prod_int_int] :
% 8.69/4.90        ( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.90       => ( P @ P5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3847_prod__cases,axiom,
% 8.69/4.90      ! [P: produc8763457246119570046nteger > $o,P5: produc8763457246119570046nteger] :
% 8.69/4.90        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.90       => ( P @ P5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3848_prod__cases,axiom,
% 8.69/4.90      ! [P: produc1908205239877642774nteger > $o,P5: produc1908205239877642774nteger] :
% 8.69/4.90        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 8.69/4.90       => ( P @ P5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3849_prod__cases,axiom,
% 8.69/4.90      ! [P: produc2285326912895808259nt_int > $o,P5: produc2285326912895808259nt_int] :
% 8.69/4.90        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 8.69/4.90       => ( P @ P5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3850_prod__cases,axiom,
% 8.69/4.90      ! [P: produc7773217078559923341nt_int > $o,P5: produc7773217078559923341nt_int] :
% 8.69/4.90        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 8.69/4.90       => ( P @ P5 ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3851_Pair__inject,axiom,
% 8.69/4.90      ! [A: int,B: int,A4: int,B4: int] :
% 8.69/4.90        ( ( ( product_Pair_int_int @ A @ B )
% 8.69/4.90          = ( product_Pair_int_int @ A4 @ B4 ) )
% 8.69/4.90       => ~ ( ( A = A4 )
% 8.69/4.90           => ( B != B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3852_Pair__inject,axiom,
% 8.69/4.90      ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc6137756002093451184nteger @ A @ B )
% 8.69/4.90          = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 8.69/4.90       => ~ ( ( A = A4 )
% 8.69/4.90           => ( B != B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3853_Pair__inject,axiom,
% 8.69/4.90      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 8.69/4.90        ( ( ( produc8603105652947943368nteger @ A @ B )
% 8.69/4.90          = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 8.69/4.90       => ~ ( ( A = A4 )
% 8.69/4.90           => ( B != B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3854_Pair__inject,axiom,
% 8.69/4.90      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 8.69/4.90          = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 8.69/4.90       => ~ ( ( A = A4 )
% 8.69/4.90           => ( B != B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3855_Pair__inject,axiom,
% 8.69/4.90      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 8.69/4.90        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 8.69/4.90          = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 8.69/4.90       => ~ ( ( A = A4 )
% 8.69/4.90           => ( B != B4 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3856_prod__cases3,axiom,
% 8.69/4.90      ! [Y: produc8763457246119570046nteger] :
% 8.69/4.90        ~ ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3857_prod__cases3,axiom,
% 8.69/4.90      ! [Y: produc1908205239877642774nteger] :
% 8.69/4.90        ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3858_prod__cases3,axiom,
% 8.69/4.90      ! [Y: produc2285326912895808259nt_int] :
% 8.69/4.90        ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3859_prod__cases3,axiom,
% 8.69/4.90      ! [Y: produc7773217078559923341nt_int] :
% 8.69/4.90        ~ ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] :
% 8.69/4.90            ( Y
% 8.69/4.90           != ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3860_prod__induct3,axiom,
% 8.69/4.90      ! [P: produc8763457246119570046nteger > $o,X: produc8763457246119570046nteger] :
% 8.69/4.90        ( ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 8.69/4.90       => ( P @ X ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3861_prod__induct3,axiom,
% 8.69/4.90      ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 8.69/4.90        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 8.69/4.90       => ( P @ X ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3862_prod__induct3,axiom,
% 8.69/4.90      ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 8.69/4.90        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 8.69/4.90       => ( P @ X ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3863_prod__induct3,axiom,
% 8.69/4.90      ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 8.69/4.90        ( ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 8.69/4.90       => ( P @ X ) ) ).
% 8.69/4.90  
% 8.69/4.90  thf(fact_3864_artanh__def,axiom,
% 8.69/4.90      ( artanh_real
% 8.69/4.90      = ( ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3865_gcd__nat__induct,axiom,
% 8.69/4.91      ! [P: nat > nat > $o,M: nat,N: nat] :
% 8.69/4.91        ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 8.69/4.91       => ( ! [M4: nat,N3: nat] :
% 8.69/4.91              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.69/4.91             => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 8.69/4.91               => ( P @ M4 @ N3 ) ) )
% 8.69/4.91         => ( P @ M @ N ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3866_concat__bit__Suc,axiom,
% 8.69/4.91      ! [N: nat,K: int,L2: int] :
% 8.69/4.91        ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 8.69/4.91        = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3867_dual__order_Orefl,axiom,
% 8.69/4.91      ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3868_dual__order_Orefl,axiom,
% 8.69/4.91      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3869_dual__order_Orefl,axiom,
% 8.69/4.91      ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3870_dual__order_Orefl,axiom,
% 8.69/4.91      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3871_dual__order_Orefl,axiom,
% 8.69/4.91      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3872_order__refl,axiom,
% 8.69/4.91      ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3873_order__refl,axiom,
% 8.69/4.91      ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3874_order__refl,axiom,
% 8.69/4.91      ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3875_order__refl,axiom,
% 8.69/4.91      ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3876_order__refl,axiom,
% 8.69/4.91      ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3877_ln__less__cancel__iff,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 8.69/4.91            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3878_ln__inj__iff,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ( ( ln_ln_real @ X )
% 8.69/4.91              = ( ln_ln_real @ Y ) )
% 8.69/4.91            = ( X = Y ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3879_concat__bit__0,axiom,
% 8.69/4.91      ! [K: int,L2: int] :
% 8.69/4.91        ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 8.69/4.91        = L2 ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3880_ln__le__cancel__iff,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 8.69/4.91            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3881_ln__less__zero__iff,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 8.69/4.91          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3882_ln__gt__zero__iff,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 8.69/4.91          = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3883_ln__eq__zero__iff,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ( ln_ln_real @ X )
% 8.69/4.91            = zero_zero_real )
% 8.69/4.91          = ( X = one_one_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3884_ln__one,axiom,
% 8.69/4.91      ( ( ln_ln_real @ one_one_real )
% 8.69/4.91      = zero_zero_real ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3885_concat__bit__nonnegative__iff,axiom,
% 8.69/4.91      ! [N: nat,K: int,L2: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 8.69/4.91        = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3886_concat__bit__negative__iff,axiom,
% 8.69/4.91      ! [N: nat,K: int,L2: int] :
% 8.69/4.91        ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 8.69/4.91        = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3887_ln__le__zero__iff,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 8.69/4.91          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3888_ln__ge__zero__iff,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 8.69/4.91          = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3889_concat__bit__assoc,axiom,
% 8.69/4.91      ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 8.69/4.91        ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 8.69/4.91        = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3890_ln__less__self,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3891_ln__bound,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3892_ln__gt__zero__imp__gt__one,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91         => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3893_ln__less__zero,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/4.91         => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3894_ln__gt__zero,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.91       => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3895_ln__ge__zero,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.91       => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3896_order__antisym__conv,axiom,
% 8.69/4.91      ! [Y: set_int,X: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ Y @ X )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3897_order__antisym__conv,axiom,
% 8.69/4.91      ! [Y: rat,X: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ Y @ X )
% 8.69/4.91       => ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3898_order__antisym__conv,axiom,
% 8.69/4.91      ! [Y: num,X: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ Y @ X )
% 8.69/4.91       => ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3899_order__antisym__conv,axiom,
% 8.69/4.91      ! [Y: nat,X: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.91       => ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3900_order__antisym__conv,axiom,
% 8.69/4.91      ! [Y: int,X: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ Y @ X )
% 8.69/4.91       => ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3901_linorder__le__cases,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ~ ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3902_linorder__le__cases,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ~ ( ord_less_eq_num @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3903_linorder__le__cases,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ~ ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3904_linorder__le__cases,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ~ ( ord_less_eq_int @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3905_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3906_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3907_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3908_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3909_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3910_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3911_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3912_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3913_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3914_ord__le__eq__subst,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3915_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3916_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3917_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3918_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3919_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3920_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: num,F: num > num,B: num,C: num] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3921_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3922_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: int,F: num > int,B: num,C: num] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3923_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3924_ord__eq__le__subst,axiom,
% 8.69/4.91      ! [A: num,F: nat > num,B: nat,C: nat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3925_linorder__linear,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91        | ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3926_linorder__linear,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91        | ( ord_less_eq_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3927_linorder__linear,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91        | ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3928_linorder__linear,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91        | ( ord_less_eq_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3929_order__eq__refl,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int] :
% 8.69/4.91        ( ( X = Y )
% 8.69/4.91       => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3930_order__eq__refl,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( X = Y )
% 8.69/4.91       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3931_order__eq__refl,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( X = Y )
% 8.69/4.91       => ( ord_less_eq_num @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3932_order__eq__refl,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( X = Y )
% 8.69/4.91       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3933_order__eq__refl,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( X = Y )
% 8.69/4.91       => ( ord_less_eq_int @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3934_order__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3935_order__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3936_order__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3937_order__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3938_order__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3939_order__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3940_order__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3941_order__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3942_order__subst2,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3943_order__subst2,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3944_order__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3945_order__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3946_order__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3947_order__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_eq_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3948_order__subst1,axiom,
% 8.69/4.91      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3949_order__subst1,axiom,
% 8.69/4.91      ! [A: num,F: num > num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3950_order__subst1,axiom,
% 8.69/4.91      ! [A: num,F: nat > num,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_eq_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3951_order__subst1,axiom,
% 8.69/4.91      ! [A: num,F: int > num,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_eq_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3952_order__subst1,axiom,
% 8.69/4.91      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3953_order__subst1,axiom,
% 8.69/4.91      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3954_Orderings_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: set_int,B2: set_int] :
% 8.69/4.91            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 8.69/4.91            & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3955_Orderings_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.91            ( ( ord_less_eq_rat @ A3 @ B2 )
% 8.69/4.91            & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3956_Orderings_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: num,B2: num] :
% 8.69/4.91            ( ( ord_less_eq_num @ A3 @ B2 )
% 8.69/4.91            & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3957_Orderings_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.91            ( ( ord_less_eq_nat @ A3 @ B2 )
% 8.69/4.91            & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3958_Orderings_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: int,B2: int] :
% 8.69/4.91            ( ( ord_less_eq_int @ A3 @ B2 )
% 8.69/4.91            & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3959_antisym,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ B @ A )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3960_antisym,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ A )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3961_antisym,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ A )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3962_antisym,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ A )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3963_antisym,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_int @ B @ A )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3964_dual__order_Otrans,axiom,
% 8.69/4.91      ! [B: set_int,A: set_int,C: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ C @ B )
% 8.69/4.91         => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3965_dual__order_Otrans,axiom,
% 8.69/4.91      ! [B: rat,A: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_rat @ C @ B )
% 8.69/4.91         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3966_dual__order_Otrans,axiom,
% 8.69/4.91      ! [B: num,A: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_num @ C @ B )
% 8.69/4.91         => ( ord_less_eq_num @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3967_dual__order_Otrans,axiom,
% 8.69/4.91      ! [B: nat,A: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_nat @ C @ B )
% 8.69/4.91         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3968_dual__order_Otrans,axiom,
% 8.69/4.91      ! [B: int,A: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_int @ C @ B )
% 8.69/4.91         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3969_dual__order_Oantisym,axiom,
% 8.69/4.91      ! [B: set_int,A: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3970_dual__order_Oantisym,axiom,
% 8.69/4.91      ! [B: rat,A: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3971_dual__order_Oantisym,axiom,
% 8.69/4.91      ! [B: num,A: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3972_dual__order_Oantisym,axiom,
% 8.69/4.91      ! [B: nat,A: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3973_dual__order_Oantisym,axiom,
% 8.69/4.91      ! [B: int,A: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ B @ A )
% 8.69/4.91       => ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91         => ( A = B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3974_dual__order_Oeq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: set_int,B2: set_int] :
% 8.69/4.91            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 8.69/4.91            & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3975_dual__order_Oeq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.91            ( ( ord_less_eq_rat @ B2 @ A3 )
% 8.69/4.91            & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3976_dual__order_Oeq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: num,B2: num] :
% 8.69/4.91            ( ( ord_less_eq_num @ B2 @ A3 )
% 8.69/4.91            & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3977_dual__order_Oeq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.91            ( ( ord_less_eq_nat @ B2 @ A3 )
% 8.69/4.91            & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3978_dual__order_Oeq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [A3: int,B2: int] :
% 8.69/4.91            ( ( ord_less_eq_int @ B2 @ A3 )
% 8.69/4.91            & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3979_linorder__wlog,axiom,
% 8.69/4.91      ! [P: rat > rat > $o,A: rat,B: rat] :
% 8.69/4.91        ( ! [A5: rat,B5: rat] :
% 8.69/4.91            ( ( ord_less_eq_rat @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: rat,B5: rat] :
% 8.69/4.91              ( ( P @ B5 @ A5 )
% 8.69/4.91             => ( P @ A5 @ B5 ) )
% 8.69/4.91         => ( P @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3980_linorder__wlog,axiom,
% 8.69/4.91      ! [P: num > num > $o,A: num,B: num] :
% 8.69/4.91        ( ! [A5: num,B5: num] :
% 8.69/4.91            ( ( ord_less_eq_num @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: num,B5: num] :
% 8.69/4.91              ( ( P @ B5 @ A5 )
% 8.69/4.91             => ( P @ A5 @ B5 ) )
% 8.69/4.91         => ( P @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3981_linorder__wlog,axiom,
% 8.69/4.91      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.69/4.91        ( ! [A5: nat,B5: nat] :
% 8.69/4.91            ( ( ord_less_eq_nat @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: nat,B5: nat] :
% 8.69/4.91              ( ( P @ B5 @ A5 )
% 8.69/4.91             => ( P @ A5 @ B5 ) )
% 8.69/4.91         => ( P @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3982_linorder__wlog,axiom,
% 8.69/4.91      ! [P: int > int > $o,A: int,B: int] :
% 8.69/4.91        ( ! [A5: int,B5: int] :
% 8.69/4.91            ( ( ord_less_eq_int @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: int,B5: int] :
% 8.69/4.91              ( ( P @ B5 @ A5 )
% 8.69/4.91             => ( P @ A5 @ B5 ) )
% 8.69/4.91         => ( P @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3983_order__trans,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int,Z: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3984_order__trans,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_rat @ Y @ Z )
% 8.69/4.91         => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3985_order__trans,axiom,
% 8.69/4.91      ! [X: num,Y: num,Z: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_num @ Y @ Z )
% 8.69/4.91         => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3986_order__trans,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,Z: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_nat @ Y @ Z )
% 8.69/4.91         => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3987_order__trans,axiom,
% 8.69/4.91      ! [X: int,Y: int,Z: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3988_order_Otrans,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int,C: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ B @ C )
% 8.69/4.91         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3989_order_Otrans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3990_order_Otrans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3991_order_Otrans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3992_order_Otrans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_int @ B @ C )
% 8.69/4.91         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3993_order__antisym,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ Y @ X )
% 8.69/4.91         => ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3994_order__antisym,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_rat @ Y @ X )
% 8.69/4.91         => ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3995_order__antisym,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_num @ Y @ X )
% 8.69/4.91         => ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3996_order__antisym,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.91         => ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3997_order__antisym,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_int @ Y @ X )
% 8.69/4.91         => ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3998_ord__le__eq__trans,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int,C: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_3999_ord__le__eq__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4000_ord__le__eq__trans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4001_ord__le__eq__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4002_ord__le__eq__trans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4003_ord__eq__le__trans,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int,C: set_int] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ B @ C )
% 8.69/4.91         => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4004_ord__eq__le__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4005_ord__eq__le__trans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ord_less_eq_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4006_ord__eq__le__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.91         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4007_ord__eq__le__trans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_eq_int @ B @ C )
% 8.69/4.91         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4008_order__class_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [X3: set_int,Y3: set_int] :
% 8.69/4.91            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 8.69/4.91            & ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4009_order__class_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [X3: rat,Y3: rat] :
% 8.69/4.91            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.69/4.91            & ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4010_order__class_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [X3: num,Y3: num] :
% 8.69/4.91            ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.69/4.91            & ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4011_order__class_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [X3: nat,Y3: nat] :
% 8.69/4.91            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.69/4.91            & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4012_order__class_Oorder__eq__iff,axiom,
% 8.69/4.91      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 8.69/4.91      = ( ^ [X3: int,Y3: int] :
% 8.69/4.91            ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.69/4.91            & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4013_le__cases3,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.91        ( ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 8.69/4.91       => ( ( ( ord_less_eq_rat @ Y @ X )
% 8.69/4.91           => ~ ( ord_less_eq_rat @ X @ Z ) )
% 8.69/4.91         => ( ( ( ord_less_eq_rat @ X @ Z )
% 8.69/4.91             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 8.69/4.91           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 8.69/4.91               => ~ ( ord_less_eq_rat @ Y @ X ) )
% 8.69/4.91             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 8.69/4.91                 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 8.69/4.91               => ~ ( ( ord_less_eq_rat @ Z @ X )
% 8.69/4.91                   => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4014_le__cases3,axiom,
% 8.69/4.91      ! [X: num,Y: num,Z: num] :
% 8.69/4.91        ( ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91         => ~ ( ord_less_eq_num @ Y @ Z ) )
% 8.69/4.91       => ( ( ( ord_less_eq_num @ Y @ X )
% 8.69/4.91           => ~ ( ord_less_eq_num @ X @ Z ) )
% 8.69/4.91         => ( ( ( ord_less_eq_num @ X @ Z )
% 8.69/4.91             => ~ ( ord_less_eq_num @ Z @ Y ) )
% 8.69/4.91           => ( ( ( ord_less_eq_num @ Z @ Y )
% 8.69/4.91               => ~ ( ord_less_eq_num @ Y @ X ) )
% 8.69/4.91             => ( ( ( ord_less_eq_num @ Y @ Z )
% 8.69/4.91                 => ~ ( ord_less_eq_num @ Z @ X ) )
% 8.69/4.91               => ~ ( ( ord_less_eq_num @ Z @ X )
% 8.69/4.91                   => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4015_le__cases3,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,Z: nat] :
% 8.69/4.91        ( ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 8.69/4.91       => ( ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.91           => ~ ( ord_less_eq_nat @ X @ Z ) )
% 8.69/4.91         => ( ( ( ord_less_eq_nat @ X @ Z )
% 8.69/4.91             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 8.69/4.91           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 8.69/4.91               => ~ ( ord_less_eq_nat @ Y @ X ) )
% 8.69/4.91             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 8.69/4.91                 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 8.69/4.91               => ~ ( ( ord_less_eq_nat @ Z @ X )
% 8.69/4.91                   => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4016_le__cases3,axiom,
% 8.69/4.91      ! [X: int,Y: int,Z: int] :
% 8.69/4.91        ( ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 8.69/4.91       => ( ( ( ord_less_eq_int @ Y @ X )
% 8.69/4.91           => ~ ( ord_less_eq_int @ X @ Z ) )
% 8.69/4.91         => ( ( ( ord_less_eq_int @ X @ Z )
% 8.69/4.91             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 8.69/4.91           => ( ( ( ord_less_eq_int @ Z @ Y )
% 8.69/4.91               => ~ ( ord_less_eq_int @ Y @ X ) )
% 8.69/4.91             => ( ( ( ord_less_eq_int @ Y @ Z )
% 8.69/4.91                 => ~ ( ord_less_eq_int @ Z @ X ) )
% 8.69/4.91               => ~ ( ( ord_less_eq_int @ Z @ X )
% 8.69/4.91                   => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4017_nle__le,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 8.69/4.91        = ( ( ord_less_eq_rat @ B @ A )
% 8.69/4.91          & ( B != A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4018_nle__le,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 8.69/4.91        = ( ( ord_less_eq_num @ B @ A )
% 8.69/4.91          & ( B != A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4019_nle__le,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 8.69/4.91        = ( ( ord_less_eq_nat @ B @ A )
% 8.69/4.91          & ( B != A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4020_nle__le,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 8.69/4.91        = ( ( ord_less_eq_int @ B @ A )
% 8.69/4.91          & ( B != A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4021_order__less__imp__not__less,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4022_order__less__imp__not__less,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4023_order__less__imp__not__less,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4024_order__less__imp__not__less,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4025_order__less__imp__not__less,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4026_order__less__imp__not__eq2,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( Y != X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4027_order__less__imp__not__eq2,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( Y != X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4028_order__less__imp__not__eq2,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( Y != X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4029_order__less__imp__not__eq2,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( Y != X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4030_order__less__imp__not__eq2,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( Y != X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4031_order__less__imp__not__eq,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4032_order__less__imp__not__eq,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4033_order__less__imp__not__eq,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4034_order__less__imp__not__eq,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4035_order__less__imp__not__eq,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4036_linorder__less__linear,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91        | ( X = Y )
% 8.69/4.91        | ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4037_linorder__less__linear,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91        | ( X = Y )
% 8.69/4.91        | ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4038_linorder__less__linear,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91        | ( X = Y )
% 8.69/4.91        | ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4039_linorder__less__linear,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91        | ( X = Y )
% 8.69/4.91        | ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4040_linorder__less__linear,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91        | ( X = Y )
% 8.69/4.91        | ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4041_order__less__imp__triv,axiom,
% 8.69/4.91      ! [X: real,Y: real,P: $o] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( ( ord_less_real @ Y @ X )
% 8.69/4.91         => P ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4042_order__less__imp__triv,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,P: $o] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_rat @ Y @ X )
% 8.69/4.91         => P ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4043_order__less__imp__triv,axiom,
% 8.69/4.91      ! [X: num,Y: num,P: $o] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_num @ Y @ X )
% 8.69/4.91         => P ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4044_order__less__imp__triv,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,P: $o] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_nat @ Y @ X )
% 8.69/4.91         => P ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4045_order__less__imp__triv,axiom,
% 8.69/4.91      ! [X: int,Y: int,P: $o] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_int @ Y @ X )
% 8.69/4.91         => P ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4046_order__less__not__sym,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4047_order__less__not__sym,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4048_order__less__not__sym,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4049_order__less__not__sym,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4050_order__less__not__sym,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4051_order__less__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4052_order__less__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4053_order__less__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > num,C: num] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4054_order__less__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4055_order__less__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > int,C: int] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4056_order__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > real,C: real] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4057_order__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4058_order__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4059_order__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4060_order__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4061_order__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: real > real,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4062_order__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: rat > real,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4063_order__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: num > real,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4064_order__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: nat > real,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4065_order__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: int > real,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4066_order__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: real > rat,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4067_order__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4068_order__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4069_order__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4070_order__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4071_order__less__irrefl,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ~ ( ord_less_real @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4072_order__less__irrefl,axiom,
% 8.69/4.91      ! [X: rat] :
% 8.69/4.91        ~ ( ord_less_rat @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4073_order__less__irrefl,axiom,
% 8.69/4.91      ! [X: num] :
% 8.69/4.91        ~ ( ord_less_num @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4074_order__less__irrefl,axiom,
% 8.69/4.91      ! [X: nat] :
% 8.69/4.91        ~ ( ord_less_nat @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4075_order__less__irrefl,axiom,
% 8.69/4.91      ! [X: int] :
% 8.69/4.91        ~ ( ord_less_int @ X @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4076_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4077_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4078_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > num,C: num] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4079_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4080_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > int,C: int] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4081_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > real,C: real] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4082_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4083_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4084_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4085_ord__less__eq__subst,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ( F @ B )
% 8.69/4.91            = C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4086_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: real,F: real > real,B: real,C: real] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4087_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: rat,F: real > rat,B: real,C: real] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4088_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: num,F: real > num,B: real,C: real] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4089_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: nat,F: real > nat,B: real,C: real] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4090_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: int,F: real > int,B: real,C: real] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4091_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: real,F: rat > real,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4092_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4093_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4094_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4095_ord__eq__less__subst,axiom,
% 8.69/4.91      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.69/4.91        ( ( A
% 8.69/4.91          = ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4096_order__less__trans,axiom,
% 8.69/4.91      ! [X: real,Y: real,Z: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( ( ord_less_real @ Y @ Z )
% 8.69/4.91         => ( ord_less_real @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4097_order__less__trans,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_rat @ Y @ Z )
% 8.69/4.91         => ( ord_less_rat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4098_order__less__trans,axiom,
% 8.69/4.91      ! [X: num,Y: num,Z: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_num @ Y @ Z )
% 8.69/4.91         => ( ord_less_num @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4099_order__less__trans,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,Z: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_nat @ Y @ Z )
% 8.69/4.91         => ( ord_less_nat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4100_order__less__trans,axiom,
% 8.69/4.91      ! [X: int,Y: int,Z: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4101_order__less__asym_H,axiom,
% 8.69/4.91      ! [A: real,B: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ~ ( ord_less_real @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4102_order__less__asym_H,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4103_order__less__asym_H,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ~ ( ord_less_num @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4104_order__less__asym_H,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4105_order__less__asym_H,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ~ ( ord_less_int @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4106_linorder__neq__iff,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91        = ( ( ord_less_real @ X @ Y )
% 8.69/4.91          | ( ord_less_real @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4107_linorder__neq__iff,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91        = ( ( ord_less_rat @ X @ Y )
% 8.69/4.91          | ( ord_less_rat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4108_linorder__neq__iff,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91        = ( ( ord_less_num @ X @ Y )
% 8.69/4.91          | ( ord_less_num @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4109_linorder__neq__iff,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91        = ( ( ord_less_nat @ X @ Y )
% 8.69/4.91          | ( ord_less_nat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4110_linorder__neq__iff,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91        = ( ( ord_less_int @ X @ Y )
% 8.69/4.91          | ( ord_less_int @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4111_order__less__asym,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4112_order__less__asym,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4113_order__less__asym,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4114_order__less__asym,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4115_order__less__asym,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4116_linorder__neqE,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91       => ( ~ ( ord_less_real @ X @ Y )
% 8.69/4.91         => ( ord_less_real @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4117_linorder__neqE,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91       => ( ~ ( ord_less_rat @ X @ Y )
% 8.69/4.91         => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4118_linorder__neqE,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91       => ( ~ ( ord_less_num @ X @ Y )
% 8.69/4.91         => ( ord_less_num @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4119_linorder__neqE,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91       => ( ~ ( ord_less_nat @ X @ Y )
% 8.69/4.91         => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4120_linorder__neqE,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( X != Y )
% 8.69/4.91       => ( ~ ( ord_less_int @ X @ Y )
% 8.69/4.91         => ( ord_less_int @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4121_dual__order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [B: real,A: real] :
% 8.69/4.91        ( ( ord_less_real @ B @ A )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4122_dual__order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [B: rat,A: rat] :
% 8.69/4.91        ( ( ord_less_rat @ B @ A )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4123_dual__order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [B: num,A: num] :
% 8.69/4.91        ( ( ord_less_num @ B @ A )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4124_dual__order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [B: nat,A: nat] :
% 8.69/4.91        ( ( ord_less_nat @ B @ A )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4125_dual__order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [B: int,A: int] :
% 8.69/4.91        ( ( ord_less_int @ B @ A )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4126_order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [A: real,B: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4127_order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4128_order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4129_order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4130_order_Ostrict__implies__not__eq,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ( A != B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4131_dual__order_Ostrict__trans,axiom,
% 8.69/4.91      ! [B: real,A: real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ B @ A )
% 8.69/4.91       => ( ( ord_less_real @ C @ B )
% 8.69/4.91         => ( ord_less_real @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4132_dual__order_Ostrict__trans,axiom,
% 8.69/4.91      ! [B: rat,A: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ B @ A )
% 8.69/4.91       => ( ( ord_less_rat @ C @ B )
% 8.69/4.91         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4133_dual__order_Ostrict__trans,axiom,
% 8.69/4.91      ! [B: num,A: num,C: num] :
% 8.69/4.91        ( ( ord_less_num @ B @ A )
% 8.69/4.91       => ( ( ord_less_num @ C @ B )
% 8.69/4.91         => ( ord_less_num @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4134_dual__order_Ostrict__trans,axiom,
% 8.69/4.91      ! [B: nat,A: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_nat @ B @ A )
% 8.69/4.91       => ( ( ord_less_nat @ C @ B )
% 8.69/4.91         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4135_dual__order_Ostrict__trans,axiom,
% 8.69/4.91      ! [B: int,A: int,C: int] :
% 8.69/4.91        ( ( ord_less_int @ B @ A )
% 8.69/4.91       => ( ( ord_less_int @ C @ B )
% 8.69/4.91         => ( ord_less_int @ C @ A ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4136_not__less__iff__gr__or__eq,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.69/4.91        = ( ( ord_less_real @ Y @ X )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4137_not__less__iff__gr__or__eq,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.69/4.91        = ( ( ord_less_rat @ Y @ X )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4138_not__less__iff__gr__or__eq,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.69/4.91        = ( ( ord_less_num @ Y @ X )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4139_not__less__iff__gr__or__eq,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.69/4.91        = ( ( ord_less_nat @ Y @ X )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4140_not__less__iff__gr__or__eq,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.69/4.91        = ( ( ord_less_int @ Y @ X )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4141_order_Ostrict__trans,axiom,
% 8.69/4.91      ! [A: real,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ord_less_real @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4142_order_Ostrict__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4143_order_Ostrict__trans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ord_less_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4144_order_Ostrict__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4145_order_Ostrict__trans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ord_less_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4146_linorder__less__wlog,axiom,
% 8.69/4.91      ! [P: real > real > $o,A: real,B: real] :
% 8.69/4.91        ( ! [A5: real,B5: real] :
% 8.69/4.91            ( ( ord_less_real @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 8.69/4.91         => ( ! [A5: real,B5: real] :
% 8.69/4.91                ( ( P @ B5 @ A5 )
% 8.69/4.91               => ( P @ A5 @ B5 ) )
% 8.69/4.91           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4147_linorder__less__wlog,axiom,
% 8.69/4.91      ! [P: rat > rat > $o,A: rat,B: rat] :
% 8.69/4.91        ( ! [A5: rat,B5: rat] :
% 8.69/4.91            ( ( ord_less_rat @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 8.69/4.91         => ( ! [A5: rat,B5: rat] :
% 8.69/4.91                ( ( P @ B5 @ A5 )
% 8.69/4.91               => ( P @ A5 @ B5 ) )
% 8.69/4.91           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4148_linorder__less__wlog,axiom,
% 8.69/4.91      ! [P: num > num > $o,A: num,B: num] :
% 8.69/4.91        ( ! [A5: num,B5: num] :
% 8.69/4.91            ( ( ord_less_num @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: num] : ( P @ A5 @ A5 )
% 8.69/4.91         => ( ! [A5: num,B5: num] :
% 8.69/4.91                ( ( P @ B5 @ A5 )
% 8.69/4.91               => ( P @ A5 @ B5 ) )
% 8.69/4.91           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4149_linorder__less__wlog,axiom,
% 8.69/4.91      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.69/4.91        ( ! [A5: nat,B5: nat] :
% 8.69/4.91            ( ( ord_less_nat @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 8.69/4.91         => ( ! [A5: nat,B5: nat] :
% 8.69/4.91                ( ( P @ B5 @ A5 )
% 8.69/4.91               => ( P @ A5 @ B5 ) )
% 8.69/4.91           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4150_linorder__less__wlog,axiom,
% 8.69/4.91      ! [P: int > int > $o,A: int,B: int] :
% 8.69/4.91        ( ! [A5: int,B5: int] :
% 8.69/4.91            ( ( ord_less_int @ A5 @ B5 )
% 8.69/4.91           => ( P @ A5 @ B5 ) )
% 8.69/4.91       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 8.69/4.91         => ( ! [A5: int,B5: int] :
% 8.69/4.91                ( ( P @ B5 @ A5 )
% 8.69/4.91               => ( P @ A5 @ B5 ) )
% 8.69/4.91           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4151_exists__least__iff,axiom,
% 8.69/4.91      ( ( ^ [P3: nat > $o] :
% 8.69/4.91          ? [X7: nat] : ( P3 @ X7 ) )
% 8.69/4.91      = ( ^ [P4: nat > $o] :
% 8.69/4.91          ? [N2: nat] :
% 8.69/4.91            ( ( P4 @ N2 )
% 8.69/4.91            & ! [M3: nat] :
% 8.69/4.91                ( ( ord_less_nat @ M3 @ N2 )
% 8.69/4.91               => ~ ( P4 @ M3 ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4152_dual__order_Oirrefl,axiom,
% 8.69/4.91      ! [A: real] :
% 8.69/4.91        ~ ( ord_less_real @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4153_dual__order_Oirrefl,axiom,
% 8.69/4.91      ! [A: rat] :
% 8.69/4.91        ~ ( ord_less_rat @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4154_dual__order_Oirrefl,axiom,
% 8.69/4.91      ! [A: num] :
% 8.69/4.91        ~ ( ord_less_num @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4155_dual__order_Oirrefl,axiom,
% 8.69/4.91      ! [A: nat] :
% 8.69/4.91        ~ ( ord_less_nat @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4156_dual__order_Oirrefl,axiom,
% 8.69/4.91      ! [A: int] :
% 8.69/4.91        ~ ( ord_less_int @ A @ A ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4157_dual__order_Oasym,axiom,
% 8.69/4.91      ! [B: real,A: real] :
% 8.69/4.91        ( ( ord_less_real @ B @ A )
% 8.69/4.91       => ~ ( ord_less_real @ A @ B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4158_dual__order_Oasym,axiom,
% 8.69/4.91      ! [B: rat,A: rat] :
% 8.69/4.91        ( ( ord_less_rat @ B @ A )
% 8.69/4.91       => ~ ( ord_less_rat @ A @ B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4159_dual__order_Oasym,axiom,
% 8.69/4.91      ! [B: num,A: num] :
% 8.69/4.91        ( ( ord_less_num @ B @ A )
% 8.69/4.91       => ~ ( ord_less_num @ A @ B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4160_dual__order_Oasym,axiom,
% 8.69/4.91      ! [B: nat,A: nat] :
% 8.69/4.91        ( ( ord_less_nat @ B @ A )
% 8.69/4.91       => ~ ( ord_less_nat @ A @ B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4161_dual__order_Oasym,axiom,
% 8.69/4.91      ! [B: int,A: int] :
% 8.69/4.91        ( ( ord_less_int @ B @ A )
% 8.69/4.91       => ~ ( ord_less_int @ A @ B ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4162_linorder__cases,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ~ ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( ( X != Y )
% 8.69/4.91         => ( ord_less_real @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4163_linorder__cases,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ~ ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( ( X != Y )
% 8.69/4.91         => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4164_linorder__cases,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ~ ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( ( X != Y )
% 8.69/4.91         => ( ord_less_num @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4165_linorder__cases,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ~ ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( ( X != Y )
% 8.69/4.91         => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4166_linorder__cases,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ~ ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( ( X != Y )
% 8.69/4.91         => ( ord_less_int @ Y @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4167_antisym__conv3,axiom,
% 8.69/4.91      ! [Y: real,X: real] :
% 8.69/4.91        ( ~ ( ord_less_real @ Y @ X )
% 8.69/4.91       => ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4168_antisym__conv3,axiom,
% 8.69/4.91      ! [Y: rat,X: rat] :
% 8.69/4.91        ( ~ ( ord_less_rat @ Y @ X )
% 8.69/4.91       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4169_antisym__conv3,axiom,
% 8.69/4.91      ! [Y: num,X: num] :
% 8.69/4.91        ( ~ ( ord_less_num @ Y @ X )
% 8.69/4.91       => ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4170_antisym__conv3,axiom,
% 8.69/4.91      ! [Y: nat,X: nat] :
% 8.69/4.91        ( ~ ( ord_less_nat @ Y @ X )
% 8.69/4.91       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4171_antisym__conv3,axiom,
% 8.69/4.91      ! [Y: int,X: int] :
% 8.69/4.91        ( ~ ( ord_less_int @ Y @ X )
% 8.69/4.91       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.69/4.91          = ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4172_less__induct,axiom,
% 8.69/4.91      ! [P: nat > $o,A: nat] :
% 8.69/4.91        ( ! [X6: nat] :
% 8.69/4.91            ( ! [Y2: nat] :
% 8.69/4.91                ( ( ord_less_nat @ Y2 @ X6 )
% 8.69/4.91               => ( P @ Y2 ) )
% 8.69/4.91           => ( P @ X6 ) )
% 8.69/4.91       => ( P @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4173_ord__less__eq__trans,axiom,
% 8.69/4.91      ! [A: real,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_real @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4174_ord__less__eq__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4175_ord__less__eq__trans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4176_ord__less__eq__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4177_ord__less__eq__trans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ( ( B = C )
% 8.69/4.91         => ( ord_less_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4178_ord__eq__less__trans,axiom,
% 8.69/4.91      ! [A: real,B: real,C: real] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ord_less_real @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4179_ord__eq__less__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat,C: rat] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4180_ord__eq__less__trans,axiom,
% 8.69/4.91      ! [A: num,B: num,C: num] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ord_less_num @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4181_ord__eq__less__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat,C: nat] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4182_ord__eq__less__trans,axiom,
% 8.69/4.91      ! [A: int,B: int,C: int] :
% 8.69/4.91        ( ( A = B )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ord_less_int @ A @ C ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4183_order_Oasym,axiom,
% 8.69/4.91      ! [A: real,B: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ~ ( ord_less_real @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4184_order_Oasym,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4185_order_Oasym,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ~ ( ord_less_num @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4186_order_Oasym,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4187_order_Oasym,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ~ ( ord_less_int @ B @ A ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4188_less__imp__neq,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4189_less__imp__neq,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4190_less__imp__neq,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4191_less__imp__neq,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4192_less__imp__neq,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( X != Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4193_dense,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ? [Z5: real] :
% 8.69/4.91            ( ( ord_less_real @ X @ Z5 )
% 8.69/4.91            & ( ord_less_real @ Z5 @ Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4194_dense,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ? [Z5: rat] :
% 8.69/4.91            ( ( ord_less_rat @ X @ Z5 )
% 8.69/4.91            & ( ord_less_rat @ Z5 @ Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4195_gt__ex,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91      ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4196_gt__ex,axiom,
% 8.69/4.91      ! [X: rat] :
% 8.69/4.91      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4197_gt__ex,axiom,
% 8.69/4.91      ! [X: nat] :
% 8.69/4.91      ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4198_gt__ex,axiom,
% 8.69/4.91      ! [X: int] :
% 8.69/4.91      ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4199_lt__ex,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91      ? [Y5: real] : ( ord_less_real @ Y5 @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4200_lt__ex,axiom,
% 8.69/4.91      ! [X: rat] :
% 8.69/4.91      ? [Y5: rat] : ( ord_less_rat @ Y5 @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4201_lt__ex,axiom,
% 8.69/4.91      ! [X: int] :
% 8.69/4.91      ? [Y5: int] : ( ord_less_int @ Y5 @ X ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4202_small__lazy_H_Ocases,axiom,
% 8.69/4.91      ! [X: product_prod_int_int] :
% 8.69/4.91        ~ ! [D3: int,I4: int] :
% 8.69/4.91            ( X
% 8.69/4.91           != ( product_Pair_int_int @ D3 @ I4 ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4203_exhaustive__int_H_Ocases,axiom,
% 8.69/4.91      ! [X: produc7773217078559923341nt_int] :
% 8.69/4.91        ~ ! [F2: int > option6357759511663192854e_term,D3: int,I4: int] :
% 8.69/4.91            ( X
% 8.69/4.91           != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4204_full__exhaustive__int_H_Ocases,axiom,
% 8.69/4.91      ! [X: produc2285326912895808259nt_int] :
% 8.69/4.91        ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I4: int] :
% 8.69/4.91            ( X
% 8.69/4.91           != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4205_ln__ge__zero__imp__ge__one,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91         => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4206_ln__add__one__self__le__self,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4207_ln__mult,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 8.69/4.91            = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4208_ln__eq__minus__one,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ( ln_ln_real @ X )
% 8.69/4.91            = ( minus_minus_real @ X @ one_one_real ) )
% 8.69/4.91         => ( X = one_one_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4209_ln__div,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 8.69/4.91            = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4210_ln__le__minus__one,axiom,
% 8.69/4.91      ! [X: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4211_ln__diff__le,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.91       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.91         => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4212_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.91       => ( ( ord_less_real @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4213_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_set_int @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4214_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_rat @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4215_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_num @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4216_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_nat @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4217_order__le__imp__less__or__eq,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_int @ X @ Y )
% 8.69/4.91          | ( X = Y ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4218_linorder__le__less__linear,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.91        | ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4219_linorder__le__less__linear,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91        | ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4220_linorder__le__less__linear,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91        | ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4221_linorder__le__less__linear,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91        | ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4222_linorder__le__less__linear,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91        | ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4223_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > real,C: real] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4224_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > real,C: real] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4225_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > real,C: real] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4226_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > real,C: real] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4227_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: int,B: int,F: int > real,C: real] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4228_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: real,B: real,F: real > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_real @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4229_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4230_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4231_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4232_order__less__le__subst2,axiom,
% 8.69/4.91      ! [A: int,B: int,F: int > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_int @ A @ B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4233_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: real,F: rat > real,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4234_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4235_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: num,F: rat > num,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4236_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_nat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4237_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: int,F: rat > int,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_int @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4238_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: real,F: num > real,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4239_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4240_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: num,F: num > num,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_num @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4241_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: nat,F: num > nat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_nat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4242_order__less__le__subst1,axiom,
% 8.69/4.91      ! [A: int,F: num > int,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_int @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4243_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > real,C: real] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4244_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4245_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4246_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4247_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: rat,B: rat,F: rat > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_eq_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4248_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > real,C: real] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_real @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4249_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_rat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4250_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_num @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4251_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_nat @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4252_order__le__less__subst2,axiom,
% 8.69/4.91      ! [A: num,B: num,F: num > int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( ord_less_int @ ( F @ B ) @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_eq_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4253_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: real > real,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4254_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: rat > real,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4255_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: num > real,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4256_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: nat > real,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4257_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: real,F: int > real,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4258_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: real > rat,B: real,C: real] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_real @ B @ C )
% 8.69/4.91         => ( ! [X6: real,Y5: real] :
% 8.69/4.91                ( ( ord_less_real @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4259_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_rat @ B @ C )
% 8.69/4.91         => ( ! [X6: rat,Y5: rat] :
% 8.69/4.91                ( ( ord_less_rat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4260_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: num > rat,B: num,C: num] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_num @ B @ C )
% 8.69/4.91         => ( ! [X6: num,Y5: num] :
% 8.69/4.91                ( ( ord_less_num @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4261_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_nat @ B @ C )
% 8.69/4.91         => ( ! [X6: nat,Y5: nat] :
% 8.69/4.91                ( ( ord_less_nat @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4262_order__le__less__subst1,axiom,
% 8.69/4.91      ! [A: rat,F: int > rat,B: int,C: int] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 8.69/4.91       => ( ( ord_less_int @ B @ C )
% 8.69/4.91         => ( ! [X6: int,Y5: int] :
% 8.69/4.91                ( ( ord_less_int @ X6 @ Y5 )
% 8.69/4.91               => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 8.69/4.91           => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4263_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: real,Y: real,Z: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_real @ Y @ Z )
% 8.69/4.91         => ( ord_less_real @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4264_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int,Z: set_int] :
% 8.69/4.91        ( ( ord_less_set_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_set_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4265_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_rat @ Y @ Z )
% 8.69/4.91         => ( ord_less_rat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4266_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: num,Y: num,Z: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_num @ Y @ Z )
% 8.69/4.91         => ( ord_less_num @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4267_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,Z: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_nat @ Y @ Z )
% 8.69/4.91         => ( ord_less_nat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4268_order__less__le__trans,axiom,
% 8.69/4.91      ! [X: int,Y: int,Z: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_eq_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4269_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: real,Y: real,Z: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.91       => ( ( ord_less_real @ Y @ Z )
% 8.69/4.91         => ( ord_less_real @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4270_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int,Z: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_set_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_set_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4271_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_rat @ Y @ Z )
% 8.69/4.91         => ( ord_less_rat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4272_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: num,Y: num,Z: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.91       => ( ( ord_less_num @ Y @ Z )
% 8.69/4.91         => ( ord_less_num @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4273_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: nat,Y: nat,Z: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.91       => ( ( ord_less_nat @ Y @ Z )
% 8.69/4.91         => ( ord_less_nat @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4274_order__le__less__trans,axiom,
% 8.69/4.91      ! [X: int,Y: int,Z: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.91       => ( ( ord_less_int @ Y @ Z )
% 8.69/4.91         => ( ord_less_int @ X @ Z ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4275_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: real,B: real] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_real @ A @ B )
% 8.69/4.91         => ( ord_less_real @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4276_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91         => ( ord_less_set_int @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4277_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4278_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91         => ( ord_less_num @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4279_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4280_order__neq__le__trans,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( A != B )
% 8.69/4.91       => ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91         => ( ord_less_int @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4281_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: real,B: real] :
% 8.69/4.91        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_real @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4282_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: set_int,B: set_int] :
% 8.69/4.91        ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_set_int @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4283_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: rat,B: rat] :
% 8.69/4.91        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_rat @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4284_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: num,B: num] :
% 8.69/4.91        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_num @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4285_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: nat,B: nat] :
% 8.69/4.91        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_nat @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4286_order__le__neq__trans,axiom,
% 8.69/4.91      ! [A: int,B: int] :
% 8.69/4.91        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.91       => ( ( A != B )
% 8.69/4.91         => ( ord_less_int @ A @ B ) ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4287_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ord_less_real @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4288_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: set_int,Y: set_int] :
% 8.69/4.91        ( ( ord_less_set_int @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4289_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ord_less_rat @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4290_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: num,Y: num] :
% 8.69/4.91        ( ( ord_less_num @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_num @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4291_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: nat,Y: nat] :
% 8.69/4.91        ( ( ord_less_nat @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4292_order__less__imp__le,axiom,
% 8.69/4.91      ! [X: int,Y: int] :
% 8.69/4.91        ( ( ord_less_int @ X @ Y )
% 8.69/4.91       => ( ord_less_eq_int @ X @ Y ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4293_linorder__not__less,axiom,
% 8.69/4.91      ! [X: real,Y: real] :
% 8.69/4.91        ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.69/4.91        = ( ord_less_eq_real @ Y @ X ) ) ).
% 8.69/4.91  
% 8.69/4.91  thf(fact_4294_linorder__not__less,axiom,
% 8.69/4.91      ! [X: rat,Y: rat] :
% 8.69/4.91        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.69/4.91        = ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4295_linorder__not__less,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.69/4.92        = ( ord_less_eq_num @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4296_linorder__not__less,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.69/4.92        = ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4297_linorder__not__less,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.69/4.92        = ( ord_less_eq_int @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4298_linorder__not__le,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 8.69/4.92        = ( ord_less_real @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4299_linorder__not__le,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 8.69/4.92        = ( ord_less_rat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4300_linorder__not__le,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 8.69/4.92        = ( ord_less_num @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4301_linorder__not__le,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 8.69/4.92        = ( ord_less_nat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4302_linorder__not__le,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 8.69/4.92        = ( ord_less_int @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4303_order__less__le,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [X3: real,Y3: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4304_order__less__le,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [X3: set_int,Y3: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4305_order__less__le,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [X3: rat,Y3: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4306_order__less__le,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [X3: num,Y3: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4307_order__less__le,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [X3: nat,Y3: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4308_order__less__le,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [X3: int,Y3: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.69/4.92            & ( X3 != Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4309_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_real
% 8.69/4.92      = ( ^ [X3: real,Y3: real] :
% 8.69/4.92            ( ( ord_less_real @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4310_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_set_int
% 8.69/4.92      = ( ^ [X3: set_int,Y3: set_int] :
% 8.69/4.92            ( ( ord_less_set_int @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4311_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_rat
% 8.69/4.92      = ( ^ [X3: rat,Y3: rat] :
% 8.69/4.92            ( ( ord_less_rat @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4312_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_num
% 8.69/4.92      = ( ^ [X3: num,Y3: num] :
% 8.69/4.92            ( ( ord_less_num @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4313_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_nat
% 8.69/4.92      = ( ^ [X3: nat,Y3: nat] :
% 8.69/4.92            ( ( ord_less_nat @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4314_order__le__less,axiom,
% 8.69/4.92      ( ord_less_eq_int
% 8.69/4.92      = ( ^ [X3: int,Y3: int] :
% 8.69/4.92            ( ( ord_less_int @ X3 @ Y3 )
% 8.69/4.92            | ( X3 = Y3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4315_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: real,A: real] :
% 8.69/4.92        ( ( ord_less_real @ B @ A )
% 8.69/4.92       => ( ord_less_eq_real @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4316_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: set_int,A: set_int] :
% 8.69/4.92        ( ( ord_less_set_int @ B @ A )
% 8.69/4.92       => ( ord_less_eq_set_int @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4317_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: rat,A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ B @ A )
% 8.69/4.92       => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4318_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: num,A: num] :
% 8.69/4.92        ( ( ord_less_num @ B @ A )
% 8.69/4.92       => ( ord_less_eq_num @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4319_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: nat,A: nat] :
% 8.69/4.92        ( ( ord_less_nat @ B @ A )
% 8.69/4.92       => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4320_dual__order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [B: int,A: int] :
% 8.69/4.92        ( ( ord_less_int @ B @ A )
% 8.69/4.92       => ( ord_less_eq_int @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4321_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( ord_less_real @ A @ B )
% 8.69/4.92       => ( ord_less_eq_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4322_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: set_int,B: set_int] :
% 8.69/4.92        ( ( ord_less_set_int @ A @ B )
% 8.69/4.92       => ( ord_less_eq_set_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4323_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( ord_less_rat @ A @ B )
% 8.69/4.92       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4324_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: num,B: num] :
% 8.69/4.92        ( ( ord_less_num @ A @ B )
% 8.69/4.92       => ( ord_less_eq_num @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4325_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( ord_less_nat @ A @ B )
% 8.69/4.92       => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4326_order_Ostrict__implies__order,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( ord_less_int @ A @ B )
% 8.69/4.92       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4327_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [B2: real,A3: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4328_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [B2: set_int,A3: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4329_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [B2: rat,A3: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4330_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [B2: num,A3: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4331_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [B2: nat,A3: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4332_dual__order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [B2: int,A3: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ B2 @ A3 )
% 8.69/4.92            & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4333_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: real,A: real,C: real] :
% 8.69/4.92        ( ( ord_less_real @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_real @ C @ B )
% 8.69/4.92         => ( ord_less_real @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4334_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: set_int,A: set_int,C: set_int] :
% 8.69/4.92        ( ( ord_less_set_int @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_set_int @ C @ B )
% 8.69/4.92         => ( ord_less_set_int @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4335_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: rat,A: rat,C: rat] :
% 8.69/4.92        ( ( ord_less_rat @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_rat @ C @ B )
% 8.69/4.92         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4336_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: num,A: num,C: num] :
% 8.69/4.92        ( ( ord_less_num @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_num @ C @ B )
% 8.69/4.92         => ( ord_less_num @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4337_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: nat,A: nat,C: nat] :
% 8.69/4.92        ( ( ord_less_nat @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_nat @ C @ B )
% 8.69/4.92         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4338_dual__order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [B: int,A: int,C: int] :
% 8.69/4.92        ( ( ord_less_int @ B @ A )
% 8.69/4.92       => ( ( ord_less_eq_int @ C @ B )
% 8.69/4.92         => ( ord_less_int @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4339_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: real,A: real,C: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ B @ A )
% 8.69/4.92       => ( ( ord_less_real @ C @ B )
% 8.69/4.92         => ( ord_less_real @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4340_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: set_int,A: set_int,C: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ B @ A )
% 8.69/4.92       => ( ( ord_less_set_int @ C @ B )
% 8.69/4.92         => ( ord_less_set_int @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4341_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: rat,A: rat,C: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ B @ A )
% 8.69/4.92       => ( ( ord_less_rat @ C @ B )
% 8.69/4.92         => ( ord_less_rat @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4342_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: num,A: num,C: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ B @ A )
% 8.69/4.92       => ( ( ord_less_num @ C @ B )
% 8.69/4.92         => ( ord_less_num @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4343_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: nat,A: nat,C: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ B @ A )
% 8.69/4.92       => ( ( ord_less_nat @ C @ B )
% 8.69/4.92         => ( ord_less_nat @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4344_dual__order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [B: int,A: int,C: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ B @ A )
% 8.69/4.92       => ( ( ord_less_int @ C @ B )
% 8.69/4.92         => ( ord_less_int @ C @ A ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4345_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [B2: real,A3: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4346_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [B2: set_int,A3: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4347_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [B2: rat,A3: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4348_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [B2: num,A3: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4349_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [B2: nat,A3: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4350_dual__order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [B2: int,A3: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ B2 @ A3 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4351_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_real
% 8.69/4.92      = ( ^ [B2: real,A3: real] :
% 8.69/4.92            ( ( ord_less_real @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4352_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_set_int
% 8.69/4.92      = ( ^ [B2: set_int,A3: set_int] :
% 8.69/4.92            ( ( ord_less_set_int @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4353_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_rat
% 8.69/4.92      = ( ^ [B2: rat,A3: rat] :
% 8.69/4.92            ( ( ord_less_rat @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4354_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_num
% 8.69/4.92      = ( ^ [B2: num,A3: num] :
% 8.69/4.92            ( ( ord_less_num @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4355_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_nat
% 8.69/4.92      = ( ^ [B2: nat,A3: nat] :
% 8.69/4.92            ( ( ord_less_nat @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4356_dual__order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_int
% 8.69/4.92      = ( ^ [B2: int,A3: int] :
% 8.69/4.92            ( ( ord_less_int @ B2 @ A3 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4357_dense__le__bounded,axiom,
% 8.69/4.92      ! [X: real,Y: real,Z: real] :
% 8.69/4.92        ( ( ord_less_real @ X @ Y )
% 8.69/4.92       => ( ! [W2: real] :
% 8.69/4.92              ( ( ord_less_real @ X @ W2 )
% 8.69/4.92             => ( ( ord_less_real @ W2 @ Y )
% 8.69/4.92               => ( ord_less_eq_real @ W2 @ Z ) ) )
% 8.69/4.92         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4358_dense__le__bounded,axiom,
% 8.69/4.92      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.92        ( ( ord_less_rat @ X @ Y )
% 8.69/4.92       => ( ! [W2: rat] :
% 8.69/4.92              ( ( ord_less_rat @ X @ W2 )
% 8.69/4.92             => ( ( ord_less_rat @ W2 @ Y )
% 8.69/4.92               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 8.69/4.92         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4359_dense__ge__bounded,axiom,
% 8.69/4.92      ! [Z: real,X: real,Y: real] :
% 8.69/4.92        ( ( ord_less_real @ Z @ X )
% 8.69/4.92       => ( ! [W2: real] :
% 8.69/4.92              ( ( ord_less_real @ Z @ W2 )
% 8.69/4.92             => ( ( ord_less_real @ W2 @ X )
% 8.69/4.92               => ( ord_less_eq_real @ Y @ W2 ) ) )
% 8.69/4.92         => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4360_dense__ge__bounded,axiom,
% 8.69/4.92      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.92        ( ( ord_less_rat @ Z @ X )
% 8.69/4.92       => ( ! [W2: rat] :
% 8.69/4.92              ( ( ord_less_rat @ Z @ W2 )
% 8.69/4.92             => ( ( ord_less_rat @ W2 @ X )
% 8.69/4.92               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 8.69/4.92         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4361_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [A3: real,B2: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4362_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [A3: set_int,B2: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4363_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4364_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [A3: num,B2: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4365_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4366_order_Ostrict__iff__not,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [A3: int,B2: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ A3 @ B2 )
% 8.69/4.92            & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4367_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: real,B: real,C: real] :
% 8.69/4.92        ( ( ord_less_real @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_real @ B @ C )
% 8.69/4.92         => ( ord_less_real @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4368_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: set_int,B: set_int,C: set_int] :
% 8.69/4.92        ( ( ord_less_set_int @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_set_int @ B @ C )
% 8.69/4.92         => ( ord_less_set_int @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4369_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: rat,B: rat,C: rat] :
% 8.69/4.92        ( ( ord_less_rat @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_rat @ B @ C )
% 8.69/4.92         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4370_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: num,B: num,C: num] :
% 8.69/4.92        ( ( ord_less_num @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_num @ B @ C )
% 8.69/4.92         => ( ord_less_num @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4371_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( ord_less_nat @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_nat @ B @ C )
% 8.69/4.92         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4372_order_Ostrict__trans2,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( ord_less_int @ A @ B )
% 8.69/4.92       => ( ( ord_less_eq_int @ B @ C )
% 8.69/4.92         => ( ord_less_int @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4373_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: real,B: real,C: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.92       => ( ( ord_less_real @ B @ C )
% 8.69/4.92         => ( ord_less_real @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4374_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: set_int,B: set_int,C: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ A @ B )
% 8.69/4.92       => ( ( ord_less_set_int @ B @ C )
% 8.69/4.92         => ( ord_less_set_int @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4375_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: rat,B: rat,C: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.92       => ( ( ord_less_rat @ B @ C )
% 8.69/4.92         => ( ord_less_rat @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4376_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: num,B: num,C: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ A @ B )
% 8.69/4.92       => ( ( ord_less_num @ B @ C )
% 8.69/4.92         => ( ord_less_num @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4377_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ A @ B )
% 8.69/4.92       => ( ( ord_less_nat @ B @ C )
% 8.69/4.92         => ( ord_less_nat @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4378_order_Ostrict__trans1,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.92       => ( ( ord_less_int @ B @ C )
% 8.69/4.92         => ( ord_less_int @ A @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4379_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [A3: real,B2: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4380_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [A3: set_int,B2: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4381_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4382_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [A3: num,B2: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4383_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4384_order_Ostrict__iff__order,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [A3: int,B2: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ A3 @ B2 )
% 8.69/4.92            & ( A3 != B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4385_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_real
% 8.69/4.92      = ( ^ [A3: real,B2: real] :
% 8.69/4.92            ( ( ord_less_real @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4386_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_set_int
% 8.69/4.92      = ( ^ [A3: set_int,B2: set_int] :
% 8.69/4.92            ( ( ord_less_set_int @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4387_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_rat
% 8.69/4.92      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.92            ( ( ord_less_rat @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4388_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_num
% 8.69/4.92      = ( ^ [A3: num,B2: num] :
% 8.69/4.92            ( ( ord_less_num @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4389_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_nat
% 8.69/4.92      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.92            ( ( ord_less_nat @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4390_order_Oorder__iff__strict,axiom,
% 8.69/4.92      ( ord_less_eq_int
% 8.69/4.92      = ( ^ [A3: int,B2: int] :
% 8.69/4.92            ( ( ord_less_int @ A3 @ B2 )
% 8.69/4.92            | ( A3 = B2 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4391_not__le__imp__less,axiom,
% 8.69/4.92      ! [Y: real,X: real] :
% 8.69/4.92        ( ~ ( ord_less_eq_real @ Y @ X )
% 8.69/4.92       => ( ord_less_real @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4392_not__le__imp__less,axiom,
% 8.69/4.92      ! [Y: rat,X: rat] :
% 8.69/4.92        ( ~ ( ord_less_eq_rat @ Y @ X )
% 8.69/4.92       => ( ord_less_rat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4393_not__le__imp__less,axiom,
% 8.69/4.92      ! [Y: num,X: num] :
% 8.69/4.92        ( ~ ( ord_less_eq_num @ Y @ X )
% 8.69/4.92       => ( ord_less_num @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4394_not__le__imp__less,axiom,
% 8.69/4.92      ! [Y: nat,X: nat] :
% 8.69/4.92        ( ~ ( ord_less_eq_nat @ Y @ X )
% 8.69/4.92       => ( ord_less_nat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4395_not__le__imp__less,axiom,
% 8.69/4.92      ! [Y: int,X: int] :
% 8.69/4.92        ( ~ ( ord_less_eq_int @ Y @ X )
% 8.69/4.92       => ( ord_less_int @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4396_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_real
% 8.69/4.92      = ( ^ [X3: real,Y3: real] :
% 8.69/4.92            ( ( ord_less_eq_real @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4397_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_set_int
% 8.69/4.92      = ( ^ [X3: set_int,Y3: set_int] :
% 8.69/4.92            ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4398_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_rat
% 8.69/4.92      = ( ^ [X3: rat,Y3: rat] :
% 8.69/4.92            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4399_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_num
% 8.69/4.92      = ( ^ [X3: num,Y3: num] :
% 8.69/4.92            ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4400_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_nat
% 8.69/4.92      = ( ^ [X3: nat,Y3: nat] :
% 8.69/4.92            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4401_less__le__not__le,axiom,
% 8.69/4.92      ( ord_less_int
% 8.69/4.92      = ( ^ [X3: int,Y3: int] :
% 8.69/4.92            ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.69/4.92            & ~ ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4402_dense__le,axiom,
% 8.69/4.92      ! [Y: real,Z: real] :
% 8.69/4.92        ( ! [X6: real] :
% 8.69/4.92            ( ( ord_less_real @ X6 @ Y )
% 8.69/4.92           => ( ord_less_eq_real @ X6 @ Z ) )
% 8.69/4.92       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4403_dense__le,axiom,
% 8.69/4.92      ! [Y: rat,Z: rat] :
% 8.69/4.92        ( ! [X6: rat] :
% 8.69/4.92            ( ( ord_less_rat @ X6 @ Y )
% 8.69/4.92           => ( ord_less_eq_rat @ X6 @ Z ) )
% 8.69/4.92       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4404_dense__ge,axiom,
% 8.69/4.92      ! [Z: real,Y: real] :
% 8.69/4.92        ( ! [X6: real] :
% 8.69/4.92            ( ( ord_less_real @ Z @ X6 )
% 8.69/4.92           => ( ord_less_eq_real @ Y @ X6 ) )
% 8.69/4.92       => ( ord_less_eq_real @ Y @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4405_dense__ge,axiom,
% 8.69/4.92      ! [Z: rat,Y: rat] :
% 8.69/4.92        ( ! [X6: rat] :
% 8.69/4.92            ( ( ord_less_rat @ Z @ X6 )
% 8.69/4.92           => ( ord_less_eq_rat @ Y @ X6 ) )
% 8.69/4.92       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4406_antisym__conv2,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4407_antisym__conv2,axiom,
% 8.69/4.92      ! [X: set_int,Y: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4408_antisym__conv2,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4409_antisym__conv2,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4410_antisym__conv2,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4411_antisym__conv2,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.92       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4412_antisym__conv1,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ~ ( ord_less_real @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4413_antisym__conv1,axiom,
% 8.69/4.92      ! [X: set_int,Y: set_int] :
% 8.69/4.92        ( ~ ( ord_less_set_int @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4414_antisym__conv1,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ~ ( ord_less_rat @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4415_antisym__conv1,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ~ ( ord_less_num @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4416_antisym__conv1,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ~ ( ord_less_nat @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4417_antisym__conv1,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ~ ( ord_less_int @ X @ Y )
% 8.69/4.92       => ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.92          = ( X = Y ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4418_nless__le,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( ~ ( ord_less_real @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_real @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4419_nless__le,axiom,
% 8.69/4.92      ! [A: set_int,B: set_int] :
% 8.69/4.92        ( ( ~ ( ord_less_set_int @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_set_int @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4420_nless__le,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( ~ ( ord_less_rat @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_rat @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4421_nless__le,axiom,
% 8.69/4.92      ! [A: num,B: num] :
% 8.69/4.92        ( ( ~ ( ord_less_num @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_num @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4422_nless__le,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( ~ ( ord_less_nat @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_nat @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4423_nless__le,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( ~ ( ord_less_int @ A @ B ) )
% 8.69/4.92        = ( ~ ( ord_less_eq_int @ A @ B )
% 8.69/4.92          | ( A = B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4424_leI,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ~ ( ord_less_real @ X @ Y )
% 8.69/4.92       => ( ord_less_eq_real @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4425_leI,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ~ ( ord_less_rat @ X @ Y )
% 8.69/4.92       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4426_leI,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ~ ( ord_less_num @ X @ Y )
% 8.69/4.92       => ( ord_less_eq_num @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4427_leI,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ~ ( ord_less_nat @ X @ Y )
% 8.69/4.92       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4428_leI,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ~ ( ord_less_int @ X @ Y )
% 8.69/4.92       => ( ord_less_eq_int @ Y @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4429_leD,axiom,
% 8.69/4.92      ! [Y: real,X: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_real @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4430_leD,axiom,
% 8.69/4.92      ! [Y: set_int,X: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4431_leD,axiom,
% 8.69/4.92      ! [Y: rat,X: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_rat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4432_leD,axiom,
% 8.69/4.92      ! [Y: num,X: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_num @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4433_leD,axiom,
% 8.69/4.92      ! [Y: nat,X: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_nat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4434_leD,axiom,
% 8.69/4.92      ! [Y: int,X: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ Y @ X )
% 8.69/4.92       => ~ ( ord_less_int @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4435_bot_Oextremum__uniqueI,axiom,
% 8.69/4.92      ! [A: set_nat] :
% 8.69/4.92        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 8.69/4.92       => ( A = bot_bot_set_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4436_bot_Oextremum__uniqueI,axiom,
% 8.69/4.92      ! [A: extended_enat] :
% 8.69/4.92        ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 8.69/4.92       => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4437_bot_Oextremum__uniqueI,axiom,
% 8.69/4.92      ! [A: set_real] :
% 8.69/4.92        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 8.69/4.92       => ( A = bot_bot_set_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4438_bot_Oextremum__uniqueI,axiom,
% 8.69/4.92      ! [A: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 8.69/4.92       => ( A = bot_bot_set_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4439_bot_Oextremum__uniqueI,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 8.69/4.92       => ( A = bot_bot_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4440_bot_Oextremum__unique,axiom,
% 8.69/4.92      ! [A: set_nat] :
% 8.69/4.92        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 8.69/4.92        = ( A = bot_bot_set_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4441_bot_Oextremum__unique,axiom,
% 8.69/4.92      ! [A: extended_enat] :
% 8.69/4.92        ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 8.69/4.92        = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4442_bot_Oextremum__unique,axiom,
% 8.69/4.92      ! [A: set_real] :
% 8.69/4.92        ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 8.69/4.92        = ( A = bot_bot_set_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4443_bot_Oextremum__unique,axiom,
% 8.69/4.92      ! [A: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 8.69/4.92        = ( A = bot_bot_set_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4444_bot_Oextremum__unique,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 8.69/4.92        = ( A = bot_bot_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4445_bot_Oextremum,axiom,
% 8.69/4.92      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4446_bot_Oextremum,axiom,
% 8.69/4.92      ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4447_bot_Oextremum,axiom,
% 8.69/4.92      ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4448_bot_Oextremum,axiom,
% 8.69/4.92      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4449_bot_Oextremum,axiom,
% 8.69/4.92      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4450_bot_Onot__eq__extremum,axiom,
% 8.69/4.92      ! [A: set_nat] :
% 8.69/4.92        ( ( A != bot_bot_set_nat )
% 8.69/4.92        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4451_bot_Onot__eq__extremum,axiom,
% 8.69/4.92      ! [A: extended_enat] :
% 8.69/4.92        ( ( A != bot_bo4199563552545308370d_enat )
% 8.69/4.92        = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4452_bot_Onot__eq__extremum,axiom,
% 8.69/4.92      ! [A: set_int] :
% 8.69/4.92        ( ( A != bot_bot_set_int )
% 8.69/4.92        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4453_bot_Onot__eq__extremum,axiom,
% 8.69/4.92      ! [A: set_real] :
% 8.69/4.92        ( ( A != bot_bot_set_real )
% 8.69/4.92        = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4454_bot_Onot__eq__extremum,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( A != bot_bot_nat )
% 8.69/4.92        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4455_bot_Oextremum__strict,axiom,
% 8.69/4.92      ! [A: set_nat] :
% 8.69/4.92        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4456_bot_Oextremum__strict,axiom,
% 8.69/4.92      ! [A: extended_enat] :
% 8.69/4.92        ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4457_bot_Oextremum__strict,axiom,
% 8.69/4.92      ! [A: set_int] :
% 8.69/4.92        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4458_bot_Oextremum__strict,axiom,
% 8.69/4.92      ! [A: set_real] :
% 8.69/4.92        ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4459_bot_Oextremum__strict,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4460_Euclid__induct,axiom,
% 8.69/4.92      ! [P: nat > nat > $o,A: nat,B: nat] :
% 8.69/4.92        ( ! [A5: nat,B5: nat] :
% 8.69/4.92            ( ( P @ A5 @ B5 )
% 8.69/4.92            = ( P @ B5 @ A5 ) )
% 8.69/4.92       => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 8.69/4.92         => ( ! [A5: nat,B5: nat] :
% 8.69/4.92                ( ( P @ A5 @ B5 )
% 8.69/4.92               => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 8.69/4.92           => ( P @ A @ B ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4461_max__def,axiom,
% 8.69/4.92      ( ord_ma741700101516333627d_enat
% 8.69/4.92      = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4462_max__def,axiom,
% 8.69/4.92      ( ord_max_Code_integer
% 8.69/4.92      = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4463_max__def,axiom,
% 8.69/4.92      ( ord_max_set_int
% 8.69/4.92      = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4464_max__def,axiom,
% 8.69/4.92      ( ord_max_rat
% 8.69/4.92      = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4465_max__def,axiom,
% 8.69/4.92      ( ord_max_num
% 8.69/4.92      = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4466_max__def,axiom,
% 8.69/4.92      ( ord_max_nat
% 8.69/4.92      = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4467_max__def,axiom,
% 8.69/4.92      ( ord_max_int
% 8.69/4.92      = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4468_max__absorb1,axiom,
% 8.69/4.92      ! [Y: extended_enat,X: extended_enat] :
% 8.69/4.92        ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 8.69/4.92       => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4469_max__absorb1,axiom,
% 8.69/4.92      ! [Y: code_integer,X: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ Y @ X )
% 8.69/4.92       => ( ( ord_max_Code_integer @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4470_max__absorb1,axiom,
% 8.69/4.92      ! [Y: set_int,X: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ Y @ X )
% 8.69/4.92       => ( ( ord_max_set_int @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4471_max__absorb1,axiom,
% 8.69/4.92      ! [Y: rat,X: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ Y @ X )
% 8.69/4.92       => ( ( ord_max_rat @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4472_max__absorb1,axiom,
% 8.69/4.92      ! [Y: num,X: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ Y @ X )
% 8.69/4.92       => ( ( ord_max_num @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4473_max__absorb1,axiom,
% 8.69/4.92      ! [Y: nat,X: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.92       => ( ( ord_max_nat @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4474_max__absorb1,axiom,
% 8.69/4.92      ! [Y: int,X: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ Y @ X )
% 8.69/4.92       => ( ( ord_max_int @ X @ Y )
% 8.69/4.92          = X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4475_max__absorb2,axiom,
% 8.69/4.92      ! [X: extended_enat,Y: extended_enat] :
% 8.69/4.92        ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 8.69/4.92       => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4476_max__absorb2,axiom,
% 8.69/4.92      ! [X: code_integer,Y: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ X @ Y )
% 8.69/4.92       => ( ( ord_max_Code_integer @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4477_max__absorb2,axiom,
% 8.69/4.92      ! [X: set_int,Y: set_int] :
% 8.69/4.92        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.92       => ( ( ord_max_set_int @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4478_max__absorb2,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.92       => ( ( ord_max_rat @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4479_max__absorb2,axiom,
% 8.69/4.92      ! [X: num,Y: num] :
% 8.69/4.92        ( ( ord_less_eq_num @ X @ Y )
% 8.69/4.92       => ( ( ord_max_num @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4480_max__absorb2,axiom,
% 8.69/4.92      ! [X: nat,Y: nat] :
% 8.69/4.92        ( ( ord_less_eq_nat @ X @ Y )
% 8.69/4.92       => ( ( ord_max_nat @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4481_max__absorb2,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ X @ Y )
% 8.69/4.92       => ( ( ord_max_int @ X @ Y )
% 8.69/4.92          = Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4482_ln__one__plus__pos__lower__bound,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.92       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.92         => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4483_ln__2__less__1,axiom,
% 8.69/4.92      ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4484_tanh__ln__real,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.92       => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 8.69/4.92          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4485_ln__one__minus__pos__lower__bound,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.92       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.92         => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4486_abs__ln__one__plus__x__minus__x__bound,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.92       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4487_even__succ__mod__exp,axiom,
% 8.69/4.92      ! [A: nat,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4488_even__succ__mod__exp,axiom,
% 8.69/4.92      ! [A: int,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4489_even__succ__mod__exp,axiom,
% 8.69/4.92      ! [A: code_integer,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4490_even__succ__div__exp,axiom,
% 8.69/4.92      ! [A: code_integer,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4491_even__succ__div__exp,axiom,
% 8.69/4.92      ! [A: nat,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4492_even__succ__div__exp,axiom,
% 8.69/4.92      ! [A: int,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.92       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.92         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.92            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4493_neg__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( ( uminus_uminus_real @ A )
% 8.69/4.92          = ( uminus_uminus_real @ B ) )
% 8.69/4.92        = ( A = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4494_neg__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( ( uminus_uminus_int @ A )
% 8.69/4.92          = ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( A = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4495_neg__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.92          = ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.92        = ( A = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4496_neg__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.92          = ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( A = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4497_neg__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( ( uminus_uminus_rat @ A )
% 8.69/4.92          = ( uminus_uminus_rat @ B ) )
% 8.69/4.92        = ( A = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4498_add_Oinverse__inverse,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4499_add_Oinverse__inverse,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4500_add_Oinverse__inverse,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 8.69/4.92        = A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4501_add_Oinverse__inverse,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4502_add_Oinverse__inverse,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = A ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4503_abs__abs,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 8.69/4.92        = ( abs_abs_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4504_abs__abs,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 8.69/4.92        = ( abs_abs_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4505_abs__abs,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 8.69/4.92        = ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4506_abs__abs,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 8.69/4.92        = ( abs_abs_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4507_abs__idempotent,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 8.69/4.92        = ( abs_abs_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4508_abs__idempotent,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 8.69/4.92        = ( abs_abs_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4509_abs__idempotent,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 8.69/4.92        = ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4510_abs__idempotent,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 8.69/4.92        = ( abs_abs_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4511_nat__dvd__1__iff__1,axiom,
% 8.69/4.92      ! [M: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 8.69/4.92        = ( M = one_one_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4512_neg__le__iff__le,axiom,
% 8.69/4.92      ! [B: real,A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_eq_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4513_neg__le__iff__le,axiom,
% 8.69/4.92      ! [B: code_integer,A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4514_neg__le__iff__le,axiom,
% 8.69/4.92      ! [B: rat,A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4515_neg__le__iff__le,axiom,
% 8.69/4.92      ! [B: int,A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_eq_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4516_neg__equal__zero,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ( uminus_uminus_real @ A )
% 8.69/4.92          = A )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4517_neg__equal__zero,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ( uminus_uminus_int @ A )
% 8.69/4.92          = A )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4518_neg__equal__zero,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.92          = A )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4519_neg__equal__zero,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ( uminus_uminus_rat @ A )
% 8.69/4.92          = A )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4520_equal__neg__zero,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( A
% 8.69/4.92          = ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4521_equal__neg__zero,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( A
% 8.69/4.92          = ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4522_equal__neg__zero,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( A
% 8.69/4.92          = ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4523_equal__neg__zero,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( A
% 8.69/4.92          = ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4524_neg__equal__0__iff__equal,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ( uminus_uminus_real @ A )
% 8.69/4.92          = zero_zero_real )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4525_neg__equal__0__iff__equal,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ( uminus_uminus_int @ A )
% 8.69/4.92          = zero_zero_int )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4526_neg__equal__0__iff__equal,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.92          = zero_zero_complex )
% 8.69/4.92        = ( A = zero_zero_complex ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4527_neg__equal__0__iff__equal,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.92          = zero_z3403309356797280102nteger )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4528_neg__equal__0__iff__equal,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ( uminus_uminus_rat @ A )
% 8.69/4.92          = zero_zero_rat )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4529_neg__0__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( zero_zero_real
% 8.69/4.92          = ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( zero_zero_real = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4530_neg__0__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( zero_zero_int
% 8.69/4.92          = ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( zero_zero_int = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4531_neg__0__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( zero_zero_complex
% 8.69/4.92          = ( uminus1482373934393186551omplex @ A ) )
% 8.69/4.92        = ( zero_zero_complex = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4532_neg__0__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( zero_z3403309356797280102nteger
% 8.69/4.92          = ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( zero_z3403309356797280102nteger = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4533_neg__0__equal__iff__equal,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( zero_zero_rat
% 8.69/4.92          = ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( zero_zero_rat = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4534_add_Oinverse__neutral,axiom,
% 8.69/4.92      ( ( uminus_uminus_real @ zero_zero_real )
% 8.69/4.92      = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4535_add_Oinverse__neutral,axiom,
% 8.69/4.92      ( ( uminus_uminus_int @ zero_zero_int )
% 8.69/4.92      = zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4536_add_Oinverse__neutral,axiom,
% 8.69/4.92      ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 8.69/4.92      = zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4537_add_Oinverse__neutral,axiom,
% 8.69/4.92      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 8.69/4.92      = zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4538_add_Oinverse__neutral,axiom,
% 8.69/4.92      ( ( uminus_uminus_rat @ zero_zero_rat )
% 8.69/4.92      = zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4539_neg__less__iff__less,axiom,
% 8.69/4.92      ! [B: real,A: real] :
% 8.69/4.92        ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4540_neg__less__iff__less,axiom,
% 8.69/4.92      ! [B: int,A: int] :
% 8.69/4.92        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4541_neg__less__iff__less,axiom,
% 8.69/4.92      ! [B: code_integer,A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4542_neg__less__iff__less,axiom,
% 8.69/4.92      ! [B: rat,A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4543_neg__numeral__eq__iff,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 8.69/4.92          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.92        = ( M = N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4544_neg__numeral__eq__iff,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 8.69/4.92          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.92        = ( M = N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4545_neg__numeral__eq__iff,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 8.69/4.92          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.92        = ( M = N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4546_neg__numeral__eq__iff,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 8.69/4.92          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.92        = ( M = N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4547_neg__numeral__eq__iff,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 8.69/4.92          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.92        = ( M = N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4548_mult__minus__left,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.92        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4549_mult__minus__left,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.92        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4550_mult__minus__left,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4551_mult__minus__left,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4552_mult__minus__left,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.92        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4553_minus__mult__minus,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.69/4.92        = ( times_times_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4554_minus__mult__minus,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( times_times_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4555_minus__mult__minus,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.92        = ( times_times_complex @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4556_minus__mult__minus,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4557_minus__mult__minus,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.69/4.92        = ( times_times_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4558_mult__minus__right,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 8.69/4.92        = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4559_mult__minus__right,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4560_mult__minus__right,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4561_mult__minus__right,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4562_mult__minus__right,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.69/4.92        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4563_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4564_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 8.69/4.92        = ( A = zero_zero_complex ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4565_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4566_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4567_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.69/4.92        = ( A = zero_zero_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4568_dvd__0__left__iff,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4569_dvd__0__right,axiom,
% 8.69/4.92      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4570_dvd__0__right,axiom,
% 8.69/4.92      ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4571_dvd__0__right,axiom,
% 8.69/4.92      ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4572_dvd__0__right,axiom,
% 8.69/4.92      ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4573_dvd__0__right,axiom,
% 8.69/4.92      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4574_dvd__0__right,axiom,
% 8.69/4.92      ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4575_add__minus__cancel,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4576_add__minus__cancel,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4577_add__minus__cancel,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4578_add__minus__cancel,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4579_add__minus__cancel,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4580_minus__add__cancel,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4581_minus__add__cancel,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4582_minus__add__cancel,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4583_minus__add__cancel,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4584_minus__add__cancel,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 8.69/4.92        = B ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4585_minus__add__distrib,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.69/4.92        = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4586_minus__add__distrib,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.69/4.92        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4587_minus__add__distrib,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.69/4.92        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4588_minus__add__distrib,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.92        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4589_minus__add__distrib,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.69/4.92        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4590_minus__diff__eq,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 8.69/4.92        = ( minus_minus_real @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4591_minus__diff__eq,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 8.69/4.92        = ( minus_minus_int @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4592_minus__diff__eq,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 8.69/4.92        = ( minus_minus_complex @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4593_minus__diff__eq,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.69/4.92        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4594_minus__diff__eq,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 8.69/4.92        = ( minus_minus_rat @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4595_div__minus__minus,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( divide_divide_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4596_div__minus__minus,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4597_dvd__1__iff__1,axiom,
% 8.69/4.92      ! [M: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.69/4.92        = ( M
% 8.69/4.92          = ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4598_dvd__1__left,axiom,
% 8.69/4.92      ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4599_dvd__add__triv__left__iff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4600_dvd__add__triv__left__iff,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.69/4.92        = ( dvd_dvd_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4601_dvd__add__triv__left__iff,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.69/4.92        = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4602_dvd__add__triv__left__iff,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.69/4.92        = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4603_dvd__add__triv__left__iff,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.69/4.92        = ( dvd_dvd_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4604_dvd__add__triv__right__iff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4605_dvd__add__triv__right__iff,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.69/4.92        = ( dvd_dvd_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4606_dvd__add__triv__right__iff,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.69/4.92        = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4607_dvd__add__triv__right__iff,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.69/4.92        = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4608_dvd__add__triv__right__iff,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.69/4.92        = ( dvd_dvd_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4609_abs__0,axiom,
% 8.69/4.92      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.69/4.92      = zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4610_abs__0,axiom,
% 8.69/4.92      ( ( abs_abs_complex @ zero_zero_complex )
% 8.69/4.92      = zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4611_abs__0,axiom,
% 8.69/4.92      ( ( abs_abs_real @ zero_zero_real )
% 8.69/4.92      = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4612_abs__0,axiom,
% 8.69/4.92      ( ( abs_abs_rat @ zero_zero_rat )
% 8.69/4.92      = zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4613_abs__0,axiom,
% 8.69/4.92      ( ( abs_abs_int @ zero_zero_int )
% 8.69/4.92      = zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4614_abs__zero,axiom,
% 8.69/4.92      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.69/4.92      = zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4615_abs__zero,axiom,
% 8.69/4.92      ( ( abs_abs_real @ zero_zero_real )
% 8.69/4.92      = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4616_abs__zero,axiom,
% 8.69/4.92      ( ( abs_abs_rat @ zero_zero_rat )
% 8.69/4.92      = zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4617_abs__zero,axiom,
% 8.69/4.92      ( ( abs_abs_int @ zero_zero_int )
% 8.69/4.92      = zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4618_abs__eq__0,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ( abs_abs_Code_integer @ A )
% 8.69/4.92          = zero_z3403309356797280102nteger )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4619_abs__eq__0,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ( abs_abs_real @ A )
% 8.69/4.92          = zero_zero_real )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4620_abs__eq__0,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ( abs_abs_rat @ A )
% 8.69/4.92          = zero_zero_rat )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4621_abs__eq__0,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ( abs_abs_int @ A )
% 8.69/4.92          = zero_zero_int )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4622_abs__0__eq,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( zero_z3403309356797280102nteger
% 8.69/4.92          = ( abs_abs_Code_integer @ A ) )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4623_abs__0__eq,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( zero_zero_real
% 8.69/4.92          = ( abs_abs_real @ A ) )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4624_abs__0__eq,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( zero_zero_rat
% 8.69/4.92          = ( abs_abs_rat @ A ) )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4625_abs__0__eq,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( zero_zero_int
% 8.69/4.92          = ( abs_abs_int @ A ) )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4626_div__dvd__div,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ A @ C )
% 8.69/4.92         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 8.69/4.92            = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4627_div__dvd__div,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.92       => ( ( dvd_dvd_nat @ A @ C )
% 8.69/4.92         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 8.69/4.92            = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4628_div__dvd__div,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.92       => ( ( dvd_dvd_int @ A @ C )
% 8.69/4.92         => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 8.69/4.92            = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4629_minus__dvd__iff,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 8.69/4.92        = ( dvd_dvd_real @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4630_minus__dvd__iff,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 8.69/4.92        = ( dvd_dvd_int @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4631_minus__dvd__iff,axiom,
% 8.69/4.92      ! [X: complex,Y: complex] :
% 8.69/4.92        ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 8.69/4.92        = ( dvd_dvd_complex @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4632_minus__dvd__iff,axiom,
% 8.69/4.92      ! [X: code_integer,Y: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4633_minus__dvd__iff,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 8.69/4.92        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4634_dvd__minus__iff,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 8.69/4.92        = ( dvd_dvd_real @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4635_dvd__minus__iff,axiom,
% 8.69/4.92      ! [X: int,Y: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 8.69/4.92        = ( dvd_dvd_int @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4636_dvd__minus__iff,axiom,
% 8.69/4.92      ! [X: complex,Y: complex] :
% 8.69/4.92        ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 8.69/4.92        = ( dvd_dvd_complex @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4637_dvd__minus__iff,axiom,
% 8.69/4.92      ! [X: code_integer,Y: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4638_dvd__minus__iff,axiom,
% 8.69/4.92      ! [X: rat,Y: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 8.69/4.92        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4639_abs__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.92        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4640_abs__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 8.69/4.92        = ( numeral_numeral_real @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4641_abs__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 8.69/4.92        = ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4642_abs__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 8.69/4.92        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4643_abs__mult__self__eq,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 8.69/4.92        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4644_abs__mult__self__eq,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 8.69/4.92        = ( times_times_real @ A @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4645_abs__mult__self__eq,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 8.69/4.92        = ( times_times_rat @ A @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4646_abs__mult__self__eq,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 8.69/4.92        = ( times_times_int @ A @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4647_abs__add__abs,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 8.69/4.92        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4648_abs__add__abs,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 8.69/4.92        = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4649_abs__add__abs,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 8.69/4.92        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4650_abs__add__abs,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 8.69/4.92        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4651_abs__1,axiom,
% 8.69/4.92      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.69/4.92      = one_one_Code_integer ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4652_abs__1,axiom,
% 8.69/4.92      ( ( abs_abs_complex @ one_one_complex )
% 8.69/4.92      = one_one_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4653_abs__1,axiom,
% 8.69/4.92      ( ( abs_abs_real @ one_one_real )
% 8.69/4.92      = one_one_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4654_abs__1,axiom,
% 8.69/4.92      ( ( abs_abs_rat @ one_one_rat )
% 8.69/4.92      = one_one_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4655_abs__1,axiom,
% 8.69/4.92      ( ( abs_abs_int @ one_one_int )
% 8.69/4.92      = one_one_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4656_abs__divide,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.92        = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4657_abs__divide,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.92        = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4658_abs__divide,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.92        = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4659_abs__minus,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( abs_abs_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4660_abs__minus,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( abs_abs_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4661_abs__minus,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 8.69/4.92        = ( abs_abs_complex @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4662_abs__minus,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4663_abs__minus,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( abs_abs_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4664_abs__minus__cancel,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( abs_abs_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4665_abs__minus__cancel,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( abs_abs_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4666_abs__minus__cancel,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4667_abs__minus__cancel,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( abs_abs_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4668_mod__minus__minus,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4669_mod__minus__minus,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4670_nat__mult__dvd__cancel__disj,axiom,
% 8.69/4.92      ! [K: nat,M: nat,N: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.69/4.92        = ( ( K = zero_zero_nat )
% 8.69/4.92          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4671_dvd__abs__iff,axiom,
% 8.69/4.92      ! [M: real,K: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 8.69/4.92        = ( dvd_dvd_real @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4672_dvd__abs__iff,axiom,
% 8.69/4.92      ! [M: int,K: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 8.69/4.92        = ( dvd_dvd_int @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4673_dvd__abs__iff,axiom,
% 8.69/4.92      ! [M: code_integer,K: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4674_dvd__abs__iff,axiom,
% 8.69/4.92      ! [M: rat,K: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 8.69/4.92        = ( dvd_dvd_rat @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4675_abs__dvd__iff,axiom,
% 8.69/4.92      ! [M: real,K: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 8.69/4.92        = ( dvd_dvd_real @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4676_abs__dvd__iff,axiom,
% 8.69/4.92      ! [M: int,K: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 8.69/4.92        = ( dvd_dvd_int @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4677_abs__dvd__iff,axiom,
% 8.69/4.92      ! [M: code_integer,K: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4678_abs__dvd__iff,axiom,
% 8.69/4.92      ! [M: rat,K: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 8.69/4.92        = ( dvd_dvd_rat @ M @ K ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4679_tanh__0,axiom,
% 8.69/4.92      ( ( tanh_complex @ zero_zero_complex )
% 8.69/4.92      = zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4680_tanh__0,axiom,
% 8.69/4.92      ( ( tanh_real @ zero_zero_real )
% 8.69/4.92      = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4681_tanh__real__zero__iff,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( ( tanh_real @ X )
% 8.69/4.92          = zero_zero_real )
% 8.69/4.92        = ( X = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4682_tanh__real__le__iff,axiom,
% 8.69/4.92      ! [X: real,Y: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 8.69/4.92        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4683_neg__less__eq__nonneg,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4684_neg__less__eq__nonneg,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4685_neg__less__eq__nonneg,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4686_neg__less__eq__nonneg,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4687_less__eq__neg__nonpos,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4688_less__eq__neg__nonpos,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4689_less__eq__neg__nonpos,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4690_less__eq__neg__nonpos,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4691_neg__le__0__iff__le,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 8.69/4.92        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4692_neg__le__0__iff__le,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4693_neg__le__0__iff__le,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.69/4.92        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4694_neg__le__0__iff__le,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.69/4.92        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4695_neg__0__le__iff__le,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4696_neg__0__le__iff__le,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4697_neg__0__le__iff__le,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4698_neg__0__le__iff__le,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4699_less__neg__neg,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4700_less__neg__neg,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4701_less__neg__neg,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4702_less__neg__neg,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4703_neg__less__pos,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 8.69/4.92        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4704_neg__less__pos,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 8.69/4.92        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4705_neg__less__pos,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.69/4.92        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4706_neg__less__pos,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.69/4.92        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4707_neg__0__less__iff__less,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4708_neg__0__less__iff__less,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4709_neg__0__less__iff__less,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4710_neg__0__less__iff__less,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4711_neg__less__0__iff__less,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 8.69/4.92        = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4712_neg__less__0__iff__less,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.69/4.92        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4713_neg__less__0__iff__less,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.69/4.92        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4714_neg__less__0__iff__less,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.69/4.92        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4715_ab__left__minus,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 8.69/4.92        = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4716_ab__left__minus,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.69/4.92        = zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4717_ab__left__minus,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 8.69/4.92        = zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4718_ab__left__minus,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.69/4.92        = zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4719_ab__left__minus,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.69/4.92        = zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4720_add_Oright__inverse,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 8.69/4.92        = zero_zero_real ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4721_add_Oright__inverse,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 8.69/4.92        = zero_zero_int ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4722_add_Oright__inverse,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 8.69/4.92        = zero_zero_complex ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4723_add_Oright__inverse,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.92        = zero_z3403309356797280102nteger ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4724_add_Oright__inverse,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.69/4.92        = zero_zero_rat ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4725_diff__0,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( minus_minus_real @ zero_zero_real @ A )
% 8.69/4.92        = ( uminus_uminus_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4726_diff__0,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( minus_minus_int @ zero_zero_int @ A )
% 8.69/4.92        = ( uminus_uminus_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4727_diff__0,axiom,
% 8.69/4.92      ! [A: complex] :
% 8.69/4.92        ( ( minus_minus_complex @ zero_zero_complex @ A )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4728_diff__0,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4729_diff__0,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 8.69/4.92        = ( uminus_uminus_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4730_verit__minus__simplify_I3_J,axiom,
% 8.69/4.92      ! [B: real] :
% 8.69/4.92        ( ( minus_minus_real @ zero_zero_real @ B )
% 8.69/4.92        = ( uminus_uminus_real @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4731_verit__minus__simplify_I3_J,axiom,
% 8.69/4.92      ! [B: int] :
% 8.69/4.92        ( ( minus_minus_int @ zero_zero_int @ B )
% 8.69/4.92        = ( uminus_uminus_int @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4732_verit__minus__simplify_I3_J,axiom,
% 8.69/4.92      ! [B: complex] :
% 8.69/4.92        ( ( minus_minus_complex @ zero_zero_complex @ B )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4733_verit__minus__simplify_I3_J,axiom,
% 8.69/4.92      ! [B: code_integer] :
% 8.69/4.92        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4734_verit__minus__simplify_I3_J,axiom,
% 8.69/4.92      ! [B: rat] :
% 8.69/4.92        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 8.69/4.92        = ( uminus_uminus_rat @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4735_add__neg__numeral__simps_I3_J,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.92        = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4736_add__neg__numeral__simps_I3_J,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.92        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4737_add__neg__numeral__simps_I3_J,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4738_add__neg__numeral__simps_I3_J,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4739_add__neg__numeral__simps_I3_J,axiom,
% 8.69/4.92      ! [M: num,N: num] :
% 8.69/4.92        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.92        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4740_dvd__times__right__cancel__iff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.92        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 8.69/4.92          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4741_dvd__times__right__cancel__iff,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( A != zero_zero_nat )
% 8.69/4.92       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 8.69/4.92          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4742_dvd__times__right__cancel__iff,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( A != zero_zero_int )
% 8.69/4.92       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 8.69/4.92          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4743_dvd__times__left__cancel__iff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.92        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 8.69/4.92          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4744_dvd__times__left__cancel__iff,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( A != zero_zero_nat )
% 8.69/4.92       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 8.69/4.92          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4745_dvd__times__left__cancel__iff,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( A != zero_zero_int )
% 8.69/4.92       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 8.69/4.92          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4746_dvd__mult__cancel__right,axiom,
% 8.69/4.92      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.69/4.92        = ( ( C = zero_z3403309356797280102nteger )
% 8.69/4.92          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4747_dvd__mult__cancel__right,axiom,
% 8.69/4.92      ! [A: complex,C: complex,B: complex] :
% 8.69/4.92        ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 8.69/4.92        = ( ( C = zero_zero_complex )
% 8.69/4.92          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4748_dvd__mult__cancel__right,axiom,
% 8.69/4.92      ! [A: real,C: real,B: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 8.69/4.92        = ( ( C = zero_zero_real )
% 8.69/4.92          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4749_dvd__mult__cancel__right,axiom,
% 8.69/4.92      ! [A: rat,C: rat,B: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 8.69/4.92        = ( ( C = zero_zero_rat )
% 8.69/4.92          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4750_dvd__mult__cancel__right,axiom,
% 8.69/4.92      ! [A: int,C: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 8.69/4.92        = ( ( C = zero_zero_int )
% 8.69/4.92          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4751_dvd__mult__cancel__left,axiom,
% 8.69/4.92      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.69/4.92        = ( ( C = zero_z3403309356797280102nteger )
% 8.69/4.92          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4752_dvd__mult__cancel__left,axiom,
% 8.69/4.92      ! [C: complex,A: complex,B: complex] :
% 8.69/4.92        ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 8.69/4.92        = ( ( C = zero_zero_complex )
% 8.69/4.92          | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4753_dvd__mult__cancel__left,axiom,
% 8.69/4.92      ! [C: real,A: real,B: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 8.69/4.92        = ( ( C = zero_zero_real )
% 8.69/4.92          | ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4754_dvd__mult__cancel__left,axiom,
% 8.69/4.92      ! [C: rat,A: rat,B: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 8.69/4.92        = ( ( C = zero_zero_rat )
% 8.69/4.92          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4755_dvd__mult__cancel__left,axiom,
% 8.69/4.92      ! [C: int,A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.69/4.92        = ( ( C = zero_zero_int )
% 8.69/4.92          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4756_mult__minus1__right,axiom,
% 8.69/4.92      ! [Z: real] :
% 8.69/4.92        ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.92        = ( uminus_uminus_real @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4757_mult__minus1__right,axiom,
% 8.69/4.92      ! [Z: int] :
% 8.69/4.92        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.92        = ( uminus_uminus_int @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4758_mult__minus1__right,axiom,
% 8.69/4.92      ! [Z: complex] :
% 8.69/4.92        ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4759_mult__minus1__right,axiom,
% 8.69/4.92      ! [Z: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4760_mult__minus1__right,axiom,
% 8.69/4.92      ! [Z: rat] :
% 8.69/4.92        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.92        = ( uminus_uminus_rat @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4761_mult__minus1,axiom,
% 8.69/4.92      ! [Z: real] :
% 8.69/4.92        ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 8.69/4.92        = ( uminus_uminus_real @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4762_mult__minus1,axiom,
% 8.69/4.92      ! [Z: int] :
% 8.69/4.92        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 8.69/4.92        = ( uminus_uminus_int @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4763_mult__minus1,axiom,
% 8.69/4.92      ! [Z: complex] :
% 8.69/4.92        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4764_mult__minus1,axiom,
% 8.69/4.92      ! [Z: code_integer] :
% 8.69/4.92        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4765_mult__minus1,axiom,
% 8.69/4.92      ! [Z: rat] :
% 8.69/4.92        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 8.69/4.92        = ( uminus_uminus_rat @ Z ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4766_abs__le__zero__iff,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 8.69/4.92        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4767_abs__le__zero__iff,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 8.69/4.92        = ( A = zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4768_abs__le__zero__iff,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 8.69/4.92        = ( A = zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4769_abs__le__zero__iff,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 8.69/4.92        = ( A = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4770_abs__le__self__iff,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 8.69/4.92        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4771_abs__le__self__iff,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4772_abs__le__self__iff,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4773_abs__le__self__iff,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 8.69/4.92        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4774_abs__of__nonneg,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.69/4.92       => ( ( abs_abs_Code_integer @ A )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4775_abs__of__nonneg,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.92       => ( ( abs_abs_real @ A )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4776_abs__of__nonneg,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.69/4.92       => ( ( abs_abs_rat @ A )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4777_abs__of__nonneg,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.69/4.92       => ( ( abs_abs_int @ A )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4778_zero__less__abs__iff,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 8.69/4.92        = ( A != zero_z3403309356797280102nteger ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4779_zero__less__abs__iff,axiom,
% 8.69/4.92      ! [A: real] :
% 8.69/4.92        ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 8.69/4.92        = ( A != zero_zero_real ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4780_zero__less__abs__iff,axiom,
% 8.69/4.92      ! [A: rat] :
% 8.69/4.92        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 8.69/4.92        = ( A != zero_zero_rat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4781_zero__less__abs__iff,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 8.69/4.92        = ( A != zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4782_uminus__add__conv__diff,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.92        = ( minus_minus_real @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4783_uminus__add__conv__diff,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.92        = ( minus_minus_int @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4784_uminus__add__conv__diff,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.69/4.92        = ( minus_minus_complex @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4785_uminus__add__conv__diff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.92        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4786_uminus__add__conv__diff,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.92        = ( minus_minus_rat @ B @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4787_diff__minus__eq__add,axiom,
% 8.69/4.92      ! [A: real,B: real] :
% 8.69/4.92        ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 8.69/4.92        = ( plus_plus_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4788_diff__minus__eq__add,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.92        = ( plus_plus_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4789_diff__minus__eq__add,axiom,
% 8.69/4.92      ! [A: complex,B: complex] :
% 8.69/4.92        ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.92        = ( plus_plus_complex @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4790_diff__minus__eq__add,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.92        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4791_diff__minus__eq__add,axiom,
% 8.69/4.92      ! [A: rat,B: rat] :
% 8.69/4.92        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.69/4.92        = ( plus_plus_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4792_divide__minus1,axiom,
% 8.69/4.92      ! [X: real] :
% 8.69/4.92        ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.92        = ( uminus_uminus_real @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4793_divide__minus1,axiom,
% 8.69/4.92      ! [X: complex] :
% 8.69/4.92        ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.92        = ( uminus1482373934393186551omplex @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4794_divide__minus1,axiom,
% 8.69/4.92      ! [X: rat] :
% 8.69/4.92        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.92        = ( uminus_uminus_rat @ X ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4795_div__minus1__right,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.92        = ( uminus_uminus_int @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4796_div__minus1__right,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.92        = ( uminus1351360451143612070nteger @ A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4797_dvd__add__times__triv__right__iff,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4798_dvd__add__times__triv__right__iff,axiom,
% 8.69/4.92      ! [A: real,B: real,C: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 8.69/4.92        = ( dvd_dvd_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4799_dvd__add__times__triv__right__iff,axiom,
% 8.69/4.92      ! [A: rat,B: rat,C: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 8.69/4.92        = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4800_dvd__add__times__triv__right__iff,axiom,
% 8.69/4.92      ! [A: nat,B: nat,C: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 8.69/4.92        = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4801_dvd__add__times__triv__right__iff,axiom,
% 8.69/4.92      ! [A: int,B: int,C: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 8.69/4.92        = ( dvd_dvd_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4802_dvd__add__times__triv__left__iff,axiom,
% 8.69/4.92      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 8.69/4.92        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4803_dvd__add__times__triv__left__iff,axiom,
% 8.69/4.92      ! [A: real,C: real,B: real] :
% 8.69/4.92        ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 8.69/4.92        = ( dvd_dvd_real @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4804_dvd__add__times__triv__left__iff,axiom,
% 8.69/4.92      ! [A: rat,C: rat,B: rat] :
% 8.69/4.92        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 8.69/4.92        = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4805_dvd__add__times__triv__left__iff,axiom,
% 8.69/4.92      ! [A: nat,C: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 8.69/4.92        = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4806_dvd__add__times__triv__left__iff,axiom,
% 8.69/4.92      ! [A: int,C: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 8.69/4.92        = ( dvd_dvd_int @ A @ B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4807_unit__prod,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.92         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4808_unit__prod,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.92       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.92         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4809_unit__prod,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.92       => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.92         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4810_dvd__div__mult__self,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.92       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4811_dvd__div__mult__self,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.92       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4812_dvd__div__mult__self,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.92       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4813_dvd__mult__div__cancel,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.92       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4814_dvd__mult__div__cancel,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.92       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4815_dvd__mult__div__cancel,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.92       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 8.69/4.92          = B ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4816_div__add,axiom,
% 8.69/4.92      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ C @ A )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.92         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.69/4.92            = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4817_div__add,axiom,
% 8.69/4.92      ! [C: nat,A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ C @ A )
% 8.69/4.92       => ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.92         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.69/4.92            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4818_div__add,axiom,
% 8.69/4.92      ! [C: int,A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ C @ A )
% 8.69/4.92       => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.92         => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.69/4.92            = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4819_unit__div,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.92         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4820_unit__div,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.92       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.92         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4821_unit__div,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.92       => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.92         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4822_unit__div__1__unit,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.92       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4823_unit__div__1__unit,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.92       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4824_unit__div__1__unit,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.92       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4825_unit__div__1__div__1,axiom,
% 8.69/4.92      ! [A: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.92       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4826_unit__div__1__div__1,axiom,
% 8.69/4.92      ! [A: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.92       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4827_unit__div__1__div__1,axiom,
% 8.69/4.92      ! [A: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.92       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 8.69/4.92          = A ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4828_div__diff,axiom,
% 8.69/4.92      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ C @ A )
% 8.69/4.92       => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.92         => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 8.69/4.92            = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4829_div__diff,axiom,
% 8.69/4.92      ! [C: int,A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ C @ A )
% 8.69/4.92       => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.92         => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 8.69/4.92            = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4830_abs__neg__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.92        = ( numeral_numeral_real @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4831_abs__neg__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.92        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4832_abs__neg__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.92        = ( numera6620942414471956472nteger @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4833_abs__neg__numeral,axiom,
% 8.69/4.92      ! [N: num] :
% 8.69/4.92        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.92        = ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4834_dvd__imp__mod__0,axiom,
% 8.69/4.92      ! [A: nat,B: nat] :
% 8.69/4.92        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.92       => ( ( modulo_modulo_nat @ B @ A )
% 8.69/4.92          = zero_zero_nat ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4835_dvd__imp__mod__0,axiom,
% 8.69/4.92      ! [A: int,B: int] :
% 8.69/4.92        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.92       => ( ( modulo_modulo_int @ B @ A )
% 8.69/4.92          = zero_zero_int ) ) ).
% 8.69/4.92  
% 8.69/4.92  thf(fact_4836_dvd__imp__mod__0,axiom,
% 8.69/4.92      ! [A: code_integer,B: code_integer] :
% 8.69/4.92        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.92       => ( ( modulo364778990260209775nteger @ B @ A )
% 8.69/4.92          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4837_abs__neg__one,axiom,
% 8.69/4.93      ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = one_one_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4838_abs__neg__one,axiom,
% 8.69/4.93      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4839_abs__neg__one,axiom,
% 8.69/4.93      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4840_abs__neg__one,axiom,
% 8.69/4.93      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = one_one_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4841_minus__mod__self1,axiom,
% 8.69/4.93      ! [B: int,A: int] :
% 8.69/4.93        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 8.69/4.93        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4842_minus__mod__self1,axiom,
% 8.69/4.93      ! [B: code_integer,A: code_integer] :
% 8.69/4.93        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 8.69/4.93        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4843_abs__power__minus,axiom,
% 8.69/4.93      ! [A: real,N: nat] :
% 8.69/4.93        ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 8.69/4.93        = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4844_abs__power__minus,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 8.69/4.93        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4845_abs__power__minus,axiom,
% 8.69/4.93      ! [A: code_integer,N: nat] :
% 8.69/4.93        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 8.69/4.93        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4846_abs__power__minus,axiom,
% 8.69/4.93      ! [A: rat,N: nat] :
% 8.69/4.93        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 8.69/4.93        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4847_real__add__minus__iff,axiom,
% 8.69/4.93      ! [X: real,A: real] :
% 8.69/4.93        ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 8.69/4.93          = zero_zero_real )
% 8.69/4.93        = ( X = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4848_tanh__real__neg__iff,axiom,
% 8.69/4.93      ! [X: real] :
% 8.69/4.93        ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 8.69/4.93        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4849_tanh__real__pos__iff,axiom,
% 8.69/4.93      ! [X: real] :
% 8.69/4.93        ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 8.69/4.93        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4850_tanh__real__nonpos__iff,axiom,
% 8.69/4.93      ! [X: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 8.69/4.93        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4851_tanh__real__nonneg__iff,axiom,
% 8.69/4.93      ! [X: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 8.69/4.93        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4852_dbl__simps_I1_J,axiom,
% 8.69/4.93      ! [K: num] :
% 8.69/4.93        ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 8.69/4.93        = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4853_dbl__simps_I1_J,axiom,
% 8.69/4.93      ! [K: num] :
% 8.69/4.93        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.93        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4854_dbl__simps_I1_J,axiom,
% 8.69/4.93      ! [K: num] :
% 8.69/4.93        ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 8.69/4.93        = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4855_dbl__simps_I1_J,axiom,
% 8.69/4.93      ! [K: num] :
% 8.69/4.93        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.69/4.93        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4856_dbl__simps_I1_J,axiom,
% 8.69/4.93      ! [K: num] :
% 8.69/4.93        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.69/4.93        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4857_add__neg__numeral__special_I7_J,axiom,
% 8.69/4.93      ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = zero_zero_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4858_add__neg__numeral__special_I7_J,axiom,
% 8.69/4.93      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = zero_zero_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4859_add__neg__numeral__special_I7_J,axiom,
% 8.69/4.93      ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93      = zero_zero_complex ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4860_add__neg__numeral__special_I7_J,axiom,
% 8.69/4.93      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = zero_z3403309356797280102nteger ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4861_add__neg__numeral__special_I7_J,axiom,
% 8.69/4.93      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = zero_zero_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4862_add__neg__numeral__special_I8_J,axiom,
% 8.69/4.93      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 8.69/4.93      = zero_zero_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4863_add__neg__numeral__special_I8_J,axiom,
% 8.69/4.93      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.69/4.93      = zero_zero_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4864_add__neg__numeral__special_I8_J,axiom,
% 8.69/4.93      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 8.69/4.93      = zero_zero_complex ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4865_add__neg__numeral__special_I8_J,axiom,
% 8.69/4.93      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 8.69/4.93      = zero_z3403309356797280102nteger ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4866_add__neg__numeral__special_I8_J,axiom,
% 8.69/4.93      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 8.69/4.93      = zero_zero_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4867_diff__numeral__special_I12_J,axiom,
% 8.69/4.93      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = zero_zero_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4868_diff__numeral__special_I12_J,axiom,
% 8.69/4.93      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = zero_zero_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4869_diff__numeral__special_I12_J,axiom,
% 8.69/4.93      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93      = zero_zero_complex ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4870_diff__numeral__special_I12_J,axiom,
% 8.69/4.93      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = zero_z3403309356797280102nteger ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4871_diff__numeral__special_I12_J,axiom,
% 8.69/4.93      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = zero_zero_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4872_neg__one__eq__numeral__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_real @ one_one_real )
% 8.69/4.93          = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4873_neg__one__eq__numeral__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_int @ one_one_int )
% 8.69/4.93          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4874_neg__one__eq__numeral__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4875_neg__one__eq__numeral__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4876_neg__one__eq__numeral__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_rat @ one_one_rat )
% 8.69/4.93          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4877_numeral__eq__neg__one__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 8.69/4.93          = ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4878_numeral__eq__neg__one__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 8.69/4.93          = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4879_numeral__eq__neg__one__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4880_numeral__eq__neg__one__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4881_numeral__eq__neg__one__iff,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 8.69/4.93          = ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93        = ( N = one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4882_zero__le__divide__abs__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 8.69/4.93        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.93          | ( B = zero_zero_real ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4883_zero__le__divide__abs__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 8.69/4.93        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.69/4.93          | ( B = zero_zero_rat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4884_divide__le__0__abs__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 8.69/4.93        = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.69/4.93          | ( B = zero_zero_real ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4885_divide__le__0__abs__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 8.69/4.93        = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.69/4.93          | ( B = zero_zero_rat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4886_minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 8.69/4.93        = one_one_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4887_minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 8.69/4.93        = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4888_minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 8.69/4.93        = one_one_complex ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4889_minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 8.69/4.93        = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4890_minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 8.69/4.93        = one_one_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4891_left__minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat,A: real] :
% 8.69/4.93        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 8.69/4.93        = A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4892_left__minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat,A: int] :
% 8.69/4.93        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 8.69/4.93        = A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4893_left__minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat,A: complex] :
% 8.69/4.93        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 8.69/4.93        = A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4894_left__minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat,A: code_integer] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 8.69/4.93        = A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4895_left__minus__one__mult__self,axiom,
% 8.69/4.93      ! [N: nat,A: rat] :
% 8.69/4.93        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 8.69/4.93        = A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4896_abs__of__nonpos,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.69/4.93       => ( ( abs_abs_real @ A )
% 8.69/4.93          = ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4897_abs__of__nonpos,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.69/4.93       => ( ( abs_abs_Code_integer @ A )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4898_abs__of__nonpos,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.69/4.93       => ( ( abs_abs_rat @ A )
% 8.69/4.93          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4899_abs__of__nonpos,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.69/4.93       => ( ( abs_abs_int @ A )
% 8.69/4.93          = ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4900_even__Suc,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4901_even__Suc__Suc__iff,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 8.69/4.93        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4902_unit__mult__div__div,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.93       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 8.69/4.93          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4903_unit__mult__div__div,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.93       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 8.69/4.93          = ( divide_divide_nat @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4904_unit__mult__div__div,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.93       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 8.69/4.93          = ( divide_divide_int @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4905_unit__div__mult__self,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.93       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 8.69/4.93          = B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4906_unit__div__mult__self,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.93       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 8.69/4.93          = B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4907_unit__div__mult__self,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.93       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 8.69/4.93          = B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4908_mod__minus1__right,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93        = zero_zero_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4909_mod__minus1__right,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93        = zero_z3403309356797280102nteger ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4910_max__number__of_I2_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93         => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93            = ( numeral_numeral_real @ U ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4911_max__number__of_I2_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93            = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4912_max__number__of_I2_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93            = ( numeral_numeral_rat @ U ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4913_max__number__of_I2_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93         => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93            = ( numeral_numeral_int @ U ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4914_max__number__of_I3_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 8.69/4.93         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 8.69/4.93            = ( numeral_numeral_real @ V ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 8.69/4.93         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 8.69/4.93            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4915_max__number__of_I3_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 8.69/4.93            = ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 8.69/4.93            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4916_max__number__of_I3_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 8.69/4.93            = ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 8.69/4.93            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4917_max__number__of_I3_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 8.69/4.93         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 8.69/4.93            = ( numeral_numeral_int @ V ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 8.69/4.93         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 8.69/4.93            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4918_max__number__of_I4_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93         => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4919_max__number__of_I4_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93         => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 8.69/4.93            = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4920_max__number__of_I4_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93         => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4921_max__number__of_I4_J,axiom,
% 8.69/4.93      ! [U: num,V: num] :
% 8.69/4.93        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 8.69/4.93        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93         => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 8.69/4.93            = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4922_pow__divides__pow__iff,axiom,
% 8.69/4.93      ! [N: nat,A: nat,B: nat] :
% 8.69/4.93        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.93       => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.69/4.93          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4923_pow__divides__pow__iff,axiom,
% 8.69/4.93      ! [N: nat,A: int,B: int] :
% 8.69/4.93        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.93       => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.69/4.93          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4924_semiring__norm_I168_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: real] :
% 8.69/4.93        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 8.69/4.93        = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4925_semiring__norm_I168_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: int] :
% 8.69/4.93        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 8.69/4.93        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4926_semiring__norm_I168_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: complex] :
% 8.69/4.93        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 8.69/4.93        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4927_semiring__norm_I168_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: code_integer] :
% 8.69/4.93        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 8.69/4.93        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4928_semiring__norm_I168_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: rat] :
% 8.69/4.93        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 8.69/4.93        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4929_diff__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.93        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4930_diff__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.93        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4931_diff__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 8.69/4.93        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4932_diff__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.93        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4933_diff__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 8.69/4.93        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4934_diff__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4935_diff__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4936_diff__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.93        = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4937_diff__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4938_diff__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4939_semiring__norm_I172_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: real] :
% 8.69/4.93        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4940_semiring__norm_I172_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: int] :
% 8.69/4.93        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4941_semiring__norm_I172_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: complex] :
% 8.69/4.93        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4942_semiring__norm_I172_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: code_integer] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4943_semiring__norm_I172_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: rat] :
% 8.69/4.93        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4944_semiring__norm_I171_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: real] :
% 8.69/4.93        ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4945_semiring__norm_I171_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: int] :
% 8.69/4.93        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4946_semiring__norm_I171_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: complex] :
% 8.69/4.93        ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4947_semiring__norm_I171_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: code_integer] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4948_semiring__norm_I171_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: rat] :
% 8.69/4.93        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 8.69/4.93        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4949_semiring__norm_I170_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: real] :
% 8.69/4.93        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 8.69/4.93        = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4950_semiring__norm_I170_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: int] :
% 8.69/4.93        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 8.69/4.93        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4951_semiring__norm_I170_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: complex] :
% 8.69/4.93        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 8.69/4.93        = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4952_semiring__norm_I170_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: code_integer] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 8.69/4.93        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4953_semiring__norm_I170_J,axiom,
% 8.69/4.93      ! [V: num,W: num,Y: rat] :
% 8.69/4.93        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 8.69/4.93        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4954_mult__neg__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4955_mult__neg__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4956_mult__neg__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.93        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4957_mult__neg__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4958_mult__neg__numeral__simps_I3_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4959_mult__neg__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.93        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4960_mult__neg__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.93        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4961_mult__neg__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 8.69/4.93        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4962_mult__neg__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.93        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4963_mult__neg__numeral__simps_I2_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 8.69/4.93        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4964_mult__neg__numeral__simps_I1_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4965_mult__neg__numeral__simps_I1_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4966_mult__neg__numeral__simps_I1_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.93        = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4967_mult__neg__numeral__simps_I1_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4968_mult__neg__numeral__simps_I1_J,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4969_artanh__minus__real,axiom,
% 8.69/4.93      ! [X: real] :
% 8.69/4.93        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.93       => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 8.69/4.93          = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4970_neg__numeral__le__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4971_neg__numeral__le__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4972_neg__numeral__le__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4973_neg__numeral__le__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( ord_less_eq_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4974_neg__numeral__less__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( ord_less_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4975_neg__numeral__less__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( ord_less_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4976_neg__numeral__less__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( ord_less_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4977_neg__numeral__less__iff,axiom,
% 8.69/4.93      ! [M: num,N: num] :
% 8.69/4.93        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( ord_less_num @ N @ M ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4978_not__neg__one__le__neg__numeral__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4979_not__neg__one__le__neg__numeral__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4980_not__neg__one__le__neg__numeral__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4981_not__neg__one__le__neg__numeral__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4982_le__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: real,B: real,W: num] :
% 8.69/4.93        ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 8.69/4.93        = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4983_le__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: rat,B: rat,W: num] :
% 8.69/4.93        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 8.69/4.93        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4984_divide__le__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: real,W: num,A: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 8.69/4.93        = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4985_divide__le__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: rat,W: num,A: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 8.69/4.93        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4986_divide__eq__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: real,W: num,A: real] :
% 8.69/4.93        ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.93          = A )
% 8.69/4.93        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.93             != zero_zero_real )
% 8.69/4.93           => ( B
% 8.69/4.93              = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 8.69/4.93          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.93              = zero_zero_real )
% 8.69/4.93           => ( A = zero_zero_real ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4987_divide__eq__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: complex,W: num,A: complex] :
% 8.69/4.93        ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.93          = A )
% 8.69/4.93        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.93             != zero_zero_complex )
% 8.69/4.93           => ( B
% 8.69/4.93              = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 8.69/4.93          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.93              = zero_zero_complex )
% 8.69/4.93           => ( A = zero_zero_complex ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4988_divide__eq__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: rat,W: num,A: rat] :
% 8.69/4.93        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 8.69/4.93          = A )
% 8.69/4.93        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.93             != zero_zero_rat )
% 8.69/4.93           => ( B
% 8.69/4.93              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 8.69/4.93          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.93              = zero_zero_rat )
% 8.69/4.93           => ( A = zero_zero_rat ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4989_eq__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: real,B: real,W: num] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 8.69/4.93        = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.93             != zero_zero_real )
% 8.69/4.93           => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.93              = B ) )
% 8.69/4.93          & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.93              = zero_zero_real )
% 8.69/4.93           => ( A = zero_zero_real ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4990_eq__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: complex,B: complex,W: num] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 8.69/4.93        = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.93             != zero_zero_complex )
% 8.69/4.93           => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.93              = B ) )
% 8.69/4.93          & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.93              = zero_zero_complex )
% 8.69/4.93           => ( A = zero_zero_complex ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4991_eq__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: rat,B: rat,W: num] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 8.69/4.93        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.93             != zero_zero_rat )
% 8.69/4.93           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 8.69/4.93              = B ) )
% 8.69/4.93          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.93              = zero_zero_rat )
% 8.69/4.93           => ( A = zero_zero_rat ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4992_neg__numeral__less__neg__one__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4993_neg__numeral__less__neg__one__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4994_neg__numeral__less__neg__one__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4995_neg__numeral__less__neg__one__iff,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93        = ( M != one ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4996_divide__less__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: real,W: num,A: real] :
% 8.69/4.93        ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 8.69/4.93        = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4997_divide__less__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [B: rat,W: num,A: rat] :
% 8.69/4.93        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 8.69/4.93        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4998_less__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: real,B: real,W: num] :
% 8.69/4.93        ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 8.69/4.93        = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_4999_less__divide__eq__numeral1_I2_J,axiom,
% 8.69/4.93      ! [A: rat,B: rat,W: num] :
% 8.69/4.93        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 8.69/4.93        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5000_even__mult__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5001_even__mult__iff,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5002_even__mult__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5003_odd__add,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 8.69/4.93        = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.93         != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5004_odd__add,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 8.69/4.93        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.93         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5005_odd__add,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 8.69/4.93        = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.93         != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5006_even__add,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5007_even__add,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5008_even__add,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 8.69/4.93        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5009_power__minus__odd,axiom,
% 8.69/4.93      ! [N: nat,A: real] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.69/4.93          = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5010_power__minus__odd,axiom,
% 8.69/4.93      ! [N: nat,A: int] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.69/4.93          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5011_power__minus__odd,axiom,
% 8.69/4.93      ! [N: nat,A: complex] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5012_power__minus__odd,axiom,
% 8.69/4.93      ! [N: nat,A: code_integer] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5013_power__minus__odd,axiom,
% 8.69/4.93      ! [N: nat,A: rat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.69/4.93          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5014_Parity_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [N: nat,A: real] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.69/4.93          = ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5015_Parity_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [N: nat,A: int] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.69/4.93          = ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5016_Parity_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [N: nat,A: complex] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.69/4.93          = ( power_power_complex @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5017_Parity_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [N: nat,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.69/4.93          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5018_Parity_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [N: nat,A: rat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.69/4.93          = ( power_power_rat @ A @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5019_power2__minus,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5020_power2__minus,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5021_power2__minus,axiom,
% 8.69/4.93      ! [A: complex] :
% 8.69/4.93        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5022_power2__minus,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5023_power2__minus,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5024_zero__less__power__abs__iff,axiom,
% 8.69/4.93      ! [A: code_integer,N: nat] :
% 8.69/4.93        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 8.69/4.93        = ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.93          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5025_zero__less__power__abs__iff,axiom,
% 8.69/4.93      ! [A: real,N: nat] :
% 8.69/4.93        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 8.69/4.93        = ( ( A != zero_zero_real )
% 8.69/4.93          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5026_zero__less__power__abs__iff,axiom,
% 8.69/4.93      ! [A: rat,N: nat] :
% 8.69/4.93        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 8.69/4.93        = ( ( A != zero_zero_rat )
% 8.69/4.93          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5027_zero__less__power__abs__iff,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 8.69/4.93        = ( ( A != zero_zero_int )
% 8.69/4.93          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5028_even__mod__2__iff,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5029_even__mod__2__iff,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5030_even__mod__2__iff,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5031_power__even__abs__numeral,axiom,
% 8.69/4.93      ! [W: num,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5032_power__even__abs__numeral,axiom,
% 8.69/4.93      ! [W: num,A: rat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5033_power__even__abs__numeral,axiom,
% 8.69/4.93      ! [W: num,A: real] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93       => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5034_power__even__abs__numeral,axiom,
% 8.69/4.93      ! [W: num,A: int] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93       => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5035_abs__power2,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5036_abs__power2,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5037_abs__power2,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5038_abs__power2,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5039_power2__abs,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5040_power2__abs,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5041_power2__abs,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5042_power2__abs,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5043_odd__Suc__div__two,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5044_even__Suc__div__two,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5045_zero__le__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: real,W: num] :
% 8.69/4.93        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5046_zero__le__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: rat,W: num] :
% 8.69/4.93        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5047_zero__le__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: int,W: num] :
% 8.69/4.93        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5048_power__less__zero__eq,axiom,
% 8.69/4.93      ! [A: real,N: nat] :
% 8.69/4.93        ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5049_power__less__zero__eq,axiom,
% 8.69/4.93      ! [A: rat,N: nat] :
% 8.69/4.93        ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5050_power__less__zero__eq,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5051_power__less__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: real,W: num] :
% 8.69/4.93        ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5052_power__less__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: rat,W: num] :
% 8.69/4.93        ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5053_power__less__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: int,W: num] :
% 8.69/4.93        ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5054_add__neg__numeral__special_I9_J,axiom,
% 8.69/4.93      ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5055_add__neg__numeral__special_I9_J,axiom,
% 8.69/4.93      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5056_add__neg__numeral__special_I9_J,axiom,
% 8.69/4.93      ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5057_add__neg__numeral__special_I9_J,axiom,
% 8.69/4.93      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5058_add__neg__numeral__special_I9_J,axiom,
% 8.69/4.93      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5059_diff__numeral__special_I11_J,axiom,
% 8.69/4.93      ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5060_diff__numeral__special_I11_J,axiom,
% 8.69/4.93      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5061_diff__numeral__special_I11_J,axiom,
% 8.69/4.93      ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93      = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5062_diff__numeral__special_I11_J,axiom,
% 8.69/4.93      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5063_diff__numeral__special_I11_J,axiom,
% 8.69/4.93      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5064_diff__numeral__special_I10_J,axiom,
% 8.69/4.93      ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 8.69/4.93      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5065_diff__numeral__special_I10_J,axiom,
% 8.69/4.93      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.69/4.93      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5066_diff__numeral__special_I10_J,axiom,
% 8.69/4.93      ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 8.69/4.93      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5067_diff__numeral__special_I10_J,axiom,
% 8.69/4.93      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 8.69/4.93      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5068_diff__numeral__special_I10_J,axiom,
% 8.69/4.93      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 8.69/4.93      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5069_minus__1__div__2__eq,axiom,
% 8.69/4.93      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5070_minus__1__div__2__eq,axiom,
% 8.69/4.93      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5071_even__plus__one__iff,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 8.69/4.93        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5072_even__plus__one__iff,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 8.69/4.93        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5073_even__plus__one__iff,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 8.69/4.93        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5074_even__diff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.69/4.93        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5075_even__diff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 8.69/4.93        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5076_neg__one__odd__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 8.69/4.93          = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5077_neg__one__odd__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 8.69/4.93          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5078_neg__one__odd__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5079_neg__one__odd__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5080_neg__one__odd__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 8.69/4.93          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5081_neg__one__even__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 8.69/4.93          = one_one_real ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5082_neg__one__even__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 8.69/4.93          = one_one_int ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5083_neg__one__even__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 8.69/4.93          = one_one_complex ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5084_neg__one__even__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 8.69/4.93          = one_one_Code_integer ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5085_neg__one__even__power,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 8.69/4.93          = one_one_rat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5086_bits__minus__1__mod__2__eq,axiom,
% 8.69/4.93      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93      = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5087_bits__minus__1__mod__2__eq,axiom,
% 8.69/4.93      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93      = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5088_minus__1__mod__2__eq,axiom,
% 8.69/4.93      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93      = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5089_minus__1__mod__2__eq,axiom,
% 8.69/4.93      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93      = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5090_odd__Suc__minus__one,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.69/4.93          = N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5091_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [A: real,N: nat] :
% 8.69/4.93        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5092_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5093_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [A: complex,N: nat] :
% 8.69/4.93        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5094_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [A: code_integer,N: nat] :
% 8.69/4.93        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5095_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.69/4.93      ! [A: rat,N: nat] :
% 8.69/4.93        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5096_even__diff__nat,axiom,
% 8.69/4.93      ! [M: nat,N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.93        = ( ( ord_less_nat @ M @ N )
% 8.69/4.93          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5097_diff__numeral__special_I3_J,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5098_diff__numeral__special_I3_J,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5099_diff__numeral__special_I3_J,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.93        = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5100_diff__numeral__special_I3_J,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.93        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5101_diff__numeral__special_I3_J,axiom,
% 8.69/4.93      ! [N: num] :
% 8.69/4.93        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.93        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5102_diff__numeral__special_I4_J,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 8.69/4.93        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5103_diff__numeral__special_I4_J,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 8.69/4.93        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5104_diff__numeral__special_I4_J,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 8.69/4.93        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5105_diff__numeral__special_I4_J,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 8.69/4.93        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5106_diff__numeral__special_I4_J,axiom,
% 8.69/4.93      ! [M: num] :
% 8.69/4.93        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 8.69/4.93        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5107_dbl__simps_I4_J,axiom,
% 8.69/4.93      ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.93      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5108_dbl__simps_I4_J,axiom,
% 8.69/4.93      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.93      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5109_dbl__simps_I4_J,axiom,
% 8.69/4.93      ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.93      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5110_dbl__simps_I4_J,axiom,
% 8.69/4.93      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.93      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5111_dbl__simps_I4_J,axiom,
% 8.69/4.93      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.93      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5112_zero__less__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: real,W: num] :
% 8.69/4.93        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( ( numeral_numeral_nat @ W )
% 8.69/4.93            = zero_zero_nat )
% 8.69/4.93          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( A != zero_zero_real ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5113_zero__less__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: rat,W: num] :
% 8.69/4.93        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( ( numeral_numeral_nat @ W )
% 8.69/4.93            = zero_zero_nat )
% 8.69/4.93          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( A != zero_zero_rat ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5114_zero__less__power__eq__numeral,axiom,
% 8.69/4.93      ! [A: int,W: num] :
% 8.69/4.93        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 8.69/4.93        = ( ( ( numeral_numeral_nat @ W )
% 8.69/4.93            = zero_zero_nat )
% 8.69/4.93          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( A != zero_zero_int ) )
% 8.69/4.93          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5115_even__succ__div__2,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5116_even__succ__div__2,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5117_even__succ__div__2,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5118_odd__succ__div__two,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5119_odd__succ__div__two,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5120_odd__succ__div__two,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5121_even__succ__div__two,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5122_even__succ__div__two,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5123_even__succ__div__two,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.93          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5124_even__power,axiom,
% 8.69/4.93      ! [A: code_integer,N: nat] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.69/4.93        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5125_even__power,axiom,
% 8.69/4.93      ! [A: nat,N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 8.69/4.93        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5126_even__power,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 8.69/4.93        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93          & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5127_power__minus1__even,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = one_one_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5128_power__minus1__even,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5129_power__minus1__even,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = one_one_complex ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5130_power__minus1__even,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5131_power__minus1__even,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.93        = one_one_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5132_odd__two__times__div__two__nat,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.93       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.93          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5133_odd__two__times__div__two__succ,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5134_odd__two__times__div__two__succ,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5135_odd__two__times__div__two__succ,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.93       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5136_power__le__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: real,W: num] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 8.69/4.93        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.69/4.93            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( A = zero_zero_real ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5137_power__le__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: rat,W: num] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 8.69/4.93        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.69/4.93            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( A = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5138_power__le__zero__eq__numeral,axiom,
% 8.69/4.93      ! [A: int,W: num] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 8.69/4.93        = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.69/4.93            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 8.69/4.93              & ( A = zero_zero_int ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5139_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 8.69/4.93        = ( N = zero_zero_nat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5140_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 8.69/4.93        = ( N = zero_zero_nat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5141_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.69/4.93      ! [N: nat] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 8.69/4.93        = ( N = zero_zero_nat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5142_dvd__div__neg,axiom,
% 8.69/4.93      ! [B: real,A: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ B @ A )
% 8.69/4.93       => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 8.69/4.93          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5143_dvd__div__neg,axiom,
% 8.69/4.93      ! [B: int,A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.93       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.93          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5144_dvd__div__neg,axiom,
% 8.69/4.93      ! [B: complex,A: complex] :
% 8.69/4.93        ( ( dvd_dvd_complex @ B @ A )
% 8.69/4.93       => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5145_dvd__div__neg,axiom,
% 8.69/4.93      ! [B: code_integer,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.93       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5146_dvd__div__neg,axiom,
% 8.69/4.93      ! [B: rat,A: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ B @ A )
% 8.69/4.93       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.69/4.93          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5147_dvd__neg__div,axiom,
% 8.69/4.93      ! [B: real,A: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ B @ A )
% 8.69/4.93       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.93          = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5148_dvd__neg__div,axiom,
% 8.69/4.93      ! [B: int,A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.93       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.93          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5149_dvd__neg__div,axiom,
% 8.69/4.93      ! [B: complex,A: complex] :
% 8.69/4.93        ( ( dvd_dvd_complex @ B @ A )
% 8.69/4.93       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.69/4.93          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5150_dvd__neg__div,axiom,
% 8.69/4.93      ! [B: code_integer,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.93       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5151_dvd__neg__div,axiom,
% 8.69/4.93      ! [B: rat,A: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ B @ A )
% 8.69/4.93       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.93          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5152_dvd__if__abs__eq,axiom,
% 8.69/4.93      ! [L2: real,K: real] :
% 8.69/4.93        ( ( ( abs_abs_real @ L2 )
% 8.69/4.93          = ( abs_abs_real @ K ) )
% 8.69/4.93       => ( dvd_dvd_real @ L2 @ K ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5153_dvd__if__abs__eq,axiom,
% 8.69/4.93      ! [L2: int,K: int] :
% 8.69/4.93        ( ( ( abs_abs_int @ L2 )
% 8.69/4.93          = ( abs_abs_int @ K ) )
% 8.69/4.93       => ( dvd_dvd_int @ L2 @ K ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5154_dvd__if__abs__eq,axiom,
% 8.69/4.93      ! [L2: code_integer,K: code_integer] :
% 8.69/4.93        ( ( ( abs_abs_Code_integer @ L2 )
% 8.69/4.93          = ( abs_abs_Code_integer @ K ) )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5155_dvd__if__abs__eq,axiom,
% 8.69/4.93      ! [L2: rat,K: rat] :
% 8.69/4.93        ( ( ( abs_abs_rat @ L2 )
% 8.69/4.93          = ( abs_abs_rat @ K ) )
% 8.69/4.93       => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5156_abs__eq__iff,axiom,
% 8.69/4.93      ! [X: real,Y: real] :
% 8.69/4.93        ( ( ( abs_abs_real @ X )
% 8.69/4.93          = ( abs_abs_real @ Y ) )
% 8.69/4.93        = ( ( X = Y )
% 8.69/4.93          | ( X
% 8.69/4.93            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5157_abs__eq__iff,axiom,
% 8.69/4.93      ! [X: int,Y: int] :
% 8.69/4.93        ( ( ( abs_abs_int @ X )
% 8.69/4.93          = ( abs_abs_int @ Y ) )
% 8.69/4.93        = ( ( X = Y )
% 8.69/4.93          | ( X
% 8.69/4.93            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5158_abs__eq__iff,axiom,
% 8.69/4.93      ! [X: code_integer,Y: code_integer] :
% 8.69/4.93        ( ( ( abs_abs_Code_integer @ X )
% 8.69/4.93          = ( abs_abs_Code_integer @ Y ) )
% 8.69/4.93        = ( ( X = Y )
% 8.69/4.93          | ( X
% 8.69/4.93            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5159_abs__eq__iff,axiom,
% 8.69/4.93      ! [X: rat,Y: rat] :
% 8.69/4.93        ( ( ( abs_abs_rat @ X )
% 8.69/4.93          = ( abs_abs_rat @ Y ) )
% 8.69/4.93        = ( ( X = Y )
% 8.69/4.93          | ( X
% 8.69/4.93            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5160_dvd__trans,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_nat @ B @ C )
% 8.69/4.93         => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5161_dvd__trans,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_int @ B @ C )
% 8.69/4.93         => ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5162_dvd__trans,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ B @ C )
% 8.69/4.93         => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5163_dvd__refl,axiom,
% 8.69/4.93      ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5164_dvd__refl,axiom,
% 8.69/4.93      ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5165_dvd__refl,axiom,
% 8.69/4.93      ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5166_minus__equation__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ( uminus_uminus_real @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( uminus_uminus_real @ B )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5167_minus__equation__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ( uminus_uminus_int @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( uminus_uminus_int @ B )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5168_minus__equation__iff,axiom,
% 8.69/4.93      ! [A: complex,B: complex] :
% 8.69/4.93        ( ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( uminus1482373934393186551omplex @ B )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5169_minus__equation__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( uminus1351360451143612070nteger @ B )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5170_minus__equation__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ( uminus_uminus_rat @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( uminus_uminus_rat @ B )
% 8.69/4.93          = A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5171_equation__minus__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( uminus_uminus_real @ B ) )
% 8.69/4.93        = ( B
% 8.69/4.93          = ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5172_equation__minus__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( uminus_uminus_int @ B ) )
% 8.69/4.93        = ( B
% 8.69/4.93          = ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5173_equation__minus__iff,axiom,
% 8.69/4.93      ! [A: complex,B: complex] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.93        = ( B
% 8.69/4.93          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5174_equation__minus__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.93        = ( B
% 8.69/4.93          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5175_equation__minus__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( uminus_uminus_rat @ B ) )
% 8.69/4.93        = ( B
% 8.69/4.93          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5176_abs__less__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_real @ A @ B )
% 8.69/4.93          & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5177_abs__less__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_int @ A @ B )
% 8.69/4.93          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5178_abs__less__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.69/4.93        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.69/4.93          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5179_abs__less__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_rat @ A @ B )
% 8.69/4.93          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5180_abs__leI,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.93       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.93         => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5181_abs__leI,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.69/4.93       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.93         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5182_abs__leI,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.93       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.93         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5183_abs__leI,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.93       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.93         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5184_abs__le__D2,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5185_abs__le__D2,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.69/4.93       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5186_abs__le__D2,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5187_abs__le__D2,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5188_abs__le__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_eq_real @ A @ B )
% 8.69/4.93          & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5189_abs__le__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.69/4.93        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.69/4.93          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5190_abs__le__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.93          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5191_abs__le__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.69/4.93        = ( ( ord_less_eq_int @ A @ B )
% 8.69/4.93          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5192_abs__ge__minus__self,axiom,
% 8.69/4.93      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5193_abs__ge__minus__self,axiom,
% 8.69/4.93      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5194_abs__ge__minus__self,axiom,
% 8.69/4.93      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5195_abs__ge__minus__self,axiom,
% 8.69/4.93      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5196_abs__minus__le__zero,axiom,
% 8.69/4.93      ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5197_abs__minus__le__zero,axiom,
% 8.69/4.93      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5198_abs__minus__le__zero,axiom,
% 8.69/4.93      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5199_abs__minus__le__zero,axiom,
% 8.69/4.93      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5200_eq__abs__iff_H,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( abs_abs_real @ B ) )
% 8.69/4.93        = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.93          & ( ( B = A )
% 8.69/4.93            | ( B
% 8.69/4.93              = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5201_eq__abs__iff_H,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( abs_abs_Code_integer @ B ) )
% 8.69/4.93        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.69/4.93          & ( ( B = A )
% 8.69/4.93            | ( B
% 8.69/4.93              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5202_eq__abs__iff_H,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( abs_abs_rat @ B ) )
% 8.69/4.93        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.69/4.93          & ( ( B = A )
% 8.69/4.93            | ( B
% 8.69/4.93              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5203_eq__abs__iff_H,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( abs_abs_int @ B ) )
% 8.69/4.93        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.69/4.93          & ( ( B = A )
% 8.69/4.93            | ( B
% 8.69/4.93              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5204_abs__eq__iff_H,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ( abs_abs_real @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.69/4.93          & ( ( A = B )
% 8.69/4.93            | ( A
% 8.69/4.93              = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5205_abs__eq__iff_H,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ( abs_abs_Code_integer @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.69/4.93          & ( ( A = B )
% 8.69/4.93            | ( A
% 8.69/4.93              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5206_abs__eq__iff_H,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ( abs_abs_rat @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.69/4.93          & ( ( A = B )
% 8.69/4.93            | ( A
% 8.69/4.93              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5207_abs__eq__iff_H,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ( abs_abs_int @ A )
% 8.69/4.93          = B )
% 8.69/4.93        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.69/4.93          & ( ( A = B )
% 8.69/4.93            | ( A
% 8.69/4.93              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5208_abs__if,axiom,
% 8.69/4.93      ( abs_abs_real
% 8.69/4.93      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5209_abs__if,axiom,
% 8.69/4.93      ( abs_abs_int
% 8.69/4.93      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5210_abs__if,axiom,
% 8.69/4.93      ( abs_abs_Code_integer
% 8.69/4.93      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5211_abs__if,axiom,
% 8.69/4.93      ( abs_abs_rat
% 8.69/4.93      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5212_abs__of__neg,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( ord_less_real @ A @ zero_zero_real )
% 8.69/4.93       => ( ( abs_abs_real @ A )
% 8.69/4.93          = ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5213_abs__of__neg,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( ord_less_int @ A @ zero_zero_int )
% 8.69/4.93       => ( ( abs_abs_int @ A )
% 8.69/4.93          = ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5214_abs__of__neg,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.69/4.93       => ( ( abs_abs_Code_integer @ A )
% 8.69/4.93          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5215_abs__of__neg,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.69/4.93       => ( ( abs_abs_rat @ A )
% 8.69/4.93          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5216_abs__if__raw,axiom,
% 8.69/4.93      ( abs_abs_real
% 8.69/4.93      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5217_abs__if__raw,axiom,
% 8.69/4.93      ( abs_abs_int
% 8.69/4.93      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5218_abs__if__raw,axiom,
% 8.69/4.93      ( abs_abs_Code_integer
% 8.69/4.93      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5219_abs__if__raw,axiom,
% 8.69/4.93      ( abs_abs_rat
% 8.69/4.93      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5220_abs__real__def,axiom,
% 8.69/4.93      ( abs_abs_real
% 8.69/4.93      = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5221_abs__le__D1,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_real @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5222_abs__le__D1,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.69/4.93       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5223_abs__le__D1,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5224_abs__le__D1,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.69/4.93       => ( ord_less_eq_int @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5225_abs__ge__self,axiom,
% 8.69/4.93      ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5226_abs__ge__self,axiom,
% 8.69/4.93      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5227_abs__ge__self,axiom,
% 8.69/4.93      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5228_abs__ge__self,axiom,
% 8.69/4.93      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5229_abs__eq__0__iff,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( ( abs_abs_Code_integer @ A )
% 8.69/4.93          = zero_z3403309356797280102nteger )
% 8.69/4.93        = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5230_abs__eq__0__iff,axiom,
% 8.69/4.93      ! [A: complex] :
% 8.69/4.93        ( ( ( abs_abs_complex @ A )
% 8.69/4.93          = zero_zero_complex )
% 8.69/4.93        = ( A = zero_zero_complex ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5231_abs__eq__0__iff,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( ( abs_abs_real @ A )
% 8.69/4.93          = zero_zero_real )
% 8.69/4.93        = ( A = zero_zero_real ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5232_abs__eq__0__iff,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( ( abs_abs_rat @ A )
% 8.69/4.93          = zero_zero_rat )
% 8.69/4.93        = ( A = zero_zero_rat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5233_abs__eq__0__iff,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( ( abs_abs_int @ A )
% 8.69/4.93          = zero_zero_int )
% 8.69/4.93        = ( A = zero_zero_int ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5234_abs__mult,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.69/4.93        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5235_abs__mult,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 8.69/4.93        = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5236_abs__mult,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 8.69/4.93        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5237_abs__mult,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 8.69/4.93        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5238_abs__one,axiom,
% 8.69/4.93      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.69/4.93      = one_one_Code_integer ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5239_abs__one,axiom,
% 8.69/4.93      ( ( abs_abs_real @ one_one_real )
% 8.69/4.93      = one_one_real ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5240_abs__one,axiom,
% 8.69/4.93      ( ( abs_abs_rat @ one_one_rat )
% 8.69/4.93      = one_one_rat ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5241_abs__one,axiom,
% 8.69/4.93      ( ( abs_abs_int @ one_one_int )
% 8.69/4.93      = one_one_int ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5242_abs__minus__commute,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.69/4.93        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5243_abs__minus__commute,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 8.69/4.93        = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5244_abs__minus__commute,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 8.69/4.93        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5245_abs__minus__commute,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 8.69/4.93        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5246_tanh__real__gt__neg1,axiom,
% 8.69/4.93      ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5247_power__abs,axiom,
% 8.69/4.93      ! [A: code_integer,N: nat] :
% 8.69/4.93        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.69/4.93        = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5248_power__abs,axiom,
% 8.69/4.93      ! [A: rat,N: nat] :
% 8.69/4.93        ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 8.69/4.93        = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5249_power__abs,axiom,
% 8.69/4.93      ! [A: real,N: nat] :
% 8.69/4.93        ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 8.69/4.93        = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5250_power__abs,axiom,
% 8.69/4.93      ! [A: int,N: nat] :
% 8.69/4.93        ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 8.69/4.93        = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5251_bot__nat__def,axiom,
% 8.69/4.93      bot_bot_nat = zero_zero_nat ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5252_dvd__0__left,axiom,
% 8.69/4.93      ! [A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 8.69/4.93       => ( A = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5253_dvd__0__left,axiom,
% 8.69/4.93      ! [A: complex] :
% 8.69/4.93        ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 8.69/4.93       => ( A = zero_zero_complex ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5254_dvd__0__left,axiom,
% 8.69/4.93      ! [A: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ zero_zero_real @ A )
% 8.69/4.93       => ( A = zero_zero_real ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5255_dvd__0__left,axiom,
% 8.69/4.93      ! [A: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 8.69/4.93       => ( A = zero_zero_rat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5256_dvd__0__left,axiom,
% 8.69/4.93      ! [A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.69/4.93       => ( A = zero_zero_nat ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5257_dvd__0__left,axiom,
% 8.69/4.93      ! [A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ zero_zero_int @ A )
% 8.69/4.93       => ( A = zero_zero_int ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5258_dvd__field__iff,axiom,
% 8.69/4.93      ( dvd_dvd_complex
% 8.69/4.93      = ( ^ [A3: complex,B2: complex] :
% 8.69/4.93            ( ( A3 = zero_zero_complex )
% 8.69/4.93           => ( B2 = zero_zero_complex ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5259_dvd__field__iff,axiom,
% 8.69/4.93      ( dvd_dvd_real
% 8.69/4.93      = ( ^ [A3: real,B2: real] :
% 8.69/4.93            ( ( A3 = zero_zero_real )
% 8.69/4.93           => ( B2 = zero_zero_real ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5260_dvd__field__iff,axiom,
% 8.69/4.93      ( dvd_dvd_rat
% 8.69/4.93      = ( ^ [A3: rat,B2: rat] :
% 8.69/4.93            ( ( A3 = zero_zero_rat )
% 8.69/4.93           => ( B2 = zero_zero_rat ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5261_dvdE,axiom,
% 8.69/4.93      ! [B: code_integer,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.93       => ~ ! [K3: code_integer] :
% 8.69/4.93              ( A
% 8.69/4.93             != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5262_dvdE,axiom,
% 8.69/4.93      ! [B: real,A: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ B @ A )
% 8.69/4.93       => ~ ! [K3: real] :
% 8.69/4.93              ( A
% 8.69/4.93             != ( times_times_real @ B @ K3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5263_dvdE,axiom,
% 8.69/4.93      ! [B: rat,A: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ B @ A )
% 8.69/4.93       => ~ ! [K3: rat] :
% 8.69/4.93              ( A
% 8.69/4.93             != ( times_times_rat @ B @ K3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5264_dvdE,axiom,
% 8.69/4.93      ! [B: nat,A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.93       => ~ ! [K3: nat] :
% 8.69/4.93              ( A
% 8.69/4.93             != ( times_times_nat @ B @ K3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5265_dvdE,axiom,
% 8.69/4.93      ! [B: int,A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.93       => ~ ! [K3: int] :
% 8.69/4.93              ( A
% 8.69/4.93             != ( times_times_int @ B @ K3 ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5266_dvdI,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,K: code_integer] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( times_3573771949741848930nteger @ B @ K ) )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5267_dvdI,axiom,
% 8.69/4.93      ! [A: real,B: real,K: real] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( times_times_real @ B @ K ) )
% 8.69/4.93       => ( dvd_dvd_real @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5268_dvdI,axiom,
% 8.69/4.93      ! [A: rat,B: rat,K: rat] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( times_times_rat @ B @ K ) )
% 8.69/4.93       => ( dvd_dvd_rat @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5269_dvdI,axiom,
% 8.69/4.93      ! [A: nat,B: nat,K: nat] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( times_times_nat @ B @ K ) )
% 8.69/4.93       => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5270_dvdI,axiom,
% 8.69/4.93      ! [A: int,B: int,K: int] :
% 8.69/4.93        ( ( A
% 8.69/4.93          = ( times_times_int @ B @ K ) )
% 8.69/4.93       => ( dvd_dvd_int @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5271_dvd__def,axiom,
% 8.69/4.93      ( dvd_dvd_Code_integer
% 8.69/4.93      = ( ^ [B2: code_integer,A3: code_integer] :
% 8.69/4.93          ? [K2: code_integer] :
% 8.69/4.93            ( A3
% 8.69/4.93            = ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5272_dvd__def,axiom,
% 8.69/4.93      ( dvd_dvd_real
% 8.69/4.93      = ( ^ [B2: real,A3: real] :
% 8.69/4.93          ? [K2: real] :
% 8.69/4.93            ( A3
% 8.69/4.93            = ( times_times_real @ B2 @ K2 ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5273_dvd__def,axiom,
% 8.69/4.93      ( dvd_dvd_rat
% 8.69/4.93      = ( ^ [B2: rat,A3: rat] :
% 8.69/4.93          ? [K2: rat] :
% 8.69/4.93            ( A3
% 8.69/4.93            = ( times_times_rat @ B2 @ K2 ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5274_dvd__def,axiom,
% 8.69/4.93      ( dvd_dvd_nat
% 8.69/4.93      = ( ^ [B2: nat,A3: nat] :
% 8.69/4.93          ? [K2: nat] :
% 8.69/4.93            ( A3
% 8.69/4.93            = ( times_times_nat @ B2 @ K2 ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5275_dvd__def,axiom,
% 8.69/4.93      ( dvd_dvd_int
% 8.69/4.93      = ( ^ [B2: int,A3: int] :
% 8.69/4.93          ? [K2: int] :
% 8.69/4.93            ( A3
% 8.69/4.93            = ( times_times_int @ B2 @ K2 ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5276_dvd__mult,axiom,
% 8.69/4.93      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ C )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5277_dvd__mult,axiom,
% 8.69/4.93      ! [A: real,C: real,B: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ C )
% 8.69/4.93       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5278_dvd__mult,axiom,
% 8.69/4.93      ! [A: rat,C: rat,B: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ C )
% 8.69/4.93       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5279_dvd__mult,axiom,
% 8.69/4.93      ! [A: nat,C: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ C )
% 8.69/4.93       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5280_dvd__mult,axiom,
% 8.69/4.93      ! [A: int,C: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ C )
% 8.69/4.93       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5281_dvd__mult2,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5282_dvd__mult2,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ B )
% 8.69/4.93       => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5283_dvd__mult2,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ B )
% 8.69/4.93       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5284_dvd__mult2,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5285_dvd__mult2,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5286_dvd__mult__left,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5287_dvd__mult__left,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_real @ A @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5288_dvd__mult__left,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_rat @ A @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5289_dvd__mult__left,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_nat @ A @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5290_dvd__mult__left,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_int @ A @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5291_dvd__triv__left,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5292_dvd__triv__left,axiom,
% 8.69/4.93      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5293_dvd__triv__left,axiom,
% 8.69/4.93      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5294_dvd__triv__left,axiom,
% 8.69/4.93      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5295_dvd__triv__left,axiom,
% 8.69/4.93      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5296_mult__dvd__mono,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ C @ D )
% 8.69/4.93         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5297_mult__dvd__mono,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real,D: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_real @ C @ D )
% 8.69/4.93         => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5298_mult__dvd__mono,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_rat @ C @ D )
% 8.69/4.93         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5299_mult__dvd__mono,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_nat @ C @ D )
% 8.69/4.93         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5300_mult__dvd__mono,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int,D: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_int @ C @ D )
% 8.69/4.93         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5301_dvd__mult__right,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5302_dvd__mult__right,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_real @ B @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5303_dvd__mult__right,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_rat @ B @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5304_dvd__mult__right,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_nat @ B @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5305_dvd__mult__right,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 8.69/4.93       => ( dvd_dvd_int @ B @ C ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5306_dvd__triv__right,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5307_dvd__triv__right,axiom,
% 8.69/4.93      ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5308_dvd__triv__right,axiom,
% 8.69/4.93      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5309_dvd__triv__right,axiom,
% 8.69/4.93      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5310_dvd__triv__right,axiom,
% 8.69/4.93      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5311_division__decomp,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.69/4.93       => ? [B7: nat,C5: nat] :
% 8.69/4.93            ( ( A
% 8.69/4.93              = ( times_times_nat @ B7 @ C5 ) )
% 8.69/4.93            & ( dvd_dvd_nat @ B7 @ B )
% 8.69/4.93            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5312_division__decomp,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 8.69/4.93       => ? [B7: int,C5: int] :
% 8.69/4.93            ( ( A
% 8.69/4.93              = ( times_times_int @ B7 @ C5 ) )
% 8.69/4.93            & ( dvd_dvd_int @ B7 @ B )
% 8.69/4.93            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5313_dvd__productE,axiom,
% 8.69/4.93      ! [P5: nat,A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 8.69/4.93       => ~ ! [X6: nat,Y5: nat] :
% 8.69/4.93              ( ( P5
% 8.69/4.93                = ( times_times_nat @ X6 @ Y5 ) )
% 8.69/4.93             => ( ( dvd_dvd_nat @ X6 @ A )
% 8.69/4.93               => ~ ( dvd_dvd_nat @ Y5 @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5314_dvd__productE,axiom,
% 8.69/4.93      ! [P5: int,A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 8.69/4.93       => ~ ! [X6: int,Y5: int] :
% 8.69/4.93              ( ( P5
% 8.69/4.93                = ( times_times_int @ X6 @ Y5 ) )
% 8.69/4.93             => ( ( dvd_dvd_int @ X6 @ A )
% 8.69/4.93               => ~ ( dvd_dvd_int @ Y5 @ B ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5315_dvd__add,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ A @ C )
% 8.69/4.93         => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5316_dvd__add,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_real @ A @ C )
% 8.69/4.93         => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5317_dvd__add,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_rat @ A @ C )
% 8.69/4.93         => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5318_dvd__add,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_nat @ A @ C )
% 8.69/4.93         => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5319_dvd__add,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_int @ A @ C )
% 8.69/4.93         => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5320_dvd__add__left__iff,axiom,
% 8.69/4.93      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ C )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5321_dvd__add__left__iff,axiom,
% 8.69/4.93      ! [A: real,C: real,B: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ C )
% 8.69/4.93       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5322_dvd__add__left__iff,axiom,
% 8.69/4.93      ! [A: rat,C: rat,B: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ C )
% 8.69/4.93       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5323_dvd__add__left__iff,axiom,
% 8.69/4.93      ! [A: nat,C: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ C )
% 8.69/4.93       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5324_dvd__add__left__iff,axiom,
% 8.69/4.93      ! [A: int,C: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ C )
% 8.69/4.93       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5325_dvd__add__right__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5326_dvd__add__right__iff,axiom,
% 8.69/4.93      ! [A: real,B: real,C: real] :
% 8.69/4.93        ( ( dvd_dvd_real @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_real @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5327_dvd__add__right__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat,C: rat] :
% 8.69/4.93        ( ( dvd_dvd_rat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5328_dvd__add__right__iff,axiom,
% 8.69/4.93      ! [A: nat,B: nat,C: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5329_dvd__add__right__iff,axiom,
% 8.69/4.93      ! [A: int,B: int,C: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 8.69/4.93          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5330_one__dvd,axiom,
% 8.69/4.93      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5331_one__dvd,axiom,
% 8.69/4.93      ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5332_one__dvd,axiom,
% 8.69/4.93      ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5333_one__dvd,axiom,
% 8.69/4.93      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5334_one__dvd,axiom,
% 8.69/4.93      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5335_one__dvd,axiom,
% 8.69/4.93      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5336_unit__imp__dvd,axiom,
% 8.69/4.93      ! [B: code_integer,A: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.93       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5337_unit__imp__dvd,axiom,
% 8.69/4.93      ! [B: nat,A: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.93       => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5338_unit__imp__dvd,axiom,
% 8.69/4.93      ! [B: int,A: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.93       => ( dvd_dvd_int @ B @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5339_dvd__unit__imp__unit,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.93         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5340_dvd__unit__imp__unit,axiom,
% 8.69/4.93      ! [A: nat,B: nat] :
% 8.69/4.93        ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.93         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5341_dvd__unit__imp__unit,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( dvd_dvd_int @ A @ B )
% 8.69/4.93       => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.93         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5342_le__minus__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 8.69/4.93        = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5343_le__minus__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.93        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5344_le__minus__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.69/4.93        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5345_le__minus__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.93        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5346_minus__le__iff,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.93        = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5347_minus__le__iff,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.93        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5348_minus__le__iff,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.93        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5349_minus__le__iff,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.93        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5350_le__imp__neg__le,axiom,
% 8.69/4.93      ! [A: real,B: real] :
% 8.69/4.93        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.93       => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5351_le__imp__neg__le,axiom,
% 8.69/4.93      ! [A: code_integer,B: code_integer] :
% 8.69/4.93        ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.69/4.93       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5352_le__imp__neg__le,axiom,
% 8.69/4.93      ! [A: rat,B: rat] :
% 8.69/4.93        ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.93       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5353_le__imp__neg__le,axiom,
% 8.69/4.93      ! [A: int,B: int] :
% 8.69/4.93        ( ( ord_less_eq_int @ A @ B )
% 8.69/4.93       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.93  
% 8.69/4.93  thf(fact_5354_dvd__diff__commute,axiom,
% 8.69/4.93      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.93        ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 8.69/4.93        = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5355_dvd__diff__commute,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 8.69/4.94        = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5356_dvd__diff,axiom,
% 8.69/4.94      ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ X @ Y )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ X @ Z )
% 8.69/4.94         => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5357_dvd__diff,axiom,
% 8.69/4.94      ! [X: real,Y: real,Z: real] :
% 8.69/4.94        ( ( dvd_dvd_real @ X @ Y )
% 8.69/4.94       => ( ( dvd_dvd_real @ X @ Z )
% 8.69/4.94         => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5358_dvd__diff,axiom,
% 8.69/4.94      ! [X: rat,Y: rat,Z: rat] :
% 8.69/4.94        ( ( dvd_dvd_rat @ X @ Y )
% 8.69/4.94       => ( ( dvd_dvd_rat @ X @ Z )
% 8.69/4.94         => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5359_dvd__diff,axiom,
% 8.69/4.94      ! [X: int,Y: int,Z: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ X @ Y )
% 8.69/4.94       => ( ( dvd_dvd_int @ X @ Z )
% 8.69/4.94         => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5360_less__minus__iff,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 8.69/4.94        = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5361_less__minus__iff,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.94        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5362_less__minus__iff,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.94        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5363_less__minus__iff,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.69/4.94        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5364_minus__less__iff,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.94        = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5365_minus__less__iff,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.94        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5366_minus__less__iff,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.94        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5367_minus__less__iff,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.94        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5368_verit__negate__coefficient_I2_J,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ord_less_real @ A @ B )
% 8.69/4.94       => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5369_verit__negate__coefficient_I2_J,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ord_less_int @ A @ B )
% 8.69/4.94       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5370_verit__negate__coefficient_I2_J,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.69/4.94       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5371_verit__negate__coefficient_I2_J,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ord_less_rat @ A @ B )
% 8.69/4.94       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5372_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94         => ( ( ( divide6298287555418463151nteger @ A @ C )
% 8.69/4.94              = ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5373_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: complex,A: complex,B: complex] :
% 8.69/4.94        ( ( dvd_dvd_complex @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_complex @ C @ B )
% 8.69/4.94         => ( ( ( divide1717551699836669952omplex @ A @ C )
% 8.69/4.94              = ( divide1717551699836669952omplex @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5374_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: real,A: real,B: real] :
% 8.69/4.94        ( ( dvd_dvd_real @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_real @ C @ B )
% 8.69/4.94         => ( ( ( divide_divide_real @ A @ C )
% 8.69/4.94              = ( divide_divide_real @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5375_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: rat,A: rat,B: rat] :
% 8.69/4.94        ( ( dvd_dvd_rat @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_rat @ C @ B )
% 8.69/4.94         => ( ( ( divide_divide_rat @ A @ C )
% 8.69/4.94              = ( divide_divide_rat @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5376_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: nat,A: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94         => ( ( ( divide_divide_nat @ A @ C )
% 8.69/4.94              = ( divide_divide_nat @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5377_dvd__div__eq__iff,axiom,
% 8.69/4.94      ! [C: int,A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ A )
% 8.69/4.94       => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94         => ( ( ( divide_divide_int @ A @ C )
% 8.69/4.94              = ( divide_divide_int @ B @ C ) )
% 8.69/4.94            = ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5378_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( divide6298287555418463151nteger @ A @ C )
% 8.69/4.94          = ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5379_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: complex,C: complex,B: complex] :
% 8.69/4.94        ( ( ( divide1717551699836669952omplex @ A @ C )
% 8.69/4.94          = ( divide1717551699836669952omplex @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_complex @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_complex @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5380_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: real,C: real,B: real] :
% 8.69/4.94        ( ( ( divide_divide_real @ A @ C )
% 8.69/4.94          = ( divide_divide_real @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_real @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_real @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5381_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: rat,C: rat,B: rat] :
% 8.69/4.94        ( ( ( divide_divide_rat @ A @ C )
% 8.69/4.94          = ( divide_divide_rat @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_rat @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_rat @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5382_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: nat,C: nat,B: nat] :
% 8.69/4.94        ( ( ( divide_divide_nat @ A @ C )
% 8.69/4.94          = ( divide_divide_nat @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_nat @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5383_dvd__div__eq__cancel,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int] :
% 8.69/4.94        ( ( ( divide_divide_int @ A @ C )
% 8.69/4.94          = ( divide_divide_int @ B @ C ) )
% 8.69/4.94       => ( ( dvd_dvd_int @ C @ A )
% 8.69/4.94         => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94           => ( A = B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5384_div__div__div__same,axiom,
% 8.69/4.94      ! [D: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ D @ B )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94         => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 8.69/4.94            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5385_div__div__div__same,axiom,
% 8.69/4.94      ! [D: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ D @ B )
% 8.69/4.94       => ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94         => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 8.69/4.94            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5386_div__div__div__same,axiom,
% 8.69/4.94      ! [D: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ D @ B )
% 8.69/4.94       => ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94         => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 8.69/4.94            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5387_neg__numeral__neq__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 8.69/4.94       != ( numeral_numeral_real @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5388_neg__numeral__neq__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 8.69/4.94       != ( numeral_numeral_int @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5389_neg__numeral__neq__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 8.69/4.94       != ( numera6690914467698888265omplex @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5390_neg__numeral__neq__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 8.69/4.94       != ( numera6620942414471956472nteger @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5391_neg__numeral__neq__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 8.69/4.94       != ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5392_numeral__neq__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( numeral_numeral_real @ M )
% 8.69/4.94       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5393_numeral__neq__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( numeral_numeral_int @ M )
% 8.69/4.94       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5394_numeral__neq__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( numera6690914467698888265omplex @ M )
% 8.69/4.94       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5395_numeral__neq__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( numera6620942414471956472nteger @ M )
% 8.69/4.94       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5396_numeral__neq__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ( ( numeral_numeral_rat @ M )
% 8.69/4.94       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5397_dvd__power__same,axiom,
% 8.69/4.94      ! [X: code_integer,Y: code_integer,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ X @ Y )
% 8.69/4.94       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5398_dvd__power__same,axiom,
% 8.69/4.94      ! [X: nat,Y: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ X @ Y )
% 8.69/4.94       => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5399_dvd__power__same,axiom,
% 8.69/4.94      ! [X: real,Y: real,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_real @ X @ Y )
% 8.69/4.94       => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5400_dvd__power__same,axiom,
% 8.69/4.94      ! [X: int,Y: int,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_int @ X @ Y )
% 8.69/4.94       => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5401_dvd__power__same,axiom,
% 8.69/4.94      ! [X: complex,Y: complex,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_complex @ X @ Y )
% 8.69/4.94       => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5402_square__eq__iff,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ( times_times_real @ A @ A )
% 8.69/4.94          = ( times_times_real @ B @ B ) )
% 8.69/4.94        = ( ( A = B )
% 8.69/4.94          | ( A
% 8.69/4.94            = ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5403_square__eq__iff,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( times_times_int @ A @ A )
% 8.69/4.94          = ( times_times_int @ B @ B ) )
% 8.69/4.94        = ( ( A = B )
% 8.69/4.94          | ( A
% 8.69/4.94            = ( uminus_uminus_int @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5404_square__eq__iff,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ( times_times_complex @ A @ A )
% 8.69/4.94          = ( times_times_complex @ B @ B ) )
% 8.69/4.94        = ( ( A = B )
% 8.69/4.94          | ( A
% 8.69/4.94            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5405_square__eq__iff,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( times_3573771949741848930nteger @ A @ A )
% 8.69/4.94          = ( times_3573771949741848930nteger @ B @ B ) )
% 8.69/4.94        = ( ( A = B )
% 8.69/4.94          | ( A
% 8.69/4.94            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5406_square__eq__iff,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ( times_times_rat @ A @ A )
% 8.69/4.94          = ( times_times_rat @ B @ B ) )
% 8.69/4.94        = ( ( A = B )
% 8.69/4.94          | ( A
% 8.69/4.94            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5407_minus__mult__commute,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 8.69/4.94        = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5408_minus__mult__commute,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.94        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5409_minus__mult__commute,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.69/4.94        = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5410_minus__mult__commute,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.94        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5411_minus__mult__commute,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.69/4.94        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5412_group__cancel_Oneg1,axiom,
% 8.69/4.94      ! [A2: real,K: real,A: real] :
% 8.69/4.94        ( ( A2
% 8.69/4.94          = ( plus_plus_real @ K @ A ) )
% 8.69/4.94       => ( ( uminus_uminus_real @ A2 )
% 8.69/4.94          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5413_group__cancel_Oneg1,axiom,
% 8.69/4.94      ! [A2: int,K: int,A: int] :
% 8.69/4.94        ( ( A2
% 8.69/4.94          = ( plus_plus_int @ K @ A ) )
% 8.69/4.94       => ( ( uminus_uminus_int @ A2 )
% 8.69/4.94          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5414_group__cancel_Oneg1,axiom,
% 8.69/4.94      ! [A2: complex,K: complex,A: complex] :
% 8.69/4.94        ( ( A2
% 8.69/4.94          = ( plus_plus_complex @ K @ A ) )
% 8.69/4.94       => ( ( uminus1482373934393186551omplex @ A2 )
% 8.69/4.94          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5415_group__cancel_Oneg1,axiom,
% 8.69/4.94      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 8.69/4.94        ( ( A2
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 8.69/4.94       => ( ( uminus1351360451143612070nteger @ A2 )
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5416_group__cancel_Oneg1,axiom,
% 8.69/4.94      ! [A2: rat,K: rat,A: rat] :
% 8.69/4.94        ( ( A2
% 8.69/4.94          = ( plus_plus_rat @ K @ A ) )
% 8.69/4.94       => ( ( uminus_uminus_rat @ A2 )
% 8.69/4.94          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5417_add_Oinverse__distrib__swap,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.69/4.94        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5418_add_Oinverse__distrib__swap,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.69/4.94        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5419_add_Oinverse__distrib__swap,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.69/4.94        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5420_add_Oinverse__distrib__swap,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.94        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5421_add_Oinverse__distrib__swap,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.69/4.94        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5422_is__num__normalize_I8_J,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.69/4.94        = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5423_is__num__normalize_I8_J,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.69/4.94        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5424_is__num__normalize_I8_J,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.69/4.94        = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5425_is__num__normalize_I8_J,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.69/4.94        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5426_is__num__normalize_I8_J,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.69/4.94        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5427_one__neq__neg__one,axiom,
% 8.69/4.94      ( one_one_real
% 8.69/4.94     != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5428_one__neq__neg__one,axiom,
% 8.69/4.94      ( one_one_int
% 8.69/4.94     != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5429_one__neq__neg__one,axiom,
% 8.69/4.94      ( one_one_complex
% 8.69/4.94     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5430_one__neq__neg__one,axiom,
% 8.69/4.94      ( one_one_Code_integer
% 8.69/4.94     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5431_one__neq__neg__one,axiom,
% 8.69/4.94      ( one_one_rat
% 8.69/4.94     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5432_minus__diff__minus,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.69/4.94        = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5433_minus__diff__minus,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 8.69/4.94        = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5434_minus__diff__minus,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.94        = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5435_minus__diff__minus,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.94        = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5436_minus__diff__minus,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.69/4.94        = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5437_minus__diff__commute,axiom,
% 8.69/4.94      ! [B: real,A: real] :
% 8.69/4.94        ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 8.69/4.94        = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5438_minus__diff__commute,axiom,
% 8.69/4.94      ! [B: int,A: int] :
% 8.69/4.94        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 8.69/4.94        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5439_minus__diff__commute,axiom,
% 8.69/4.94      ! [B: complex,A: complex] :
% 8.69/4.94        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 8.69/4.94        = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5440_minus__diff__commute,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 8.69/4.94        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5441_minus__diff__commute,axiom,
% 8.69/4.94      ! [B: rat,A: rat] :
% 8.69/4.94        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 8.69/4.94        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5442_minus__divide__right,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.94        = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5443_minus__divide__right,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.94        = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5444_minus__divide__right,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.94        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5445_minus__divide__divide,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.69/4.94        = ( divide_divide_real @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5446_minus__divide__divide,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.94        = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5447_minus__divide__divide,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.69/4.94        = ( divide_divide_rat @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5448_minus__divide__left,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.94        = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5449_minus__divide__left,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.94        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5450_minus__divide__left,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.94        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5451_div__minus__right,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.94        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5452_div__minus__right,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.94        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5453_gcd__nat_Oextremum,axiom,
% 8.69/4.94      ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5454_gcd__nat_Oextremum__strict,axiom,
% 8.69/4.94      ! [A: nat] :
% 8.69/4.94        ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.69/4.94          & ( zero_zero_nat != A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5455_gcd__nat_Oextremum__unique,axiom,
% 8.69/4.94      ! [A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.69/4.94        = ( A = zero_zero_nat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5456_gcd__nat_Onot__eq__extremum,axiom,
% 8.69/4.94      ! [A: nat] :
% 8.69/4.94        ( ( A != zero_zero_nat )
% 8.69/4.94        = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 8.69/4.94          & ( A != zero_zero_nat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5457_gcd__nat_Oextremum__uniqueI,axiom,
% 8.69/4.94      ! [A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.69/4.94       => ( A = zero_zero_nat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5458_mod__mod__cancel,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 8.69/4.94          = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5459_mod__mod__cancel,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 8.69/4.94          = ( modulo_modulo_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5460_mod__mod__cancel,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 8.69/4.94          = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5461_dvd__mod,axiom,
% 8.69/4.94      ! [K: nat,M: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ K @ M )
% 8.69/4.94       => ( ( dvd_dvd_nat @ K @ N )
% 8.69/4.94         => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5462_dvd__mod,axiom,
% 8.69/4.94      ! [K: int,M: int,N: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ K @ M )
% 8.69/4.94       => ( ( dvd_dvd_int @ K @ N )
% 8.69/4.94         => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5463_dvd__mod,axiom,
% 8.69/4.94      ! [K: code_integer,M: code_integer,N: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ K @ M )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ K @ N )
% 8.69/4.94         => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5464_dvd__mod__imp__dvd,axiom,
% 8.69/4.94      ! [C: nat,A: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 8.69/4.94       => ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94         => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5465_dvd__mod__imp__dvd,axiom,
% 8.69/4.94      ! [C: int,A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 8.69/4.94       => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94         => ( dvd_dvd_int @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5466_dvd__mod__imp__dvd,axiom,
% 8.69/4.94      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94         => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5467_dvd__mod__iff,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 8.69/4.94          = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5468_dvd__mod__iff,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 8.69/4.94          = ( dvd_dvd_int @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5469_dvd__mod__iff,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5470_mod__minus__right,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.94        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5471_mod__minus__right,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.94        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5472_mod__minus__cong,axiom,
% 8.69/4.94      ! [A: int,B: int,A4: int] :
% 8.69/4.94        ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.94          = ( modulo_modulo_int @ A4 @ B ) )
% 8.69/4.94       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.94          = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5473_mod__minus__cong,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,A4: code_integer] :
% 8.69/4.94        ( ( ( modulo364778990260209775nteger @ A @ B )
% 8.69/4.94          = ( modulo364778990260209775nteger @ A4 @ B ) )
% 8.69/4.94       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.69/4.94          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5474_mod__minus__eq,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 8.69/4.94        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5475_mod__minus__eq,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 8.69/4.94        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5476_dvd__diff__nat,axiom,
% 8.69/4.94      ! [K: nat,M: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ K @ M )
% 8.69/4.94       => ( ( dvd_dvd_nat @ K @ N )
% 8.69/4.94         => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5477_zdvd__zdiffD,axiom,
% 8.69/4.94      ! [K: int,M: int,N: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 8.69/4.94       => ( ( dvd_dvd_int @ K @ N )
% 8.69/4.94         => ( dvd_dvd_int @ K @ M ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5478_bot__enat__def,axiom,
% 8.69/4.94      bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5479_even__minus,axiom,
% 8.69/4.94      ! [A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 8.69/4.94        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5480_even__minus,axiom,
% 8.69/4.94      ! [A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.69/4.94        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5481_subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ord_le211207098394363844omplex
% 8.69/4.94          @ ( collect_complex
% 8.69/4.94            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 8.69/4.94          @ ( collect_complex
% 8.69/4.94            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 8.69/4.94        = ( dvd_dvd_complex @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5482_subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( ord_less_eq_set_nat
% 8.69/4.94          @ ( collect_nat
% 8.69/4.94            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 8.69/4.94          @ ( collect_nat
% 8.69/4.94            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 8.69/4.94        = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5483_subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ord_le7084787975880047091nteger
% 8.69/4.94          @ ( collect_Code_integer
% 8.69/4.94            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 8.69/4.94          @ ( collect_Code_integer
% 8.69/4.94            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 8.69/4.94        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5484_subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ord_less_eq_set_int
% 8.69/4.94          @ ( collect_int
% 8.69/4.94            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 8.69/4.94          @ ( collect_int
% 8.69/4.94            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 8.69/4.94        = ( dvd_dvd_int @ A @ B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5485_strict__subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ord_less_set_complex
% 8.69/4.94          @ ( collect_complex
% 8.69/4.94            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 8.69/4.94          @ ( collect_complex
% 8.69/4.94            @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 8.69/4.94        = ( ( dvd_dvd_complex @ A @ B )
% 8.69/4.94          & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5486_strict__subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( ord_less_set_nat
% 8.69/4.94          @ ( collect_nat
% 8.69/4.94            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 8.69/4.94          @ ( collect_nat
% 8.69/4.94            @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 8.69/4.94        = ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.94          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5487_strict__subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ord_less_set_int
% 8.69/4.94          @ ( collect_int
% 8.69/4.94            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 8.69/4.94          @ ( collect_int
% 8.69/4.94            @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 8.69/4.94        = ( ( dvd_dvd_int @ A @ B )
% 8.69/4.94          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5488_strict__subset__divisors__dvd,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ord_le1307284697595431911nteger
% 8.69/4.94          @ ( collect_Code_integer
% 8.69/4.94            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 8.69/4.94          @ ( collect_Code_integer
% 8.69/4.94            @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 8.69/4.94        = ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.94          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5489_power__even__abs,axiom,
% 8.69/4.94      ! [N: nat,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 8.69/4.94          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5490_power__even__abs,axiom,
% 8.69/4.94      ! [N: nat,A: rat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 8.69/4.94          = ( power_power_rat @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5491_power__even__abs,axiom,
% 8.69/4.94      ! [N: nat,A: real] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 8.69/4.94          = ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5492_power__even__abs,axiom,
% 8.69/4.94      ! [N: nat,A: int] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 8.69/4.94          = ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5493_abs__ge__zero,axiom,
% 8.69/4.94      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5494_abs__ge__zero,axiom,
% 8.69/4.94      ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5495_abs__ge__zero,axiom,
% 8.69/4.94      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5496_abs__ge__zero,axiom,
% 8.69/4.94      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5497_abs__of__pos,axiom,
% 8.69/4.94      ! [A: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.69/4.94       => ( ( abs_abs_Code_integer @ A )
% 8.69/4.94          = A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5498_abs__of__pos,axiom,
% 8.69/4.94      ! [A: real] :
% 8.69/4.94        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.94       => ( ( abs_abs_real @ A )
% 8.69/4.94          = A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5499_abs__of__pos,axiom,
% 8.69/4.94      ! [A: rat] :
% 8.69/4.94        ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.69/4.94       => ( ( abs_abs_rat @ A )
% 8.69/4.94          = A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5500_abs__of__pos,axiom,
% 8.69/4.94      ! [A: int] :
% 8.69/4.94        ( ( ord_less_int @ zero_zero_int @ A )
% 8.69/4.94       => ( ( abs_abs_int @ A )
% 8.69/4.94          = A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5501_abs__not__less__zero,axiom,
% 8.69/4.94      ! [A: code_integer] :
% 8.69/4.94        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5502_abs__not__less__zero,axiom,
% 8.69/4.94      ! [A: real] :
% 8.69/4.94        ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5503_abs__not__less__zero,axiom,
% 8.69/4.94      ! [A: rat] :
% 8.69/4.94        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5504_abs__not__less__zero,axiom,
% 8.69/4.94      ! [A: int] :
% 8.69/4.94        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5505_uminus__power__if,axiom,
% 8.69/4.94      ! [N: nat,A: real] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.69/4.94            = ( power_power_real @ A @ N ) ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.69/4.94            = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5506_uminus__power__if,axiom,
% 8.69/4.94      ! [N: nat,A: int] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.69/4.94            = ( power_power_int @ A @ N ) ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.69/4.94            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5507_uminus__power__if,axiom,
% 8.69/4.94      ! [N: nat,A: complex] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.69/4.94            = ( power_power_complex @ A @ N ) ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.69/4.94            = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5508_uminus__power__if,axiom,
% 8.69/4.94      ! [N: nat,A: code_integer] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.69/4.94            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.69/4.94            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5509_uminus__power__if,axiom,
% 8.69/4.94      ! [N: nat,A: rat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.69/4.94            = ( power_power_rat @ A @ N ) ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.69/4.94            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5510_abs__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5511_abs__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5512_abs__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5513_abs__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5514_abs__mult__less,axiom,
% 8.69/4.94      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 8.69/4.94       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 8.69/4.94         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5515_abs__mult__less,axiom,
% 8.69/4.94      ! [A: real,C: real,B: real,D: real] :
% 8.69/4.94        ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 8.69/4.94       => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 8.69/4.94         => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5516_abs__mult__less,axiom,
% 8.69/4.94      ! [A: rat,C: rat,B: rat,D: rat] :
% 8.69/4.94        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 8.69/4.94       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 8.69/4.94         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5517_abs__mult__less,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int,D: int] :
% 8.69/4.94        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 8.69/4.94       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 8.69/4.94         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5518_abs__triangle__ineq2__sym,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5519_abs__triangle__ineq2__sym,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5520_abs__triangle__ineq2__sym,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5521_abs__triangle__ineq2__sym,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5522_abs__triangle__ineq3,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5523_abs__triangle__ineq3,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5524_abs__triangle__ineq3,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5525_abs__triangle__ineq3,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5526_abs__triangle__ineq2,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5527_abs__triangle__ineq2,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5528_abs__triangle__ineq2,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5529_abs__triangle__ineq2,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5530_nonzero__abs__divide,axiom,
% 8.69/4.94      ! [B: real,A: real] :
% 8.69/4.94        ( ( B != zero_zero_real )
% 8.69/4.94       => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.94          = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5531_nonzero__abs__divide,axiom,
% 8.69/4.94      ! [B: rat,A: rat] :
% 8.69/4.94        ( ( B != zero_zero_rat )
% 8.69/4.94       => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.94          = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5532_not__is__unit__0,axiom,
% 8.69/4.94      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5533_not__is__unit__0,axiom,
% 8.69/4.94      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5534_not__is__unit__0,axiom,
% 8.69/4.94      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5535_pinf_I9_J,axiom,
% 8.69/4.94      ! [D: code_integer,S: code_integer] :
% 8.69/4.94      ? [Z5: code_integer] :
% 8.69/4.94      ! [X4: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5536_pinf_I9_J,axiom,
% 8.69/4.94      ! [D: real,S: real] :
% 8.69/4.94      ? [Z5: real] :
% 8.69/4.94      ! [X4: real] :
% 8.69/4.94        ( ( ord_less_real @ Z5 @ X4 )
% 8.69/4.94       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5537_pinf_I9_J,axiom,
% 8.69/4.94      ! [D: rat,S: rat] :
% 8.69/4.94      ? [Z5: rat] :
% 8.69/4.94      ! [X4: rat] :
% 8.69/4.94        ( ( ord_less_rat @ Z5 @ X4 )
% 8.69/4.94       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5538_pinf_I9_J,axiom,
% 8.69/4.94      ! [D: nat,S: nat] :
% 8.69/4.94      ? [Z5: nat] :
% 8.69/4.94      ! [X4: nat] :
% 8.69/4.94        ( ( ord_less_nat @ Z5 @ X4 )
% 8.69/4.94       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5539_pinf_I9_J,axiom,
% 8.69/4.94      ! [D: int,S: int] :
% 8.69/4.94      ? [Z5: int] :
% 8.69/4.94      ! [X4: int] :
% 8.69/4.94        ( ( ord_less_int @ Z5 @ X4 )
% 8.69/4.94       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5540_pinf_I10_J,axiom,
% 8.69/4.94      ! [D: code_integer,S: code_integer] :
% 8.69/4.94      ? [Z5: code_integer] :
% 8.69/4.94      ! [X4: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5541_pinf_I10_J,axiom,
% 8.69/4.94      ! [D: real,S: real] :
% 8.69/4.94      ? [Z5: real] :
% 8.69/4.94      ! [X4: real] :
% 8.69/4.94        ( ( ord_less_real @ Z5 @ X4 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5542_pinf_I10_J,axiom,
% 8.69/4.94      ! [D: rat,S: rat] :
% 8.69/4.94      ? [Z5: rat] :
% 8.69/4.94      ! [X4: rat] :
% 8.69/4.94        ( ( ord_less_rat @ Z5 @ X4 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5543_pinf_I10_J,axiom,
% 8.69/4.94      ! [D: nat,S: nat] :
% 8.69/4.94      ? [Z5: nat] :
% 8.69/4.94      ! [X4: nat] :
% 8.69/4.94        ( ( ord_less_nat @ Z5 @ X4 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5544_pinf_I10_J,axiom,
% 8.69/4.94      ! [D: int,S: int] :
% 8.69/4.94      ? [Z5: int] :
% 8.69/4.94      ! [X4: int] :
% 8.69/4.94        ( ( ord_less_int @ Z5 @ X4 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5545_minf_I9_J,axiom,
% 8.69/4.94      ! [D: code_integer,S: code_integer] :
% 8.69/4.94      ? [Z5: code_integer] :
% 8.69/4.94      ! [X4: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5546_minf_I9_J,axiom,
% 8.69/4.94      ! [D: real,S: real] :
% 8.69/4.94      ? [Z5: real] :
% 8.69/4.94      ! [X4: real] :
% 8.69/4.94        ( ( ord_less_real @ X4 @ Z5 )
% 8.69/4.94       => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5547_minf_I9_J,axiom,
% 8.69/4.94      ! [D: rat,S: rat] :
% 8.69/4.94      ? [Z5: rat] :
% 8.69/4.94      ! [X4: rat] :
% 8.69/4.94        ( ( ord_less_rat @ X4 @ Z5 )
% 8.69/4.94       => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5548_minf_I9_J,axiom,
% 8.69/4.94      ! [D: nat,S: nat] :
% 8.69/4.94      ? [Z5: nat] :
% 8.69/4.94      ! [X4: nat] :
% 8.69/4.94        ( ( ord_less_nat @ X4 @ Z5 )
% 8.69/4.94       => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5549_minf_I9_J,axiom,
% 8.69/4.94      ! [D: int,S: int] :
% 8.69/4.94      ? [Z5: int] :
% 8.69/4.94      ! [X4: int] :
% 8.69/4.94        ( ( ord_less_int @ X4 @ Z5 )
% 8.69/4.94       => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 8.69/4.94          = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5550_minf_I10_J,axiom,
% 8.69/4.94      ! [D: code_integer,S: code_integer] :
% 8.69/4.94      ? [Z5: code_integer] :
% 8.69/4.94      ! [X4: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5551_minf_I10_J,axiom,
% 8.69/4.94      ! [D: real,S: real] :
% 8.69/4.94      ? [Z5: real] :
% 8.69/4.94      ! [X4: real] :
% 8.69/4.94        ( ( ord_less_real @ X4 @ Z5 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5552_minf_I10_J,axiom,
% 8.69/4.94      ! [D: rat,S: rat] :
% 8.69/4.94      ? [Z5: rat] :
% 8.69/4.94      ! [X4: rat] :
% 8.69/4.94        ( ( ord_less_rat @ X4 @ Z5 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5553_minf_I10_J,axiom,
% 8.69/4.94      ! [D: nat,S: nat] :
% 8.69/4.94      ? [Z5: nat] :
% 8.69/4.94      ! [X4: nat] :
% 8.69/4.94        ( ( ord_less_nat @ X4 @ Z5 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5554_minf_I10_J,axiom,
% 8.69/4.94      ! [D: int,S: int] :
% 8.69/4.94      ? [Z5: int] :
% 8.69/4.94      ! [X4: int] :
% 8.69/4.94        ( ( ord_less_int @ X4 @ Z5 )
% 8.69/4.94       => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 8.69/4.94          = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5555_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 8.69/4.94            = zero_z3403309356797280102nteger )
% 8.69/4.94          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5556_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: complex,A: complex] :
% 8.69/4.94        ( ( dvd_dvd_complex @ B @ A )
% 8.69/4.94       => ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.69/4.94            = zero_zero_complex )
% 8.69/4.94          = ( A = zero_zero_complex ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5557_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: real,A: real] :
% 8.69/4.94        ( ( dvd_dvd_real @ B @ A )
% 8.69/4.94       => ( ( ( divide_divide_real @ A @ B )
% 8.69/4.94            = zero_zero_real )
% 8.69/4.94          = ( A = zero_zero_real ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5558_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: rat,A: rat] :
% 8.69/4.94        ( ( dvd_dvd_rat @ B @ A )
% 8.69/4.94       => ( ( ( divide_divide_rat @ A @ B )
% 8.69/4.94            = zero_zero_rat )
% 8.69/4.94          = ( A = zero_zero_rat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5559_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94       => ( ( ( divide_divide_nat @ A @ B )
% 8.69/4.94            = zero_zero_nat )
% 8.69/4.94          = ( A = zero_zero_nat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5560_dvd__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94       => ( ( ( divide_divide_int @ A @ B )
% 8.69/4.94            = zero_zero_int )
% 8.69/4.94          = ( A = zero_zero_int ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5561_is__unit__mult__iff,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 8.69/4.94        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5562_is__unit__mult__iff,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 8.69/4.94        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5563_is__unit__mult__iff,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 8.69/4.94        = ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5564_dvd__mult__unit__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5565_dvd__mult__unit__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5566_dvd__mult__unit__iff,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5567_mult__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5568_mult__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5569_mult__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5570_dvd__mult__unit__iff_H,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5571_dvd__mult__unit__iff_H,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.69/4.94          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5572_dvd__mult__unit__iff_H,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 8.69/4.94          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5573_mult__unit__dvd__iff_H,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5574_mult__unit__dvd__iff_H,axiom,
% 8.69/4.94      ! [A: nat,B: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5575_mult__unit__dvd__iff_H,axiom,
% 8.69/4.94      ! [A: int,B: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5576_unit__mult__left__cancel,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 8.69/4.94            = ( times_3573771949741848930nteger @ A @ C ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5577_unit__mult__left__cancel,axiom,
% 8.69/4.94      ! [A: nat,B: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94       => ( ( ( times_times_nat @ A @ B )
% 8.69/4.94            = ( times_times_nat @ A @ C ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5578_unit__mult__left__cancel,axiom,
% 8.69/4.94      ! [A: int,B: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94       => ( ( ( times_times_int @ A @ B )
% 8.69/4.94            = ( times_times_int @ A @ C ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5579_unit__mult__right__cancel,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 8.69/4.94            = ( times_3573771949741848930nteger @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5580_unit__mult__right__cancel,axiom,
% 8.69/4.94      ! [A: nat,B: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94       => ( ( ( times_times_nat @ B @ A )
% 8.69/4.94            = ( times_times_nat @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5581_unit__mult__right__cancel,axiom,
% 8.69/4.94      ! [A: int,B: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94       => ( ( ( times_times_int @ B @ A )
% 8.69/4.94            = ( times_times_int @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5582_dvd__div__mult,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 8.69/4.94          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5583_dvd__div__mult,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 8.69/4.94          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5584_dvd__div__mult,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 8.69/4.94          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5585_div__mult__swap,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.94          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5586_div__mult__swap,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 8.69/4.94          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5587_div__mult__swap,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 8.69/4.94          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5588_div__div__eq__right,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.94            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5589_div__div__eq__right,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 8.69/4.94            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5590_div__div__eq__right,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 8.69/4.94            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5591_dvd__div__mult2__eq,axiom,
% 8.69/4.94      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 8.69/4.94       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.69/4.94          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5592_dvd__div__mult2__eq,axiom,
% 8.69/4.94      ! [B: nat,C: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 8.69/4.94       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.69/4.94          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5593_dvd__div__mult2__eq,axiom,
% 8.69/4.94      ! [B: int,C: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 8.69/4.94       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.69/4.94          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5594_dvd__mult__imp__div,axiom,
% 8.69/4.94      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 8.69/4.94       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5595_dvd__mult__imp__div,axiom,
% 8.69/4.94      ! [A: nat,C: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 8.69/4.94       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5596_dvd__mult__imp__div,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 8.69/4.94       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5597_div__mult__div__if__dvd,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ D @ C )
% 8.69/4.94         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 8.69/4.94            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5598_div__mult__div__if__dvd,axiom,
% 8.69/4.94      ! [B: nat,A: nat,D: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94       => ( ( dvd_dvd_nat @ D @ C )
% 8.69/4.94         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 8.69/4.94            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5599_div__mult__div__if__dvd,axiom,
% 8.69/4.94      ! [B: int,A: int,D: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94       => ( ( dvd_dvd_int @ D @ C )
% 8.69/4.94         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 8.69/4.94            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5600_not__numeral__le__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5601_not__numeral__le__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5602_not__numeral__le__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5603_not__numeral__le__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5604_neg__numeral__le__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5605_neg__numeral__le__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5606_neg__numeral__le__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5607_neg__numeral__le__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5608_zero__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( zero_zero_real
% 8.69/4.94       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5609_zero__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( zero_zero_int
% 8.69/4.94       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5610_zero__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( zero_zero_complex
% 8.69/4.94       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5611_zero__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( zero_z3403309356797280102nteger
% 8.69/4.94       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5612_zero__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( zero_zero_rat
% 8.69/4.94       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5613_div__plus__div__distrib__dvd__right,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5614_div__plus__div__distrib__dvd__right,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.69/4.94          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5615_div__plus__div__distrib__dvd__right,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.69/4.94          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5616_div__plus__div__distrib__dvd__left,axiom,
% 8.69/4.94      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ C @ A )
% 8.69/4.94       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5617_div__plus__div__distrib__dvd__left,axiom,
% 8.69/4.94      ! [C: nat,A: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ C @ A )
% 8.69/4.94       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 8.69/4.94          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5618_div__plus__div__distrib__dvd__left,axiom,
% 8.69/4.94      ! [C: int,A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ C @ A )
% 8.69/4.94       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 8.69/4.94          = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5619_unit__div__cancel,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 8.69/4.94            = ( divide6298287555418463151nteger @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5620_unit__div__cancel,axiom,
% 8.69/4.94      ! [A: nat,B: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94       => ( ( ( divide_divide_nat @ B @ A )
% 8.69/4.94            = ( divide_divide_nat @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5621_unit__div__cancel,axiom,
% 8.69/4.94      ! [A: int,B: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94       => ( ( ( divide_divide_int @ B @ A )
% 8.69/4.94            = ( divide_divide_int @ C @ A ) )
% 8.69/4.94          = ( B = C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5622_div__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5623_div__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5624_div__unit__dvd__iff,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 8.69/4.94          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5625_dvd__div__unit__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5626_dvd__div__unit__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5627_dvd__div__unit__iff,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 8.69/4.94          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5628_neg__numeral__less__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5629_neg__numeral__less__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5630_neg__numeral__less__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5631_neg__numeral__less__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5632_not__numeral__less__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5633_not__numeral__less__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5634_not__numeral__less__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5635_not__numeral__less__neg__numeral,axiom,
% 8.69/4.94      ! [M: num,N: num] :
% 8.69/4.94        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5636_le__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5637_le__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5638_le__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5639_le__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5640_le__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5641_le__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5642_le__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5643_le__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5644_neg__eq__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ( uminus_uminus_real @ A )
% 8.69/4.94          = B )
% 8.69/4.94        = ( ( plus_plus_real @ A @ B )
% 8.69/4.94          = zero_zero_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5645_neg__eq__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( uminus_uminus_int @ A )
% 8.69/4.94          = B )
% 8.69/4.94        = ( ( plus_plus_int @ A @ B )
% 8.69/4.94          = zero_zero_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5646_neg__eq__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.94          = B )
% 8.69/4.94        = ( ( plus_plus_complex @ A @ B )
% 8.69/4.94          = zero_zero_complex ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5647_neg__eq__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.94          = B )
% 8.69/4.94        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5648_neg__eq__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ( uminus_uminus_rat @ A )
% 8.69/4.94          = B )
% 8.69/4.94        = ( ( plus_plus_rat @ A @ B )
% 8.69/4.94          = zero_zero_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5649_eq__neg__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( A
% 8.69/4.94          = ( uminus_uminus_real @ B ) )
% 8.69/4.94        = ( ( plus_plus_real @ A @ B )
% 8.69/4.94          = zero_zero_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5650_eq__neg__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( A
% 8.69/4.94          = ( uminus_uminus_int @ B ) )
% 8.69/4.94        = ( ( plus_plus_int @ A @ B )
% 8.69/4.94          = zero_zero_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5651_eq__neg__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( A
% 8.69/4.94          = ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.94        = ( ( plus_plus_complex @ A @ B )
% 8.69/4.94          = zero_zero_complex ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5652_eq__neg__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( A
% 8.69/4.94          = ( uminus1351360451143612070nteger @ B ) )
% 8.69/4.94        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5653_eq__neg__iff__add__eq__0,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( A
% 8.69/4.94          = ( uminus_uminus_rat @ B ) )
% 8.69/4.94        = ( ( plus_plus_rat @ A @ B )
% 8.69/4.94          = zero_zero_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5654_add_Oinverse__unique,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ( plus_plus_real @ A @ B )
% 8.69/4.94          = zero_zero_real )
% 8.69/4.94       => ( ( uminus_uminus_real @ A )
% 8.69/4.94          = B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5655_add_Oinverse__unique,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( plus_plus_int @ A @ B )
% 8.69/4.94          = zero_zero_int )
% 8.69/4.94       => ( ( uminus_uminus_int @ A )
% 8.69/4.94          = B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5656_add_Oinverse__unique,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ( plus_plus_complex @ A @ B )
% 8.69/4.94          = zero_zero_complex )
% 8.69/4.94       => ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.94          = B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5657_add_Oinverse__unique,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger )
% 8.69/4.94       => ( ( uminus1351360451143612070nteger @ A )
% 8.69/4.94          = B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5658_add_Oinverse__unique,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ( plus_plus_rat @ A @ B )
% 8.69/4.94          = zero_zero_rat )
% 8.69/4.94       => ( ( uminus_uminus_rat @ A )
% 8.69/4.94          = B ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5659_ab__group__add__class_Oab__left__minus,axiom,
% 8.69/4.94      ! [A: real] :
% 8.69/4.94        ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 8.69/4.94        = zero_zero_real ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5660_ab__group__add__class_Oab__left__minus,axiom,
% 8.69/4.94      ! [A: int] :
% 8.69/4.94        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.69/4.94        = zero_zero_int ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5661_ab__group__add__class_Oab__left__minus,axiom,
% 8.69/4.94      ! [A: complex] :
% 8.69/4.94        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 8.69/4.94        = zero_zero_complex ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5662_ab__group__add__class_Oab__left__minus,axiom,
% 8.69/4.94      ! [A: code_integer] :
% 8.69/4.94        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.69/4.94        = zero_z3403309356797280102nteger ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5663_ab__group__add__class_Oab__left__minus,axiom,
% 8.69/4.94      ! [A: rat] :
% 8.69/4.94        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.69/4.94        = zero_zero_rat ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5664_add__eq__0__iff,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ( plus_plus_real @ A @ B )
% 8.69/4.94          = zero_zero_real )
% 8.69/4.94        = ( B
% 8.69/4.94          = ( uminus_uminus_real @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5665_add__eq__0__iff,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( plus_plus_int @ A @ B )
% 8.69/4.94          = zero_zero_int )
% 8.69/4.94        = ( B
% 8.69/4.94          = ( uminus_uminus_int @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5666_add__eq__0__iff,axiom,
% 8.69/4.94      ! [A: complex,B: complex] :
% 8.69/4.94        ( ( ( plus_plus_complex @ A @ B )
% 8.69/4.94          = zero_zero_complex )
% 8.69/4.94        = ( B
% 8.69/4.94          = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5667_add__eq__0__iff,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger )
% 8.69/4.94        = ( B
% 8.69/4.94          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5668_add__eq__0__iff,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ( plus_plus_rat @ A @ B )
% 8.69/4.94          = zero_zero_rat )
% 8.69/4.94        = ( B
% 8.69/4.94          = ( uminus_uminus_rat @ A ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5669_zero__neq__neg__one,axiom,
% 8.69/4.94      ( zero_zero_real
% 8.69/4.94     != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5670_zero__neq__neg__one,axiom,
% 8.69/4.94      ( zero_zero_int
% 8.69/4.94     != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5671_zero__neq__neg__one,axiom,
% 8.69/4.94      ( zero_zero_complex
% 8.69/4.94     != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5672_zero__neq__neg__one,axiom,
% 8.69/4.94      ( zero_z3403309356797280102nteger
% 8.69/4.94     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5673_zero__neq__neg__one,axiom,
% 8.69/4.94      ( zero_zero_rat
% 8.69/4.94     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5674_less__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5675_less__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5676_less__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5677_less__minus__one__simps_I2_J,axiom,
% 8.69/4.94      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5678_less__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5679_less__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5680_less__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5681_less__minus__one__simps_I4_J,axiom,
% 8.69/4.94      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5682_numeral__times__minus__swap,axiom,
% 8.69/4.94      ! [W: num,X: real] :
% 8.69/4.94        ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 8.69/4.94        = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5683_numeral__times__minus__swap,axiom,
% 8.69/4.94      ! [W: num,X: int] :
% 8.69/4.94        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 8.69/4.94        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5684_numeral__times__minus__swap,axiom,
% 8.69/4.94      ! [W: num,X: complex] :
% 8.69/4.94        ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 8.69/4.94        = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5685_numeral__times__minus__swap,axiom,
% 8.69/4.94      ! [W: num,X: code_integer] :
% 8.69/4.94        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 8.69/4.94        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5686_numeral__times__minus__swap,axiom,
% 8.69/4.94      ! [W: num,X: rat] :
% 8.69/4.94        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 8.69/4.94        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5687_div__power,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94       => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 8.69/4.94          = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5688_div__power,axiom,
% 8.69/4.94      ! [B: nat,A: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94       => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 8.69/4.94          = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5689_div__power,axiom,
% 8.69/4.94      ! [B: int,A: int,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94       => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 8.69/4.94          = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5690_nonzero__minus__divide__divide,axiom,
% 8.69/4.94      ! [B: real,A: real] :
% 8.69/4.94        ( ( B != zero_zero_real )
% 8.69/4.94       => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.69/4.94          = ( divide_divide_real @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5691_nonzero__minus__divide__divide,axiom,
% 8.69/4.94      ! [B: complex,A: complex] :
% 8.69/4.94        ( ( B != zero_zero_complex )
% 8.69/4.94       => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.69/4.94          = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5692_nonzero__minus__divide__divide,axiom,
% 8.69/4.94      ! [B: rat,A: rat] :
% 8.69/4.94        ( ( B != zero_zero_rat )
% 8.69/4.94       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.69/4.94          = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5693_nonzero__minus__divide__right,axiom,
% 8.69/4.94      ! [B: real,A: real] :
% 8.69/4.94        ( ( B != zero_zero_real )
% 8.69/4.94       => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.94          = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5694_nonzero__minus__divide__right,axiom,
% 8.69/4.94      ! [B: complex,A: complex] :
% 8.69/4.94        ( ( B != zero_zero_complex )
% 8.69/4.94       => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.94          = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5695_nonzero__minus__divide__right,axiom,
% 8.69/4.94      ! [B: rat,A: rat] :
% 8.69/4.94        ( ( B != zero_zero_rat )
% 8.69/4.94       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.94          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5696_one__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( one_one_real
% 8.69/4.94       != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5697_one__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( one_one_int
% 8.69/4.94       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5698_one__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( one_one_complex
% 8.69/4.94       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5699_one__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( one_one_Code_integer
% 8.69/4.94       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5700_one__neq__neg__numeral,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( one_one_rat
% 8.69/4.94       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5701_numeral__neq__neg__one,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( ( numeral_numeral_real @ N )
% 8.69/4.94       != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5702_numeral__neq__neg__one,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( ( numeral_numeral_int @ N )
% 8.69/4.94       != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5703_numeral__neq__neg__one,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( ( numera6690914467698888265omplex @ N )
% 8.69/4.94       != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5704_numeral__neq__neg__one,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( ( numera6620942414471956472nteger @ N )
% 8.69/4.94       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5705_numeral__neq__neg__one,axiom,
% 8.69/4.94      ! [N: num] :
% 8.69/4.94        ( ( numeral_numeral_rat @ N )
% 8.69/4.94       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5706_square__eq__1__iff,axiom,
% 8.69/4.94      ! [X: real] :
% 8.69/4.94        ( ( ( times_times_real @ X @ X )
% 8.69/4.94          = one_one_real )
% 8.69/4.94        = ( ( X = one_one_real )
% 8.69/4.94          | ( X
% 8.69/4.94            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5707_square__eq__1__iff,axiom,
% 8.69/4.94      ! [X: int] :
% 8.69/4.94        ( ( ( times_times_int @ X @ X )
% 8.69/4.94          = one_one_int )
% 8.69/4.94        = ( ( X = one_one_int )
% 8.69/4.94          | ( X
% 8.69/4.94            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5708_square__eq__1__iff,axiom,
% 8.69/4.94      ! [X: complex] :
% 8.69/4.94        ( ( ( times_times_complex @ X @ X )
% 8.69/4.94          = one_one_complex )
% 8.69/4.94        = ( ( X = one_one_complex )
% 8.69/4.94          | ( X
% 8.69/4.94            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5709_square__eq__1__iff,axiom,
% 8.69/4.94      ! [X: code_integer] :
% 8.69/4.94        ( ( ( times_3573771949741848930nteger @ X @ X )
% 8.69/4.94          = one_one_Code_integer )
% 8.69/4.94        = ( ( X = one_one_Code_integer )
% 8.69/4.94          | ( X
% 8.69/4.94            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5710_square__eq__1__iff,axiom,
% 8.69/4.94      ! [X: rat] :
% 8.69/4.94        ( ( ( times_times_rat @ X @ X )
% 8.69/4.94          = one_one_rat )
% 8.69/4.94        = ( ( X = one_one_rat )
% 8.69/4.94          | ( X
% 8.69/4.94            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5711_mod__eq__0__iff__dvd,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( ( modulo_modulo_nat @ A @ B )
% 8.69/4.94          = zero_zero_nat )
% 8.69/4.94        = ( dvd_dvd_nat @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5712_mod__eq__0__iff__dvd,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.94          = zero_zero_int )
% 8.69/4.94        = ( dvd_dvd_int @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5713_mod__eq__0__iff__dvd,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( modulo364778990260209775nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger )
% 8.69/4.94        = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5714_dvd__eq__mod__eq__0,axiom,
% 8.69/4.94      ( dvd_dvd_nat
% 8.69/4.94      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.94            ( ( modulo_modulo_nat @ B2 @ A3 )
% 8.69/4.94            = zero_zero_nat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5715_dvd__eq__mod__eq__0,axiom,
% 8.69/4.94      ( dvd_dvd_int
% 8.69/4.94      = ( ^ [A3: int,B2: int] :
% 8.69/4.94            ( ( modulo_modulo_int @ B2 @ A3 )
% 8.69/4.94            = zero_zero_int ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5716_dvd__eq__mod__eq__0,axiom,
% 8.69/4.94      ( dvd_dvd_Code_integer
% 8.69/4.94      = ( ^ [A3: code_integer,B2: code_integer] :
% 8.69/4.94            ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 8.69/4.94            = zero_z3403309356797280102nteger ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5717_mod__0__imp__dvd,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( ( modulo_modulo_nat @ A @ B )
% 8.69/4.94          = zero_zero_nat )
% 8.69/4.94       => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5718_mod__0__imp__dvd,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.94          = zero_zero_int )
% 8.69/4.94       => ( dvd_dvd_int @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5719_mod__0__imp__dvd,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( modulo364778990260209775nteger @ A @ B )
% 8.69/4.94          = zero_z3403309356797280102nteger )
% 8.69/4.94       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5720_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_real
% 8.69/4.94      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5721_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_int
% 8.69/4.94      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5722_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_complex
% 8.69/4.94      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5723_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_8373710615458151222nteger
% 8.69/4.94      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5724_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_rat
% 8.69/4.94      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5725_diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_real
% 8.69/4.94      = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5726_diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_int
% 8.69/4.94      = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5727_diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_complex
% 8.69/4.94      = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5728_diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_8373710615458151222nteger
% 8.69/4.94      = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5729_diff__conv__add__uminus,axiom,
% 8.69/4.94      ( minus_minus_rat
% 8.69/4.94      = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5730_group__cancel_Osub2,axiom,
% 8.69/4.94      ! [B3: real,K: real,B: real,A: real] :
% 8.69/4.94        ( ( B3
% 8.69/4.94          = ( plus_plus_real @ K @ B ) )
% 8.69/4.94       => ( ( minus_minus_real @ A @ B3 )
% 8.69/4.94          = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5731_group__cancel_Osub2,axiom,
% 8.69/4.94      ! [B3: int,K: int,B: int,A: int] :
% 8.69/4.94        ( ( B3
% 8.69/4.94          = ( plus_plus_int @ K @ B ) )
% 8.69/4.94       => ( ( minus_minus_int @ A @ B3 )
% 8.69/4.94          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5732_group__cancel_Osub2,axiom,
% 8.69/4.94      ! [B3: complex,K: complex,B: complex,A: complex] :
% 8.69/4.94        ( ( B3
% 8.69/4.94          = ( plus_plus_complex @ K @ B ) )
% 8.69/4.94       => ( ( minus_minus_complex @ A @ B3 )
% 8.69/4.94          = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5733_group__cancel_Osub2,axiom,
% 8.69/4.94      ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( B3
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 8.69/4.94       => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 8.69/4.94          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5734_group__cancel_Osub2,axiom,
% 8.69/4.94      ! [B3: rat,K: rat,B: rat,A: rat] :
% 8.69/4.94        ( ( B3
% 8.69/4.94          = ( plus_plus_rat @ K @ B ) )
% 8.69/4.94       => ( ( minus_minus_rat @ A @ B3 )
% 8.69/4.94          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5735_le__imp__power__dvd,axiom,
% 8.69/4.94      ! [M: nat,N: nat,A: code_integer] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5736_le__imp__power__dvd,axiom,
% 8.69/4.94      ! [M: nat,N: nat,A: nat] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5737_le__imp__power__dvd,axiom,
% 8.69/4.94      ! [M: nat,N: nat,A: real] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5738_le__imp__power__dvd,axiom,
% 8.69/4.94      ! [M: nat,N: nat,A: int] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5739_le__imp__power__dvd,axiom,
% 8.69/4.94      ! [M: nat,N: nat,A: complex] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5740_power__le__dvd,axiom,
% 8.69/4.94      ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 8.69/4.94       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5741_power__le__dvd,axiom,
% 8.69/4.94      ! [A: nat,N: nat,B: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 8.69/4.94       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94         => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5742_power__le__dvd,axiom,
% 8.69/4.94      ! [A: real,N: nat,B: real,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 8.69/4.94       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94         => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5743_power__le__dvd,axiom,
% 8.69/4.94      ! [A: int,N: nat,B: int,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 8.69/4.94       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94         => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5744_power__le__dvd,axiom,
% 8.69/4.94      ! [A: complex,N: nat,B: complex,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 8.69/4.94       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94         => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5745_dvd__power__le,axiom,
% 8.69/4.94      ! [X: code_integer,Y: code_integer,N: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ X @ Y )
% 8.69/4.94       => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94         => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5746_dvd__power__le,axiom,
% 8.69/4.94      ! [X: nat,Y: nat,N: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ X @ Y )
% 8.69/4.94       => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5747_dvd__power__le,axiom,
% 8.69/4.94      ! [X: real,Y: real,N: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_real @ X @ Y )
% 8.69/4.94       => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94         => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5748_dvd__power__le,axiom,
% 8.69/4.94      ! [X: int,Y: int,N: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_int @ X @ Y )
% 8.69/4.94       => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94         => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5749_dvd__power__le,axiom,
% 8.69/4.94      ! [X: complex,Y: complex,N: nat,M: nat] :
% 8.69/4.94        ( ( dvd_dvd_complex @ X @ Y )
% 8.69/4.94       => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94         => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5750_mod__eq__dvd__iff,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int] :
% 8.69/4.94        ( ( ( modulo_modulo_int @ A @ C )
% 8.69/4.94          = ( modulo_modulo_int @ B @ C ) )
% 8.69/4.94        = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5751_mod__eq__dvd__iff,axiom,
% 8.69/4.94      ! [A: code_integer,C: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( modulo364778990260209775nteger @ A @ C )
% 8.69/4.94          = ( modulo364778990260209775nteger @ B @ C ) )
% 8.69/4.94        = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5752_dvd__minus__mod,axiom,
% 8.69/4.94      ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5753_dvd__minus__mod,axiom,
% 8.69/4.94      ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5754_dvd__minus__mod,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5755_nat__dvd__not__less,axiom,
% 8.69/4.94      ! [M: nat,N: nat] :
% 8.69/4.94        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.94       => ( ( ord_less_nat @ M @ N )
% 8.69/4.94         => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5756_dvd__pos__nat,axiom,
% 8.69/4.94      ! [N: nat,M: nat] :
% 8.69/4.94        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.94       => ( ( dvd_dvd_nat @ M @ N )
% 8.69/4.94         => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5757_sin__bound__lemma,axiom,
% 8.69/4.94      ! [X: real,Y: real,U: real,V: real] :
% 8.69/4.94        ( ( X = Y )
% 8.69/4.94       => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 8.69/4.94         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5758_dvd__minus__self,axiom,
% 8.69/4.94      ! [M: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 8.69/4.94        = ( ( ord_less_nat @ N @ M )
% 8.69/4.94          | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5759_zdvd__antisym__nonneg,axiom,
% 8.69/4.94      ! [M: int,N: int] :
% 8.69/4.94        ( ( ord_less_eq_int @ zero_zero_int @ M )
% 8.69/4.94       => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.69/4.94         => ( ( dvd_dvd_int @ M @ N )
% 8.69/4.94           => ( ( dvd_dvd_int @ N @ M )
% 8.69/4.94             => ( M = N ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5760_less__eq__dvd__minus,axiom,
% 8.69/4.94      ! [M: nat,N: nat] :
% 8.69/4.94        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.94       => ( ( dvd_dvd_nat @ M @ N )
% 8.69/4.94          = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5761_dvd__diffD1,axiom,
% 8.69/4.94      ! [K: nat,M: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.94       => ( ( dvd_dvd_nat @ K @ M )
% 8.69/4.94         => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94           => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5762_dvd__diffD,axiom,
% 8.69/4.94      ! [K: nat,M: nat,N: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.94       => ( ( dvd_dvd_nat @ K @ N )
% 8.69/4.94         => ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.94           => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5763_zdvd__not__zless,axiom,
% 8.69/4.94      ! [M: int,N: int] :
% 8.69/4.94        ( ( ord_less_int @ zero_zero_int @ M )
% 8.69/4.94       => ( ( ord_less_int @ M @ N )
% 8.69/4.94         => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5764_bezout__lemma__nat,axiom,
% 8.69/4.94      ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ D @ A )
% 8.69/4.94       => ( ( dvd_dvd_nat @ D @ B )
% 8.69/4.94         => ( ( ( ( times_times_nat @ A @ X )
% 8.69/4.94                = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 8.69/4.94              | ( ( times_times_nat @ B @ X )
% 8.69/4.94                = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 8.69/4.94           => ? [X6: nat,Y5: nat] :
% 8.69/4.94                ( ( dvd_dvd_nat @ D @ A )
% 8.69/4.94                & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 8.69/4.94                & ( ( ( times_times_nat @ A @ X6 )
% 8.69/4.94                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D ) )
% 8.69/4.94                  | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X6 )
% 8.69/4.94                    = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5765_bezout__add__nat,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94      ? [D3: nat,X6: nat,Y5: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ D3 @ A )
% 8.69/4.94        & ( dvd_dvd_nat @ D3 @ B )
% 8.69/4.94        & ( ( ( times_times_nat @ A @ X6 )
% 8.69/4.94            = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) )
% 8.69/4.94          | ( ( times_times_nat @ B @ X6 )
% 8.69/4.94            = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5766_zdvd__mult__cancel,axiom,
% 8.69/4.94      ! [K: int,M: int,N: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 8.69/4.94       => ( ( K != zero_zero_int )
% 8.69/4.94         => ( dvd_dvd_int @ M @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5767_zdvd__mono,axiom,
% 8.69/4.94      ! [K: int,M: int,T: int] :
% 8.69/4.94        ( ( K != zero_zero_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ M @ T )
% 8.69/4.94          = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5768_bezout1__nat,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94      ? [D3: nat,X6: nat,Y5: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ D3 @ A )
% 8.69/4.94        & ( dvd_dvd_nat @ D3 @ B )
% 8.69/4.94        & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 8.69/4.94            = D3 )
% 8.69/4.94          | ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 8.69/4.94            = D3 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5769_real__minus__mult__self__le,axiom,
% 8.69/4.94      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5770_zdvd__period,axiom,
% 8.69/4.94      ! [A: int,D: int,X: int,T: int,C: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ D )
% 8.69/4.94       => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 8.69/4.94          = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5771_zdvd__reduce,axiom,
% 8.69/4.94      ! [K: int,N: int,M: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 8.69/4.94        = ( dvd_dvd_int @ K @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5772_power__mono__even,axiom,
% 8.69/4.94      ! [N: nat,A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 8.69/4.94         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5773_power__mono__even,axiom,
% 8.69/4.94      ! [N: nat,A: real,B: real] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 8.69/4.94         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5774_power__mono__even,axiom,
% 8.69/4.94      ! [N: nat,A: rat,B: rat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 8.69/4.94         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5775_power__mono__even,axiom,
% 8.69/4.94      ! [N: nat,A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94       => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 8.69/4.94         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5776_minus__real__def,axiom,
% 8.69/4.94      ( minus_minus_real
% 8.69/4.94      = ( ^ [X3: real,Y3: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5777_minus__one__power__iff,axiom,
% 8.69/4.94      ! [N: nat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 8.69/4.94            = one_one_real ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 8.69/4.94            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5778_minus__one__power__iff,axiom,
% 8.69/4.94      ! [N: nat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 8.69/4.94            = one_one_int ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 8.69/4.94            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5779_minus__one__power__iff,axiom,
% 8.69/4.94      ! [N: nat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 8.69/4.94            = one_one_complex ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 8.69/4.94            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5780_minus__one__power__iff,axiom,
% 8.69/4.94      ! [N: nat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 8.69/4.94            = one_one_Code_integer ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 8.69/4.94            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5781_minus__one__power__iff,axiom,
% 8.69/4.94      ! [N: nat] :
% 8.69/4.94        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 8.69/4.94            = one_one_rat ) )
% 8.69/4.94        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.94         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 8.69/4.94            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5782_tanh__real__lt__1,axiom,
% 8.69/4.94      ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5783_dense__eq0__I,axiom,
% 8.69/4.94      ! [X: real] :
% 8.69/4.94        ( ! [E2: real] :
% 8.69/4.94            ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.69/4.94           => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 8.69/4.94       => ( X = zero_zero_real ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5784_dense__eq0__I,axiom,
% 8.69/4.94      ! [X: rat] :
% 8.69/4.94        ( ! [E2: rat] :
% 8.69/4.94            ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.69/4.94           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 8.69/4.94       => ( X = zero_zero_rat ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5785_abs__eq__mult,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.69/4.94            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 8.69/4.94          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.69/4.94            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 8.69/4.94       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.69/4.94          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5786_abs__eq__mult,axiom,
% 8.69/4.94      ! [A: real,B: real] :
% 8.69/4.94        ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.94            | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.69/4.94          & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.69/4.94            | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 8.69/4.94       => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 8.69/4.94          = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5787_abs__eq__mult,axiom,
% 8.69/4.94      ! [A: rat,B: rat] :
% 8.69/4.94        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.69/4.94            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.69/4.94          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.69/4.94            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.69/4.94       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 8.69/4.94          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5788_abs__eq__mult,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.69/4.94            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.69/4.94          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.69/4.94            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.69/4.94       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 8.69/4.94          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5789_abs__mult__pos,axiom,
% 8.69/4.94      ! [X: code_integer,Y: code_integer] :
% 8.69/4.94        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 8.69/4.94       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 8.69/4.94          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5790_abs__mult__pos,axiom,
% 8.69/4.94      ! [X: real,Y: real] :
% 8.69/4.94        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.94       => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 8.69/4.94          = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5791_abs__mult__pos,axiom,
% 8.69/4.94      ! [X: rat,Y: rat] :
% 8.69/4.94        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.69/4.94       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 8.69/4.94          = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5792_abs__mult__pos,axiom,
% 8.69/4.94      ! [X: int,Y: int] :
% 8.69/4.94        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/4.94       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 8.69/4.94          = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5793_abs__div__pos,axiom,
% 8.69/4.94      ! [Y: real,X: real] :
% 8.69/4.94        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.94       => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 8.69/4.94          = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5794_abs__div__pos,axiom,
% 8.69/4.94      ! [Y: rat,X: rat] :
% 8.69/4.94        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.69/4.94       => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 8.69/4.94          = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5795_zero__le__power__abs,axiom,
% 8.69/4.94      ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5796_zero__le__power__abs,axiom,
% 8.69/4.94      ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5797_zero__le__power__abs,axiom,
% 8.69/4.94      ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5798_zero__le__power__abs,axiom,
% 8.69/4.94      ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5799_abs__triangle__ineq4,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5800_abs__triangle__ineq4,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5801_abs__triangle__ineq4,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5802_abs__triangle__ineq4,axiom,
% 8.69/4.94      ! [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 ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5803_abs__diff__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5804_abs__diff__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5805_abs__diff__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5806_abs__diff__triangle__ineq,axiom,
% 8.69/4.94      ! [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 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5807_abs__diff__le__iff,axiom,
% 8.69/4.94      ! [X: code_integer,A: code_integer,R: code_integer] :
% 8.69/4.94        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 8.69/4.94          & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5808_abs__diff__le__iff,axiom,
% 8.69/4.94      ! [X: real,A: real,R: real] :
% 8.69/4.94        ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5809_abs__diff__le__iff,axiom,
% 8.69/4.94      ! [X: rat,A: rat,R: rat] :
% 8.69/4.94        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5810_abs__diff__le__iff,axiom,
% 8.69/4.94      ! [X: int,A: int,R: int] :
% 8.69/4.94        ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5811_abs__diff__less__iff,axiom,
% 8.69/4.94      ! [X: code_integer,A: code_integer,R: code_integer] :
% 8.69/4.94        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 8.69/4.94          & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5812_abs__diff__less__iff,axiom,
% 8.69/4.94      ! [X: real,A: real,R: real] :
% 8.69/4.94        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5813_abs__diff__less__iff,axiom,
% 8.69/4.94      ! [X: rat,A: rat,R: rat] :
% 8.69/4.94        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5814_abs__diff__less__iff,axiom,
% 8.69/4.94      ! [X: int,A: int,R: int] :
% 8.69/4.94        ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 8.69/4.94        = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 8.69/4.94          & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5815_finite__divisors__int,axiom,
% 8.69/4.94      ! [I: int] :
% 8.69/4.94        ( ( I != zero_zero_int )
% 8.69/4.94       => ( finite_finite_int
% 8.69/4.94          @ ( collect_int
% 8.69/4.94            @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5816_div2__even__ext__nat,axiom,
% 8.69/4.94      ! [X: nat,Y: nat] :
% 8.69/4.94        ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.94          = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.94       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 8.69/4.94            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 8.69/4.94         => ( X = Y ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5817_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: code_integer > $o,L2: code_integer] :
% 8.69/4.94        ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: code_integer] :
% 8.69/4.94              ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5818_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: complex > $o,L2: complex] :
% 8.69/4.94        ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: complex] :
% 8.69/4.94              ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5819_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: real > $o,L2: real] :
% 8.69/4.94        ( ( ? [X3: real] : ( P @ ( times_times_real @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: real] :
% 8.69/4.94              ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5820_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: rat > $o,L2: rat] :
% 8.69/4.94        ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: rat] :
% 8.69/4.94              ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5821_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: nat > $o,L2: nat] :
% 8.69/4.94        ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: nat] :
% 8.69/4.94              ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5822_unity__coeff__ex,axiom,
% 8.69/4.94      ! [P: int > $o,L2: int] :
% 8.69/4.94        ( ( ? [X3: int] : ( P @ ( times_times_int @ L2 @ X3 ) ) )
% 8.69/4.94        = ( ? [X3: int] :
% 8.69/4.94              ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 8.69/4.94              & ( P @ X3 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5823_unit__dvdE,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.94       => ~ ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.94           => ! [C2: code_integer] :
% 8.69/4.94                ( B
% 8.69/4.94               != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5824_unit__dvdE,axiom,
% 8.69/4.94      ! [A: nat,B: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.94       => ~ ( ( A != zero_zero_nat )
% 8.69/4.94           => ! [C2: nat] :
% 8.69/4.94                ( B
% 8.69/4.94               != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5825_unit__dvdE,axiom,
% 8.69/4.94      ! [A: int,B: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.94       => ~ ( ( A != zero_zero_int )
% 8.69/4.94           => ! [C2: int] :
% 8.69/4.94                ( B
% 8.69/4.94               != ( times_times_int @ A @ C2 ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5826_dvd__div__eq__mult,axiom,
% 8.69/4.94      ! [A: code_integer,B: code_integer,C: code_integer] :
% 8.69/4.94        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.94         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 8.69/4.94              = C )
% 8.69/4.94            = ( B
% 8.69/4.94              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5827_dvd__div__eq__mult,axiom,
% 8.69/4.94      ! [A: nat,B: nat,C: nat] :
% 8.69/4.94        ( ( A != zero_zero_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.94         => ( ( ( divide_divide_nat @ B @ A )
% 8.69/4.94              = C )
% 8.69/4.94            = ( B
% 8.69/4.94              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5828_dvd__div__eq__mult,axiom,
% 8.69/4.94      ! [A: int,B: int,C: int] :
% 8.69/4.94        ( ( A != zero_zero_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ A @ B )
% 8.69/4.94         => ( ( ( divide_divide_int @ B @ A )
% 8.69/4.94              = C )
% 8.69/4.94            = ( B
% 8.69/4.94              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5829_div__dvd__iff__mult,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.94        ( ( B != zero_z3403309356797280102nteger )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.94         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 8.69/4.94            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5830_div__dvd__iff__mult,axiom,
% 8.69/4.94      ! [B: nat,A: nat,C: nat] :
% 8.69/4.94        ( ( B != zero_zero_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.94         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 8.69/4.94            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5831_div__dvd__iff__mult,axiom,
% 8.69/4.94      ! [B: int,A: int,C: int] :
% 8.69/4.94        ( ( B != zero_zero_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ B @ A )
% 8.69/4.94         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 8.69/4.94            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5832_dvd__div__iff__mult,axiom,
% 8.69/4.94      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( C != zero_z3403309356797280102nteger )
% 8.69/4.94       => ( ( dvd_dvd_Code_integer @ C @ B )
% 8.69/4.94         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.94            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5833_dvd__div__iff__mult,axiom,
% 8.69/4.94      ! [C: nat,B: nat,A: nat] :
% 8.69/4.94        ( ( C != zero_zero_nat )
% 8.69/4.94       => ( ( dvd_dvd_nat @ C @ B )
% 8.69/4.94         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 8.69/4.94            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5834_dvd__div__iff__mult,axiom,
% 8.69/4.94      ! [C: int,B: int,A: int] :
% 8.69/4.94        ( ( C != zero_zero_int )
% 8.69/4.94       => ( ( dvd_dvd_int @ C @ B )
% 8.69/4.94         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 8.69/4.94            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5835_dvd__div__div__eq__mult,axiom,
% 8.69/4.94      ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 8.69/4.94        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.94       => ( ( C != zero_z3403309356797280102nteger )
% 8.69/4.94         => ( ( dvd_dvd_Code_integer @ A @ B )
% 8.69/4.94           => ( ( dvd_dvd_Code_integer @ C @ D )
% 8.69/4.94             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 8.69/4.94                  = ( divide6298287555418463151nteger @ D @ C ) )
% 8.69/4.94                = ( ( times_3573771949741848930nteger @ B @ C )
% 8.69/4.94                  = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5836_dvd__div__div__eq__mult,axiom,
% 8.69/4.94      ! [A: nat,C: nat,B: nat,D: nat] :
% 8.69/4.94        ( ( A != zero_zero_nat )
% 8.69/4.94       => ( ( C != zero_zero_nat )
% 8.69/4.94         => ( ( dvd_dvd_nat @ A @ B )
% 8.69/4.94           => ( ( dvd_dvd_nat @ C @ D )
% 8.69/4.94             => ( ( ( divide_divide_nat @ B @ A )
% 8.69/4.94                  = ( divide_divide_nat @ D @ C ) )
% 8.69/4.94                = ( ( times_times_nat @ B @ C )
% 8.69/4.94                  = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5837_dvd__div__div__eq__mult,axiom,
% 8.69/4.94      ! [A: int,C: int,B: int,D: int] :
% 8.69/4.94        ( ( A != zero_zero_int )
% 8.69/4.94       => ( ( C != zero_zero_int )
% 8.69/4.94         => ( ( dvd_dvd_int @ A @ B )
% 8.69/4.94           => ( ( dvd_dvd_int @ C @ D )
% 8.69/4.94             => ( ( ( divide_divide_int @ B @ A )
% 8.69/4.94                  = ( divide_divide_int @ D @ C ) )
% 8.69/4.94                = ( ( times_times_int @ B @ C )
% 8.69/4.94                  = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5838_unit__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: code_integer,A: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.94       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 8.69/4.94            = zero_z3403309356797280102nteger )
% 8.69/4.94          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5839_unit__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: nat,A: nat] :
% 8.69/4.94        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.94       => ( ( ( divide_divide_nat @ A @ B )
% 8.69/4.94            = zero_zero_nat )
% 8.69/4.94          = ( A = zero_zero_nat ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5840_unit__div__eq__0__iff,axiom,
% 8.69/4.94      ! [B: int,A: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.94       => ( ( ( divide_divide_int @ A @ B )
% 8.69/4.94            = zero_zero_int )
% 8.69/4.94          = ( A = zero_zero_int ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5841_even__numeral,axiom,
% 8.69/4.94      ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5842_even__numeral,axiom,
% 8.69/4.94      ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5843_even__numeral,axiom,
% 8.69/4.94      ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5844_inf__period_I3_J,axiom,
% 8.69/4.94      ! [D: code_integer,D4: code_integer,T: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 8.69/4.94       => ! [X4: code_integer,K4: code_integer] :
% 8.69/4.94            ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) )
% 8.69/4.94            = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5845_inf__period_I3_J,axiom,
% 8.69/4.94      ! [D: real,D4: real,T: real] :
% 8.69/4.94        ( ( dvd_dvd_real @ D @ D4 )
% 8.69/4.94       => ! [X4: real,K4: real] :
% 8.69/4.94            ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) )
% 8.69/4.94            = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5846_inf__period_I3_J,axiom,
% 8.69/4.94      ! [D: rat,D4: rat,T: rat] :
% 8.69/4.94        ( ( dvd_dvd_rat @ D @ D4 )
% 8.69/4.94       => ! [X4: rat,K4: rat] :
% 8.69/4.94            ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) )
% 8.69/4.94            = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5847_inf__period_I3_J,axiom,
% 8.69/4.94      ! [D: int,D4: int,T: int] :
% 8.69/4.94        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.94       => ! [X4: int,K4: int] :
% 8.69/4.94            ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.69/4.94            = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5848_inf__period_I4_J,axiom,
% 8.69/4.94      ! [D: code_integer,D4: code_integer,T: code_integer] :
% 8.69/4.94        ( ( dvd_dvd_Code_integer @ D @ D4 )
% 8.69/4.94       => ! [X4: code_integer,K4: code_integer] :
% 8.69/4.94            ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) ) )
% 8.69/4.94            = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5849_inf__period_I4_J,axiom,
% 8.69/4.94      ! [D: real,D4: real,T: real] :
% 8.69/4.94        ( ( dvd_dvd_real @ D @ D4 )
% 8.69/4.94       => ! [X4: real,K4: real] :
% 8.69/4.94            ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) ) )
% 8.69/4.94            = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 8.69/4.94  
% 8.69/4.94  thf(fact_5850_inf__period_I4_J,axiom,
% 8.69/4.94      ! [D: rat,D4: rat,T: rat] :
% 8.69/4.94        ( ( dvd_dvd_rat @ D @ D4 )
% 8.69/4.94       => ! [X4: rat,K4: rat] :
% 8.69/4.94            ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) ) )
% 8.69/4.95            = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5851_inf__period_I4_J,axiom,
% 8.69/4.95      ! [D: int,D4: int,T: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.95       => ! [X4: int,K4: int] :
% 8.69/4.95            ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) ) )
% 8.69/4.95            = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5852_not__zero__le__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5853_not__zero__le__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5854_not__zero__le__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5855_not__zero__le__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5856_neg__numeral__le__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5857_neg__numeral__le__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5858_neg__numeral__le__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5859_neg__numeral__le__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5860_unit__eq__div1,axiom,
% 8.69/4.95      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 8.69/4.95            = C )
% 8.69/4.95          = ( A
% 8.69/4.95            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5861_unit__eq__div1,axiom,
% 8.69/4.95      ! [B: nat,A: nat,C: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95       => ( ( ( divide_divide_nat @ A @ B )
% 8.69/4.95            = C )
% 8.69/4.95          = ( A
% 8.69/4.95            = ( times_times_nat @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5862_unit__eq__div1,axiom,
% 8.69/4.95      ! [B: int,A: int,C: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95       => ( ( ( divide_divide_int @ A @ B )
% 8.69/4.95            = C )
% 8.69/4.95          = ( A
% 8.69/4.95            = ( times_times_int @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5863_unit__eq__div2,axiom,
% 8.69/4.95      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95       => ( ( A
% 8.69/4.95            = ( divide6298287555418463151nteger @ C @ B ) )
% 8.69/4.95          = ( ( times_3573771949741848930nteger @ A @ B )
% 8.69/4.95            = C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5864_unit__eq__div2,axiom,
% 8.69/4.95      ! [B: nat,A: nat,C: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95       => ( ( A
% 8.69/4.95            = ( divide_divide_nat @ C @ B ) )
% 8.69/4.95          = ( ( times_times_nat @ A @ B )
% 8.69/4.95            = C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5865_unit__eq__div2,axiom,
% 8.69/4.95      ! [B: int,A: int,C: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95       => ( ( A
% 8.69/4.95            = ( divide_divide_int @ C @ B ) )
% 8.69/4.95          = ( ( times_times_int @ A @ B )
% 8.69/4.95            = C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5866_div__mult__unit2,axiom,
% 8.69/4.95      ! [C: code_integer,B: code_integer,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 8.69/4.95       => ( ( dvd_dvd_Code_integer @ B @ A )
% 8.69/4.95         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.69/4.95            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5867_div__mult__unit2,axiom,
% 8.69/4.95      ! [C: nat,B: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 8.69/4.95       => ( ( dvd_dvd_nat @ B @ A )
% 8.69/4.95         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.69/4.95            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5868_div__mult__unit2,axiom,
% 8.69/4.95      ! [C: int,B: int,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ C @ one_one_int )
% 8.69/4.95       => ( ( dvd_dvd_int @ B @ A )
% 8.69/4.95         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.69/4.95            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5869_unit__div__commute,axiom,
% 8.69/4.95      ! [B: code_integer,A: code_integer,C: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 8.69/4.95          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5870_unit__div__commute,axiom,
% 8.69/4.95      ! [B: nat,A: nat,C: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 8.69/4.95          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5871_unit__div__commute,axiom,
% 8.69/4.95      ! [B: int,A: int,C: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 8.69/4.95          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5872_unit__div__mult__swap,axiom,
% 8.69/4.95      ! [C: code_integer,A: code_integer,B: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 8.69/4.95       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 8.69/4.95          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5873_unit__div__mult__swap,axiom,
% 8.69/4.95      ! [C: nat,A: nat,B: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 8.69/4.95       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 8.69/4.95          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5874_unit__div__mult__swap,axiom,
% 8.69/4.95      ! [C: int,A: int,B: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ C @ one_one_int )
% 8.69/4.95       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 8.69/4.95          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5875_is__unit__div__mult2__eq,axiom,
% 8.69/4.95      ! [B: code_integer,C: code_integer,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 8.69/4.95         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 8.69/4.95            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5876_is__unit__div__mult2__eq,axiom,
% 8.69/4.95      ! [B: nat,C: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 8.69/4.95         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 8.69/4.95            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5877_is__unit__div__mult2__eq,axiom,
% 8.69/4.95      ! [B: int,C: int,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95       => ( ( dvd_dvd_int @ C @ one_one_int )
% 8.69/4.95         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 8.69/4.95            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5878_neg__numeral__less__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5879_neg__numeral__less__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5880_neg__numeral__less__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5881_neg__numeral__less__zero,axiom,
% 8.69/4.95      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5882_not__zero__less__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5883_not__zero__less__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5884_not__zero__less__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5885_not__zero__less__neg__numeral,axiom,
% 8.69/4.95      ! [N: num] :
% 8.69/4.95        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5886_le__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5887_le__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5888_le__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5889_le__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5890_le__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5891_le__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5892_le__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5893_le__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5894_less__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5895_less__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5896_less__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5897_less__minus__one__simps_I3_J,axiom,
% 8.69/4.95      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5898_less__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5899_less__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5900_less__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5901_less__minus__one__simps_I1_J,axiom,
% 8.69/4.95      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5902_not__one__le__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5903_not__one__le__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5904_not__one__le__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5905_not__one__le__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5906_not__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5907_not__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5908_not__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5909_not__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5910_neg__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5911_neg__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5912_neg__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5913_neg__numeral__le__neg__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5914_neg__one__le__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5915_neg__one__le__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5916_neg__one__le__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5917_neg__one__le__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5918_neg__numeral__le__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5919_neg__numeral__le__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5920_neg__numeral__le__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5921_neg__numeral__le__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5922_neg__numeral__less__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5923_neg__numeral__less__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5924_neg__numeral__less__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5925_neg__numeral__less__one,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5926_neg__one__less__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5927_neg__one__less__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5928_neg__one__less__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5929_neg__one__less__numeral,axiom,
% 8.69/4.95      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5930_not__numeral__less__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5931_not__numeral__less__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5932_not__numeral__less__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5933_not__numeral__less__neg__one,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5934_not__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5935_not__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5936_not__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5937_not__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5938_not__neg__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5939_not__neg__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5940_not__neg__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5941_not__neg__one__less__neg__numeral,axiom,
% 8.69/4.95      ! [M: num] :
% 8.69/4.95        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5942_is__unit__power__iff,axiom,
% 8.69/4.95      ! [A: code_integer,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 8.69/4.95        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5943_is__unit__power__iff,axiom,
% 8.69/4.95      ! [A: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 8.69/4.95        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5944_is__unit__power__iff,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 8.69/4.95        = ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5945_unit__imp__mod__eq__0,axiom,
% 8.69/4.95      ! [B: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95       => ( ( modulo_modulo_nat @ A @ B )
% 8.69/4.95          = zero_zero_nat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5946_unit__imp__mod__eq__0,axiom,
% 8.69/4.95      ! [B: int,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95       => ( ( modulo_modulo_int @ A @ B )
% 8.69/4.95          = zero_zero_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5947_unit__imp__mod__eq__0,axiom,
% 8.69/4.95      ! [B: code_integer,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95       => ( ( modulo364778990260209775nteger @ A @ B )
% 8.69/4.95          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5948_eq__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: real,B: real,C: real] :
% 8.69/4.95        ( ( A
% 8.69/4.95          = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_real )
% 8.69/4.95           => ( ( times_times_real @ A @ C )
% 8.69/4.95              = ( uminus_uminus_real @ B ) ) )
% 8.69/4.95          & ( ( C = zero_zero_real )
% 8.69/4.95           => ( A = zero_zero_real ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5949_eq__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: complex,B: complex,C: complex] :
% 8.69/4.95        ( ( A
% 8.69/4.95          = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_complex )
% 8.69/4.95           => ( ( times_times_complex @ A @ C )
% 8.69/4.95              = ( uminus1482373934393186551omplex @ B ) ) )
% 8.69/4.95          & ( ( C = zero_zero_complex )
% 8.69/4.95           => ( A = zero_zero_complex ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5950_eq__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: rat,B: rat,C: rat] :
% 8.69/4.95        ( ( A
% 8.69/4.95          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_rat )
% 8.69/4.95           => ( ( times_times_rat @ A @ C )
% 8.69/4.95              = ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95          & ( ( C = zero_zero_rat )
% 8.69/4.95           => ( A = zero_zero_rat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5951_minus__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: real,C: real,A: real] :
% 8.69/4.95        ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 8.69/4.95          = A )
% 8.69/4.95        = ( ( ( C != zero_zero_real )
% 8.69/4.95           => ( ( uminus_uminus_real @ B )
% 8.69/4.95              = ( times_times_real @ A @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_real )
% 8.69/4.95           => ( A = zero_zero_real ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5952_minus__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: complex,C: complex,A: complex] :
% 8.69/4.95        ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 8.69/4.95          = A )
% 8.69/4.95        = ( ( ( C != zero_zero_complex )
% 8.69/4.95           => ( ( uminus1482373934393186551omplex @ B )
% 8.69/4.95              = ( times_times_complex @ A @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_complex )
% 8.69/4.95           => ( A = zero_zero_complex ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5953_minus__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: rat,C: rat,A: rat] :
% 8.69/4.95        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 8.69/4.95          = A )
% 8.69/4.95        = ( ( ( C != zero_zero_rat )
% 8.69/4.95           => ( ( uminus_uminus_rat @ B )
% 8.69/4.95              = ( times_times_rat @ A @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_rat )
% 8.69/4.95           => ( A = zero_zero_rat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5954_nonzero__neg__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: real,A: real,C: real] :
% 8.69/4.95        ( ( B != zero_zero_real )
% 8.69/4.95       => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.95            = C )
% 8.69/4.95          = ( ( uminus_uminus_real @ A )
% 8.69/4.95            = ( times_times_real @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5955_nonzero__neg__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: complex,A: complex,C: complex] :
% 8.69/4.95        ( ( B != zero_zero_complex )
% 8.69/4.95       => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.95            = C )
% 8.69/4.95          = ( ( uminus1482373934393186551omplex @ A )
% 8.69/4.95            = ( times_times_complex @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5956_nonzero__neg__divide__eq__eq,axiom,
% 8.69/4.95      ! [B: rat,A: rat,C: rat] :
% 8.69/4.95        ( ( B != zero_zero_rat )
% 8.69/4.95       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.69/4.95            = C )
% 8.69/4.95          = ( ( uminus_uminus_rat @ A )
% 8.69/4.95            = ( times_times_rat @ C @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5957_nonzero__neg__divide__eq__eq2,axiom,
% 8.69/4.95      ! [B: real,C: real,A: real] :
% 8.69/4.95        ( ( B != zero_zero_real )
% 8.69/4.95       => ( ( C
% 8.69/4.95            = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 8.69/4.95          = ( ( times_times_real @ C @ B )
% 8.69/4.95            = ( uminus_uminus_real @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5958_nonzero__neg__divide__eq__eq2,axiom,
% 8.69/4.95      ! [B: complex,C: complex,A: complex] :
% 8.69/4.95        ( ( B != zero_zero_complex )
% 8.69/4.95       => ( ( C
% 8.69/4.95            = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/4.95          = ( ( times_times_complex @ C @ B )
% 8.69/4.95            = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5959_nonzero__neg__divide__eq__eq2,axiom,
% 8.69/4.95      ! [B: rat,C: rat,A: rat] :
% 8.69/4.95        ( ( B != zero_zero_rat )
% 8.69/4.95       => ( ( C
% 8.69/4.95            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 8.69/4.95          = ( ( times_times_rat @ C @ B )
% 8.69/4.95            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5960_mult__1s__ring__1_I2_J,axiom,
% 8.69/4.95      ! [B: real] :
% 8.69/4.95        ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 8.69/4.95        = ( uminus_uminus_real @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5961_mult__1s__ring__1_I2_J,axiom,
% 8.69/4.95      ! [B: int] :
% 8.69/4.95        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 8.69/4.95        = ( uminus_uminus_int @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5962_mult__1s__ring__1_I2_J,axiom,
% 8.69/4.95      ! [B: complex] :
% 8.69/4.95        ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 8.69/4.95        = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5963_mult__1s__ring__1_I2_J,axiom,
% 8.69/4.95      ! [B: code_integer] :
% 8.69/4.95        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 8.69/4.95        = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5964_mult__1s__ring__1_I2_J,axiom,
% 8.69/4.95      ! [B: rat] :
% 8.69/4.95        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 8.69/4.95        = ( uminus_uminus_rat @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5965_mult__1s__ring__1_I1_J,axiom,
% 8.69/4.95      ! [B: real] :
% 8.69/4.95        ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 8.69/4.95        = ( uminus_uminus_real @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5966_mult__1s__ring__1_I1_J,axiom,
% 8.69/4.95      ! [B: int] :
% 8.69/4.95        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 8.69/4.95        = ( uminus_uminus_int @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5967_mult__1s__ring__1_I1_J,axiom,
% 8.69/4.95      ! [B: complex] :
% 8.69/4.95        ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 8.69/4.95        = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5968_mult__1s__ring__1_I1_J,axiom,
% 8.69/4.95      ! [B: code_integer] :
% 8.69/4.95        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 8.69/4.95        = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5969_mult__1s__ring__1_I1_J,axiom,
% 8.69/4.95      ! [B: rat] :
% 8.69/4.95        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 8.69/4.95        = ( uminus_uminus_rat @ B ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5970_divide__eq__minus__1__iff,axiom,
% 8.69/4.95      ! [A: real,B: real] :
% 8.69/4.95        ( ( ( divide_divide_real @ A @ B )
% 8.69/4.95          = ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.95        = ( ( B != zero_zero_real )
% 8.69/4.95          & ( A
% 8.69/4.95            = ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5971_divide__eq__minus__1__iff,axiom,
% 8.69/4.95      ! [A: complex,B: complex] :
% 8.69/4.95        ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.69/4.95          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.95        = ( ( B != zero_zero_complex )
% 8.69/4.95          & ( A
% 8.69/4.95            = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5972_divide__eq__minus__1__iff,axiom,
% 8.69/4.95      ! [A: rat,B: rat] :
% 8.69/4.95        ( ( ( divide_divide_rat @ A @ B )
% 8.69/4.95          = ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.95        = ( ( B != zero_zero_rat )
% 8.69/4.95          & ( A
% 8.69/4.95            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5973_uminus__numeral__One,axiom,
% 8.69/4.95      ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 8.69/4.95      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5974_uminus__numeral__One,axiom,
% 8.69/4.95      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 8.69/4.95      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5975_uminus__numeral__One,axiom,
% 8.69/4.95      ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 8.69/4.95      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5976_uminus__numeral__One,axiom,
% 8.69/4.95      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 8.69/4.95      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5977_uminus__numeral__One,axiom,
% 8.69/4.95      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 8.69/4.95      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5978_power__minus,axiom,
% 8.69/4.95      ! [A: real,N: nat] :
% 8.69/4.95        ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.69/4.95        = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5979_power__minus,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.69/4.95        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5980_power__minus,axiom,
% 8.69/4.95      ! [A: complex,N: nat] :
% 8.69/4.95        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.69/4.95        = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5981_power__minus,axiom,
% 8.69/4.95      ! [A: code_integer,N: nat] :
% 8.69/4.95        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.69/4.95        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5982_power__minus,axiom,
% 8.69/4.95      ! [A: rat,N: nat] :
% 8.69/4.95        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.69/4.95        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5983_power__minus__Bit0,axiom,
% 8.69/4.95      ! [X: real,K: num] :
% 8.69/4.95        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5984_power__minus__Bit0,axiom,
% 8.69/4.95      ! [X: int,K: num] :
% 8.69/4.95        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5985_power__minus__Bit0,axiom,
% 8.69/4.95      ! [X: complex,K: num] :
% 8.69/4.95        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5986_power__minus__Bit0,axiom,
% 8.69/4.95      ! [X: code_integer,K: num] :
% 8.69/4.95        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5987_power__minus__Bit0,axiom,
% 8.69/4.95      ! [X: rat,K: num] :
% 8.69/4.95        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5988_lemma__interval__lt,axiom,
% 8.69/4.95      ! [A: real,X: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ A @ X )
% 8.69/4.95       => ( ( ord_less_real @ X @ B )
% 8.69/4.95         => ? [D3: real] :
% 8.69/4.95              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/4.95              & ! [Y2: real] :
% 8.69/4.95                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 8.69/4.95                 => ( ( ord_less_real @ A @ Y2 )
% 8.69/4.95                    & ( ord_less_real @ Y2 @ B ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5989_dvd__imp__le,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ K @ N )
% 8.69/4.95       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95         => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5990_dvd__mult__cancel,axiom,
% 8.69/4.95      ! [K: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.69/4.95       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.95         => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5991_nat__mult__dvd__cancel1,axiom,
% 8.69/4.95      ! [K: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.95       => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 8.69/4.95          = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5992_bezout__add__strong__nat,axiom,
% 8.69/4.95      ! [A: nat,B: nat] :
% 8.69/4.95        ( ( A != zero_zero_nat )
% 8.69/4.95       => ? [D3: nat,X6: nat,Y5: nat] :
% 8.69/4.95            ( ( dvd_dvd_nat @ D3 @ A )
% 8.69/4.95            & ( dvd_dvd_nat @ D3 @ B )
% 8.69/4.95            & ( ( times_times_nat @ A @ X6 )
% 8.69/4.95              = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5993_zdvd__imp__le,axiom,
% 8.69/4.95      ! [Z: int,N: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ Z @ N )
% 8.69/4.95       => ( ( ord_less_int @ zero_zero_int @ N )
% 8.69/4.95         => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5994_mod__greater__zero__iff__not__dvd,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 8.69/4.95        = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5995_real__0__less__add__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 8.69/4.95        = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5996_real__add__less__0__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 8.69/4.95        = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5997_real__add__le__0__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 8.69/4.95        = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5998_real__0__le__add__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 8.69/4.95        = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_5999_mod__eq__dvd__iff__nat,axiom,
% 8.69/4.95      ! [N: nat,M: nat,Q2: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.95       => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 8.69/4.95            = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.69/4.95          = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6000_prod__decode__aux_Ocases,axiom,
% 8.69/4.95      ! [X: product_prod_nat_nat] :
% 8.69/4.95        ~ ! [K3: nat,M4: nat] :
% 8.69/4.95            ( X
% 8.69/4.95           != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6001_finite__divisors__nat,axiom,
% 8.69/4.95      ! [M: nat] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.95       => ( finite_finite_nat
% 8.69/4.95          @ ( collect_nat
% 8.69/4.95            @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6002_abs__add__one__gt__zero,axiom,
% 8.69/4.95      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6003_abs__add__one__gt__zero,axiom,
% 8.69/4.95      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6004_abs__add__one__gt__zero,axiom,
% 8.69/4.95      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6005_abs__add__one__gt__zero,axiom,
% 8.69/4.95      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6006_even__zero,axiom,
% 8.69/4.95      dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6007_even__zero,axiom,
% 8.69/4.95      dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6008_even__zero,axiom,
% 8.69/4.95      dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6009_is__unitE,axiom,
% 8.69/4.95      ! [A: code_integer,C: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.69/4.95       => ~ ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.95           => ! [B5: code_integer] :
% 8.69/4.95                ( ( B5 != zero_z3403309356797280102nteger )
% 8.69/4.95               => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 8.69/4.95                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 8.69/4.95                      = B5 )
% 8.69/4.95                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 8.69/4.95                        = A )
% 8.69/4.95                     => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 8.69/4.95                          = one_one_Code_integer )
% 8.69/4.95                       => ( ( divide6298287555418463151nteger @ C @ A )
% 8.69/4.95                         != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6010_is__unitE,axiom,
% 8.69/4.95      ! [A: nat,C: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.69/4.95       => ~ ( ( A != zero_zero_nat )
% 8.69/4.95           => ! [B5: nat] :
% 8.69/4.95                ( ( B5 != zero_zero_nat )
% 8.69/4.95               => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 8.69/4.95                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 8.69/4.95                      = B5 )
% 8.69/4.95                   => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 8.69/4.95                        = A )
% 8.69/4.95                     => ( ( ( times_times_nat @ A @ B5 )
% 8.69/4.95                          = one_one_nat )
% 8.69/4.95                       => ( ( divide_divide_nat @ C @ A )
% 8.69/4.95                         != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6011_is__unitE,axiom,
% 8.69/4.95      ! [A: int,C: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ A @ one_one_int )
% 8.69/4.95       => ~ ( ( A != zero_zero_int )
% 8.69/4.95           => ! [B5: int] :
% 8.69/4.95                ( ( B5 != zero_zero_int )
% 8.69/4.95               => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 8.69/4.95                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 8.69/4.95                      = B5 )
% 8.69/4.95                   => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 8.69/4.95                        = A )
% 8.69/4.95                     => ( ( ( times_times_int @ A @ B5 )
% 8.69/4.95                          = one_one_int )
% 8.69/4.95                       => ( ( divide_divide_int @ C @ A )
% 8.69/4.95                         != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6012_is__unit__div__mult__cancel__left,axiom,
% 8.69/4.95      ! [A: code_integer,B: code_integer] :
% 8.69/4.95        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.95       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.69/4.95            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6013_is__unit__div__mult__cancel__left,axiom,
% 8.69/4.95      ! [A: nat,B: nat] :
% 8.69/4.95        ( ( A != zero_zero_nat )
% 8.69/4.95       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 8.69/4.95            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6014_is__unit__div__mult__cancel__left,axiom,
% 8.69/4.95      ! [A: int,B: int] :
% 8.69/4.95        ( ( A != zero_zero_int )
% 8.69/4.95       => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 8.69/4.95            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6015_is__unit__div__mult__cancel__right,axiom,
% 8.69/4.95      ! [A: code_integer,B: code_integer] :
% 8.69/4.95        ( ( A != zero_z3403309356797280102nteger )
% 8.69/4.95       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.69/4.95         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 8.69/4.95            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6016_is__unit__div__mult__cancel__right,axiom,
% 8.69/4.95      ! [A: nat,B: nat] :
% 8.69/4.95        ( ( A != zero_zero_nat )
% 8.69/4.95       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.69/4.95         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 8.69/4.95            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6017_is__unit__div__mult__cancel__right,axiom,
% 8.69/4.95      ! [A: int,B: int] :
% 8.69/4.95        ( ( A != zero_zero_int )
% 8.69/4.95       => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.69/4.95         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 8.69/4.95            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6018_evenE,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: code_integer] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6019_evenE,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: nat] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6020_evenE,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: int] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6021_odd__even__add,axiom,
% 8.69/4.95      ! [A: code_integer,B: code_integer] :
% 8.69/4.95        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 8.69/4.95         => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6022_odd__even__add,axiom,
% 8.69/4.95      ! [A: nat,B: nat] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.69/4.95         => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6023_odd__even__add,axiom,
% 8.69/4.95      ! [A: int,B: int] :
% 8.69/4.95        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 8.69/4.95         => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6024_odd__one,axiom,
% 8.69/4.95      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6025_odd__one,axiom,
% 8.69/4.95      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6026_odd__one,axiom,
% 8.69/4.95      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6027_bit__eq__rec,axiom,
% 8.69/4.95      ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 8.69/4.95      = ( ^ [A3: code_integer,B2: code_integer] :
% 8.69/4.95            ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 8.69/4.95              = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 8.69/4.95            & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95              = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6028_bit__eq__rec,axiom,
% 8.69/4.95      ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 8.69/4.95      = ( ^ [A3: nat,B2: nat] :
% 8.69/4.95            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 8.69/4.95              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 8.69/4.95            & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95              = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6029_bit__eq__rec,axiom,
% 8.69/4.95      ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 8.69/4.95      = ( ^ [A3: int,B2: int] :
% 8.69/4.95            ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 8.69/4.95              = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 8.69/4.95            & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95              = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6030_dvd__power__iff,axiom,
% 8.69/4.95      ! [X: code_integer,M: nat,N: nat] :
% 8.69/4.95        ( ( X != zero_z3403309356797280102nteger )
% 8.69/4.95       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 8.69/4.95          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 8.69/4.95            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6031_dvd__power__iff,axiom,
% 8.69/4.95      ! [X: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( X != zero_zero_nat )
% 8.69/4.95       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 8.69/4.95          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 8.69/4.95            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6032_dvd__power__iff,axiom,
% 8.69/4.95      ! [X: int,M: nat,N: nat] :
% 8.69/4.95        ( ( X != zero_zero_int )
% 8.69/4.95       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 8.69/4.95          = ( ( dvd_dvd_int @ X @ one_one_int )
% 8.69/4.95            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6033_less__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: real,B: real,C: real] :
% 8.69/4.95        ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6034_less__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: rat,B: rat,C: rat] :
% 8.69/4.95        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6035_minus__divide__less__eq,axiom,
% 8.69/4.95      ! [B: real,C: real,A: real] :
% 8.69/4.95        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6036_minus__divide__less__eq,axiom,
% 8.69/4.95      ! [B: rat,C: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6037_neg__less__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: real,A: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6038_neg__less__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6039_neg__minus__divide__less__eq,axiom,
% 8.69/4.95      ! [C: real,B: real,A: real] :
% 8.69/4.95        ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6040_neg__minus__divide__less__eq,axiom,
% 8.69/4.95      ! [C: rat,B: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6041_pos__less__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: real,A: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95       => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6042_pos__less__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6043_pos__minus__divide__less__eq,axiom,
% 8.69/4.95      ! [C: real,B: real,A: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95       => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6044_pos__minus__divide__less__eq,axiom,
% 8.69/4.95      ! [C: rat,B: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6045_divide__eq__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: real,C: real,W: num] :
% 8.69/4.95        ( ( ( divide_divide_real @ B @ C )
% 8.69/4.95          = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_real )
% 8.69/4.95           => ( B
% 8.69/4.95              = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_real )
% 8.69/4.95           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.95              = zero_zero_real ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6046_divide__eq__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: complex,C: complex,W: num] :
% 8.69/4.95        ( ( ( divide1717551699836669952omplex @ B @ C )
% 8.69/4.95          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_complex )
% 8.69/4.95           => ( B
% 8.69/4.95              = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_complex )
% 8.69/4.95           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.95              = zero_zero_complex ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6047_divide__eq__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: rat,C: rat,W: num] :
% 8.69/4.95        ( ( ( divide_divide_rat @ B @ C )
% 8.69/4.95          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 8.69/4.95        = ( ( ( C != zero_zero_rat )
% 8.69/4.95           => ( B
% 8.69/4.95              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ( C = zero_zero_rat )
% 8.69/4.95           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.95              = zero_zero_rat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6048_eq__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: real,C: real] :
% 8.69/4.95        ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.95          = ( divide_divide_real @ B @ C ) )
% 8.69/4.95        = ( ( ( C != zero_zero_real )
% 8.69/4.95           => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 8.69/4.95              = B ) )
% 8.69/4.95          & ( ( C = zero_zero_real )
% 8.69/4.95           => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.95              = zero_zero_real ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6049_eq__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: complex,C: complex] :
% 8.69/4.95        ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.95          = ( divide1717551699836669952omplex @ B @ C ) )
% 8.69/4.95        = ( ( ( C != zero_zero_complex )
% 8.69/4.95           => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 8.69/4.95              = B ) )
% 8.69/4.95          & ( ( C = zero_zero_complex )
% 8.69/4.95           => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.95              = zero_zero_complex ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6050_eq__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: rat,C: rat] :
% 8.69/4.95        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.95          = ( divide_divide_rat @ B @ C ) )
% 8.69/4.95        = ( ( ( C != zero_zero_rat )
% 8.69/4.95           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 8.69/4.95              = B ) )
% 8.69/4.95          & ( ( C = zero_zero_rat )
% 8.69/4.95           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 8.69/4.95              = zero_zero_rat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6051_minus__divide__add__eq__iff,axiom,
% 8.69/4.95      ! [Z: real,X: real,Y: real] :
% 8.69/4.95        ( ( Z != zero_zero_real )
% 8.69/4.95       => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6052_minus__divide__add__eq__iff,axiom,
% 8.69/4.95      ! [Z: complex,X: complex,Y: complex] :
% 8.69/4.95        ( ( Z != zero_zero_complex )
% 8.69/4.95       => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6053_minus__divide__add__eq__iff,axiom,
% 8.69/4.95      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.95        ( ( Z != zero_zero_rat )
% 8.69/4.95       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6054_add__divide__eq__if__simps_I3_J,axiom,
% 8.69/4.95      ! [Z: real,A: real,B: real] :
% 8.69/4.95        ( ( ( Z = zero_zero_real )
% 8.69/4.95         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 8.69/4.95            = B ) )
% 8.69/4.95        & ( ( Z != zero_zero_real )
% 8.69/4.95         => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6055_add__divide__eq__if__simps_I3_J,axiom,
% 8.69/4.95      ! [Z: complex,A: complex,B: complex] :
% 8.69/4.95        ( ( ( Z = zero_zero_complex )
% 8.69/4.95         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 8.69/4.95            = B ) )
% 8.69/4.95        & ( ( Z != zero_zero_complex )
% 8.69/4.95         => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6056_add__divide__eq__if__simps_I3_J,axiom,
% 8.69/4.95      ! [Z: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ( Z = zero_zero_rat )
% 8.69/4.95         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 8.69/4.95            = B ) )
% 8.69/4.95        & ( ( Z != zero_zero_rat )
% 8.69/4.95         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6057_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: code_integer] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_Code_integer ) )
% 8.69/4.95       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6058_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: rat] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_rat ) )
% 8.69/4.95       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6059_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: nat] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_nat ) )
% 8.69/4.95       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6060_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: real] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_real ) )
% 8.69/4.95       => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6061_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: int] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_int ) )
% 8.69/4.95       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6062_dvd__power,axiom,
% 8.69/4.95      ! [N: nat,X: complex] :
% 8.69/4.95        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          | ( X = one_one_complex ) )
% 8.69/4.95       => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6063_add__divide__eq__if__simps_I6_J,axiom,
% 8.69/4.95      ! [Z: real,A: real,B: real] :
% 8.69/4.95        ( ( ( Z = zero_zero_real )
% 8.69/4.95         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 8.69/4.95            = ( uminus_uminus_real @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_real )
% 8.69/4.95         => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6064_add__divide__eq__if__simps_I6_J,axiom,
% 8.69/4.95      ! [Z: complex,A: complex,B: complex] :
% 8.69/4.95        ( ( ( Z = zero_zero_complex )
% 8.69/4.95         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 8.69/4.95            = ( uminus1482373934393186551omplex @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_complex )
% 8.69/4.95         => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6065_add__divide__eq__if__simps_I6_J,axiom,
% 8.69/4.95      ! [Z: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ( Z = zero_zero_rat )
% 8.69/4.95         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 8.69/4.95            = ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_rat )
% 8.69/4.95         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 8.69/4.95            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6066_add__divide__eq__if__simps_I5_J,axiom,
% 8.69/4.95      ! [Z: real,A: real,B: real] :
% 8.69/4.95        ( ( ( Z = zero_zero_real )
% 8.69/4.95         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 8.69/4.95            = ( uminus_uminus_real @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_real )
% 8.69/4.95         => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 8.69/4.95            = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6067_add__divide__eq__if__simps_I5_J,axiom,
% 8.69/4.95      ! [Z: complex,A: complex,B: complex] :
% 8.69/4.95        ( ( ( Z = zero_zero_complex )
% 8.69/4.95         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 8.69/4.95            = ( uminus1482373934393186551omplex @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_complex )
% 8.69/4.95         => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 8.69/4.95            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6068_add__divide__eq__if__simps_I5_J,axiom,
% 8.69/4.95      ! [Z: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ( Z = zero_zero_rat )
% 8.69/4.95         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 8.69/4.95            = ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95        & ( ( Z != zero_zero_rat )
% 8.69/4.95         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 8.69/4.95            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6069_minus__divide__diff__eq__iff,axiom,
% 8.69/4.95      ! [Z: real,X: real,Y: real] :
% 8.69/4.95        ( ( Z != zero_zero_real )
% 8.69/4.95       => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6070_minus__divide__diff__eq__iff,axiom,
% 8.69/4.95      ! [Z: complex,X: complex,Y: complex] :
% 8.69/4.95        ( ( Z != zero_zero_complex )
% 8.69/4.95       => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6071_minus__divide__diff__eq__iff,axiom,
% 8.69/4.95      ! [Z: rat,X: rat,Y: rat] :
% 8.69/4.95        ( ( Z != zero_zero_rat )
% 8.69/4.95       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 8.69/4.95          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6072_power2__eq__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          | ( X
% 8.69/4.95            = ( uminus_uminus_real @ Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6073_power2__eq__iff,axiom,
% 8.69/4.95      ! [X: int,Y: int] :
% 8.69/4.95        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          | ( X
% 8.69/4.95            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6074_power2__eq__iff,axiom,
% 8.69/4.95      ! [X: complex,Y: complex] :
% 8.69/4.95        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          | ( X
% 8.69/4.95            = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6075_power2__eq__iff,axiom,
% 8.69/4.95      ! [X: code_integer,Y: code_integer] :
% 8.69/4.95        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          | ( X
% 8.69/4.95            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6076_power2__eq__iff,axiom,
% 8.69/4.95      ! [X: rat,Y: rat] :
% 8.69/4.95        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          | ( X
% 8.69/4.95            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6077_lemma__interval,axiom,
% 8.69/4.95      ! [A: real,X: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ A @ X )
% 8.69/4.95       => ( ( ord_less_real @ X @ B )
% 8.69/4.95         => ? [D3: real] :
% 8.69/4.95              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/4.95              & ! [Y2: real] :
% 8.69/4.95                  ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 8.69/4.95                 => ( ( ord_less_eq_real @ A @ Y2 )
% 8.69/4.95                    & ( ord_less_eq_real @ Y2 @ B ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6078_even__even__mod__4__iff,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6079_dvd__mult__cancel1,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.95       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 8.69/4.95          = ( N = one_one_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6080_dvd__mult__cancel2,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.95       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 8.69/4.95          = ( N = one_one_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6081_dvd__minus__add,axiom,
% 8.69/4.95      ! [Q2: nat,N: nat,R: nat,M: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ Q2 @ N )
% 8.69/4.95       => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 8.69/4.95         => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 8.69/4.95            = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6082_power__dvd__imp__le,axiom,
% 8.69/4.95      ! [I: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 8.69/4.95       => ( ( ord_less_nat @ one_one_nat @ I )
% 8.69/4.95         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6083_mod__nat__eqI,axiom,
% 8.69/4.95      ! [R: nat,N: nat,M: nat] :
% 8.69/4.95        ( ( ord_less_nat @ R @ N )
% 8.69/4.95       => ( ( ord_less_eq_nat @ R @ M )
% 8.69/4.95         => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 8.69/4.95           => ( ( modulo_modulo_nat @ M @ N )
% 8.69/4.95              = R ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6084_ln__add__one__self__le__self2,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.95       => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6085_mod__int__pos__iff,axiom,
% 8.69/4.95      ! [K: int,L2: int] :
% 8.69/4.95        ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 8.69/4.95        = ( ( dvd_dvd_int @ L2 @ K )
% 8.69/4.95          | ( ( L2 = zero_zero_int )
% 8.69/4.95            & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 8.69/4.95          | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6086_aset_I10_J,axiom,
% 8.69/4.95      ! [D: int,D4: int,A2: set_int,T: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.95       => ! [X4: int] :
% 8.69/4.95            ( ! [Xa3: int] :
% 8.69/4.95                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.69/4.95               => ! [Xb2: int] :
% 8.69/4.95                    ( ( member_int @ Xb2 @ A2 )
% 8.69/4.95                   => ( X4
% 8.69/4.95                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.69/4.95           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.69/4.95             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6087_aset_I9_J,axiom,
% 8.69/4.95      ! [D: int,D4: int,A2: set_int,T: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.95       => ! [X4: int] :
% 8.69/4.95            ( ! [Xa3: int] :
% 8.69/4.95                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.69/4.95               => ! [Xb2: int] :
% 8.69/4.95                    ( ( member_int @ Xb2 @ A2 )
% 8.69/4.95                   => ( X4
% 8.69/4.95                     != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 8.69/4.95           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.69/4.95             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6088_bset_I10_J,axiom,
% 8.69/4.95      ! [D: int,D4: int,B3: set_int,T: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.95       => ! [X4: int] :
% 8.69/4.95            ( ! [Xa3: int] :
% 8.69/4.95                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.69/4.95               => ! [Xb2: int] :
% 8.69/4.95                    ( ( member_int @ Xb2 @ B3 )
% 8.69/4.95                   => ( X4
% 8.69/4.95                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.69/4.95           => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.69/4.95             => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6089_bset_I9_J,axiom,
% 8.69/4.95      ! [D: int,D4: int,B3: set_int,T: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ D @ D4 )
% 8.69/4.95       => ! [X4: int] :
% 8.69/4.95            ( ! [Xa3: int] :
% 8.69/4.95                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 8.69/4.95               => ! [Xb2: int] :
% 8.69/4.95                    ( ( member_int @ Xb2 @ B3 )
% 8.69/4.95                   => ( X4
% 8.69/4.95                     != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 8.69/4.95           => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 8.69/4.95             => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6090_abs__le__square__iff,axiom,
% 8.69/4.95      ! [X: code_integer,Y: code_integer] :
% 8.69/4.95        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 8.69/4.95        = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6091_abs__le__square__iff,axiom,
% 8.69/4.95      ! [X: real,Y: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 8.69/4.95        = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6092_abs__le__square__iff,axiom,
% 8.69/4.95      ! [X: rat,Y: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 8.69/4.95        = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6093_abs__le__square__iff,axiom,
% 8.69/4.95      ! [X: int,Y: int] :
% 8.69/4.95        ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 8.69/4.95        = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6094_abs__square__eq__1,axiom,
% 8.69/4.95      ! [X: code_integer] :
% 8.69/4.95        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_Code_integer )
% 8.69/4.95        = ( ( abs_abs_Code_integer @ X )
% 8.69/4.95          = one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6095_abs__square__eq__1,axiom,
% 8.69/4.95      ! [X: rat] :
% 8.69/4.95        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_rat )
% 8.69/4.95        = ( ( abs_abs_rat @ X )
% 8.69/4.95          = one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6096_abs__square__eq__1,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_real )
% 8.69/4.95        = ( ( abs_abs_real @ X )
% 8.69/4.95          = one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6097_abs__square__eq__1,axiom,
% 8.69/4.95      ! [X: int] :
% 8.69/4.95        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_int )
% 8.69/4.95        = ( ( abs_abs_int @ X )
% 8.69/4.95          = one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6098_even__two__times__div__two,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = A ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6099_even__two__times__div__two,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = A ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6100_even__two__times__div__two,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = A ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6101_even__iff__mod__2__eq__zero,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = zero_zero_nat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6102_even__iff__mod__2__eq__zero,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95          = zero_zero_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6103_even__iff__mod__2__eq__zero,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6104_le__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: real,B: real,C: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6105_le__minus__divide__eq,axiom,
% 8.69/4.95      ! [A: rat,B: rat,C: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6106_minus__divide__le__eq,axiom,
% 8.69/4.95      ! [B: real,C: real,A: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6107_minus__divide__le__eq,axiom,
% 8.69/4.95      ! [B: rat,C: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6108_neg__le__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: real,A: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6109_neg__le__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6110_neg__minus__divide__le__eq,axiom,
% 8.69/4.95      ! [C: real,B: real,A: real] :
% 8.69/4.95        ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6111_neg__minus__divide__le__eq,axiom,
% 8.69/4.95      ! [C: rat,B: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6112_pos__le__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: real,A: real,B: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95       => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6113_pos__le__minus__divide__eq,axiom,
% 8.69/4.95      ! [C: rat,A: rat,B: rat] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 8.69/4.95          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6114_pos__minus__divide__le__eq,axiom,
% 8.69/4.95      ! [C: real,B: real,A: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6115_pos__minus__divide__le__eq,axiom,
% 8.69/4.95      ! [C: rat,B: rat,A: rat] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 8.69/4.95          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6116_odd__iff__mod__2__eq__one,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.95        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_nat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6117_odd__iff__mod__2__eq__one,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.95        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6118_odd__iff__mod__2__eq__one,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.95        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6119_less__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: real,C: real] :
% 8.69/4.95        ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6120_less__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: rat,C: rat] :
% 8.69/4.95        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6121_divide__less__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: real,C: real,W: num] :
% 8.69/4.95        ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6122_divide__less__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: rat,C: rat,W: num] :
% 8.69/4.95        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6123_power__mono__odd,axiom,
% 8.69/4.95      ! [N: nat,A: real,B: real] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_real @ A @ B )
% 8.69/4.95         => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6124_power__mono__odd,axiom,
% 8.69/4.95      ! [N: nat,A: rat,B: rat] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_rat @ A @ B )
% 8.69/4.95         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6125_power__mono__odd,axiom,
% 8.69/4.95      ! [N: nat,A: int,B: int] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_int @ A @ B )
% 8.69/4.95         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6126_power2__eq__1__iff,axiom,
% 8.69/4.95      ! [A: real] :
% 8.69/4.95        ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_real )
% 8.69/4.95        = ( ( A = one_one_real )
% 8.69/4.95          | ( A
% 8.69/4.95            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6127_power2__eq__1__iff,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_int )
% 8.69/4.95        = ( ( A = one_one_int )
% 8.69/4.95          | ( A
% 8.69/4.95            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6128_power2__eq__1__iff,axiom,
% 8.69/4.95      ! [A: complex] :
% 8.69/4.95        ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_complex )
% 8.69/4.95        = ( ( A = one_one_complex )
% 8.69/4.95          | ( A
% 8.69/4.95            = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6129_power2__eq__1__iff,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_Code_integer )
% 8.69/4.95        = ( ( A = one_one_Code_integer )
% 8.69/4.95          | ( A
% 8.69/4.95            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6130_power2__eq__1__iff,axiom,
% 8.69/4.95      ! [A: rat] :
% 8.69/4.95        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95          = one_one_rat )
% 8.69/4.95        = ( ( A = one_one_rat )
% 8.69/4.95          | ( A
% 8.69/4.95            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6131_odd__pos,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6132_dvd__power__iff__le,axiom,
% 8.69/4.95      ! [K: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.69/4.95       => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 8.69/4.95          = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6133_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.95       => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 8.69/4.95          = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6134_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.95       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 8.69/4.95          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6135_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.95       => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 8.69/4.95          = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6136_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.95       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 8.69/4.95          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6137_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.69/4.95      ! [K: nat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.95       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 8.69/4.95          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6138_even__unset__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          | ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6139_even__unset__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          | ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6140_even__unset__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          | ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6141_even__set__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          & ( M != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6142_even__set__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          & ( M != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6143_even__set__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95          & ( M != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6144_realpow__square__minus__le,axiom,
% 8.69/4.95      ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6145_even__flip__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: code_integer] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         != ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6146_even__flip__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         != ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6147_even__flip__bit__iff,axiom,
% 8.69/4.95      ! [M: nat,A: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         != ( M = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6148_even__diff__iff,axiom,
% 8.69/4.95      ! [K: int,L2: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 8.69/4.95        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6149_ln__one__minus__pos__upper__bound,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.95       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/4.95         => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6150_abs__sqrt__wlog,axiom,
% 8.69/4.95      ! [P: code_integer > code_integer > $o,X: code_integer] :
% 8.69/4.95        ( ! [X6: code_integer] :
% 8.69/4.95            ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X6 )
% 8.69/4.95           => ( P @ X6 @ ( power_8256067586552552935nteger @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.95       => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6151_abs__sqrt__wlog,axiom,
% 8.69/4.95      ! [P: real > real > $o,X: real] :
% 8.69/4.95        ( ! [X6: real] :
% 8.69/4.95            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 8.69/4.95           => ( P @ X6 @ ( power_power_real @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.95       => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6152_abs__sqrt__wlog,axiom,
% 8.69/4.95      ! [P: rat > rat > $o,X: rat] :
% 8.69/4.95        ( ! [X6: rat] :
% 8.69/4.95            ( ( ord_less_eq_rat @ zero_zero_rat @ X6 )
% 8.69/4.95           => ( P @ X6 @ ( power_power_rat @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.95       => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6153_abs__sqrt__wlog,axiom,
% 8.69/4.95      ! [P: int > int > $o,X: int] :
% 8.69/4.95        ( ! [X6: int] :
% 8.69/4.95            ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 8.69/4.95           => ( P @ X6 @ ( power_power_int @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.95       => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6154_power2__le__iff__abs__le,axiom,
% 8.69/4.95      ! [Y: code_integer,X: code_integer] :
% 8.69/4.95        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.69/4.95       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6155_power2__le__iff__abs__le,axiom,
% 8.69/4.95      ! [Y: real,X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.95       => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6156_power2__le__iff__abs__le,axiom,
% 8.69/4.95      ! [Y: rat,X: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.69/4.95       => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6157_power2__le__iff__abs__le,axiom,
% 8.69/4.95      ! [Y: int,X: int] :
% 8.69/4.95        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.95       => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6158_abs__square__le__1,axiom,
% 8.69/4.95      ! [X: code_integer] :
% 8.69/4.95        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 8.69/4.95        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6159_abs__square__le__1,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 8.69/4.95        = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6160_abs__square__le__1,axiom,
% 8.69/4.95      ! [X: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 8.69/4.95        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6161_abs__square__le__1,axiom,
% 8.69/4.95      ! [X: int] :
% 8.69/4.95        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 8.69/4.95        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6162_abs__square__less__1,axiom,
% 8.69/4.95      ! [X: code_integer] :
% 8.69/4.95        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 8.69/4.95        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6163_abs__square__less__1,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 8.69/4.95        = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6164_abs__square__less__1,axiom,
% 8.69/4.95      ! [X: rat] :
% 8.69/4.95        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 8.69/4.95        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6165_abs__square__less__1,axiom,
% 8.69/4.95      ! [X: int] :
% 8.69/4.95        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 8.69/4.95        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6166_oddE,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: code_integer] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6167_oddE,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: nat] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6168_oddE,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95       => ~ ! [B5: int] :
% 8.69/4.95              ( A
% 8.69/4.95             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6169_mod2__eq__if,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95            = zero_zero_nat ) )
% 8.69/4.95        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95            = one_one_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6170_mod2__eq__if,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95            = zero_zero_int ) )
% 8.69/4.95        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95            = one_one_int ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6171_mod2__eq__if,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95            = zero_z3403309356797280102nteger ) )
% 8.69/4.95        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95            = one_one_Code_integer ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6172_parity__cases,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95           != zero_zero_nat ) )
% 8.69/4.95       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.95           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95             != one_one_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6173_parity__cases,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95           != zero_zero_int ) )
% 8.69/4.95       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.95           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95             != one_one_int ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6174_parity__cases,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95           != zero_z3403309356797280102nteger ) )
% 8.69/4.95       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.95           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95             != one_one_Code_integer ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6175_le__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: real,C: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6176_le__divide__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [W: num,B: rat,C: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6177_divide__le__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: real,C: real,W: num] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.95        = ( ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 8.69/4.95           => ( ( ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 8.69/4.95              & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 8.69/4.95               => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6178_divide__le__eq__numeral_I2_J,axiom,
% 8.69/4.95      ! [B: rat,C: rat,W: num] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 8.69/4.95        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 8.69/4.95          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 8.69/4.95           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 8.69/4.95              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 8.69/4.95               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6179_zero__le__power__eq,axiom,
% 8.69/4.95      ! [A: real,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6180_zero__le__power__eq,axiom,
% 8.69/4.95      ! [A: rat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6181_zero__le__power__eq,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.69/4.95        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6182_zero__le__odd__power,axiom,
% 8.69/4.95      ! [N: nat,A: real] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.69/4.95          = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6183_zero__le__odd__power,axiom,
% 8.69/4.95      ! [N: nat,A: rat] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.69/4.95          = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6184_zero__le__odd__power,axiom,
% 8.69/4.95      ! [N: nat,A: int] :
% 8.69/4.95        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.69/4.95          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6185_zero__le__even__power,axiom,
% 8.69/4.95      ! [N: nat,A: real] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6186_zero__le__even__power,axiom,
% 8.69/4.95      ! [N: nat,A: rat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6187_zero__le__even__power,axiom,
% 8.69/4.95      ! [N: nat,A: int] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95       => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6188_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.95       => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.95         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6189_square__le__1,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.95       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.95         => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6190_square__le__1,axiom,
% 8.69/4.95      ! [X: code_integer] :
% 8.69/4.95        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 8.69/4.95       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 8.69/4.95         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6191_square__le__1,axiom,
% 8.69/4.95      ! [X: rat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 8.69/4.95       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 8.69/4.95         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6192_square__le__1,axiom,
% 8.69/4.95      ! [X: int] :
% 8.69/4.95        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 8.69/4.95       => ( ( ord_less_eq_int @ X @ one_one_int )
% 8.69/4.95         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6193_minus__power__mult__self,axiom,
% 8.69/4.95      ! [A: real,N: nat] :
% 8.69/4.95        ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 8.69/4.95        = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6194_minus__power__mult__self,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 8.69/4.95        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6195_minus__power__mult__self,axiom,
% 8.69/4.95      ! [A: complex,N: nat] :
% 8.69/4.95        ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 8.69/4.95        = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6196_minus__power__mult__self,axiom,
% 8.69/4.95      ! [A: code_integer,N: nat] :
% 8.69/4.95        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 8.69/4.95        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6197_minus__power__mult__self,axiom,
% 8.69/4.95      ! [A: rat,N: nat] :
% 8.69/4.95        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 8.69/4.95        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6198_list__decode_Ocases,axiom,
% 8.69/4.95      ! [X: nat] :
% 8.69/4.95        ( ( X != zero_zero_nat )
% 8.69/4.95       => ~ ! [N3: nat] :
% 8.69/4.95              ( X
% 8.69/4.95             != ( suc @ N3 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6199_zero__less__power__eq,axiom,
% 8.69/4.95      ! [A: real,N: nat] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.69/4.95        = ( ( N = zero_zero_nat )
% 8.69/4.95          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( A != zero_zero_real ) )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6200_zero__less__power__eq,axiom,
% 8.69/4.95      ! [A: rat,N: nat] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.69/4.95        = ( ( N = zero_zero_nat )
% 8.69/4.95          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( A != zero_zero_rat ) )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6201_zero__less__power__eq,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.69/4.95        = ( ( N = zero_zero_nat )
% 8.69/4.95          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( A != zero_zero_int ) )
% 8.69/4.95          | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6202_power__minus1__odd,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6203_power__minus1__odd,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6204_power__minus1__odd,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6205_power__minus1__odd,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6206_power__minus1__odd,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6207_eq__diff__eq_H,axiom,
% 8.69/4.95      ! [X: real,Y: real,Z: real] :
% 8.69/4.95        ( ( X
% 8.69/4.95          = ( minus_minus_real @ Y @ Z ) )
% 8.69/4.95        = ( Y
% 8.69/4.95          = ( plus_plus_real @ X @ Z ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6208_even__mask__div__iff_H,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6209_even__mask__div__iff_H,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6210_even__mask__div__iff_H,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6211_power__le__zero__eq,axiom,
% 8.69/4.95      ! [A: real,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 8.69/4.95        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.69/4.95            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( A = zero_zero_real ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6212_power__le__zero__eq,axiom,
% 8.69/4.95      ! [A: rat,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 8.69/4.95        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.69/4.95            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( A = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6213_power__le__zero__eq,axiom,
% 8.69/4.95      ! [A: int,N: nat] :
% 8.69/4.95        ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 8.69/4.95        = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.95          & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.69/4.95            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95              & ( A = zero_zero_int ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6214_even__mod__4__div__2,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.95          = ( suc @ zero_zero_nat ) )
% 8.69/4.95       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6215_even__mask__div__iff,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_z3403309356797280102nteger )
% 8.69/4.95          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6216_even__mask__div__iff,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_zero_nat )
% 8.69/4.95          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6217_even__mask__div__iff,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_zero_int )
% 8.69/4.95          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6218_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.95       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.95         => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6219_even__mult__exp__div__exp__iff,axiom,
% 8.69/4.95      ! [A: code_integer,M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ord_less_nat @ N @ M )
% 8.69/4.95          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_z3403309356797280102nteger )
% 8.69/4.95          | ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.95            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6220_even__mult__exp__div__exp__iff,axiom,
% 8.69/4.95      ! [A: nat,M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ord_less_nat @ N @ M )
% 8.69/4.95          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_zero_nat )
% 8.69/4.95          | ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.95            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6221_even__mult__exp__div__exp__iff,axiom,
% 8.69/4.95      ! [A: int,M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.95        = ( ( ord_less_nat @ N @ M )
% 8.69/4.95          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.69/4.95            = zero_zero_int )
% 8.69/4.95          | ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.95            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6222_compl__le__compl__iff,axiom,
% 8.69/4.95      ! [X: set_int,Y: set_int] :
% 8.69/4.95        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 8.69/4.95        = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6223_signed__take__bit__rec,axiom,
% 8.69/4.95      ( bit_ri6519982836138164636nteger
% 8.69/4.95      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6224_signed__take__bit__rec,axiom,
% 8.69/4.95      ( bit_ri631733984087533419it_int
% 8.69/4.95      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6225_triangle__def,axiom,
% 8.69/4.95      ( nat_triangle
% 8.69/4.95      = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6226_arctan__double,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.95       => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 8.69/4.95          = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6227_vebt__buildup_Oelims,axiom,
% 8.69/4.95      ! [X: nat,Y: vEBT_VEBT] :
% 8.69/4.95        ( ( ( vEBT_vebt_buildup @ X )
% 8.69/4.95          = Y )
% 8.69/4.95       => ( ( ( X = zero_zero_nat )
% 8.69/4.95           => ( Y
% 8.69/4.95             != ( vEBT_Leaf @ $false @ $false ) ) )
% 8.69/4.95         => ( ( ( X
% 8.69/4.95                = ( suc @ zero_zero_nat ) )
% 8.69/4.95             => ( Y
% 8.69/4.95               != ( vEBT_Leaf @ $false @ $false ) ) )
% 8.69/4.95           => ~ ! [Va2: nat] :
% 8.69/4.95                  ( ( X
% 8.69/4.95                    = ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.95                 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.95                       => ( Y
% 8.69/4.95                          = ( 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 ) ) ) ) ) ) )
% 8.69/4.95                      & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.95                       => ( Y
% 8.69/4.95                          = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6228_flip__bit__0,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 8.69/4.95        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6229_flip__bit__0,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 8.69/4.95        = ( 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 ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6230_flip__bit__0,axiom,
% 8.69/4.95      ! [A: nat] :
% 8.69/4.95        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 8.69/4.95        = ( 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 ) ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6231_intind,axiom,
% 8.69/4.95      ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( P @ X )
% 8.69/4.95         => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6232_intind,axiom,
% 8.69/4.95      ! [I: nat,N: nat,P: int > $o,X: int] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( P @ X )
% 8.69/4.95         => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6233_intind,axiom,
% 8.69/4.95      ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( P @ X )
% 8.69/4.95         => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6234_Compl__anti__mono,axiom,
% 8.69/4.95      ! [A2: set_int,B3: set_int] :
% 8.69/4.95        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.69/4.95       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6235_Compl__subset__Compl__iff,axiom,
% 8.69/4.95      ! [A2: set_int,B3: set_int] :
% 8.69/4.95        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 8.69/4.95        = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6236_of__bool__less__eq__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 8.69/4.95        = ( P
% 8.69/4.95         => Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6237_of__bool__less__eq__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 8.69/4.95        = ( P
% 8.69/4.95         => Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6238_of__bool__less__eq__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 8.69/4.95        = ( P
% 8.69/4.95         => Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6239_of__bool__less__eq__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 8.69/4.95        = ( P
% 8.69/4.95         => Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6240_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n1201886186963655149omplex @ $false )
% 8.69/4.95      = zero_zero_complex ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6241_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n3304061248610475627l_real @ $false )
% 8.69/4.95      = zero_zero_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6242_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n2052037380579107095ol_rat @ $false )
% 8.69/4.95      = zero_zero_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6243_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n2687167440665602831ol_nat @ $false )
% 8.69/4.95      = zero_zero_nat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6244_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n2684676970156552555ol_int @ $false )
% 8.69/4.95      = zero_zero_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6245_of__bool__eq_I1_J,axiom,
% 8.69/4.95      ( ( zero_n356916108424825756nteger @ $false )
% 8.69/4.95      = zero_z3403309356797280102nteger ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6246_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n1201886186963655149omplex @ P )
% 8.69/4.95          = zero_zero_complex )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6247_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n3304061248610475627l_real @ P )
% 8.69/4.95          = zero_zero_real )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6248_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 8.69/4.95          = zero_zero_rat )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6249_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 8.69/4.95          = zero_zero_nat )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6250_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2684676970156552555ol_int @ P )
% 8.69/4.95          = zero_zero_int )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6251_of__bool__eq__0__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n356916108424825756nteger @ P )
% 8.69/4.95          = zero_z3403309356797280102nteger )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6252_of__bool__less__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 8.69/4.95        = ( ~ P
% 8.69/4.95          & Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6253_of__bool__less__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 8.69/4.95        = ( ~ P
% 8.69/4.95          & Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6254_of__bool__less__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 8.69/4.95        = ( ~ P
% 8.69/4.95          & Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6255_of__bool__less__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 8.69/4.95        = ( ~ P
% 8.69/4.95          & Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6256_of__bool__less__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 8.69/4.95        = ( ~ P
% 8.69/4.95          & Q ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6257_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n1201886186963655149omplex @ P )
% 8.69/4.95          = one_one_complex )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6258_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n3304061248610475627l_real @ P )
% 8.69/4.95          = one_one_real )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6259_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 8.69/4.95          = one_one_rat )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6260_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 8.69/4.95          = one_one_nat )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6261_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n2684676970156552555ol_int @ P )
% 8.69/4.95          = one_one_int )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6262_of__bool__eq__1__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ( zero_n356916108424825756nteger @ P )
% 8.69/4.95          = one_one_Code_integer )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6263_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n1201886186963655149omplex @ $true )
% 8.69/4.95      = one_one_complex ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6264_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n3304061248610475627l_real @ $true )
% 8.69/4.95      = one_one_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6265_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n2052037380579107095ol_rat @ $true )
% 8.69/4.95      = one_one_rat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6266_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n2687167440665602831ol_nat @ $true )
% 8.69/4.95      = one_one_nat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6267_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n2684676970156552555ol_int @ $true )
% 8.69/4.95      = one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6268_of__bool__eq_I2_J,axiom,
% 8.69/4.95      ( ( zero_n356916108424825756nteger @ $true )
% 8.69/4.95      = one_one_Code_integer ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6269_signed__take__bit__of__0,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 8.69/4.95        = zero_zero_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6270_replicate__eq__replicate,axiom,
% 8.69/4.95      ! [M: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 8.69/4.95        ( ( ( replicate_VEBT_VEBT @ M @ X )
% 8.69/4.95          = ( replicate_VEBT_VEBT @ N @ Y ) )
% 8.69/4.95        = ( ( M = N )
% 8.69/4.95          & ( ( M != zero_zero_nat )
% 8.69/4.95           => ( X = Y ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6271_abs__bool__eq,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 8.69/4.95        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6272_abs__bool__eq,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 8.69/4.95        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6273_abs__bool__eq,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 8.69/4.95        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6274_abs__bool__eq,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 8.69/4.95        = ( zero_n356916108424825756nteger @ P ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6275_zdvd1__eq,axiom,
% 8.69/4.95      ! [X: int] :
% 8.69/4.95        ( ( dvd_dvd_int @ X @ one_one_int )
% 8.69/4.95        = ( ( abs_abs_int @ X )
% 8.69/4.95          = one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6276_length__replicate,axiom,
% 8.69/4.95      ! [N: nat,X: vEBT_VEBT] :
% 8.69/4.95        ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.69/4.95        = N ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6277_length__replicate,axiom,
% 8.69/4.95      ! [N: nat,X: $o] :
% 8.69/4.95        ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 8.69/4.95        = N ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6278_length__replicate,axiom,
% 8.69/4.95      ! [N: nat,X: nat] :
% 8.69/4.95        ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 8.69/4.95        = N ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6279_length__replicate,axiom,
% 8.69/4.95      ! [N: nat,X: int] :
% 8.69/4.95        ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 8.69/4.95        = N ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6280_arctan__eq__zero__iff,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ( arctan @ X )
% 8.69/4.95          = zero_zero_real )
% 8.69/4.95        = ( X = zero_zero_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6281_arctan__zero__zero,axiom,
% 8.69/4.95      ( ( arctan @ zero_zero_real )
% 8.69/4.95      = zero_zero_real ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6282_of__bool__or__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n2687167440665602831ol_nat
% 8.69/4.95          @ ( P
% 8.69/4.95            | Q ) )
% 8.69/4.95        = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6283_of__bool__or__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n2684676970156552555ol_int
% 8.69/4.95          @ ( P
% 8.69/4.95            | Q ) )
% 8.69/4.95        = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6284_of__bool__or__iff,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n356916108424825756nteger
% 8.69/4.95          @ ( P
% 8.69/4.95            | Q ) )
% 8.69/4.95        = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6285_triangle__0,axiom,
% 8.69/4.95      ( ( nat_triangle @ zero_zero_nat )
% 8.69/4.95      = zero_zero_nat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6286_zero__less__of__bool__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6287_zero__less__of__bool__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6288_zero__less__of__bool__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6289_zero__less__of__bool__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6290_zero__less__of__bool__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 8.69/4.95        = P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6291_of__bool__less__one__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6292_of__bool__less__one__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6293_of__bool__less__one__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6294_of__bool__less__one__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6295_of__bool__less__one__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 8.69/4.95        = ~ P ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6296_of__bool__not__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( zero_n1201886186963655149omplex @ ~ P )
% 8.69/4.95        = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6297_of__bool__not__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( zero_n3304061248610475627l_real @ ~ P )
% 8.69/4.95        = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6298_of__bool__not__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 8.69/4.95        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6299_of__bool__not__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 8.69/4.95        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6300_of__bool__not__iff,axiom,
% 8.69/4.95      ! [P: $o] :
% 8.69/4.95        ( ( zero_n356916108424825756nteger @ ~ P )
% 8.69/4.95        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6301_Suc__0__mod__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/4.95        = ( zero_n2687167440665602831ol_nat
% 8.69/4.95          @ ( N
% 8.69/4.95           != ( suc @ zero_zero_nat ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6302_zabs__less__one__iff,axiom,
% 8.69/4.95      ! [Z: int] :
% 8.69/4.95        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 8.69/4.95        = ( Z = zero_zero_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6303_signed__take__bit__Suc__1,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 8.69/4.95        = one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6304_signed__take__bit__of__minus__1,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.95        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6305_signed__take__bit__of__minus__1,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.95        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6306_signed__take__bit__numeral__of__1,axiom,
% 8.69/4.95      ! [K: num] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 8.69/4.95        = one_one_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6307_Ball__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: int,P: int > $o] :
% 8.69/4.95        ( ( ! [X3: int] :
% 8.69/4.95              ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 8.69/4.95             => ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6308_Ball__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: nat,P: nat > $o] :
% 8.69/4.95        ( ( ! [X3: nat] :
% 8.69/4.95              ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 8.69/4.95             => ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6309_Ball__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 8.69/4.95        ( ( ! [X3: vEBT_VEBT] :
% 8.69/4.95              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 8.69/4.95             => ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6310_Bex__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: int,P: int > $o] :
% 8.69/4.95        ( ( ? [X3: int] :
% 8.69/4.95              ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 8.69/4.95              & ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6311_Bex__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: nat,P: nat > $o] :
% 8.69/4.95        ( ( ? [X3: nat] :
% 8.69/4.95              ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 8.69/4.95              & ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6312_Bex__set__replicate,axiom,
% 8.69/4.95      ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 8.69/4.95        ( ( ? [X3: vEBT_VEBT] :
% 8.69/4.95              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 8.69/4.95              & ( P @ X3 ) ) )
% 8.69/4.95        = ( ( P @ A )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6313_in__set__replicate,axiom,
% 8.69/4.95      ! [X: complex,N: nat,Y: complex] :
% 8.69/4.95        ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6314_in__set__replicate,axiom,
% 8.69/4.95      ! [X: real,N: nat,Y: real] :
% 8.69/4.95        ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6315_in__set__replicate,axiom,
% 8.69/4.95      ! [X: set_nat,N: nat,Y: set_nat] :
% 8.69/4.95        ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6316_in__set__replicate,axiom,
% 8.69/4.95      ! [X: int,N: nat,Y: int] :
% 8.69/4.95        ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6317_in__set__replicate,axiom,
% 8.69/4.95      ! [X: nat,N: nat,Y: nat] :
% 8.69/4.95        ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6318_in__set__replicate,axiom,
% 8.69/4.95      ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 8.69/4.95        ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 8.69/4.95        = ( ( X = Y )
% 8.69/4.95          & ( N != zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6319_zero__less__arctan__iff,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 8.69/4.95        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6320_arctan__less__zero__iff,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 8.69/4.95        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6321_nth__replicate,axiom,
% 8.69/4.95      ! [I: nat,N: nat,X: nat] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I )
% 8.69/4.95          = X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6322_nth__replicate,axiom,
% 8.69/4.95      ! [I: nat,N: nat,X: int] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( nth_int @ ( replicate_int @ N @ X ) @ I )
% 8.69/4.95          = X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6323_nth__replicate,axiom,
% 8.69/4.95      ! [I: nat,N: nat,X: vEBT_VEBT] :
% 8.69/4.95        ( ( ord_less_nat @ I @ N )
% 8.69/4.95       => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I )
% 8.69/4.95          = X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6324_arctan__le__zero__iff,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 8.69/4.95        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6325_zero__le__arctan__iff,axiom,
% 8.69/4.95      ! [X: real] :
% 8.69/4.95        ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 8.69/4.95        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6326_triangle__Suc,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( nat_triangle @ ( suc @ N ) )
% 8.69/4.95        = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6327_signed__take__bit__Suc__minus__bit0,axiom,
% 8.69/4.95      ! [N: nat,K: num] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/4.95        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6328_signed__take__bit__Suc__bit0,axiom,
% 8.69/4.95      ! [N: nat,K: num] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 8.69/4.95        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6329_odd__of__bool__self,axiom,
% 8.69/4.95      ! [P5: $o] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P5 ) ) )
% 8.69/4.95        = P5 ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6330_odd__of__bool__self,axiom,
% 8.69/4.95      ! [P5: $o] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P5 ) ) )
% 8.69/4.95        = P5 ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6331_odd__of__bool__self,axiom,
% 8.69/4.95      ! [P5: $o] :
% 8.69/4.95        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P5 ) ) )
% 8.69/4.95        = P5 ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6332_of__bool__half__eq__0,axiom,
% 8.69/4.95      ! [B: $o] :
% 8.69/4.95        ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.95        = zero_zero_nat ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6333_of__bool__half__eq__0,axiom,
% 8.69/4.95      ! [B: $o] :
% 8.69/4.95        ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.95        = zero_zero_int ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6334_of__bool__half__eq__0,axiom,
% 8.69/4.95      ! [B: $o] :
% 8.69/4.95        ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.95        = zero_z3403309356797280102nteger ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6335_signed__take__bit__0,axiom,
% 8.69/4.95      ! [A: code_integer] :
% 8.69/4.95        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 8.69/4.95        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6336_signed__take__bit__0,axiom,
% 8.69/4.95      ! [A: int] :
% 8.69/4.95        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 8.69/4.95        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6337_one__div__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6338_one__div__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6339_one__div__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6340_bits__1__div__exp,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6341_bits__1__div__exp,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6342_bits__1__div__exp,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6343_one__mod__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6344_one__mod__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6345_one__mod__2__pow__eq,axiom,
% 8.69/4.95      ! [N: nat] :
% 8.69/4.95        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.95        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6346_dvd__antisym,axiom,
% 8.69/4.95      ! [M: nat,N: nat] :
% 8.69/4.95        ( ( dvd_dvd_nat @ M @ N )
% 8.69/4.95       => ( ( dvd_dvd_nat @ N @ M )
% 8.69/4.95         => ( M = N ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6347_of__bool__eq__iff,axiom,
% 8.69/4.95      ! [P5: $o,Q2: $o] :
% 8.69/4.95        ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 8.69/4.95          = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 8.69/4.95        = ( P5 = Q2 ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6348_of__bool__eq__iff,axiom,
% 8.69/4.95      ! [P5: $o,Q2: $o] :
% 8.69/4.95        ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 8.69/4.95          = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 8.69/4.95        = ( P5 = Q2 ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6349_of__bool__eq__iff,axiom,
% 8.69/4.95      ! [P5: $o,Q2: $o] :
% 8.69/4.95        ( ( ( zero_n356916108424825756nteger @ P5 )
% 8.69/4.95          = ( zero_n356916108424825756nteger @ Q2 ) )
% 8.69/4.95        = ( P5 = Q2 ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6350_zabs__def,axiom,
% 8.69/4.95      ( abs_abs_int
% 8.69/4.95      = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6351_of__bool__conj,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n3304061248610475627l_real
% 8.69/4.95          @ ( P
% 8.69/4.95            & Q ) )
% 8.69/4.95        = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6352_of__bool__conj,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n2052037380579107095ol_rat
% 8.69/4.95          @ ( P
% 8.69/4.95            & Q ) )
% 8.69/4.95        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 8.69/4.95  
% 8.69/4.95  thf(fact_6353_of__bool__conj,axiom,
% 8.69/4.95      ! [P: $o,Q: $o] :
% 8.69/4.95        ( ( zero_n2687167440665602831ol_nat
% 8.69/4.95          @ ( P
% 8.69/4.95            & Q ) )
% 8.69/4.95        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6354_of__bool__conj,axiom,
% 8.69/4.96      ! [P: $o,Q: $o] :
% 8.69/4.96        ( ( zero_n2684676970156552555ol_int
% 8.69/4.96          @ ( P
% 8.69/4.96            & Q ) )
% 8.69/4.96        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6355_of__bool__conj,axiom,
% 8.69/4.96      ! [P: $o,Q: $o] :
% 8.69/4.96        ( ( zero_n356916108424825756nteger
% 8.69/4.96          @ ( P
% 8.69/4.96            & Q ) )
% 8.69/4.96        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6356_signed__take__bit__mult,axiom,
% 8.69/4.96      ! [N: nat,K: int,L2: int] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 8.69/4.96        = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6357_signed__take__bit__add,axiom,
% 8.69/4.96      ! [N: nat,K: int,L2: int] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 8.69/4.96        = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6358_uminus__int__code_I1_J,axiom,
% 8.69/4.96      ( ( uminus_uminus_int @ zero_zero_int )
% 8.69/4.96      = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6359_abs__div,axiom,
% 8.69/4.96      ! [Y: int,X: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ Y @ X )
% 8.69/4.96       => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 8.69/4.96          = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6360_signed__take__bit__diff,axiom,
% 8.69/4.96      ! [N: nat,K: int,L2: int] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 8.69/4.96        = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6361_arctan__monotone_H,axiom,
% 8.69/4.96      ! [X: real,Y: real] :
% 8.69/4.96        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.96       => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6362_arctan__le__iff,axiom,
% 8.69/4.96      ! [X: real,Y: real] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 8.69/4.96        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6363_zero__less__eq__of__bool,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6364_zero__less__eq__of__bool,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6365_zero__less__eq__of__bool,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6366_zero__less__eq__of__bool,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6367_zero__less__eq__of__bool,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6368_of__bool__less__eq__one,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6369_of__bool__less__eq__one,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6370_of__bool__less__eq__one,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6371_of__bool__less__eq__one,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6372_of__bool__less__eq__one,axiom,
% 8.69/4.96      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6373_of__bool__def,axiom,
% 8.69/4.96      ( zero_n1201886186963655149omplex
% 8.69/4.96      = ( ^ [P2: $o] : ( if_complex @ P2 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6374_of__bool__def,axiom,
% 8.69/4.96      ( zero_n3304061248610475627l_real
% 8.69/4.96      = ( ^ [P2: $o] : ( if_real @ P2 @ one_one_real @ zero_zero_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6375_of__bool__def,axiom,
% 8.69/4.96      ( zero_n2052037380579107095ol_rat
% 8.69/4.96      = ( ^ [P2: $o] : ( if_rat @ P2 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6376_of__bool__def,axiom,
% 8.69/4.96      ( zero_n2687167440665602831ol_nat
% 8.69/4.96      = ( ^ [P2: $o] : ( if_nat @ P2 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6377_of__bool__def,axiom,
% 8.69/4.96      ( zero_n2684676970156552555ol_int
% 8.69/4.96      = ( ^ [P2: $o] : ( if_int @ P2 @ one_one_int @ zero_zero_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6378_of__bool__def,axiom,
% 8.69/4.96      ( zero_n356916108424825756nteger
% 8.69/4.96      = ( ^ [P2: $o] : ( if_Code_integer @ P2 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6379_split__of__bool,axiom,
% 8.69/4.96      ! [P: complex > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_complex ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6380_split__of__bool,axiom,
% 8.69/4.96      ! [P: real > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_real ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6381_split__of__bool,axiom,
% 8.69/4.96      ! [P: rat > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_rat ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6382_split__of__bool,axiom,
% 8.69/4.96      ! [P: nat > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_nat ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_zero_nat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6383_split__of__bool,axiom,
% 8.69/4.96      ! [P: int > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_int ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_zero_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6384_split__of__bool,axiom,
% 8.69/4.96      ! [P: code_integer > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 8.69/4.96        = ( ( P5
% 8.69/4.96           => ( P @ one_one_Code_integer ) )
% 8.69/4.96          & ( ~ P5
% 8.69/4.96           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6385_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: complex > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_complex ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6386_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: real > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_real ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6387_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: rat > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_rat ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6388_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: nat > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_nat ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6389_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: int > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_int ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6390_split__of__bool__asm,axiom,
% 8.69/4.96      ! [P: code_integer > $o,P5: $o] :
% 8.69/4.96        ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 8.69/4.96        = ( ~ ( ( P5
% 8.69/4.96                & ~ ( P @ one_one_Code_integer ) )
% 8.69/4.96              | ( ~ P5
% 8.69/4.96                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6391_dvd__imp__le__int,axiom,
% 8.69/4.96      ! [I: int,D: int] :
% 8.69/4.96        ( ( I != zero_zero_int )
% 8.69/4.96       => ( ( dvd_dvd_int @ D @ I )
% 8.69/4.96         => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6392_replicate__length__same,axiom,
% 8.69/4.96      ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.69/4.96        ( ! [X6: vEBT_VEBT] :
% 8.69/4.96            ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.69/4.96           => ( X6 = X ) )
% 8.69/4.96       => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X )
% 8.69/4.96          = Xs ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6393_replicate__length__same,axiom,
% 8.69/4.96      ! [Xs: list_o,X: $o] :
% 8.69/4.96        ( ! [X6: $o] :
% 8.69/4.96            ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 8.69/4.96           => ( X6 = X ) )
% 8.69/4.96       => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X )
% 8.69/4.96          = Xs ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6394_replicate__length__same,axiom,
% 8.69/4.96      ! [Xs: list_nat,X: nat] :
% 8.69/4.96        ( ! [X6: nat] :
% 8.69/4.96            ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 8.69/4.96           => ( X6 = X ) )
% 8.69/4.96       => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X )
% 8.69/4.96          = Xs ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6395_replicate__length__same,axiom,
% 8.69/4.96      ! [Xs: list_int,X: int] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 8.69/4.96           => ( X6 = X ) )
% 8.69/4.96       => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X )
% 8.69/4.96          = Xs ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6396_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_complex,N: nat,X: complex] :
% 8.69/4.96        ( ( ( size_s3451745648224563538omplex @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: complex] :
% 8.69/4.96              ( ( member_complex @ Y5 @ ( set_complex2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_complex @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6397_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_real,N: nat,X: real] :
% 8.69/4.96        ( ( ( size_size_list_real @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: real] :
% 8.69/4.96              ( ( member_real @ Y5 @ ( set_real2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_real @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6398_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_set_nat,N: nat,X: set_nat] :
% 8.69/4.96        ( ( ( size_s3254054031482475050et_nat @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: set_nat] :
% 8.69/4.96              ( ( member_set_nat @ Y5 @ ( set_set_nat2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6399_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 8.69/4.96        ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: vEBT_VEBT] :
% 8.69/4.96              ( ( member_VEBT_VEBT @ Y5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6400_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_o,N: nat,X: $o] :
% 8.69/4.96        ( ( ( size_size_list_o @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: $o] :
% 8.69/4.96              ( ( member_o @ Y5 @ ( set_o2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_o @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6401_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_nat,N: nat,X: nat] :
% 8.69/4.96        ( ( ( size_size_list_nat @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: nat] :
% 8.69/4.96              ( ( member_nat @ Y5 @ ( set_nat2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_nat @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6402_replicate__eqI,axiom,
% 8.69/4.96      ! [Xs: list_int,N: nat,X: int] :
% 8.69/4.96        ( ( ( size_size_list_int @ Xs )
% 8.69/4.96          = N )
% 8.69/4.96       => ( ! [Y5: int] :
% 8.69/4.96              ( ( member_int @ Y5 @ ( set_int2 @ Xs ) )
% 8.69/4.96             => ( Y5 = X ) )
% 8.69/4.96         => ( Xs
% 8.69/4.96            = ( replicate_int @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6403_abs__zmult__eq__1,axiom,
% 8.69/4.96      ! [M: int,N: int] :
% 8.69/4.96        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 8.69/4.96          = one_one_int )
% 8.69/4.96       => ( ( abs_abs_int @ M )
% 8.69/4.96          = one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6404_subset__Compl__self__eq,axiom,
% 8.69/4.96      ! [A2: set_nat] :
% 8.69/4.96        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 8.69/4.96        = ( A2 = bot_bot_set_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6405_subset__Compl__self__eq,axiom,
% 8.69/4.96      ! [A2: set_real] :
% 8.69/4.96        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 8.69/4.96        = ( A2 = bot_bot_set_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6406_subset__Compl__self__eq,axiom,
% 8.69/4.96      ! [A2: set_int] :
% 8.69/4.96        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 8.69/4.96        = ( A2 = bot_bot_set_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6407_zmult__eq__1__iff,axiom,
% 8.69/4.96      ! [M: int,N: int] :
% 8.69/4.96        ( ( ( times_times_int @ M @ N )
% 8.69/4.96          = one_one_int )
% 8.69/4.96        = ( ( ( M = one_one_int )
% 8.69/4.96            & ( N = one_one_int ) )
% 8.69/4.96          | ( ( M
% 8.69/4.96              = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.96            & ( N
% 8.69/4.96              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6408_pos__zmult__eq__1__iff__lemma,axiom,
% 8.69/4.96      ! [M: int,N: int] :
% 8.69/4.96        ( ( ( times_times_int @ M @ N )
% 8.69/4.96          = one_one_int )
% 8.69/4.96       => ( ( M = one_one_int )
% 8.69/4.96          | ( M
% 8.69/4.96            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6409_minus__int__code_I2_J,axiom,
% 8.69/4.96      ! [L2: int] :
% 8.69/4.96        ( ( minus_minus_int @ zero_zero_int @ L2 )
% 8.69/4.96        = ( uminus_uminus_int @ L2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6410_zmod__zminus1__not__zero,axiom,
% 8.69/4.96      ! [K: int,L2: int] :
% 8.69/4.96        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 8.69/4.96         != zero_zero_int )
% 8.69/4.96       => ( ( modulo_modulo_int @ K @ L2 )
% 8.69/4.96         != zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6411_zmod__zminus2__not__zero,axiom,
% 8.69/4.96      ! [K: int,L2: int] :
% 8.69/4.96        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 8.69/4.96         != zero_zero_int )
% 8.69/4.96       => ( ( modulo_modulo_int @ K @ L2 )
% 8.69/4.96         != zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6412_signed__take__bit__int__less__eq__self__iff,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 8.69/4.96        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6413_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 8.69/4.96      ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6414_signed__take__bit__int__greater__self__iff,axiom,
% 8.69/4.96      ! [K: int,N: nat] :
% 8.69/4.96        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 8.69/4.96        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6415_signed__take__bit__int__eq__self,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 8.69/4.96       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 8.69/4.96            = K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6416_signed__take__bit__int__eq__self__iff,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 8.69/4.96          = K )
% 8.69/4.96        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 8.69/4.96          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6417_zdvd__mult__cancel1,axiom,
% 8.69/4.96      ! [M: int,N: int] :
% 8.69/4.96        ( ( M != zero_zero_int )
% 8.69/4.96       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 8.69/4.96          = ( ( abs_abs_int @ N )
% 8.69/4.96            = one_one_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6418_abs__mod__less,axiom,
% 8.69/4.96      ! [L2: int,K: int] :
% 8.69/4.96        ( ( L2 != zero_zero_int )
% 8.69/4.96       => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6419_zmod__zminus1__eq__if,axiom,
% 8.69/4.96      ! [A: int,B: int] :
% 8.69/4.96        ( ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96            = zero_zero_int )
% 8.69/4.96         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.96            = zero_zero_int ) )
% 8.69/4.96        & ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96           != zero_zero_int )
% 8.69/4.96         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.96            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6420_zmod__zminus2__eq__if,axiom,
% 8.69/4.96      ! [A: int,B: int] :
% 8.69/4.96        ( ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96            = zero_zero_int )
% 8.69/4.96         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.96            = zero_zero_int ) )
% 8.69/4.96        & ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96           != zero_zero_int )
% 8.69/4.96         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.96            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6421_even__abs__add__iff,axiom,
% 8.69/4.96      ! [K: int,L2: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 8.69/4.96        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6422_even__add__abs__iff,axiom,
% 8.69/4.96      ! [K: int,L2: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 8.69/4.96        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6423_signed__take__bit__int__greater__eq,axiom,
% 8.69/4.96      ! [K: int,N: nat] :
% 8.69/4.96        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.96       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6424_verit__less__mono__div__int2,axiom,
% 8.69/4.96      ! [A2: int,B3: int,N: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ A2 @ B3 )
% 8.69/4.96       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 8.69/4.96         => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6425_div__eq__minus1,axiom,
% 8.69/4.96      ! [B: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/4.96       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.69/4.96          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6426_of__bool__odd__eq__mod__2,axiom,
% 8.69/4.96      ! [A: nat] :
% 8.69/4.96        ( ( zero_n2687167440665602831ol_nat
% 8.69/4.96          @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.96        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6427_of__bool__odd__eq__mod__2,axiom,
% 8.69/4.96      ! [A: int] :
% 8.69/4.96        ( ( zero_n2684676970156552555ol_int
% 8.69/4.96          @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.96        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6428_of__bool__odd__eq__mod__2,axiom,
% 8.69/4.96      ! [A: code_integer] :
% 8.69/4.96        ( ( zero_n356916108424825756nteger
% 8.69/4.96          @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 8.69/4.96        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6429_signed__take__bit__int__less__exp,axiom,
% 8.69/4.96      ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6430_even__signed__take__bit__iff,axiom,
% 8.69/4.96      ! [M: nat,A: code_integer] :
% 8.69/4.96        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 8.69/4.96        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6431_even__signed__take__bit__iff,axiom,
% 8.69/4.96      ! [M: nat,A: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 8.69/4.96        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6432_minus__mod__int__eq,axiom,
% 8.69/4.96      ! [L2: int,K: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 8.69/4.96       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 8.69/4.96          = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6433_zmod__minus1,axiom,
% 8.69/4.96      ! [B: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/4.96       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.69/4.96          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6434_zdiv__zminus1__eq__if,axiom,
% 8.69/4.96      ! [B: int,A: int] :
% 8.69/4.96        ( ( B != zero_zero_int )
% 8.69/4.96       => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96              = zero_zero_int )
% 8.69/4.96           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.96              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.69/4.96          & ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96             != zero_zero_int )
% 8.69/4.96           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.69/4.96              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6435_zdiv__zminus2__eq__if,axiom,
% 8.69/4.96      ! [B: int,A: int] :
% 8.69/4.96        ( ( B != zero_zero_int )
% 8.69/4.96       => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96              = zero_zero_int )
% 8.69/4.96           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.96              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.69/4.96          & ( ( ( modulo_modulo_int @ A @ B )
% 8.69/4.96             != zero_zero_int )
% 8.69/4.96           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.69/4.96              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6436_zminus1__lemma,axiom,
% 8.69/4.96      ! [A: int,B: int,Q2: int,R: int] :
% 8.69/4.96        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.96       => ( ( B != zero_zero_int )
% 8.69/4.96         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6437_bits__induct,axiom,
% 8.69/4.96      ! [P: nat > $o,A: nat] :
% 8.69/4.96        ( ! [A5: nat] :
% 8.69/4.96            ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.96              = A5 )
% 8.69/4.96           => ( P @ A5 ) )
% 8.69/4.96       => ( ! [A5: nat,B5: $o] :
% 8.69/4.96              ( ( P @ A5 )
% 8.69/4.96             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.96                  = A5 )
% 8.69/4.96               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 8.69/4.96         => ( P @ A ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6438_bits__induct,axiom,
% 8.69/4.96      ! [P: int > $o,A: int] :
% 8.69/4.96        ( ! [A5: int] :
% 8.69/4.96            ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96              = A5 )
% 8.69/4.96           => ( P @ A5 ) )
% 8.69/4.96       => ( ! [A5: int,B5: $o] :
% 8.69/4.96              ( ( P @ A5 )
% 8.69/4.96             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = A5 )
% 8.69/4.96               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 8.69/4.96         => ( P @ A ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6439_bits__induct,axiom,
% 8.69/4.96      ! [P: code_integer > $o,A: code_integer] :
% 8.69/4.96        ( ! [A5: code_integer] :
% 8.69/4.96            ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.96              = A5 )
% 8.69/4.96           => ( P @ A5 ) )
% 8.69/4.96       => ( ! [A5: code_integer,B5: $o] :
% 8.69/4.96              ( ( P @ A5 )
% 8.69/4.96             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.96                  = A5 )
% 8.69/4.96               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 8.69/4.96         => ( P @ A ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6440_nat__intermed__int__val,axiom,
% 8.69/4.96      ! [M: nat,N: nat,F: nat > int,K: int] :
% 8.69/4.96        ( ! [I4: nat] :
% 8.69/4.96            ( ( ( ord_less_eq_nat @ M @ I4 )
% 8.69/4.96              & ( ord_less_nat @ I4 @ N ) )
% 8.69/4.96           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 8.69/4.96       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.96         => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 8.69/4.96           => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.69/4.96             => ? [I4: nat] :
% 8.69/4.96                  ( ( ord_less_eq_nat @ M @ I4 )
% 8.69/4.96                  & ( ord_less_eq_nat @ I4 @ N )
% 8.69/4.96                  & ( ( F @ I4 )
% 8.69/4.96                    = K ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6441_decr__lemma,axiom,
% 8.69/4.96      ! [D: int,X: int,Z: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ D )
% 8.69/4.96       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6442_incr__lemma,axiom,
% 8.69/4.96      ! [D: int,Z: int,X: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ D )
% 8.69/4.96       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6443_signed__take__bit__int__less__self__iff,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6444_signed__take__bit__int__greater__eq__self__iff,axiom,
% 8.69/4.96      ! [K: int,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 8.69/4.96        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6445_minus__1__div__exp__eq__int,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6446_div__pos__neg__trivial,axiom,
% 8.69/4.96      ! [K: int,L2: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ K )
% 8.69/4.96       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 8.69/4.96         => ( ( divide_divide_int @ K @ L2 )
% 8.69/4.96            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6447_compl__mono,axiom,
% 8.69/4.96      ! [X: set_int,Y: set_int] :
% 8.69/4.96        ( ( ord_less_eq_set_int @ X @ Y )
% 8.69/4.96       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6448_compl__le__swap1,axiom,
% 8.69/4.96      ! [Y: set_int,X: set_int] :
% 8.69/4.96        ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 8.69/4.96       => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6449_compl__le__swap2,axiom,
% 8.69/4.96      ! [Y: set_int,X: set_int] :
% 8.69/4.96        ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 8.69/4.96       => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6450_exp__mod__exp,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6451_exp__mod__exp,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6452_exp__mod__exp,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6453_nat__ivt__aux,axiom,
% 8.69/4.96      ! [N: nat,F: nat > int,K: int] :
% 8.69/4.96        ( ! [I4: nat] :
% 8.69/4.96            ( ( ord_less_nat @ I4 @ N )
% 8.69/4.96           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 8.69/4.96       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 8.69/4.96         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.69/4.96           => ? [I4: nat] :
% 8.69/4.96                ( ( ord_less_eq_nat @ I4 @ N )
% 8.69/4.96                & ( ( F @ I4 )
% 8.69/4.96                  = K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6454_signed__take__bit__int__less__eq,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 8.69/4.96       => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6455_int__bit__induct,axiom,
% 8.69/4.96      ! [P: int > $o,K: int] :
% 8.69/4.96        ( ( P @ zero_zero_int )
% 8.69/4.96       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.96         => ( ! [K3: int] :
% 8.69/4.96                ( ( P @ K3 )
% 8.69/4.96               => ( ( K3 != zero_zero_int )
% 8.69/4.96                 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.96           => ( ! [K3: int] :
% 8.69/4.96                  ( ( P @ K3 )
% 8.69/4.96                 => ( ( K3
% 8.69/4.96                     != ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.96                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 8.69/4.96             => ( P @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6456_nat0__intermed__int__val,axiom,
% 8.69/4.96      ! [N: nat,F: nat > int,K: int] :
% 8.69/4.96        ( ! [I4: nat] :
% 8.69/4.96            ( ( ord_less_nat @ I4 @ N )
% 8.69/4.96           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 8.69/4.96       => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 8.69/4.96         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 8.69/4.96           => ? [I4: nat] :
% 8.69/4.96                ( ( ord_less_eq_nat @ I4 @ N )
% 8.69/4.96                & ( ( F @ I4 )
% 8.69/4.96                  = K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6457_exp__div__exp__eq,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_times_nat
% 8.69/4.96          @ ( zero_n2687167440665602831ol_nat
% 8.69/4.96            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 8.69/4.96               != zero_zero_nat )
% 8.69/4.96              & ( ord_less_eq_nat @ N @ M ) ) )
% 8.69/4.96          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6458_exp__div__exp__eq,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_times_int
% 8.69/4.96          @ ( zero_n2684676970156552555ol_int
% 8.69/4.96            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 8.69/4.96               != zero_zero_int )
% 8.69/4.96              & ( ord_less_eq_nat @ N @ M ) ) )
% 8.69/4.96          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6459_exp__div__exp__eq,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.96        = ( times_3573771949741848930nteger
% 8.69/4.96          @ ( zero_n356916108424825756nteger
% 8.69/4.96            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 8.69/4.96               != zero_z3403309356797280102nteger )
% 8.69/4.96              & ( ord_less_eq_nat @ N @ M ) ) )
% 8.69/4.96          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6460_arctan__add,axiom,
% 8.69/4.96      ! [X: real,Y: real] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.96       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.96         => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 8.69/4.96            = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6461_vebt__buildup_Osimps_I3_J,axiom,
% 8.69/4.96      ! [Va: nat] :
% 8.69/4.96        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.69/4.96         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 8.69/4.96            = ( 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 ) ) ) ) ) ) )
% 8.69/4.96        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.69/4.96         => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 8.69/4.96            = ( 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 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6462_diff__shunt__var,axiom,
% 8.69/4.96      ! [X: set_real,Y: set_real] :
% 8.69/4.96        ( ( ( minus_minus_set_real @ X @ Y )
% 8.69/4.96          = bot_bot_set_real )
% 8.69/4.96        = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6463_diff__shunt__var,axiom,
% 8.69/4.96      ! [X: set_nat,Y: set_nat] :
% 8.69/4.96        ( ( ( minus_minus_set_nat @ X @ Y )
% 8.69/4.96          = bot_bot_set_nat )
% 8.69/4.96        = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6464_diff__shunt__var,axiom,
% 8.69/4.96      ! [X: set_int,Y: set_int] :
% 8.69/4.96        ( ( ( minus_minus_set_int @ X @ Y )
% 8.69/4.96          = bot_bot_set_int )
% 8.69/4.96        = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6465_signed__take__bit__Suc,axiom,
% 8.69/4.96      ! [N: nat,A: code_integer] :
% 8.69/4.96        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 8.69/4.96        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6466_signed__take__bit__Suc,axiom,
% 8.69/4.96      ! [N: nat,A: int] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 8.69/4.96        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6467_Divides_Oadjust__div__eq,axiom,
% 8.69/4.96      ! [Q2: int,R: int] :
% 8.69/4.96        ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 8.69/4.96        = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6468_vebt__buildup_Opelims,axiom,
% 8.69/4.96      ! [X: nat,Y: vEBT_VEBT] :
% 8.69/4.96        ( ( ( vEBT_vebt_buildup @ X )
% 8.69/4.96          = Y )
% 8.69/4.96       => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 8.69/4.96         => ( ( ( X = zero_zero_nat )
% 8.69/4.96             => ( ( Y
% 8.69/4.96                  = ( vEBT_Leaf @ $false @ $false ) )
% 8.69/4.96               => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 8.69/4.96           => ( ( ( X
% 8.69/4.96                  = ( suc @ zero_zero_nat ) )
% 8.69/4.96               => ( ( Y
% 8.69/4.96                    = ( vEBT_Leaf @ $false @ $false ) )
% 8.69/4.96                 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 8.69/4.96             => ~ ! [Va2: nat] :
% 8.69/4.96                    ( ( X
% 8.69/4.96                      = ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.96                   => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.96                         => ( Y
% 8.69/4.96                            = ( 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 ) ) ) ) ) ) )
% 8.69/4.96                        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 8.69/4.96                         => ( Y
% 8.69/4.96                            = ( 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 ) ) ) ) ) ) ) ) )
% 8.69/4.96                     => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6469_option_Osize__gen_I2_J,axiom,
% 8.69/4.96      ! [X: nat > nat,X22: nat] :
% 8.69/4.96        ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 8.69/4.96        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6470_option_Osize__gen_I2_J,axiom,
% 8.69/4.96      ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 8.69/4.96        ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 8.69/4.96        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6471_option_Osize__gen_I2_J,axiom,
% 8.69/4.96      ! [X: num > nat,X22: num] :
% 8.69/4.96        ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 8.69/4.96        = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6472_set__decode__0,axiom,
% 8.69/4.96      ! [X: nat] :
% 8.69/4.96        ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 8.69/4.96        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6473_set__decode__Suc,axiom,
% 8.69/4.96      ! [N: nat,X: nat] :
% 8.69/4.96        ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 8.69/4.96        = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6474_add__scale__eq__noteq,axiom,
% 8.69/4.96      ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
% 8.69/4.96        ( ( R != zero_zero_complex )
% 8.69/4.96       => ( ( ( A = B )
% 8.69/4.96            & ( C != D ) )
% 8.69/4.96         => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 8.69/4.96           != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6475_add__scale__eq__noteq,axiom,
% 8.69/4.96      ! [R: real,A: real,B: real,C: real,D: real] :
% 8.69/4.96        ( ( R != zero_zero_real )
% 8.69/4.96       => ( ( ( A = B )
% 8.69/4.96            & ( C != D ) )
% 8.69/4.96         => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 8.69/4.96           != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6476_add__scale__eq__noteq,axiom,
% 8.69/4.96      ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 8.69/4.96        ( ( R != zero_zero_rat )
% 8.69/4.96       => ( ( ( A = B )
% 8.69/4.96            & ( C != D ) )
% 8.69/4.96         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 8.69/4.96           != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6477_add__scale__eq__noteq,axiom,
% 8.69/4.96      ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 8.69/4.96        ( ( R != zero_zero_nat )
% 8.69/4.96       => ( ( ( A = B )
% 8.69/4.96            & ( C != D ) )
% 8.69/4.96         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 8.69/4.96           != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6478_add__scale__eq__noteq,axiom,
% 8.69/4.96      ! [R: int,A: int,B: int,C: int,D: int] :
% 8.69/4.96        ( ( R != zero_zero_int )
% 8.69/4.96       => ( ( ( A = B )
% 8.69/4.96            & ( C != D ) )
% 8.69/4.96         => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 8.69/4.96           != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6479_set__decode__zero,axiom,
% 8.69/4.96      ( ( nat_set_decode @ zero_zero_nat )
% 8.69/4.96      = bot_bot_set_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6480_signed__take__bit__minus,axiom,
% 8.69/4.96      ! [N: nat,K: int] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 8.69/4.96        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6481_subset__decode__imp__le,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 8.69/4.96       => ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6482_add__0__iff,axiom,
% 8.69/4.96      ! [B: complex,A: complex] :
% 8.69/4.96        ( ( B
% 8.69/4.96          = ( plus_plus_complex @ B @ A ) )
% 8.69/4.96        = ( A = zero_zero_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6483_add__0__iff,axiom,
% 8.69/4.96      ! [B: real,A: real] :
% 8.69/4.96        ( ( B
% 8.69/4.96          = ( plus_plus_real @ B @ A ) )
% 8.69/4.96        = ( A = zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6484_add__0__iff,axiom,
% 8.69/4.96      ! [B: rat,A: rat] :
% 8.69/4.96        ( ( B
% 8.69/4.96          = ( plus_plus_rat @ B @ A ) )
% 8.69/4.96        = ( A = zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6485_add__0__iff,axiom,
% 8.69/4.96      ! [B: nat,A: nat] :
% 8.69/4.96        ( ( B
% 8.69/4.96          = ( plus_plus_nat @ B @ A ) )
% 8.69/4.96        = ( A = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6486_add__0__iff,axiom,
% 8.69/4.96      ! [B: int,A: int] :
% 8.69/4.96        ( ( B
% 8.69/4.96          = ( plus_plus_int @ B @ A ) )
% 8.69/4.96        = ( A = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6487_crossproduct__eq,axiom,
% 8.69/4.96      ! [W: real,Y: real,X: real,Z: real] :
% 8.69/4.96        ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 8.69/4.96          = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 8.69/4.96        = ( ( W = X )
% 8.69/4.96          | ( Y = Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6488_crossproduct__eq,axiom,
% 8.69/4.96      ! [W: rat,Y: rat,X: rat,Z: rat] :
% 8.69/4.96        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 8.69/4.96          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 8.69/4.96        = ( ( W = X )
% 8.69/4.96          | ( Y = Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6489_crossproduct__eq,axiom,
% 8.69/4.96      ! [W: nat,Y: nat,X: nat,Z: nat] :
% 8.69/4.96        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 8.69/4.96          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 8.69/4.96        = ( ( W = X )
% 8.69/4.96          | ( Y = Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6490_crossproduct__eq,axiom,
% 8.69/4.96      ! [W: int,Y: int,X: int,Z: int] :
% 8.69/4.96        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 8.69/4.96          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 8.69/4.96        = ( ( W = X )
% 8.69/4.96          | ( Y = Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6491_crossproduct__noteq,axiom,
% 8.69/4.96      ! [A: real,B: real,C: real,D: real] :
% 8.69/4.96        ( ( ( A != B )
% 8.69/4.96          & ( C != D ) )
% 8.69/4.96        = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 8.69/4.96         != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6492_crossproduct__noteq,axiom,
% 8.69/4.96      ! [A: rat,B: rat,C: rat,D: rat] :
% 8.69/4.96        ( ( ( A != B )
% 8.69/4.96          & ( C != D ) )
% 8.69/4.96        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 8.69/4.96         != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6493_crossproduct__noteq,axiom,
% 8.69/4.96      ! [A: nat,B: nat,C: nat,D: nat] :
% 8.69/4.96        ( ( ( A != B )
% 8.69/4.96          & ( C != D ) )
% 8.69/4.96        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 8.69/4.96         != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6494_crossproduct__noteq,axiom,
% 8.69/4.96      ! [A: int,B: int,C: int,D: int] :
% 8.69/4.96        ( ( ( A != B )
% 8.69/4.96          & ( C != D ) )
% 8.69/4.96        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 8.69/4.96         != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6495_option_Osize__gen_I1_J,axiom,
% 8.69/4.96      ! [X: nat > nat] :
% 8.69/4.96        ( ( size_option_nat @ X @ none_nat )
% 8.69/4.96        = ( suc @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6496_option_Osize__gen_I1_J,axiom,
% 8.69/4.96      ! [X: product_prod_nat_nat > nat] :
% 8.69/4.96        ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 8.69/4.96        = ( suc @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6497_option_Osize__gen_I1_J,axiom,
% 8.69/4.96      ! [X: num > nat] :
% 8.69/4.96        ( ( size_option_num @ X @ none_num )
% 8.69/4.96        = ( suc @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6498_set__decode__def,axiom,
% 8.69/4.96      ( nat_set_decode
% 8.69/4.96      = ( ^ [X3: nat] :
% 8.69/4.96            ( collect_nat
% 8.69/4.96            @ ^ [N2: nat] :
% 8.69/4.96                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6499_signed__take__bit__Suc__minus__bit1,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/4.96        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6500_infinite__int__iff__unbounded__le,axiom,
% 8.69/4.96      ! [S2: set_int] :
% 8.69/4.96        ( ( ~ ( finite_finite_int @ S2 ) )
% 8.69/4.96        = ( ! [M3: int] :
% 8.69/4.96            ? [N2: int] :
% 8.69/4.96              ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N2 ) )
% 8.69/4.96              & ( member_int @ N2 @ S2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6501_of__int__code__if,axiom,
% 8.69/4.96      ( ring_1_of_int_real
% 8.69/4.96      = ( ^ [K2: int] :
% 8.69/4.96            ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 8.69/4.96            @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/4.96              @ ( if_real
% 8.69/4.96                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = zero_zero_int )
% 8.69/4.96                @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96                @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6502_of__int__code__if,axiom,
% 8.69/4.96      ( ring_1_of_int_int
% 8.69/4.96      = ( ^ [K2: int] :
% 8.69/4.96            ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 8.69/4.96            @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/4.96              @ ( if_int
% 8.69/4.96                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = zero_zero_int )
% 8.69/4.96                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96                @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6503_of__int__code__if,axiom,
% 8.69/4.96      ( ring_17405671764205052669omplex
% 8.69/4.96      = ( ^ [K2: int] :
% 8.69/4.96            ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 8.69/4.96            @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/4.96              @ ( if_complex
% 8.69/4.96                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = zero_zero_int )
% 8.69/4.96                @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96                @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6504_of__int__code__if,axiom,
% 8.69/4.96      ( ring_18347121197199848620nteger
% 8.69/4.96      = ( ^ [K2: int] :
% 8.69/4.96            ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 8.69/4.96            @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/4.96              @ ( if_Code_integer
% 8.69/4.96                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = zero_zero_int )
% 8.69/4.96                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6505_of__int__code__if,axiom,
% 8.69/4.96      ( ring_1_of_int_rat
% 8.69/4.96      = ( ^ [K2: int] :
% 8.69/4.96            ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 8.69/4.96            @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/4.96              @ ( if_rat
% 8.69/4.96                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96                  = zero_zero_int )
% 8.69/4.96                @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96                @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6506_one__div__minus__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6507_minus__one__div__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6508_semiring__norm_I90_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( bit1 @ M )
% 8.69/4.96          = ( bit1 @ N ) )
% 8.69/4.96        = ( M = N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6509_semiring__norm_I88_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( bit0 @ M )
% 8.69/4.96       != ( bit1 @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6510_semiring__norm_I89_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( bit1 @ M )
% 8.69/4.96       != ( bit0 @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6511_semiring__norm_I84_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( one
% 8.69/4.96       != ( bit1 @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6512_semiring__norm_I86_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( bit1 @ M )
% 8.69/4.96       != one ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6513_semiring__norm_I80_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( ord_less_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6514_semiring__norm_I73_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6515_of__int__eq__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ Z )
% 8.69/4.96          = zero_zero_int )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6516_of__int__eq__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ Z )
% 8.69/4.96          = zero_zero_real )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6517_of__int__eq__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ Z )
% 8.69/4.96          = zero_zero_complex )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6518_of__int__eq__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ Z )
% 8.69/4.96          = zero_zero_rat )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6519_of__int__0__eq__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( zero_zero_int
% 8.69/4.96          = ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6520_of__int__0__eq__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( zero_zero_real
% 8.69/4.96          = ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6521_of__int__0__eq__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( zero_zero_complex
% 8.69/4.96          = ( ring_17405671764205052669omplex @ Z ) )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6522_of__int__0__eq__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( zero_zero_rat
% 8.69/4.96          = ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( Z = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6523_of__int__0,axiom,
% 8.69/4.96      ( ( ring_1_of_int_int @ zero_zero_int )
% 8.69/4.96      = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6524_of__int__0,axiom,
% 8.69/4.96      ( ( ring_1_of_int_real @ zero_zero_int )
% 8.69/4.96      = zero_zero_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6525_of__int__0,axiom,
% 8.69/4.96      ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 8.69/4.96      = zero_zero_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6526_of__int__0,axiom,
% 8.69/4.96      ( ( ring_1_of_int_rat @ zero_zero_int )
% 8.69/4.96      = zero_zero_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6527_of__int__eq__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ Z )
% 8.69/4.96          = ( numera6690914467698888265omplex @ N ) )
% 8.69/4.96        = ( Z
% 8.69/4.96          = ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6528_of__int__eq__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ Z )
% 8.69/4.96          = ( numeral_numeral_real @ N ) )
% 8.69/4.96        = ( Z
% 8.69/4.96          = ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6529_of__int__eq__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ Z )
% 8.69/4.96          = ( numeral_numeral_rat @ N ) )
% 8.69/4.96        = ( Z
% 8.69/4.96          = ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6530_of__int__eq__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ Z )
% 8.69/4.96          = ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( Z
% 8.69/4.96          = ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6531_of__int__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numera6690914467698888265omplex @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6532_of__int__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numeral_numeral_real @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6533_of__int__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numeral_numeral_rat @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6534_of__int__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numeral_numeral_int @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6535_of__int__le__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6536_of__int__le__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6537_of__int__le__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6538_of__int__less__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6539_of__int__less__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6540_of__int__less__iff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_int @ W @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6541_of__int__eq__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ Z )
% 8.69/4.96          = one_one_int )
% 8.69/4.96        = ( Z = one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6542_of__int__eq__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ Z )
% 8.69/4.96          = one_one_real )
% 8.69/4.96        = ( Z = one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6543_of__int__eq__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ Z )
% 8.69/4.96          = one_one_complex )
% 8.69/4.96        = ( Z = one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6544_of__int__eq__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ Z )
% 8.69/4.96          = one_one_rat )
% 8.69/4.96        = ( Z = one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6545_of__int__1,axiom,
% 8.69/4.96      ( ( ring_1_of_int_int @ one_one_int )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6546_of__int__1,axiom,
% 8.69/4.96      ( ( ring_1_of_int_real @ one_one_int )
% 8.69/4.96      = one_one_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6547_of__int__1,axiom,
% 8.69/4.96      ( ( ring_17405671764205052669omplex @ one_one_int )
% 8.69/4.96      = one_one_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6548_of__int__1,axiom,
% 8.69/4.96      ( ( ring_1_of_int_rat @ one_one_int )
% 8.69/4.96      = one_one_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6549_of__int__mult,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 8.69/4.96        = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6550_of__int__mult,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 8.69/4.96        = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6551_of__int__mult,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 8.69/4.96        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6552_of__int__mult,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 8.69/4.96        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6553_of__int__add,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 8.69/4.96        = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6554_of__int__add,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 8.69/4.96        = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6555_of__int__add,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 8.69/4.96        = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6556_of__int__add,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 8.69/4.96        = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6557_of__int__diff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 8.69/4.96        = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6558_of__int__diff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 8.69/4.96        = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6559_of__int__diff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 8.69/4.96        = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6560_of__int__diff,axiom,
% 8.69/4.96      ! [W: int,Z: int] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 8.69/4.96        = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6561_semiring__norm_I9_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6562_semiring__norm_I7_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6563_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ X )
% 8.69/4.96          = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 8.69/4.96        = ( X
% 8.69/4.96          = ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6564_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ X )
% 8.69/4.96          = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 8.69/4.96        = ( X
% 8.69/4.96          = ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6565_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ X )
% 8.69/4.96          = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 8.69/4.96        = ( X
% 8.69/4.96          = ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6566_of__int__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ X )
% 8.69/4.96          = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 8.69/4.96        = ( X
% 8.69/4.96          = ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6567_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 8.69/4.96          = ( ring_1_of_int_rat @ X ) )
% 8.69/4.96        = ( ( power_power_int @ B @ W )
% 8.69/4.96          = X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6568_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 8.69/4.96          = ( ring_1_of_int_real @ X ) )
% 8.69/4.96        = ( ( power_power_int @ B @ W )
% 8.69/4.96          = X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6569_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 8.69/4.96          = ( ring_1_of_int_int @ X ) )
% 8.69/4.96        = ( ( power_power_int @ B @ W )
% 8.69/4.96          = X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6570_of__int__eq__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 8.69/4.96          = ( ring_17405671764205052669omplex @ X ) )
% 8.69/4.96        = ( ( power_power_int @ B @ W )
% 8.69/4.96          = X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6571_of__int__power,axiom,
% 8.69/4.96      ! [Z: int,N: nat] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 8.69/4.96        = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6572_of__int__power,axiom,
% 8.69/4.96      ! [Z: int,N: nat] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 8.69/4.96        = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6573_of__int__power,axiom,
% 8.69/4.96      ! [Z: int,N: nat] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 8.69/4.96        = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6574_of__int__power,axiom,
% 8.69/4.96      ! [Z: int,N: nat] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 8.69/4.96        = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6575_semiring__norm_I15_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6576_semiring__norm_I14_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6577_semiring__norm_I81_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( ord_less_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6578_semiring__norm_I72_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6579_semiring__norm_I77_J,axiom,
% 8.69/4.96      ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6580_semiring__norm_I70_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6581_zdiv__numeral__Bit1,axiom,
% 8.69/4.96      ! [V: num,W: num] :
% 8.69/4.96        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 8.69/4.96        = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6582_semiring__norm_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 8.69/4.96        = ( bit1 @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6583_semiring__norm_I4_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 8.69/4.96        = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6584_semiring__norm_I5_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 8.69/4.96        = ( bit1 @ M ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6585_semiring__norm_I8_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 8.69/4.96        = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6586_semiring__norm_I10_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6587_semiring__norm_I16_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6588_semiring__norm_I79_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96        = ( ord_less_eq_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6589_semiring__norm_I74_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( ord_less_num @ M @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6590_of__int__0__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6591_of__int__0__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6592_of__int__0__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6593_of__int__le__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6594_of__int__le__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6595_of__int__le__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6596_of__int__0__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6597_of__int__0__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6598_of__int__0__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6599_of__int__less__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 8.69/4.96        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6600_of__int__less__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 8.69/4.96        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6601_of__int__less__0__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 8.69/4.96        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6602_of__int__le__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6603_of__int__le__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6604_of__int__le__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6605_of__int__numeral__le__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6606_of__int__numeral__le__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6607_of__int__numeral__le__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6608_of__int__numeral__less__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6609_of__int__numeral__less__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6610_of__int__numeral__less__iff,axiom,
% 8.69/4.96      ! [N: num,Z: int] :
% 8.69/4.96        ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6611_of__int__less__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.96        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6612_of__int__less__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 8.69/4.96        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6613_of__int__less__numeral__iff,axiom,
% 8.69/4.96      ! [Z: int,N: num] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6614_of__int__1__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6615_of__int__1__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6616_of__int__1__le__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6617_of__int__le__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6618_of__int__le__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6619_of__int__le__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 8.69/4.96        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6620_of__int__less__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 8.69/4.96        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6621_of__int__less__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 8.69/4.96        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6622_of__int__less__1__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 8.69/4.96        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6623_of__int__1__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 8.69/4.96        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6624_of__int__1__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 8.69/4.96        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6625_of__int__1__less__iff,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 8.69/4.96        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6626_dvd__numeral__simp,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6627_dvd__numeral__simp,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.69/4.96        = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6628_dvd__numeral__simp,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.96        = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6629_divmod__algorithm__code_I2_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ M @ one )
% 8.69/4.96        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6630_divmod__algorithm__code_I2_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( unique5055182867167087721od_nat @ M @ one )
% 8.69/4.96        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6631_divmod__algorithm__code_I2_J,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( unique3479559517661332726nteger @ M @ one )
% 8.69/4.96        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6632_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ Y )
% 8.69/4.96          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6633_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ Y )
% 8.69/4.96          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6634_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ Y )
% 8.69/4.96          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6635_of__int__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ Y )
% 8.69/4.96          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6636_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 8.69/4.96          = ( ring_17405671764205052669omplex @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6637_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 8.69/4.96          = ( ring_1_of_int_real @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6638_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 8.69/4.96          = ( ring_1_of_int_rat @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6639_numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.96          = ( ring_1_of_int_int @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6640_of__int__le__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6641_of__int__le__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6642_of__int__le__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6643_of__int__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6644_of__int__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6645_of__int__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6646_of__int__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6647_of__int__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6648_of__int__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: int,B: int,W: nat] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 8.69/4.96        = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6649_of__int__less__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6650_of__int__less__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6651_of__int__less__of__int__power__cancel__iff,axiom,
% 8.69/4.96      ! [B: int,W: nat,X: int] :
% 8.69/4.96        ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6652_div__Suc__eq__div__add3,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.69/4.96        = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6653_Suc__div__eq__add3__div__numeral,axiom,
% 8.69/4.96      ! [M: nat,V: num] :
% 8.69/4.96        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 8.69/4.96        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6654_divmod__algorithm__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 8.69/4.96        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6655_divmod__algorithm__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 8.69/4.96        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6656_divmod__algorithm__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6657_mod__Suc__eq__mod__add3,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.69/4.96        = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6658_Suc__mod__eq__add3__mod__numeral,axiom,
% 8.69/4.96      ! [M: nat,V: num] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 8.69/4.96        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6659_divmod__algorithm__code_I4_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 8.69/4.96        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6660_divmod__algorithm__code_I4_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 8.69/4.96        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6661_divmod__algorithm__code_I4_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 8.69/4.96        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6662_minus__numeral__div__numeral,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6663_numeral__div__minus__numeral,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6664_of__int__le__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6665_of__int__le__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6666_of__int__le__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6667_numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6668_numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6669_numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6670_of__int__less__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6671_of__int__less__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6672_of__int__less__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6673_numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6674_numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6675_numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6676_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_real @ Y )
% 8.69/4.96          = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6677_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_int @ Y )
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6678_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_17405671764205052669omplex @ Y )
% 8.69/4.96          = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6679_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_18347121197199848620nteger @ Y )
% 8.69/4.96          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6680_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [Y: int,X: num,N: nat] :
% 8.69/4.96        ( ( ( ring_1_of_int_rat @ Y )
% 8.69/4.96          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 8.69/4.96        = ( Y
% 8.69/4.96          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6681_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 8.69/4.96          = ( ring_1_of_int_real @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6682_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = ( ring_1_of_int_int @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6683_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 8.69/4.96          = ( ring_17405671764205052669omplex @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6684_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 8.69/4.96          = ( ring_18347121197199848620nteger @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6685_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,Y: int] :
% 8.69/4.96        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 8.69/4.96          = ( ring_1_of_int_rat @ Y ) )
% 8.69/4.96        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 8.69/4.96          = Y ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6686_zmod__numeral__Bit1,axiom,
% 8.69/4.96      ! [V: num,W: num] :
% 8.69/4.96        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 8.69/4.96        = ( 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 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6687_divmod__algorithm__code_I8_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6688_divmod__algorithm__code_I8_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6689_divmod__algorithm__code_I8_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_num @ M @ N )
% 8.69/4.96         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6690_divmod__algorithm__code_I7_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6691_divmod__algorithm__code_I7_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6692_divmod__algorithm__code_I7_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 8.69/4.96        & ( ~ ( ord_less_eq_num @ M @ N )
% 8.69/4.96         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 8.69/4.96            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6693_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6694_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6695_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6696_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.69/4.96        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6697_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6698_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6699_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6700_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6701_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6702_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6703_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6704_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 8.69/4.96      ! [A: int,X: num,N: nat] :
% 8.69/4.96        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 8.69/4.96        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6705_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6706_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6707_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6708_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 8.69/4.96      ! [X: num,N: nat,A: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 8.69/4.96        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6709_signed__take__bit__Suc__bit1,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6710_mult__of__int__commute,axiom,
% 8.69/4.96      ! [X: int,Y: complex] :
% 8.69/4.96        ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 8.69/4.96        = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6711_mult__of__int__commute,axiom,
% 8.69/4.96      ! [X: int,Y: real] :
% 8.69/4.96        ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 8.69/4.96        = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6712_mult__of__int__commute,axiom,
% 8.69/4.96      ! [X: int,Y: rat] :
% 8.69/4.96        ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 8.69/4.96        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6713_mult__of__int__commute,axiom,
% 8.69/4.96      ! [X: int,Y: int] :
% 8.69/4.96        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 8.69/4.96        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6714_verit__eq__simplify_I14_J,axiom,
% 8.69/4.96      ! [X22: num,X32: num] :
% 8.69/4.96        ( ( bit0 @ X22 )
% 8.69/4.96       != ( bit1 @ X32 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6715_verit__eq__simplify_I12_J,axiom,
% 8.69/4.96      ! [X32: num] :
% 8.69/4.96        ( one
% 8.69/4.96       != ( bit1 @ X32 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6716_num_Oexhaust,axiom,
% 8.69/4.96      ! [Y: num] :
% 8.69/4.96        ( ( Y != one )
% 8.69/4.96       => ( ! [X23: num] :
% 8.69/4.96              ( Y
% 8.69/4.96             != ( bit0 @ X23 ) )
% 8.69/4.96         => ~ ! [X33: num] :
% 8.69/4.96                ( Y
% 8.69/4.96               != ( bit1 @ X33 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6717_xor__num_Ocases,axiom,
% 8.69/4.96      ! [X: product_prod_num_num] :
% 8.69/4.96        ( ( X
% 8.69/4.96         != ( product_Pair_num_num @ one @ one ) )
% 8.69/4.96       => ( ! [N3: num] :
% 8.69/4.96              ( X
% 8.69/4.96             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 8.69/4.96         => ( ! [N3: num] :
% 8.69/4.96                ( X
% 8.69/4.96               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 8.69/4.96           => ( ! [M4: num] :
% 8.69/4.96                  ( X
% 8.69/4.96                 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 8.69/4.96             => ( ! [M4: num,N3: num] :
% 8.69/4.96                    ( X
% 8.69/4.96                   != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 8.69/4.96               => ( ! [M4: num,N3: num] :
% 8.69/4.96                      ( X
% 8.69/4.96                     != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 8.69/4.96                 => ( ! [M4: num] :
% 8.69/4.96                        ( X
% 8.69/4.96                       != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 8.69/4.96                   => ( ! [M4: num,N3: num] :
% 8.69/4.96                          ( X
% 8.69/4.96                         != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 8.69/4.96                     => ~ ! [M4: num,N3: num] :
% 8.69/4.96                            ( X
% 8.69/4.96                           != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6718_numeral__Bit1,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6719_numeral__Bit1,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6720_numeral__Bit1,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6721_numeral__Bit1,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6722_numeral__Bit1,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6723_eval__nat__numeral_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.69/4.96        = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6724_cong__exp__iff__simps_I10_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6725_cong__exp__iff__simps_I10_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6726_cong__exp__iff__simps_I10_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6727_cong__exp__iff__simps_I12_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6728_cong__exp__iff__simps_I12_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6729_cong__exp__iff__simps_I12_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6730_cong__exp__iff__simps_I13_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.69/4.96          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6731_cong__exp__iff__simps_I13_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 8.69/4.96          = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6732_cong__exp__iff__simps_I13_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 8.69/4.96          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6733_power__minus__Bit1,axiom,
% 8.69/4.96      ! [X: real,K: num] :
% 8.69/4.96        ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6734_power__minus__Bit1,axiom,
% 8.69/4.96      ! [X: int,K: num] :
% 8.69/4.96        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6735_power__minus__Bit1,axiom,
% 8.69/4.96      ! [X: complex,K: num] :
% 8.69/4.96        ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6736_power__minus__Bit1,axiom,
% 8.69/4.96      ! [X: code_integer,K: num] :
% 8.69/4.96        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6737_power__minus__Bit1,axiom,
% 8.69/4.96      ! [X: rat,K: num] :
% 8.69/4.96        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6738_real__of__int__div4,axiom,
% 8.69/4.96      ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6739_real__of__int__div,axiom,
% 8.69/4.96      ! [D: int,N: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ D @ N )
% 8.69/4.96       => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 8.69/4.96          = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6740_numeral__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6741_numeral__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6742_numeral__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6743_numeral__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6744_numeral__code_I3_J,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 8.69/4.96        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6745_power__numeral__odd,axiom,
% 8.69/4.96      ! [Z: complex,W: num] :
% 8.69/4.96        ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 8.69/4.96        = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6746_power__numeral__odd,axiom,
% 8.69/4.96      ! [Z: real,W: num] :
% 8.69/4.96        ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 8.69/4.96        = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6747_power__numeral__odd,axiom,
% 8.69/4.96      ! [Z: rat,W: num] :
% 8.69/4.96        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 8.69/4.96        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6748_power__numeral__odd,axiom,
% 8.69/4.96      ! [Z: nat,W: num] :
% 8.69/4.96        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 8.69/4.96        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6749_power__numeral__odd,axiom,
% 8.69/4.96      ! [Z: int,W: num] :
% 8.69/4.96        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 8.69/4.96        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6750_of__int__nonneg,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6751_of__int__nonneg,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6752_of__int__nonneg,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6753_of__int__leD,axiom,
% 8.69/4.96      ! [N: int,X: code_integer] :
% 8.69/4.96        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6754_of__int__leD,axiom,
% 8.69/4.96      ! [N: int,X: real] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6755_of__int__leD,axiom,
% 8.69/4.96      ! [N: int,X: rat] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6756_of__int__leD,axiom,
% 8.69/4.96      ! [N: int,X: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6757_of__int__pos,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6758_of__int__pos,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6759_of__int__pos,axiom,
% 8.69/4.96      ! [Z: int] :
% 8.69/4.96        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/4.96       => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6760_of__int__lessD,axiom,
% 8.69/4.96      ! [N: int,X: code_integer] :
% 8.69/4.96        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6761_of__int__lessD,axiom,
% 8.69/4.96      ! [N: int,X: real] :
% 8.69/4.96        ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6762_of__int__lessD,axiom,
% 8.69/4.96      ! [N: int,X: rat] :
% 8.69/4.96        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6763_of__int__lessD,axiom,
% 8.69/4.96      ! [N: int,X: int] :
% 8.69/4.96        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 8.69/4.96       => ( ( N = zero_zero_int )
% 8.69/4.96          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6764_of__int__neg__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6765_of__int__neg__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6766_of__int__neg__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6767_of__int__neg__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6768_of__int__neg__numeral,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6769_numeral__Bit1__div__2,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.96        = ( numeral_numeral_nat @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6770_numeral__Bit1__div__2,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.96        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6771_odd__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6772_odd__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6773_odd__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6774_cong__exp__iff__simps_I3_J,axiom,
% 8.69/4.96      ! [N: num,Q2: num] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6775_cong__exp__iff__simps_I3_J,axiom,
% 8.69/4.96      ! [N: num,Q2: num] :
% 8.69/4.96        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6776_cong__exp__iff__simps_I3_J,axiom,
% 8.69/4.96      ! [N: num,Q2: num] :
% 8.69/4.96        ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96       != zero_z3403309356797280102nteger ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6777_power3__eq__cube,axiom,
% 8.69/4.96      ! [A: complex] :
% 8.69/4.96        ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96        = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6778_power3__eq__cube,axiom,
% 8.69/4.96      ! [A: real] :
% 8.69/4.96        ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96        = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6779_power3__eq__cube,axiom,
% 8.69/4.96      ! [A: rat] :
% 8.69/4.96        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6780_power3__eq__cube,axiom,
% 8.69/4.96      ! [A: nat] :
% 8.69/4.96        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6781_power3__eq__cube,axiom,
% 8.69/4.96      ! [A: int] :
% 8.69/4.96        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6782_numeral__3__eq__3,axiom,
% 8.69/4.96      ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 8.69/4.96      = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6783_Suc3__eq__add__3,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( suc @ ( suc @ ( suc @ N ) ) )
% 8.69/4.96        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6784_int__le__real__less,axiom,
% 8.69/4.96      ( ord_less_eq_int
% 8.69/4.96      = ( ^ [N2: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6785_int__less__real__le,axiom,
% 8.69/4.96      ( ord_less_int
% 8.69/4.96      = ( ^ [N2: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6786_real__of__int__div__aux,axiom,
% 8.69/4.96      ! [X: int,D: int] :
% 8.69/4.96        ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 8.69/4.96        = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6787_num_Osize_I6_J,axiom,
% 8.69/4.96      ! [X32: num] :
% 8.69/4.96        ( ( size_size_num @ ( bit1 @ X32 ) )
% 8.69/4.96        = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6788_cong__exp__iff__simps_I7_J,axiom,
% 8.69/4.96      ! [Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.69/4.96          = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6789_cong__exp__iff__simps_I7_J,axiom,
% 8.69/4.96      ! [Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 8.69/4.96          = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6790_cong__exp__iff__simps_I7_J,axiom,
% 8.69/4.96      ! [Q2: num,N: num] :
% 8.69/4.96        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 8.69/4.96          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6791_cong__exp__iff__simps_I11_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num] :
% 8.69/4.96        ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.69/4.96          = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6792_cong__exp__iff__simps_I11_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num] :
% 8.69/4.96        ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 8.69/4.96          = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6793_cong__exp__iff__simps_I11_J,axiom,
% 8.69/4.96      ! [M: num,Q2: num] :
% 8.69/4.96        ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 8.69/4.96          = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 8.69/4.96        = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 8.69/4.96          = zero_z3403309356797280102nteger ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6794_Suc__div__eq__add3__div,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 8.69/4.96        = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6795_real__of__int__div2,axiom,
% 8.69/4.96      ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6796_Suc__mod__eq__add3__mod,axiom,
% 8.69/4.96      ! [M: nat,N: nat] :
% 8.69/4.96        ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 8.69/4.96        = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6797_real__of__int__div3,axiom,
% 8.69/4.96      ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6798_divmod__int__def,axiom,
% 8.69/4.96      ( unique5052692396658037445od_int
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6799_divmod__def,axiom,
% 8.69/4.96      ( unique5052692396658037445od_int
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6800_divmod__def,axiom,
% 8.69/4.96      ( unique5055182867167087721od_nat
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6801_divmod__def,axiom,
% 8.69/4.96      ( unique3479559517661332726nteger
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6802_even__of__int__iff,axiom,
% 8.69/4.96      ! [K: int] :
% 8.69/4.96        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 8.69/4.96        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6803_even__of__int__iff,axiom,
% 8.69/4.96      ! [K: int] :
% 8.69/4.96        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 8.69/4.96        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6804_mod__exhaust__less__4,axiom,
% 8.69/4.96      ! [M: nat] :
% 8.69/4.96        ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.96          = zero_zero_nat )
% 8.69/4.96        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.96          = one_one_nat )
% 8.69/4.96        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.96          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.96        | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.96          = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6805_infinite__nat__iff__unbounded,axiom,
% 8.69/4.96      ! [S2: set_nat] :
% 8.69/4.96        ( ( ~ ( finite_finite_nat @ S2 ) )
% 8.69/4.96        = ( ! [M3: nat] :
% 8.69/4.96            ? [N2: nat] :
% 8.69/4.96              ( ( ord_less_nat @ M3 @ N2 )
% 8.69/4.96              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6806_unbounded__k__infinite,axiom,
% 8.69/4.96      ! [K: nat,S2: set_nat] :
% 8.69/4.96        ( ! [M4: nat] :
% 8.69/4.96            ( ( ord_less_nat @ K @ M4 )
% 8.69/4.96           => ? [N7: nat] :
% 8.69/4.96                ( ( ord_less_nat @ M4 @ N7 )
% 8.69/4.96                & ( member_nat @ N7 @ S2 ) ) )
% 8.69/4.96       => ~ ( finite_finite_nat @ S2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6807_infinite__nat__iff__unbounded__le,axiom,
% 8.69/4.96      ! [S2: set_nat] :
% 8.69/4.96        ( ( ~ ( finite_finite_nat @ S2 ) )
% 8.69/4.96        = ( ! [M3: nat] :
% 8.69/4.96            ? [N2: nat] :
% 8.69/4.96              ( ( ord_less_eq_nat @ M3 @ N2 )
% 8.69/4.96              & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6808_odd__mod__4__div__2,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.96          = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.69/4.96       => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6809_divmod__divmod__step,axiom,
% 8.69/4.96      ( unique5055182867167087721od_nat
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6810_divmod__divmod__step,axiom,
% 8.69/4.96      ( unique5052692396658037445od_int
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6811_divmod__divmod__step,axiom,
% 8.69/4.96      ( unique3479559517661332726nteger
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6812_floor__exists,axiom,
% 8.69/4.96      ! [X: real] :
% 8.69/4.96      ? [Z5: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 8.69/4.96        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6813_floor__exists,axiom,
% 8.69/4.96      ! [X: rat] :
% 8.69/4.96      ? [Z5: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 8.69/4.96        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6814_floor__exists1,axiom,
% 8.69/4.96      ! [X: real] :
% 8.69/4.96      ? [X6: int] :
% 8.69/4.96        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X6 ) @ X )
% 8.69/4.96        & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 8.69/4.96        & ! [Y2: int] :
% 8.69/4.96            ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ X )
% 8.69/4.96              & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 8.69/4.96           => ( Y2 = X6 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6815_floor__exists1,axiom,
% 8.69/4.96      ! [X: rat] :
% 8.69/4.96      ? [X6: int] :
% 8.69/4.96        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X6 ) @ X )
% 8.69/4.96        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 8.69/4.96        & ! [Y2: int] :
% 8.69/4.96            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ X )
% 8.69/4.96              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 8.69/4.96           => ( Y2 = X6 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6816_signed__take__bit__numeral__minus__bit1,axiom,
% 8.69/4.96      ! [L2: num,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/4.96        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6817_dbl__dec__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.96      = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6818_dbl__dec__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.96      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6819_dbl__dec__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.96      = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6820_dbl__dec__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.96      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6821_dbl__dec__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.96      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6822_signed__take__bit__numeral__bit1,axiom,
% 8.69/4.96      ! [L2: num,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.69/4.96        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6823_dbl__inc__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 8.69/4.96      = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6824_dbl__inc__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 8.69/4.96      = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6825_dbl__inc__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 8.69/4.96      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6826_dbl__inc__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 8.69/4.96      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6827_dbl__dec__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 8.69/4.96      = one_one_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6828_dbl__dec__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 8.69/4.96      = one_one_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6829_dbl__dec__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 8.69/4.96      = one_one_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6830_dbl__dec__simps_I3_J,axiom,
% 8.69/4.96      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6831_pred__numeral__simps_I1_J,axiom,
% 8.69/4.96      ( ( pred_numeral @ one )
% 8.69/4.96      = zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6832_Suc__eq__numeral,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( ( suc @ N )
% 8.69/4.96          = ( numeral_numeral_nat @ K ) )
% 8.69/4.96        = ( N
% 8.69/4.96          = ( pred_numeral @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6833_eq__numeral__Suc,axiom,
% 8.69/4.96      ! [K: num,N: nat] :
% 8.69/4.96        ( ( ( numeral_numeral_nat @ K )
% 8.69/4.96          = ( suc @ N ) )
% 8.69/4.96        = ( ( pred_numeral @ K )
% 8.69/4.96          = N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6834_dbl__inc__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 8.69/4.96      = one_one_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6835_dbl__inc__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 8.69/4.96      = one_one_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6836_dbl__inc__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 8.69/4.96      = one_one_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6837_dbl__inc__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6838_dbl__inc__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.96      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6839_dbl__inc__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.96      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6840_dbl__inc__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.96      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6841_dbl__inc__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.96      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6842_dbl__inc__simps_I4_J,axiom,
% 8.69/4.96      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.96      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6843_dbl__inc__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 8.69/4.96        = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6844_dbl__inc__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 8.69/4.96        = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6845_dbl__inc__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 8.69/4.96        = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6846_dbl__inc__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6847_less__Suc__numeral,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.69/4.96        = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6848_less__numeral__Suc,axiom,
% 8.69/4.96      ! [K: num,N: nat] :
% 8.69/4.96        ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.69/4.96        = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6849_pred__numeral__simps_I3_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( pred_numeral @ ( bit1 @ K ) )
% 8.69/4.96        = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6850_le__numeral__Suc,axiom,
% 8.69/4.96      ! [K: num,N: nat] :
% 8.69/4.96        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.69/4.96        = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6851_le__Suc__numeral,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.69/4.96        = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6852_diff__numeral__Suc,axiom,
% 8.69/4.96      ! [K: num,N: nat] :
% 8.69/4.96        ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.69/4.96        = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6853_diff__Suc__numeral,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.69/4.96        = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6854_max__numeral__Suc,axiom,
% 8.69/4.96      ! [K: num,N: nat] :
% 8.69/4.96        ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.69/4.96        = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6855_max__Suc__numeral,axiom,
% 8.69/4.96      ! [N: nat,K: num] :
% 8.69/4.96        ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.69/4.96        = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6856_dbl__dec__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 8.69/4.96      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6857_dbl__dec__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 8.69/4.96      = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6858_dbl__dec__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 8.69/4.96      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6859_dbl__dec__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 8.69/4.96      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6860_dbl__dec__simps_I2_J,axiom,
% 8.69/4.96      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 8.69/4.96      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6861_dbl__dec__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6862_dbl__dec__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6863_dbl__dec__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 8.69/4.96        = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6864_dbl__dec__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.69/4.96        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6865_dbl__dec__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6866_dbl__inc__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6867_dbl__inc__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6868_dbl__inc__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 8.69/4.96        = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6869_dbl__inc__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 8.69/4.96        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6870_dbl__inc__simps_I1_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.69/4.96        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6871_signed__take__bit__numeral__bit0,axiom,
% 8.69/4.96      ! [L2: num,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 8.69/4.96        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6872_signed__take__bit__numeral__minus__bit0,axiom,
% 8.69/4.96      ! [L2: num,K: num] :
% 8.69/4.96        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/4.96        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6873_numeral__eq__Suc,axiom,
% 8.69/4.96      ( numeral_numeral_nat
% 8.69/4.96      = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6874_pred__numeral__def,axiom,
% 8.69/4.96      ( pred_numeral
% 8.69/4.96      = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6875_dbl__inc__def,axiom,
% 8.69/4.96      ( neg_nu8557863876264182079omplex
% 8.69/4.96      = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6876_dbl__inc__def,axiom,
% 8.69/4.96      ( neg_nu8295874005876285629c_real
% 8.69/4.96      = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6877_dbl__inc__def,axiom,
% 8.69/4.96      ( neg_nu5219082963157363817nc_rat
% 8.69/4.96      = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6878_dbl__inc__def,axiom,
% 8.69/4.96      ( neg_nu5851722552734809277nc_int
% 8.69/4.96      = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6879_divmod_H__nat__def,axiom,
% 8.69/4.96      ( unique5055182867167087721od_nat
% 8.69/4.96      = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6880_dbl__dec__def,axiom,
% 8.69/4.96      ( neg_nu6511756317524482435omplex
% 8.69/4.96      = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6881_dbl__dec__def,axiom,
% 8.69/4.96      ( neg_nu6075765906172075777c_real
% 8.69/4.96      = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6882_dbl__dec__def,axiom,
% 8.69/4.96      ( neg_nu3179335615603231917ec_rat
% 8.69/4.96      = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6883_dbl__dec__def,axiom,
% 8.69/4.96      ( neg_nu3811975205180677377ec_int
% 8.69/4.96      = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6884_exists__least__lemma,axiom,
% 8.69/4.96      ! [P: nat > $o] :
% 8.69/4.96        ( ~ ( P @ zero_zero_nat )
% 8.69/4.96       => ( ? [X_12: nat] : ( P @ X_12 )
% 8.69/4.96         => ? [N3: nat] :
% 8.69/4.96              ( ~ ( P @ N3 )
% 8.69/4.96              & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6885_ex__le__of__int,axiom,
% 8.69/4.96      ! [X: real] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6886_ex__le__of__int,axiom,
% 8.69/4.96      ! [X: rat] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6887_ex__of__int__less,axiom,
% 8.69/4.96      ! [X: real] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z5 ) @ X ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6888_ex__of__int__less,axiom,
% 8.69/4.96      ! [X: rat] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z5 ) @ X ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6889_ex__less__of__int,axiom,
% 8.69/4.96      ! [X: real] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6890_ex__less__of__int,axiom,
% 8.69/4.96      ! [X: rat] :
% 8.69/4.96      ? [Z5: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6891_round__unique,axiom,
% 8.69/4.96      ! [X: real,Y: int] :
% 8.69/4.96        ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 8.69/4.96       => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96         => ( ( archim8280529875227126926d_real @ X )
% 8.69/4.96            = Y ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6892_round__unique,axiom,
% 8.69/4.96      ! [X: rat,Y: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 8.69/4.96       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.96         => ( ( archim7778729529865785530nd_rat @ X )
% 8.69/4.96            = Y ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6893_round__unique_H,axiom,
% 8.69/4.96      ! [X: real,N: int] :
% 8.69/4.96        ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.96       => ( ( archim8280529875227126926d_real @ X )
% 8.69/4.96          = N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6894_round__unique_H,axiom,
% 8.69/4.96      ! [X: rat,N: int] :
% 8.69/4.96        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 8.69/4.96       => ( ( archim7778729529865785530nd_rat @ X )
% 8.69/4.96          = N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6895_of__int__round__abs__le,axiom,
% 8.69/4.96      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6896_of__int__round__abs__le,axiom,
% 8.69/4.96      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6897_of__int__round__gt,axiom,
% 8.69/4.96      ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6898_of__int__round__gt,axiom,
% 8.69/4.96      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6899_of__int__round__ge,axiom,
% 8.69/4.96      ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6900_of__int__round__ge,axiom,
% 8.69/4.96      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6901_of__int__round__le,axiom,
% 8.69/4.96      ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6902_of__int__round__le,axiom,
% 8.69/4.96      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6903_round__0,axiom,
% 8.69/4.96      ( ( archim8280529875227126926d_real @ zero_zero_real )
% 8.69/4.96      = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6904_round__0,axiom,
% 8.69/4.96      ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 8.69/4.96      = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6905_round__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 8.69/4.96        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6906_round__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 8.69/4.96        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6907_round__1,axiom,
% 8.69/4.96      ( ( archim8280529875227126926d_real @ one_one_real )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6908_round__1,axiom,
% 8.69/4.96      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6909_round__neg__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6910_round__neg__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.96        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6911_round__mono,axiom,
% 8.69/4.96      ! [X: rat,Y: rat] :
% 8.69/4.96        ( ( ord_less_eq_rat @ X @ Y )
% 8.69/4.96       => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6912_round__diff__minimal,axiom,
% 8.69/4.96      ! [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 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6913_round__diff__minimal,axiom,
% 8.69/4.96      ! [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 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6914_divmod__BitM__2__eq,axiom,
% 8.69/4.96      ! [M: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 8.69/4.96        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6915_divmod__algorithm__code_I6_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc4245557441103728435nt_int
% 8.69/4.96          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 8.69/4.96          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6916_divmod__algorithm__code_I6_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc2626176000494625587at_nat
% 8.69/4.96          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 8.69/4.96          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6917_divmod__algorithm__code_I6_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc6916734918728496179nteger
% 8.69/4.96          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 8.69/4.96          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6918_Sum__Icc__int,axiom,
% 8.69/4.96      ! [M: int,N: int] :
% 8.69/4.96        ( ( ord_less_eq_int @ M @ N )
% 8.69/4.96       => ( ( groups4538972089207619220nt_int
% 8.69/4.96            @ ^ [X3: int] : X3
% 8.69/4.96            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 8.69/4.96          = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6919_divmod__step__def,axiom,
% 8.69/4.96      ( unique5026877609467782581ep_nat
% 8.69/4.96      = ( ^ [L: num] :
% 8.69/4.96            ( produc2626176000494625587at_nat
% 8.69/4.96            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6920_divmod__step__def,axiom,
% 8.69/4.96      ( unique5024387138958732305ep_int
% 8.69/4.96      = ( ^ [L: num] :
% 8.69/4.96            ( produc4245557441103728435nt_int
% 8.69/4.96            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6921_divmod__step__def,axiom,
% 8.69/4.96      ( unique4921790084139445826nteger
% 8.69/4.96      = ( ^ [L: num] :
% 8.69/4.96            ( produc6916734918728496179nteger
% 8.69/4.96            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6922_even__set__encode__iff,axiom,
% 8.69/4.96      ! [A2: set_nat] :
% 8.69/4.96        ( ( finite_finite_nat @ A2 )
% 8.69/4.96       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 8.69/4.96          = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6923_mask__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 8.69/4.96        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6924_mask__numeral,axiom,
% 8.69/4.96      ! [N: num] :
% 8.69/4.96        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 8.69/4.96        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6925_mask__nat__positive__iff,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.69/4.96        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6926_sum_Oneutral__const,axiom,
% 8.69/4.96      ! [A2: set_int] :
% 8.69/4.96        ( ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [Uu3: int] : zero_zero_int
% 8.69/4.96          @ A2 )
% 8.69/4.96        = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6927_sum_Oneutral__const,axiom,
% 8.69/4.96      ! [A2: set_complex] :
% 8.69/4.96        ( ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [Uu3: complex] : zero_zero_complex
% 8.69/4.96          @ A2 )
% 8.69/4.96        = zero_zero_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6928_sum_Oneutral__const,axiom,
% 8.69/4.96      ! [A2: set_nat] :
% 8.69/4.96        ( ( groups3542108847815614940at_nat
% 8.69/4.96          @ ^ [Uu3: nat] : zero_zero_nat
% 8.69/4.96          @ A2 )
% 8.69/4.96        = zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6929_sum_Oneutral__const,axiom,
% 8.69/4.96      ! [A2: set_nat] :
% 8.69/4.96        ( ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [Uu3: nat] : zero_zero_real
% 8.69/4.96          @ A2 )
% 8.69/4.96        = zero_zero_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6930_case__prod__conv,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 8.69/4.96        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 8.69/4.96        = ( F @ A @ B ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6931_case__prod__conv,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 8.69/4.96        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 8.69/4.96        = ( F @ A @ B ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6932_case__prod__conv,axiom,
% 8.69/4.96      ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 8.69/4.96        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 8.69/4.96        = ( F @ A @ B ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6933_case__prod__conv,axiom,
% 8.69/4.96      ! [F: int > int > $o,A: int,B: int] :
% 8.69/4.96        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 8.69/4.96        = ( F @ A @ B ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6934_case__prod__conv,axiom,
% 8.69/4.96      ! [F: int > int > int,A: int,B: int] :
% 8.69/4.96        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 8.69/4.96        = ( F @ A @ B ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6935_sum_Oempty,axiom,
% 8.69/4.96      ! [G: nat > complex] :
% 8.69/4.96        ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 8.69/4.96        = zero_zero_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6936_sum_Oempty,axiom,
% 8.69/4.96      ! [G: nat > rat] :
% 8.69/4.96        ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 8.69/4.96        = zero_zero_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6937_sum_Oempty,axiom,
% 8.69/4.96      ! [G: nat > int] :
% 8.69/4.96        ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 8.69/4.96        = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6938_sum_Oempty,axiom,
% 8.69/4.96      ! [G: int > complex] :
% 8.69/4.96        ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 8.69/4.96        = zero_zero_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6939_sum_Oempty,axiom,
% 8.69/4.96      ! [G: int > real] :
% 8.69/4.96        ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 8.69/4.96        = zero_zero_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6940_sum_Oempty,axiom,
% 8.69/4.96      ! [G: int > rat] :
% 8.69/4.96        ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 8.69/4.96        = zero_zero_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6941_sum_Oempty,axiom,
% 8.69/4.96      ! [G: int > nat] :
% 8.69/4.96        ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 8.69/4.96        = zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6942_sum_Oempty,axiom,
% 8.69/4.96      ! [G: real > complex] :
% 8.69/4.96        ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 8.69/4.96        = zero_zero_complex ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6943_sum_Oempty,axiom,
% 8.69/4.96      ! [G: real > real] :
% 8.69/4.96        ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 8.69/4.96        = zero_zero_real ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6944_sum_Oempty,axiom,
% 8.69/4.96      ! [G: real > rat] :
% 8.69/4.96        ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 8.69/4.96        = zero_zero_rat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6945_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_nat,G: nat > complex] :
% 8.69/4.96        ( ~ ( finite_finite_nat @ A2 )
% 8.69/4.96       => ( ( groups2073611262835488442omplex @ G @ A2 )
% 8.69/4.96          = zero_zero_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6946_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_int,G: int > complex] :
% 8.69/4.96        ( ~ ( finite_finite_int @ A2 )
% 8.69/4.96       => ( ( groups3049146728041665814omplex @ G @ A2 )
% 8.69/4.96          = zero_zero_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6947_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_int,G: int > real] :
% 8.69/4.96        ( ~ ( finite_finite_int @ A2 )
% 8.69/4.96       => ( ( groups8778361861064173332t_real @ G @ A2 )
% 8.69/4.96          = zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6948_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_complex,G: complex > real] :
% 8.69/4.96        ( ~ ( finite3207457112153483333omplex @ A2 )
% 8.69/4.96       => ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.96          = zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6949_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_nat,G: nat > rat] :
% 8.69/4.96        ( ~ ( finite_finite_nat @ A2 )
% 8.69/4.96       => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 8.69/4.96          = zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6950_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_int,G: int > rat] :
% 8.69/4.96        ( ~ ( finite_finite_int @ A2 )
% 8.69/4.96       => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 8.69/4.96          = zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6951_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_complex,G: complex > rat] :
% 8.69/4.96        ( ~ ( finite3207457112153483333omplex @ A2 )
% 8.69/4.96       => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.96          = zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6952_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_int,G: int > nat] :
% 8.69/4.96        ( ~ ( finite_finite_int @ A2 )
% 8.69/4.96       => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 8.69/4.96          = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6953_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_complex,G: complex > nat] :
% 8.69/4.96        ( ~ ( finite3207457112153483333omplex @ A2 )
% 8.69/4.96       => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 8.69/4.96          = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6954_sum_Oinfinite,axiom,
% 8.69/4.96      ! [A2: set_nat,G: nat > int] :
% 8.69/4.96        ( ~ ( finite_finite_nat @ A2 )
% 8.69/4.96       => ( ( groups3539618377306564664at_int @ G @ A2 )
% 8.69/4.96          = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6955_sum__eq__0__iff,axiom,
% 8.69/4.96      ! [F3: set_int,F: int > nat] :
% 8.69/4.96        ( ( finite_finite_int @ F3 )
% 8.69/4.96       => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 8.69/4.96            = zero_zero_nat )
% 8.69/4.96          = ( ! [X3: int] :
% 8.69/4.96                ( ( member_int @ X3 @ F3 )
% 8.69/4.96               => ( ( F @ X3 )
% 8.69/4.96                  = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6956_sum__eq__0__iff,axiom,
% 8.69/4.96      ! [F3: set_complex,F: complex > nat] :
% 8.69/4.96        ( ( finite3207457112153483333omplex @ F3 )
% 8.69/4.96       => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 8.69/4.96            = zero_zero_nat )
% 8.69/4.96          = ( ! [X3: complex] :
% 8.69/4.96                ( ( member_complex @ X3 @ F3 )
% 8.69/4.96               => ( ( F @ X3 )
% 8.69/4.96                  = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6957_sum__eq__0__iff,axiom,
% 8.69/4.96      ! [F3: set_nat,F: nat > nat] :
% 8.69/4.96        ( ( finite_finite_nat @ F3 )
% 8.69/4.96       => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 8.69/4.96            = zero_zero_nat )
% 8.69/4.96          = ( ! [X3: nat] :
% 8.69/4.96                ( ( member_nat @ X3 @ F3 )
% 8.69/4.96               => ( ( F @ X3 )
% 8.69/4.96                  = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6958_mask__eq__0__iff,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( ( bit_se2002935070580805687sk_nat @ N )
% 8.69/4.96          = zero_zero_nat )
% 8.69/4.96        = ( N = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6959_mask__eq__0__iff,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( ( bit_se2000444600071755411sk_int @ N )
% 8.69/4.96          = zero_zero_int )
% 8.69/4.96        = ( N = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6960_mask__0,axiom,
% 8.69/4.96      ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 8.69/4.96      = zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6961_mask__0,axiom,
% 8.69/4.96      ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 8.69/4.96      = zero_zero_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6962_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > complex] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups5754745047067104278omplex
% 8.69/4.96                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups5754745047067104278omplex
% 8.69/4.96                @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6963_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_nat,A: nat,B: nat > complex] :
% 8.69/4.96        ( ( finite_finite_nat @ S2 )
% 8.69/4.96       => ( ( ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2073611262835488442omplex
% 8.69/4.96                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2073611262835488442omplex
% 8.69/4.96                @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6964_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > complex] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3049146728041665814omplex
% 8.69/4.96                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3049146728041665814omplex
% 8.69/4.96                @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6965_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > real] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups8097168146408367636l_real
% 8.69/4.96                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups8097168146408367636l_real
% 8.69/4.96                @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6966_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > real] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups8778361861064173332t_real
% 8.69/4.96                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups8778361861064173332t_real
% 8.69/4.96                @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6967_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_complex,A: complex,B: complex > real] :
% 8.69/4.96        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.96       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5808333547571424918x_real
% 8.69/4.96                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5808333547571424918x_real
% 8.69/4.96                @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6968_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > rat] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups1300246762558778688al_rat
% 8.69/4.96                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups1300246762558778688al_rat
% 8.69/4.96                @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6969_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_nat,A: nat,B: nat > rat] :
% 8.69/4.96        ( ( finite_finite_nat @ S2 )
% 8.69/4.96       => ( ( ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2906978787729119204at_rat
% 8.69/4.96                @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2906978787729119204at_rat
% 8.69/4.96                @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6970_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > rat] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3906332499630173760nt_rat
% 8.69/4.96                @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3906332499630173760nt_rat
% 8.69/4.96                @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6971_sum_Odelta_H,axiom,
% 8.69/4.96      ! [S2: set_complex,A: complex,B: complex > rat] :
% 8.69/4.96        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.96       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5058264527183730370ex_rat
% 8.69/4.96                @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5058264527183730370ex_rat
% 8.69/4.96                @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6972_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > complex] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups5754745047067104278omplex
% 8.69/4.96                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups5754745047067104278omplex
% 8.69/4.96                @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6973_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_nat,A: nat,B: nat > complex] :
% 8.69/4.96        ( ( finite_finite_nat @ S2 )
% 8.69/4.96       => ( ( ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2073611262835488442omplex
% 8.69/4.96                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2073611262835488442omplex
% 8.69/4.96                @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6974_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > complex] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3049146728041665814omplex
% 8.69/4.96                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3049146728041665814omplex
% 8.69/4.96                @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_complex ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6975_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > real] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups8097168146408367636l_real
% 8.69/4.96                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups8097168146408367636l_real
% 8.69/4.96                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6976_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > real] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups8778361861064173332t_real
% 8.69/4.96                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups8778361861064173332t_real
% 8.69/4.96                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6977_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_complex,A: complex,B: complex > real] :
% 8.69/4.96        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.96       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5808333547571424918x_real
% 8.69/4.96                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5808333547571424918x_real
% 8.69/4.96                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_real ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6978_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_real,A: real,B: real > rat] :
% 8.69/4.96        ( ( finite_finite_real @ S2 )
% 8.69/4.96       => ( ( ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups1300246762558778688al_rat
% 8.69/4.96                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.96           => ( ( groups1300246762558778688al_rat
% 8.69/4.96                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6979_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_nat,A: nat,B: nat > rat] :
% 8.69/4.96        ( ( finite_finite_nat @ S2 )
% 8.69/4.96       => ( ( ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2906978787729119204at_rat
% 8.69/4.96                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_nat @ A @ S2 )
% 8.69/4.96           => ( ( groups2906978787729119204at_rat
% 8.69/4.96                @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6980_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_int,A: int,B: int > rat] :
% 8.69/4.96        ( ( finite_finite_int @ S2 )
% 8.69/4.96       => ( ( ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3906332499630173760nt_rat
% 8.69/4.96                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.96           => ( ( groups3906332499630173760nt_rat
% 8.69/4.96                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6981_sum_Odelta,axiom,
% 8.69/4.96      ! [S2: set_complex,A: complex,B: complex > rat] :
% 8.69/4.96        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.96       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5058264527183730370ex_rat
% 8.69/4.96                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = ( B @ A ) ) )
% 8.69/4.96          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.96           => ( ( groups5058264527183730370ex_rat
% 8.69/4.96                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 8.69/4.96                @ S2 )
% 8.69/4.96              = zero_zero_rat ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6982_sum__abs,axiom,
% 8.69/4.96      ! [F: int > int,A2: set_int] :
% 8.69/4.96        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 8.69/4.96        @ ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6983_sum__abs,axiom,
% 8.69/4.96      ! [F: nat > real,A2: set_nat] :
% 8.69/4.96        ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 8.69/4.96        @ ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6984_set__encode__empty,axiom,
% 8.69/4.96      ( ( nat_set_encode @ bot_bot_set_nat )
% 8.69/4.96      = zero_zero_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6985_dbl__dec__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 8.69/4.96        = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6986_dbl__dec__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 8.69/4.96        = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6987_dbl__dec__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 8.69/4.96        = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6988_dbl__dec__simps_I5_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 8.69/4.96        = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6989_mask__Suc__0,axiom,
% 8.69/4.96      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 8.69/4.96      = one_one_nat ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6990_mask__Suc__0,axiom,
% 8.69/4.96      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 8.69/4.96      = one_one_int ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6991_sum__abs__ge__zero,axiom,
% 8.69/4.96      ! [F: int > int,A2: set_int] :
% 8.69/4.96        ( ord_less_eq_int @ zero_zero_int
% 8.69/4.96        @ ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6992_sum__abs__ge__zero,axiom,
% 8.69/4.96      ! [F: nat > real,A2: set_nat] :
% 8.69/4.96        ( ord_less_eq_real @ zero_zero_real
% 8.69/4.96        @ ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6993_pred__numeral__simps_I2_J,axiom,
% 8.69/4.96      ! [K: num] :
% 8.69/4.96        ( ( pred_numeral @ ( bit0 @ K ) )
% 8.69/4.96        = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6994_divmod__algorithm__code_I5_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc4245557441103728435nt_int
% 8.69/4.96          @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 8.69/4.96          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6995_divmod__algorithm__code_I5_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc2626176000494625587at_nat
% 8.69/4.96          @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 8.69/4.96          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6996_divmod__algorithm__code_I5_J,axiom,
% 8.69/4.96      ! [M: num,N: num] :
% 8.69/4.96        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 8.69/4.96        = ( produc6916734918728496179nteger
% 8.69/4.96          @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 8.69/4.96          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6997_sum_Oneutral,axiom,
% 8.69/4.96      ! [A2: set_int,G: int > int] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ( G @ X6 )
% 8.69/4.96              = zero_zero_int ) )
% 8.69/4.96       => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 8.69/4.96          = zero_zero_int ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6998_sum_Oneutral,axiom,
% 8.69/4.96      ! [A2: set_complex,G: complex > complex] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ( G @ X6 )
% 8.69/4.96              = zero_zero_complex ) )
% 8.69/4.96       => ( ( groups7754918857620584856omplex @ G @ A2 )
% 8.69/4.96          = zero_zero_complex ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_6999_sum_Oneutral,axiom,
% 8.69/4.96      ! [A2: set_nat,G: nat > nat] :
% 8.69/4.96        ( ! [X6: nat] :
% 8.69/4.96            ( ( member_nat @ X6 @ A2 )
% 8.69/4.96           => ( ( G @ X6 )
% 8.69/4.96              = zero_zero_nat ) )
% 8.69/4.96       => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 8.69/4.96          = zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7000_sum_Oneutral,axiom,
% 8.69/4.96      ! [A2: set_nat,G: nat > real] :
% 8.69/4.96        ( ! [X6: nat] :
% 8.69/4.96            ( ( member_nat @ X6 @ A2 )
% 8.69/4.96           => ( ( G @ X6 )
% 8.69/4.96              = zero_zero_real ) )
% 8.69/4.96       => ( ( groups6591440286371151544t_real @ G @ A2 )
% 8.69/4.96          = zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7001_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: real > complex,A2: set_real] :
% 8.69/4.96        ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 8.69/4.96         != zero_zero_complex )
% 8.69/4.96       => ~ ! [A5: real] :
% 8.69/4.96              ( ( member_real @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7002_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: nat > complex,A2: set_nat] :
% 8.69/4.96        ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 8.69/4.96         != zero_zero_complex )
% 8.69/4.96       => ~ ! [A5: nat] :
% 8.69/4.96              ( ( member_nat @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7003_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: int > complex,A2: set_int] :
% 8.69/4.96        ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 8.69/4.96         != zero_zero_complex )
% 8.69/4.96       => ~ ! [A5: int] :
% 8.69/4.96              ( ( member_int @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_complex ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7004_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: complex > real,A2: set_complex] :
% 8.69/4.96        ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.96         != zero_zero_real )
% 8.69/4.96       => ~ ! [A5: complex] :
% 8.69/4.96              ( ( member_complex @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7005_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: real > real,A2: set_real] :
% 8.69/4.96        ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 8.69/4.96         != zero_zero_real )
% 8.69/4.96       => ~ ! [A5: real] :
% 8.69/4.96              ( ( member_real @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7006_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: int > real,A2: set_int] :
% 8.69/4.96        ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 8.69/4.96         != zero_zero_real )
% 8.69/4.96       => ~ ! [A5: int] :
% 8.69/4.96              ( ( member_int @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_real ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7007_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: complex > rat,A2: set_complex] :
% 8.69/4.96        ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.96         != zero_zero_rat )
% 8.69/4.96       => ~ ! [A5: complex] :
% 8.69/4.96              ( ( member_complex @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7008_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: real > rat,A2: set_real] :
% 8.69/4.96        ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 8.69/4.96         != zero_zero_rat )
% 8.69/4.96       => ~ ! [A5: real] :
% 8.69/4.96              ( ( member_real @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7009_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: nat > rat,A2: set_nat] :
% 8.69/4.96        ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 8.69/4.96         != zero_zero_rat )
% 8.69/4.96       => ~ ! [A5: nat] :
% 8.69/4.96              ( ( member_nat @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7010_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.69/4.96      ! [G: int > rat,A2: set_int] :
% 8.69/4.96        ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 8.69/4.96         != zero_zero_rat )
% 8.69/4.96       => ~ ! [A5: int] :
% 8.69/4.96              ( ( member_int @ A5 @ A2 )
% 8.69/4.96             => ( ( G @ A5 )
% 8.69/4.96                = zero_zero_rat ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7011_of__int__mask__eq,axiom,
% 8.69/4.96      ! [N: nat] :
% 8.69/4.96        ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 8.69/4.96        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7012_old_Oprod_Ocase,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 8.69/4.96        ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 8.69/4.96        = ( F @ X1 @ X22 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7013_old_Oprod_Ocase,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 8.69/4.96        ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 8.69/4.96        = ( F @ X1 @ X22 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7014_old_Oprod_Ocase,axiom,
% 8.69/4.96      ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 8.69/4.96        ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 8.69/4.96        = ( F @ X1 @ X22 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7015_old_Oprod_Ocase,axiom,
% 8.69/4.96      ! [F: int > int > $o,X1: int,X22: int] :
% 8.69/4.96        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 8.69/4.96        = ( F @ X1 @ X22 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7016_old_Oprod_Ocase,axiom,
% 8.69/4.96      ! [F: int > int > int,X1: int,X22: int] :
% 8.69/4.96        ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 8.69/4.96        = ( F @ X1 @ X22 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7017_less__eq__mask,axiom,
% 8.69/4.96      ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7018_semiring__norm_I26_J,axiom,
% 8.69/4.96      ( ( bitM @ one )
% 8.69/4.96      = one ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7019_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 8.69/4.96        ( ! [I4: complex] :
% 8.69/4.96            ( ( member_complex @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7020_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_real,F: real > rat,G: real > rat] :
% 8.69/4.96        ( ! [I4: real] :
% 8.69/4.96            ( ( member_real @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7021_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 8.69/4.96        ( ! [I4: nat] :
% 8.69/4.96            ( ( member_nat @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7022_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_int,F: int > rat,G: int > rat] :
% 8.69/4.96        ( ! [I4: int] :
% 8.69/4.96            ( ( member_int @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7023_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 8.69/4.96        ( ! [I4: complex] :
% 8.69/4.96            ( ( member_complex @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7024_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_real,F: real > nat,G: real > nat] :
% 8.69/4.96        ( ! [I4: real] :
% 8.69/4.96            ( ( member_real @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7025_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_int,F: int > nat,G: int > nat] :
% 8.69/4.96        ( ! [I4: int] :
% 8.69/4.96            ( ( member_int @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7026_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_complex,F: complex > int,G: complex > int] :
% 8.69/4.96        ( ! [I4: complex] :
% 8.69/4.96            ( ( member_complex @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7027_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_real,F: real > int,G: real > int] :
% 8.69/4.96        ( ! [I4: real] :
% 8.69/4.96            ( ( member_real @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7028_sum__mono,axiom,
% 8.69/4.96      ! [K5: set_nat,F: nat > int,G: nat > int] :
% 8.69/4.96        ( ! [I4: nat] :
% 8.69/4.96            ( ( member_nat @ I4 @ K5 )
% 8.69/4.96           => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7029_sum__distrib__left,axiom,
% 8.69/4.96      ! [R: int,F: int > int,A2: set_int] :
% 8.69/4.96        ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 8.69/4.96        = ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7030_sum__distrib__left,axiom,
% 8.69/4.96      ! [R: complex,F: complex > complex,A2: set_complex] :
% 8.69/4.96        ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 8.69/4.96        = ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7031_sum__distrib__left,axiom,
% 8.69/4.96      ! [R: nat,F: nat > nat,A2: set_nat] :
% 8.69/4.96        ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 8.69/4.96        = ( groups3542108847815614940at_nat
% 8.69/4.96          @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7032_sum__distrib__left,axiom,
% 8.69/4.96      ! [R: real,F: nat > real,A2: set_nat] :
% 8.69/4.96        ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 8.69/4.96        = ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7033_sum__distrib__right,axiom,
% 8.69/4.96      ! [F: int > int,A2: set_int,R: int] :
% 8.69/4.96        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7034_sum__distrib__right,axiom,
% 8.69/4.96      ! [F: complex > complex,A2: set_complex,R: complex] :
% 8.69/4.96        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7035_sum__distrib__right,axiom,
% 8.69/4.96      ! [F: nat > nat,A2: set_nat,R: nat] :
% 8.69/4.96        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups3542108847815614940at_nat
% 8.69/4.96          @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7036_sum__distrib__right,axiom,
% 8.69/4.96      ! [F: nat > real,A2: set_nat,R: real] :
% 8.69/4.96        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7037_sum__product,axiom,
% 8.69/4.96      ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 8.69/4.96        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 8.69/4.96        = ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [I5: int] :
% 8.69/4.96              ( groups4538972089207619220nt_int
% 8.69/4.96              @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 8.69/4.96              @ B3 )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7038_sum__product,axiom,
% 8.69/4.96      ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 8.69/4.96        ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 8.69/4.96        = ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [I5: complex] :
% 8.69/4.96              ( groups7754918857620584856omplex
% 8.69/4.96              @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 8.69/4.96              @ B3 )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7039_sum__product,axiom,
% 8.69/4.96      ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 8.69/4.96        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 8.69/4.96        = ( groups3542108847815614940at_nat
% 8.69/4.96          @ ^ [I5: nat] :
% 8.69/4.96              ( groups3542108847815614940at_nat
% 8.69/4.96              @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 8.69/4.96              @ B3 )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7040_sum__product,axiom,
% 8.69/4.96      ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 8.69/4.96        ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 8.69/4.96        = ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [I5: nat] :
% 8.69/4.96              ( groups6591440286371151544t_real
% 8.69/4.96              @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 8.69/4.96              @ B3 )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7041_sum_Odistrib,axiom,
% 8.69/4.96      ! [G: int > int,H2: int > int,A2: set_int] :
% 8.69/4.96        ( ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7042_sum_Odistrib,axiom,
% 8.69/4.96      ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 8.69/4.96        ( ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [X3: complex] : ( plus_plus_complex @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7043_sum_Odistrib,axiom,
% 8.69/4.96      ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 8.69/4.96        ( ( groups3542108847815614940at_nat
% 8.69/4.96          @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7044_sum_Odistrib,axiom,
% 8.69/4.96      ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 8.69/4.96        ( ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [X3: nat] : ( plus_plus_real @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7045_sum__subtractf,axiom,
% 8.69/4.96      ! [F: int > int,G: int > int,A2: set_int] :
% 8.69/4.96        ( ( groups4538972089207619220nt_int
% 8.69/4.96          @ ^ [X3: int] : ( minus_minus_int @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7046_sum__subtractf,axiom,
% 8.69/4.96      ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 8.69/4.96        ( ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [X3: complex] : ( minus_minus_complex @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7047_sum__subtractf,axiom,
% 8.69/4.96      ! [F: nat > real,G: nat > real,A2: set_nat] :
% 8.69/4.96        ( ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [X3: nat] : ( minus_minus_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.96          @ A2 )
% 8.69/4.96        = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7048_sum__divide__distrib,axiom,
% 8.69/4.96      ! [F: complex > complex,A2: set_complex,R: complex] :
% 8.69/4.96        ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups7754918857620584856omplex
% 8.69/4.96          @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7049_sum__divide__distrib,axiom,
% 8.69/4.96      ! [F: nat > real,A2: set_nat,R: real] :
% 8.69/4.96        ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 8.69/4.96        = ( groups6591440286371151544t_real
% 8.69/4.96          @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 8.69/4.96          @ A2 ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7050_mod__sum__eq,axiom,
% 8.69/4.96      ! [F: int > int,A: int,A2: set_int] :
% 8.69/4.96        ( ( modulo_modulo_int
% 8.69/4.96          @ ( groups4538972089207619220nt_int
% 8.69/4.96            @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 8.69/4.96            @ A2 )
% 8.69/4.96          @ A )
% 8.69/4.96        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7051_mod__sum__eq,axiom,
% 8.69/4.96      ! [F: nat > nat,A: nat,A2: set_nat] :
% 8.69/4.96        ( ( modulo_modulo_nat
% 8.69/4.96          @ ( groups3542108847815614940at_nat
% 8.69/4.96            @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 8.69/4.96            @ A2 )
% 8.69/4.96          @ A )
% 8.69/4.96        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7052_case__prodE2,axiom,
% 8.69/4.96      ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 8.69/4.96        ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 8.69/4.96       => ~ ! [X6: nat,Y5: nat] :
% 8.69/4.96              ( ( Z
% 8.69/4.96                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 8.69/4.96             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7053_case__prodE2,axiom,
% 8.69/4.96      ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 8.69/4.96        ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 8.69/4.96       => ~ ! [X6: nat,Y5: nat] :
% 8.69/4.96              ( ( Z
% 8.69/4.96                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 8.69/4.96             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7054_case__prodE2,axiom,
% 8.69/4.96      ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 8.69/4.96        ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 8.69/4.96       => ~ ! [X6: int,Y5: int] :
% 8.69/4.96              ( ( Z
% 8.69/4.96                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.96             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7055_case__prodE2,axiom,
% 8.69/4.96      ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 8.69/4.96        ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 8.69/4.96       => ~ ! [X6: int,Y5: int] :
% 8.69/4.96              ( ( Z
% 8.69/4.96                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.96             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7056_case__prodE2,axiom,
% 8.69/4.96      ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 8.69/4.96        ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 8.69/4.96       => ~ ! [X6: int,Y5: int] :
% 8.69/4.96              ( ( Z
% 8.69/4.96                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.96             => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7057_case__prod__eta,axiom,
% 8.69/4.96      ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 8.69/4.96        ( ( produc27273713700761075at_nat
% 8.69/4.96          @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 8.69/4.96        = F ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7058_case__prod__eta,axiom,
% 8.69/4.96      ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 8.69/4.96        ( ( produc8739625826339149834_nat_o
% 8.69/4.96          @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 8.69/4.96        = F ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7059_case__prod__eta,axiom,
% 8.69/4.96      ! [F: product_prod_int_int > product_prod_int_int] :
% 8.69/4.96        ( ( produc4245557441103728435nt_int
% 8.69/4.96          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 8.69/4.96        = F ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7060_case__prod__eta,axiom,
% 8.69/4.96      ! [F: product_prod_int_int > $o] :
% 8.69/4.96        ( ( produc4947309494688390418_int_o
% 8.69/4.96          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 8.69/4.96        = F ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7061_case__prod__eta,axiom,
% 8.69/4.96      ! [F: product_prod_int_int > int] :
% 8.69/4.96        ( ( produc8211389475949308722nt_int
% 8.69/4.96          @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 8.69/4.96        = F ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7062_cond__case__prod__eta,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 8.69/4.96        ( ! [X6: nat,Y5: nat] :
% 8.69/4.96            ( ( F @ X6 @ Y5 )
% 8.69/4.96            = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 8.69/4.96       => ( ( produc27273713700761075at_nat @ F )
% 8.69/4.96          = G ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7063_cond__case__prod__eta,axiom,
% 8.69/4.96      ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 8.69/4.96        ( ! [X6: nat,Y5: nat] :
% 8.69/4.96            ( ( F @ X6 @ Y5 )
% 8.69/4.96            = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 8.69/4.96       => ( ( produc8739625826339149834_nat_o @ F )
% 8.69/4.96          = G ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7064_cond__case__prod__eta,axiom,
% 8.69/4.96      ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 8.69/4.96        ( ! [X6: int,Y5: int] :
% 8.69/4.96            ( ( F @ X6 @ Y5 )
% 8.69/4.96            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 8.69/4.96       => ( ( produc4245557441103728435nt_int @ F )
% 8.69/4.96          = G ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7065_cond__case__prod__eta,axiom,
% 8.69/4.96      ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 8.69/4.96        ( ! [X6: int,Y5: int] :
% 8.69/4.96            ( ( F @ X6 @ Y5 )
% 8.69/4.96            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 8.69/4.96       => ( ( produc4947309494688390418_int_o @ F )
% 8.69/4.96          = G ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7066_cond__case__prod__eta,axiom,
% 8.69/4.96      ! [F: int > int > int,G: product_prod_int_int > int] :
% 8.69/4.96        ( ! [X6: int,Y5: int] :
% 8.69/4.96            ( ( F @ X6 @ Y5 )
% 8.69/4.96            = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 8.69/4.96       => ( ( produc8211389475949308722nt_int @ F )
% 8.69/4.96          = G ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7067_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > real] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 8.69/4.96       => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7068_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > real] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 8.69/4.96       => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7069_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > real] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 8.69/4.96       => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7070_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > rat] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7071_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > rat] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7072_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_nat,F: nat > rat] :
% 8.69/4.96        ( ! [X6: nat] :
% 8.69/4.96            ( ( member_nat @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7073_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > rat] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 8.69/4.96       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7074_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > nat] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7075_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > nat] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7076_sum__nonpos,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > nat] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 8.69/4.96       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7077_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > real] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7078_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > real] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7079_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > real] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7080_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > rat] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7081_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > rat] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7082_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_nat,F: nat > rat] :
% 8.69/4.96        ( ! [X6: nat] :
% 8.69/4.96            ( ( member_nat @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7083_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > rat] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7084_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_complex,F: complex > nat] :
% 8.69/4.96        ( ! [X6: complex] :
% 8.69/4.96            ( ( member_complex @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7085_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_real,F: real > nat] :
% 8.69/4.96        ( ! [X6: real] :
% 8.69/4.96            ( ( member_real @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7086_sum__nonneg,axiom,
% 8.69/4.96      ! [A2: set_int,F: int > nat] :
% 8.69/4.96        ( ! [X6: int] :
% 8.69/4.96            ( ( member_int @ X6 @ A2 )
% 8.69/4.96           => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.96       => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7087_sum__mono__inv,axiom,
% 8.69/4.96      ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 8.69/4.96        ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 8.69/4.96          = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 8.69/4.96       => ( ! [I4: real] :
% 8.69/4.96              ( ( member_real @ I4 @ I6 )
% 8.69/4.96             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96         => ( ( member_real @ I @ I6 )
% 8.69/4.96           => ( ( finite_finite_real @ I6 )
% 8.69/4.96             => ( ( F @ I )
% 8.69/4.96                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7088_sum__mono__inv,axiom,
% 8.69/4.96      ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 8.69/4.96        ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 8.69/4.96          = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 8.69/4.96       => ( ! [I4: nat] :
% 8.69/4.96              ( ( member_nat @ I4 @ I6 )
% 8.69/4.96             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96         => ( ( member_nat @ I @ I6 )
% 8.69/4.96           => ( ( finite_finite_nat @ I6 )
% 8.69/4.96             => ( ( F @ I )
% 8.69/4.96                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7089_sum__mono__inv,axiom,
% 8.69/4.96      ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 8.69/4.96        ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 8.69/4.96          = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 8.69/4.96       => ( ! [I4: int] :
% 8.69/4.96              ( ( member_int @ I4 @ I6 )
% 8.69/4.96             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.96         => ( ( member_int @ I @ I6 )
% 8.69/4.96           => ( ( finite_finite_int @ I6 )
% 8.69/4.96             => ( ( F @ I )
% 8.69/4.96                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.96  
% 8.69/4.96  thf(fact_7090_sum__mono__inv,axiom,
% 8.69/4.96      ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 8.69/4.97        ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 8.69/4.97          = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_complex @ I @ I6 )
% 8.69/4.97           => ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7091_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 8.69/4.97        ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 8.69/4.97          = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_real @ I @ I6 )
% 8.69/4.97           => ( ( finite_finite_real @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7092_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 8.69/4.97        ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 8.69/4.97          = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_int @ I @ I6 )
% 8.69/4.97           => ( ( finite_finite_int @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7093_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 8.69/4.97        ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 8.69/4.97          = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_complex @ I @ I6 )
% 8.69/4.97           => ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7094_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: real > int,I6: set_real,G: real > int,I: real] :
% 8.69/4.97        ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 8.69/4.97          = ( groups1932886352136224148al_int @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_real @ I @ I6 )
% 8.69/4.97           => ( ( finite_finite_real @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7095_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: nat > int,I6: set_nat,G: nat > int,I: nat] :
% 8.69/4.97        ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 8.69/4.97          = ( groups3539618377306564664at_int @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: nat] :
% 8.69/4.97              ( ( member_nat @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_nat @ I @ I6 )
% 8.69/4.97           => ( ( finite_finite_nat @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7096_sum__mono__inv,axiom,
% 8.69/4.97      ! [F: complex > int,I6: set_complex,G: complex > int,I: complex] :
% 8.69/4.97        ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 8.69/4.97          = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ I6 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 8.69/4.97         => ( ( member_complex @ I @ I6 )
% 8.69/4.97           => ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = ( G @ I ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7097_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_real,G: real > complex,P: real > $o] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( groups5754745047067104278omplex @ G
% 8.69/4.97            @ ( collect_real
% 8.69/4.97              @ ^ [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups5754745047067104278omplex
% 8.69/4.97            @ ^ [X3: real] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7098_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( groups2073611262835488442omplex @ G
% 8.69/4.97            @ ( collect_nat
% 8.69/4.97              @ ^ [X3: nat] :
% 8.69/4.97                  ( ( member_nat @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups2073611262835488442omplex
% 8.69/4.97            @ ^ [X3: nat] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7099_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > complex,P: int > $o] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups3049146728041665814omplex @ G
% 8.69/4.97            @ ( collect_int
% 8.69/4.97              @ ^ [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups3049146728041665814omplex
% 8.69/4.97            @ ^ [X3: int] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7100_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_real,G: real > real,P: real > $o] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( groups8097168146408367636l_real @ G
% 8.69/4.97            @ ( collect_real
% 8.69/4.97              @ ^ [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups8097168146408367636l_real
% 8.69/4.97            @ ^ [X3: real] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7101_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > real,P: int > $o] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups8778361861064173332t_real @ G
% 8.69/4.97            @ ( collect_int
% 8.69/4.97              @ ^ [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups8778361861064173332t_real
% 8.69/4.97            @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7102_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5808333547571424918x_real @ G
% 8.69/4.97            @ ( collect_complex
% 8.69/4.97              @ ^ [X3: complex] :
% 8.69/4.97                  ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups5808333547571424918x_real
% 8.69/4.97            @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7103_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_real,G: real > rat,P: real > $o] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( groups1300246762558778688al_rat @ G
% 8.69/4.97            @ ( collect_real
% 8.69/4.97              @ ^ [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups1300246762558778688al_rat
% 8.69/4.97            @ ^ [X3: real] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7104_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( groups2906978787729119204at_rat @ G
% 8.69/4.97            @ ( collect_nat
% 8.69/4.97              @ ^ [X3: nat] :
% 8.69/4.97                  ( ( member_nat @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups2906978787729119204at_rat
% 8.69/4.97            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7105_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > rat,P: int > $o] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups3906332499630173760nt_rat @ G
% 8.69/4.97            @ ( collect_int
% 8.69/4.97              @ ^ [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups3906332499630173760nt_rat
% 8.69/4.97            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7106_sum_Ointer__filter,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > rat,P: complex > $o] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5058264527183730370ex_rat @ G
% 8.69/4.97            @ ( collect_complex
% 8.69/4.97              @ ^ [X3: complex] :
% 8.69/4.97                  ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                  & ( P @ X3 ) ) ) )
% 8.69/4.97          = ( groups5058264527183730370ex_rat
% 8.69/4.97            @ ^ [X3: complex] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 8.69/4.97            @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7107_mask__nonnegative__int,axiom,
% 8.69/4.97      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7108_not__mask__negative__int,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7109_semiring__norm_I28_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bitM @ ( bit1 @ N ) )
% 8.69/4.97        = ( bit1 @ ( bit0 @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7110_semiring__norm_I27_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bitM @ ( bit0 @ N ) )
% 8.69/4.97        = ( bit1 @ ( bitM @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7111_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ! [X6: real] :
% 8.69/4.97              ( ( member_real @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97            = ( ! [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7112_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97            = ( ! [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7113_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97            = ( ! [X3: complex] :
% 8.69/4.97                  ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_real ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7114_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ! [X6: real] :
% 8.69/4.97              ( ( member_real @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97            = ( ! [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7115_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ! [X6: nat] :
% 8.69/4.97              ( ( member_nat @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97            = ( ! [X3: nat] :
% 8.69/4.97                  ( ( member_nat @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7116_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97            = ( ! [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7117_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97            = ( ! [X3: complex] :
% 8.69/4.97                  ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7118_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ! [X6: real] :
% 8.69/4.97              ( ( member_real @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97            = ( ! [X3: real] :
% 8.69/4.97                  ( ( member_real @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_nat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7119_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97            = ( ! [X3: int] :
% 8.69/4.97                  ( ( member_int @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_nat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7120_sum__nonneg__eq__0__iff,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.97         => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97            = ( ! [X3: complex] :
% 8.69/4.97                  ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                 => ( ( F @ X3 )
% 8.69/4.97                    = zero_zero_nat ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7121_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ( finite_finite_int @ T )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S )
% 8.69/4.97                 => ? [Xa: int] :
% 8.69/4.97                      ( ( member_int @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7122_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S )
% 8.69/4.97                 => ? [Xa: complex] :
% 8.69/4.97                      ( ( member_complex @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7123_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ( finite_finite_int @ T )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S )
% 8.69/4.97                 => ? [Xa: int] :
% 8.69/4.97                      ( ( member_int @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7124_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S )
% 8.69/4.97                 => ? [Xa: complex] :
% 8.69/4.97                      ( ( member_complex @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7125_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ S )
% 8.69/4.97       => ( ( finite_finite_nat @ T )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S )
% 8.69/4.97                 => ? [Xa: nat] :
% 8.69/4.97                      ( ( member_nat @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7126_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ S )
% 8.69/4.97       => ( ( finite_finite_int @ T )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S )
% 8.69/4.97                 => ? [Xa: int] :
% 8.69/4.97                      ( ( member_int @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7127_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ S )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S )
% 8.69/4.97                 => ? [Xa: complex] :
% 8.69/4.97                      ( ( member_complex @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7128_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ( finite_finite_nat @ T )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S )
% 8.69/4.97                 => ? [Xa: nat] :
% 8.69/4.97                      ( ( member_nat @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7129_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ( finite_finite_int @ T )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S )
% 8.69/4.97                 => ? [Xa: int] :
% 8.69/4.97                      ( ( member_int @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7130_sum__le__included,axiom,
% 8.69/4.97      ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ T )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S )
% 8.69/4.97                 => ? [Xa: complex] :
% 8.69/4.97                      ( ( member_complex @ Xa @ T )
% 8.69/4.97                      & ( ( I @ Xa )
% 8.69/4.97                        = X6 )
% 8.69/4.97                      & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 8.69/4.97             => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7131_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > real,G: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: int] :
% 8.69/4.97                ( ( member_int @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7132_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: complex] :
% 8.69/4.97                ( ( member_complex @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7133_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ! [X6: nat] :
% 8.69/4.97              ( ( member_nat @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: nat] :
% 8.69/4.97                ( ( member_nat @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7134_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > rat,G: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: int] :
% 8.69/4.97                ( ( member_int @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7135_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: complex] :
% 8.69/4.97                ( ( member_complex @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7136_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > nat,G: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: int] :
% 8.69/4.97                ( ( member_int @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7137_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: complex] :
% 8.69/4.97                ( ( member_complex @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7138_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > int,G: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ! [X6: nat] :
% 8.69/4.97              ( ( member_nat @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: nat] :
% 8.69/4.97                ( ( member_nat @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7139_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > int,G: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ! [X6: complex] :
% 8.69/4.97              ( ( member_complex @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: complex] :
% 8.69/4.97                ( ( member_complex @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7140_sum__strict__mono__ex1,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > int,G: int > int] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ! [X6: int] :
% 8.69/4.97              ( ( member_int @ X6 @ A2 )
% 8.69/4.97             => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97         => ( ? [X4: int] :
% 8.69/4.97                ( ( member_int @ X4 @ A2 )
% 8.69/4.97                & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 8.69/4.97           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7141_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 8.69/4.97        ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 8.69/4.97       => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_nat @ S2 )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7142_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 8.69/4.97        ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 8.69/4.97       => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_int @ S2 )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7143_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 8.69/4.97        ( ( R4 @ zero_zero_real @ zero_zero_real )
% 8.69/4.97       => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_int @ S2 )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7144_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 8.69/4.97        ( ( R4 @ zero_zero_real @ zero_zero_real )
% 8.69/4.97       => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7145_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 8.69/4.97        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 8.69/4.97       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_nat @ S2 )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7146_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 8.69/4.97        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 8.69/4.97       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_int @ S2 )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7147_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 8.69/4.97        ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 8.69/4.97       => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7148_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 8.69/4.97        ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 8.69/4.97       => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_int @ S2 )
% 8.69/4.97           => ( ! [X6: int] :
% 8.69/4.97                  ( ( member_int @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7149_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 8.69/4.97        ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 8.69/4.97       => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7150_sum_Orelated,axiom,
% 8.69/4.97      ! [R4: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 8.69/4.97        ( ( R4 @ zero_zero_int @ zero_zero_int )
% 8.69/4.97       => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 8.69/4.97              ( ( ( R4 @ X15 @ X23 )
% 8.69/4.97                & ( R4 @ Y15 @ Y23 ) )
% 8.69/4.97             => ( R4 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 8.69/4.97         => ( ( finite_finite_nat @ S2 )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S2 )
% 8.69/4.97                 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97             => ( R4 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7151_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > real,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7152_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > real,G: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_int )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7153_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > real,G: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_real )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7154_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7155_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_nat )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7156_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > rat,G: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_int )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7157_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > rat,G: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_real )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7158_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7159_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > nat,G: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_int )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7160_sum__strict__mono,axiom,
% 8.69/4.97      ! [A2: set_real,F: real > nat,G: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ A2 )
% 8.69/4.97       => ( ( A2 != bot_bot_set_real )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ A2 )
% 8.69/4.97               => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 8.69/4.97           => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7161_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 8.69/4.97        ( ( finite_finite_real @ S4 )
% 8.69/4.97       => ( ( finite_finite_real @ T4 )
% 8.69/4.97         => ( ! [A5: real] :
% 8.69/4.97                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: real] :
% 8.69/4.97                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: real] :
% 8.69/4.97                        ( ( member_real @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_complex ) )
% 8.69/4.97                   => ( ! [B5: real] :
% 8.69/4.97                          ( ( member_real @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_complex ) )
% 8.69/4.97                     => ( ! [A5: real] :
% 8.69/4.97                            ( ( member_real @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 8.69/4.97                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7162_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 8.69/4.97        ( ( finite_finite_real @ S4 )
% 8.69/4.97       => ( ( finite_finite_int @ T4 )
% 8.69/4.97         => ( ! [A5: real] :
% 8.69/4.97                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: int] :
% 8.69/4.97                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: int] :
% 8.69/4.97                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: real] :
% 8.69/4.97                        ( ( member_real @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_complex ) )
% 8.69/4.97                   => ( ! [B5: int] :
% 8.69/4.97                          ( ( member_int @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_complex ) )
% 8.69/4.97                     => ( ! [A5: real] :
% 8.69/4.97                            ( ( member_real @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups5754745047067104278omplex @ G @ S2 )
% 8.69/4.97                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7163_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 8.69/4.97        ( ( finite_finite_int @ S4 )
% 8.69/4.97       => ( ( finite_finite_real @ T4 )
% 8.69/4.97         => ( ! [A5: int] :
% 8.69/4.97                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: int] :
% 8.69/4.97                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: real] :
% 8.69/4.97                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: int] :
% 8.69/4.97                        ( ( member_int @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_complex ) )
% 8.69/4.97                   => ( ! [B5: real] :
% 8.69/4.97                          ( ( member_real @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_complex ) )
% 8.69/4.97                     => ( ! [A5: int] :
% 8.69/4.97                            ( ( member_int @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 8.69/4.97                          = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7164_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 8.69/4.97        ( ( finite_finite_int @ S4 )
% 8.69/4.97       => ( ( finite_finite_int @ T4 )
% 8.69/4.97         => ( ! [A5: int] :
% 8.69/4.97                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: int] :
% 8.69/4.97                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: int] :
% 8.69/4.97                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: int] :
% 8.69/4.97                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: int] :
% 8.69/4.97                        ( ( member_int @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_complex ) )
% 8.69/4.97                   => ( ! [B5: int] :
% 8.69/4.97                          ( ( member_int @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_complex ) )
% 8.69/4.97                     => ( ! [A5: int] :
% 8.69/4.97                            ( ( member_int @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups3049146728041665814omplex @ G @ S2 )
% 8.69/4.97                          = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7165_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > real,H2: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ S4 )
% 8.69/4.97       => ( ( finite_finite_real @ T4 )
% 8.69/4.97         => ( ! [A5: real] :
% 8.69/4.97                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: real] :
% 8.69/4.97                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: real] :
% 8.69/4.97                        ( ( member_real @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: real] :
% 8.69/4.97                          ( ( member_real @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: real] :
% 8.69/4.97                            ( ( member_real @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 8.69/4.97                          = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7166_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > real,H2: int > real] :
% 8.69/4.97        ( ( finite_finite_real @ S4 )
% 8.69/4.97       => ( ( finite_finite_int @ T4 )
% 8.69/4.97         => ( ! [A5: real] :
% 8.69/4.97                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: int] :
% 8.69/4.97                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: int] :
% 8.69/4.97                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: real] :
% 8.69/4.97                        ( ( member_real @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: int] :
% 8.69/4.97                          ( ( member_int @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: real] :
% 8.69/4.97                            ( ( member_real @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 8.69/4.97                          = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7167_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > real,H2: complex > real] :
% 8.69/4.97        ( ( finite_finite_real @ S4 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T4 )
% 8.69/4.97         => ( ! [A5: real] :
% 8.69/4.97                ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: complex] :
% 8.69/4.97                      ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: real] :
% 8.69/4.97                        ( ( member_real @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: complex] :
% 8.69/4.97                          ( ( member_complex @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: real] :
% 8.69/4.97                            ( ( member_real @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8097168146408367636l_real @ G @ S2 )
% 8.69/4.97                          = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7168_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > real,H2: real > real] :
% 8.69/4.97        ( ( finite_finite_int @ S4 )
% 8.69/4.97       => ( ( finite_finite_real @ T4 )
% 8.69/4.97         => ( ! [A5: int] :
% 8.69/4.97                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: int] :
% 8.69/4.97                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: real] :
% 8.69/4.97                      ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: int] :
% 8.69/4.97                        ( ( member_int @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: real] :
% 8.69/4.97                          ( ( member_real @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: int] :
% 8.69/4.97                            ( ( member_int @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 8.69/4.97                          = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7169_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > real,H2: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ S4 )
% 8.69/4.97       => ( ( finite_finite_int @ T4 )
% 8.69/4.97         => ( ! [A5: int] :
% 8.69/4.97                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: int] :
% 8.69/4.97                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: int] :
% 8.69/4.97                    ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: int] :
% 8.69/4.97                      ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: int] :
% 8.69/4.97                        ( ( member_int @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: int] :
% 8.69/4.97                          ( ( member_int @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: int] :
% 8.69/4.97                            ( ( member_int @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 8.69/4.97                          = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7170_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.69/4.97      ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > real,H2: complex > real] :
% 8.69/4.97        ( ( finite_finite_int @ S4 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ T4 )
% 8.69/4.97         => ( ! [A5: int] :
% 8.69/4.97                ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97               => ( ( I @ ( J @ A5 ) )
% 8.69/4.97                  = A5 ) )
% 8.69/4.97           => ( ! [A5: int] :
% 8.69/4.97                  ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 8.69/4.97                 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 8.69/4.97                   => ( ( J @ ( I @ B5 ) )
% 8.69/4.97                      = B5 ) )
% 8.69/4.97               => ( ! [B5: complex] :
% 8.69/4.97                      ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 8.69/4.97                     => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 8.69/4.97                 => ( ! [A5: int] :
% 8.69/4.97                        ( ( member_int @ A5 @ S4 )
% 8.69/4.97                       => ( ( G @ A5 )
% 8.69/4.97                          = zero_zero_real ) )
% 8.69/4.97                   => ( ! [B5: complex] :
% 8.69/4.97                          ( ( member_complex @ B5 @ T4 )
% 8.69/4.97                         => ( ( H2 @ B5 )
% 8.69/4.97                            = zero_zero_real ) )
% 8.69/4.97                     => ( ! [A5: int] :
% 8.69/4.97                            ( ( member_int @ A5 @ S2 )
% 8.69/4.97                           => ( ( H2 @ ( J @ A5 ) )
% 8.69/4.97                              = ( G @ A5 ) ) )
% 8.69/4.97                       => ( ( groups8778361861064173332t_real @ G @ S2 )
% 8.69/4.97                          = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7171_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_real,F: real > real,B3: real,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7172_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_int,F: int > real,B3: real,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7173_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > real,B3: real,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7174_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_real,F: real > rat,B3: rat,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7175_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_nat,F: nat > rat,B3: rat,I: nat] :
% 8.69/4.97        ( ( finite_finite_nat @ S )
% 8.69/4.97       => ( ! [I4: nat] :
% 8.69/4.97              ( ( member_nat @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_nat @ I @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7176_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_int,F: int > rat,B3: rat,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7177_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > rat,B3: rat,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7178_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_real,F: real > nat,B3: nat,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7179_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_int,F: int > nat,B3: nat,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7180_sum__nonneg__leq__bound,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > nat,B3: nat,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 8.69/4.97              = B3 )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7181_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_real,F: real > real,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups8097168146408367636l_real @ F @ S )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_real ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7182_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_int,F: int > real,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups8778361861064173332t_real @ F @ S )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_real ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7183_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > real,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5808333547571424918x_real @ F @ S )
% 8.69/4.97              = zero_zero_real )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_real ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7184_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_real,F: real > rat,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7185_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_nat,F: nat > rat,I: nat] :
% 8.69/4.97        ( ( finite_finite_nat @ S )
% 8.69/4.97       => ( ! [I4: nat] :
% 8.69/4.97              ( ( member_nat @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97           => ( ( member_nat @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7186_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_int,F: int > rat,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7187_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > rat,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 8.69/4.97              = zero_zero_rat )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_rat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7188_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_real,F: real > nat,I: real] :
% 8.69/4.97        ( ( finite_finite_real @ S )
% 8.69/4.97       => ( ! [I4: real] :
% 8.69/4.97              ( ( member_real @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97           => ( ( member_real @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7189_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_int,F: int > nat,I: int] :
% 8.69/4.97        ( ( finite_finite_int @ S )
% 8.69/4.97       => ( ! [I4: int] :
% 8.69/4.97              ( ( member_int @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97           => ( ( member_int @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7190_sum__nonneg__0,axiom,
% 8.69/4.97      ! [S: set_complex,F: complex > nat,I: complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ S )
% 8.69/4.97       => ( ! [I4: complex] :
% 8.69/4.97              ( ( member_complex @ I4 @ S )
% 8.69/4.97             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97         => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 8.69/4.97              = zero_zero_nat )
% 8.69/4.97           => ( ( member_complex @ I @ S )
% 8.69/4.97             => ( ( F @ I )
% 8.69/4.97                = zero_zero_nat ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7191_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > complex] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups3049146728041665814omplex @ G
% 8.69/4.97            @ ( minus_minus_set_int @ A2
% 8.69/4.97              @ ( collect_int
% 8.69/4.97                @ ^ [X3: int] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_complex ) ) ) )
% 8.69/4.97          = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7192_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups8778361861064173332t_real @ G
% 8.69/4.97            @ ( minus_minus_set_int @ A2
% 8.69/4.97              @ ( collect_int
% 8.69/4.97                @ ^ [X3: int] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_real ) ) ) )
% 8.69/4.97          = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7193_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5808333547571424918x_real @ G
% 8.69/4.97            @ ( minus_811609699411566653omplex @ A2
% 8.69/4.97              @ ( collect_complex
% 8.69/4.97                @ ^ [X3: complex] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_real ) ) ) )
% 8.69/4.97          = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7194_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups3906332499630173760nt_rat @ G
% 8.69/4.97            @ ( minus_minus_set_int @ A2
% 8.69/4.97              @ ( collect_int
% 8.69/4.97                @ ^ [X3: int] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) )
% 8.69/4.97          = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7195_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5058264527183730370ex_rat @ G
% 8.69/4.97            @ ( minus_811609699411566653omplex @ A2
% 8.69/4.97              @ ( collect_complex
% 8.69/4.97                @ ^ [X3: complex] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) )
% 8.69/4.97          = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7196_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( groups4541462559716669496nt_nat @ G
% 8.69/4.97            @ ( minus_minus_set_int @ A2
% 8.69/4.97              @ ( collect_int
% 8.69/4.97                @ ^ [X3: int] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_nat ) ) ) )
% 8.69/4.97          = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7197_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5693394587270226106ex_nat @ G
% 8.69/4.97            @ ( minus_811609699411566653omplex @ A2
% 8.69/4.97              @ ( collect_complex
% 8.69/4.97                @ ^ [X3: complex] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_nat ) ) ) )
% 8.69/4.97          = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7198_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( groups5690904116761175830ex_int @ G
% 8.69/4.97            @ ( minus_811609699411566653omplex @ A2
% 8.69/4.97              @ ( collect_complex
% 8.69/4.97                @ ^ [X3: complex] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_int ) ) ) )
% 8.69/4.97          = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7199_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_nat,G: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( groups2073611262835488442omplex @ G
% 8.69/4.97            @ ( minus_minus_set_nat @ A2
% 8.69/4.97              @ ( collect_nat
% 8.69/4.97                @ ^ [X3: nat] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_complex ) ) ) )
% 8.69/4.97          = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7200_sum_Osetdiff__irrelevant,axiom,
% 8.69/4.97      ! [A2: set_nat,G: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( groups2906978787729119204at_rat @ G
% 8.69/4.97            @ ( minus_minus_set_nat @ A2
% 8.69/4.97              @ ( collect_nat
% 8.69/4.97                @ ^ [X3: nat] :
% 8.69/4.97                    ( ( G @ X3 )
% 8.69/4.97                    = zero_zero_rat ) ) ) )
% 8.69/4.97          = ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7201_less__mask,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/4.97       => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7202_eval__nat__numeral_I2_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.69/4.97        = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7203_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_real,I: real,F: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( member_real @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: real] :
% 8.69/4.97                  ( ( member_real @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7204_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_int,I: int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( member_int @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: int] :
% 8.69/4.97                  ( ( member_int @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7205_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_complex,I: complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( member_complex @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: complex] :
% 8.69/4.97                  ( ( member_complex @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7206_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_real,I: real,F: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( member_real @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: real] :
% 8.69/4.97                  ( ( member_real @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7207_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_nat,I: nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ I6 )
% 8.69/4.97       => ( ( member_nat @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: nat] :
% 8.69/4.97                  ( ( member_nat @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7208_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_int,I: int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( member_int @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: int] :
% 8.69/4.97                  ( ( member_int @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7209_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_complex,I: complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( member_complex @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: complex] :
% 8.69/4.97                  ( ( member_complex @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7210_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_real,I: real,F: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( member_real @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: real] :
% 8.69/4.97                  ( ( member_real @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7211_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_int,I: int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( member_int @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: int] :
% 8.69/4.97                  ( ( member_int @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7212_sum__pos2,axiom,
% 8.69/4.97      ! [I6: set_complex,I: complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( member_complex @ I @ I6 )
% 8.69/4.97         => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 8.69/4.97           => ( ! [I4: complex] :
% 8.69/4.97                  ( ( member_complex @ I4 @ I6 )
% 8.69/4.97                 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97             => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7213_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7214_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_int )
% 8.69/4.97         => ( ! [I4: int] :
% 8.69/4.97                ( ( member_int @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7215_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_real,F: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_real )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7216_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7217_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_nat )
% 8.69/4.97         => ( ! [I4: nat] :
% 8.69/4.97                ( ( member_nat @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7218_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_int )
% 8.69/4.97         => ( ! [I4: int] :
% 8.69/4.97                ( ( member_int @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7219_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_real,F: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_real )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7220_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_complex )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7221_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_int )
% 8.69/4.97         => ( ! [I4: int] :
% 8.69/4.97                ( ( member_int @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7222_sum__pos,axiom,
% 8.69/4.97      ! [I6: set_real,F: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ I6 )
% 8.69/4.97       => ( ( I6 != bot_bot_set_real )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 8.69/4.97           => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7223_set__encode__inf,axiom,
% 8.69/4.97      ! [A2: set_nat] :
% 8.69/4.97        ( ~ ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( nat_set_encode @ A2 )
% 8.69/4.97          = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7224_BitM__plus__one,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 8.69/4.97        = ( bit0 @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7225_one__plus__BitM,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 8.69/4.97        = ( bit0 @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7226_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5754745047067104278omplex @ G @ T3 )
% 8.69/4.97                = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7227_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups8097168146408367636l_real @ G @ T3 )
% 8.69/4.97                = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7228_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5808333547571424918x_real @ G @ T3 )
% 8.69/4.97                = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7229_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 8.69/4.97                = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7230_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 8.69/4.97                = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7231_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 8.69/4.97                = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7232_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 8.69/4.97                = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7233_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,G: real > int,H2: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1932886352136224148al_int @ G @ T3 )
% 8.69/4.97                = ( groups1932886352136224148al_int @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7234_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 8.69/4.97                = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7235_sum_Omono__neutral__cong__right,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > complex,H2: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups2073611262835488442omplex @ G @ T3 )
% 8.69/4.97                = ( groups2073611262835488442omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7236_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5754745047067104278omplex @ G @ S2 )
% 8.69/4.97                = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7237_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups8097168146408367636l_real @ G @ S2 )
% 8.69/4.97                = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7238_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5808333547571424918x_real @ G @ S2 )
% 8.69/4.97                = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7239_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 8.69/4.97                = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7240_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 8.69/4.97                = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7241_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 8.69/4.97                = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7242_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 8.69/4.97                = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7243_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_real,S2: set_real,H2: real > int,G: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: real] :
% 8.69/4.97                ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ! [X6: real] :
% 8.69/4.97                  ( ( member_real @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups1932886352136224148al_int @ G @ S2 )
% 8.69/4.97                = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7244_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ! [X6: complex] :
% 8.69/4.97                  ( ( member_complex @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 8.69/4.97                = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7245_sum_Omono__neutral__cong__left,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( H2 @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ! [X6: nat] :
% 8.69/4.97                  ( ( member_nat @ X6 @ S2 )
% 8.69/4.97                 => ( ( G @ X6 )
% 8.69/4.97                    = ( H2 @ X6 ) ) )
% 8.69/4.97             => ( ( groups2073611262835488442omplex @ G @ S2 )
% 8.69/4.97                = ( groups2073611262835488442omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7246_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ( groups5808333547571424918x_real @ G @ T3 )
% 8.69/4.97              = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7247_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 8.69/4.97              = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7248_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 8.69/4.97              = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7249_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 8.69/4.97              = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7250_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ( groups2073611262835488442omplex @ G @ T3 )
% 8.69/4.97              = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7251_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 8.69/4.97              = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7252_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ( groups3539618377306564664at_int @ G @ T3 )
% 8.69/4.97              = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7253_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > complex] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ( groups3049146728041665814omplex @ G @ T3 )
% 8.69/4.97              = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7254_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ( groups8778361861064173332t_real @ G @ T3 )
% 8.69/4.97              = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7255_sum_Omono__neutral__right,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 8.69/4.97              = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7256_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ( groups5808333547571424918x_real @ G @ S2 )
% 8.69/4.97              = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7257_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 8.69/4.97              = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7258_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_nat ) )
% 8.69/4.97           => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 8.69/4.97              = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7259_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ T3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: complex] :
% 8.69/4.97                ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 8.69/4.97              = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7260_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ( groups2073611262835488442omplex @ G @ S2 )
% 8.69/4.97              = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7261_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 8.69/4.97              = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7262_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: nat] :
% 8.69/4.97                ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_int ) )
% 8.69/4.97           => ( ( groups3539618377306564664at_int @ G @ S2 )
% 8.69/4.97              = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7263_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > complex] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_complex ) )
% 8.69/4.97           => ( ( groups3049146728041665814omplex @ G @ S2 )
% 8.69/4.97              = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7264_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_real ) )
% 8.69/4.97           => ( ( groups8778361861064173332t_real @ G @ S2 )
% 8.69/4.97              = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7265_sum_Omono__neutral__left,axiom,
% 8.69/4.97      ! [T3: set_int,S2: set_int,G: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ T3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 8.69/4.97         => ( ! [X6: int] :
% 8.69/4.97                ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 8.69/4.97               => ( ( G @ X6 )
% 8.69/4.97                  = zero_zero_rat ) )
% 8.69/4.97           => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 8.69/4.97              = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7266_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_complex ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_complex ) )
% 8.69/4.97               => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 8.69/4.97                    = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 8.69/4.97                    = ( groups5754745047067104278omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7267_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_real ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_real ) )
% 8.69/4.97               => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 8.69/4.97                    = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 8.69/4.97                    = ( groups8097168146408367636l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7268_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_real ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_real ) )
% 8.69/4.97               => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 8.69/4.97                    = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.97                    = ( groups5808333547571424918x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7269_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_rat ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_rat ) )
% 8.69/4.97               => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 8.69/4.97                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 8.69/4.97                    = ( groups1300246762558778688al_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7270_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_rat ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_rat ) )
% 8.69/4.97               => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 8.69/4.97                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.97                    = ( groups5058264527183730370ex_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7271_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_nat ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_nat ) )
% 8.69/4.97               => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 8.69/4.97                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 8.69/4.97                    = ( groups1935376822645274424al_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7272_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_nat ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_nat ) )
% 8.69/4.97               => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 8.69/4.97                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 8.69/4.97                    = ( groups5693394587270226106ex_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7273_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_int ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_int ) )
% 8.69/4.97               => ( ( ( groups1932886352136224148al_int @ G @ C4 )
% 8.69/4.97                    = ( groups1932886352136224148al_int @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 8.69/4.97                    = ( groups1932886352136224148al_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7274_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_int ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_int ) )
% 8.69/4.97               => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 8.69/4.97                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 8.69/4.97                    = ( groups5690904116761175830ex_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7275_sum_Osame__carrierI,axiom,
% 8.69/4.97      ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: nat] :
% 8.69/4.97                  ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_complex ) )
% 8.69/4.97             => ( ! [B5: nat] :
% 8.69/4.97                    ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_complex ) )
% 8.69/4.97               => ( ( ( groups2073611262835488442omplex @ G @ C4 )
% 8.69/4.97                    = ( groups2073611262835488442omplex @ H2 @ C4 ) )
% 8.69/4.97                 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 8.69/4.97                    = ( groups2073611262835488442omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7276_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_complex ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_complex ) )
% 8.69/4.97               => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 8.69/4.97                    = ( groups5754745047067104278omplex @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups5754745047067104278omplex @ G @ C4 )
% 8.69/4.97                    = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7277_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_real ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_real ) )
% 8.69/4.97               => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 8.69/4.97                    = ( groups8097168146408367636l_real @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups8097168146408367636l_real @ G @ C4 )
% 8.69/4.97                    = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7278_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_real ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_real ) )
% 8.69/4.97               => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.97                    = ( groups5808333547571424918x_real @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups5808333547571424918x_real @ G @ C4 )
% 8.69/4.97                    = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7279_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_rat ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_rat ) )
% 8.69/4.97               => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 8.69/4.97                    = ( groups1300246762558778688al_rat @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 8.69/4.97                    = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7280_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_rat ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_rat ) )
% 8.69/4.97               => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.97                    = ( groups5058264527183730370ex_rat @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 8.69/4.97                    = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7281_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_nat ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_nat ) )
% 8.69/4.97               => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 8.69/4.97                    = ( groups1935376822645274424al_nat @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 8.69/4.97                    = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7282_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_nat ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_nat ) )
% 8.69/4.97               => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 8.69/4.97                    = ( groups5693394587270226106ex_nat @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 8.69/4.97                    = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7283_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: real] :
% 8.69/4.97                  ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_int ) )
% 8.69/4.97             => ( ! [B5: real] :
% 8.69/4.97                    ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_int ) )
% 8.69/4.97               => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 8.69/4.97                    = ( groups1932886352136224148al_int @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups1932886352136224148al_int @ G @ C4 )
% 8.69/4.97                    = ( groups1932886352136224148al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7284_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ C4 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: complex] :
% 8.69/4.97                  ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_int ) )
% 8.69/4.97             => ( ! [B5: complex] :
% 8.69/4.97                    ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_int ) )
% 8.69/4.97               => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 8.69/4.97                    = ( groups5690904116761175830ex_int @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 8.69/4.97                    = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7285_sum_Osame__carrier,axiom,
% 8.69/4.97      ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 8.69/4.97        ( ( finite_finite_nat @ C4 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 8.69/4.97         => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 8.69/4.97           => ( ! [A5: nat] :
% 8.69/4.97                  ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 8.69/4.97                 => ( ( G @ A5 )
% 8.69/4.97                    = zero_zero_complex ) )
% 8.69/4.97             => ( ! [B5: nat] :
% 8.69/4.97                    ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 8.69/4.97                   => ( ( H2 @ B5 )
% 8.69/4.97                      = zero_zero_complex ) )
% 8.69/4.97               => ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 8.69/4.97                    = ( groups2073611262835488442omplex @ H2 @ B3 ) )
% 8.69/4.97                  = ( ( groups2073611262835488442omplex @ G @ C4 )
% 8.69/4.97                    = ( groups2073611262835488442omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7286_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 8.69/4.97        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.97            = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7287_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 8.69/4.97        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.97            = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7288_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 8.69/4.97        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 8.69/4.97            = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7289_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 8.69/4.97        ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97       => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 8.69/4.97            = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7290_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 8.69/4.97        ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_nat @ A2 )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 8.69/4.97            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7291_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 8.69/4.97        ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_nat @ A2 )
% 8.69/4.97         => ( ( groups3539618377306564664at_int @ G @ A2 )
% 8.69/4.97            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7292_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_int,A2: set_int,G: int > real] :
% 8.69/4.97        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_int @ A2 )
% 8.69/4.97         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 8.69/4.97            = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7293_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_int,A2: set_int,G: int > rat] :
% 8.69/4.97        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_int @ A2 )
% 8.69/4.97         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 8.69/4.97            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7294_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_int,A2: set_int,G: int > nat] :
% 8.69/4.97        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_int @ A2 )
% 8.69/4.97         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 8.69/4.97            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7295_sum_Osubset__diff,axiom,
% 8.69/4.97      ! [B3: set_int,A2: set_int,G: int > int] :
% 8.69/4.97        ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97       => ( ( finite_finite_int @ A2 )
% 8.69/4.97         => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 8.69/4.97            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7296_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_complex,B3: set_complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97         => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7297_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97         => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7298_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97         => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7299_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7300_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97         => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7301_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_int,B3: set_int,F: int > real] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97         => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7302_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_int,B3: set_int,F: int > rat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97         => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7303_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_int,B3: set_int,F: int > int] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97         => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7304_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97         => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7305_sum__diff,axiom,
% 8.69/4.97      ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97         => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7306_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,F: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: real] :
% 8.69/4.97                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7307_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: complex] :
% 8.69/4.97                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7308_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,F: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: real] :
% 8.69/4.97                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7309_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: complex] :
% 8.69/4.97                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7310_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: nat] :
% 8.69/4.97                ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7311_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,F: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: real] :
% 8.69/4.97                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7312_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: complex] :
% 8.69/4.97                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7313_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,F: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: real] :
% 8.69/4.97                ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7314_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,F: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: complex] :
% 8.69/4.97                ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7315_sum__mono2,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,F: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.97         => ( ! [B5: nat] :
% 8.69/4.97                ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 8.69/4.97               => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 8.69/4.97           => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7316_numeral__BitM,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 8.69/4.97        = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7317_numeral__BitM,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( numeral_numeral_real @ ( bitM @ N ) )
% 8.69/4.97        = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7318_numeral__BitM,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 8.69/4.97        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7319_numeral__BitM,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 8.69/4.97        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7320_odd__numeral__BitM,axiom,
% 8.69/4.97      ! [W: num] :
% 8.69/4.97        ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7321_odd__numeral__BitM,axiom,
% 8.69/4.97      ! [W: num] :
% 8.69/4.97        ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7322_odd__numeral__BitM,axiom,
% 8.69/4.97      ! [W: num] :
% 8.69/4.97        ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7323_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: real] :
% 8.69/4.97                    ( ( member_real @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7324_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: complex] :
% 8.69/4.97                    ( ( member_complex @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7325_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: real] :
% 8.69/4.97                    ( ( member_real @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7326_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: complex] :
% 8.69/4.97                    ( ( member_complex @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7327_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 8.69/4.97        ( ( finite_finite_nat @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.97         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: nat] :
% 8.69/4.97                    ( ( member_nat @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7328_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: real] :
% 8.69/4.97                    ( ( member_real @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7329_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: complex] :
% 8.69/4.97                    ( ( member_complex @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7330_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 8.69/4.97        ( ( finite_finite_real @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.97         => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: real] :
% 8.69/4.97                    ( ( member_real @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7331_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 8.69/4.97         => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: complex] :
% 8.69/4.97                    ( ( member_complex @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7332_sum__strict__mono2,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 8.69/4.97        ( ( finite_finite_nat @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.97         => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 8.69/4.97           => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 8.69/4.97             => ( ! [X6: nat] :
% 8.69/4.97                    ( ( member_nat @ X6 @ B3 )
% 8.69/4.97                   => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 8.69/4.97               => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7333_Suc__mask__eq__exp,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.69/4.97        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7334_mask__nat__less__exp,axiom,
% 8.69/4.97      ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7335_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 8.69/4.97        ( ! [I4: complex] :
% 8.69/4.97            ( ( member_complex @ I4 @ I6 )
% 8.69/4.97           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 8.69/4.97            = one_one_Code_integer )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_le3102999989581377725nteger
% 8.69/4.97              @ ( abs_abs_Code_integer
% 8.69/4.97                @ ( minus_8373710615458151222nteger
% 8.69/4.97                  @ ( groups6621422865394947399nteger
% 8.69/4.97                    @ ^ [I5: complex] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7336_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 8.69/4.97        ( ! [I4: real] :
% 8.69/4.97            ( ( member_real @ I4 @ I6 )
% 8.69/4.97           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 8.69/4.97            = one_one_Code_integer )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_le3102999989581377725nteger
% 8.69/4.97              @ ( abs_abs_Code_integer
% 8.69/4.97                @ ( minus_8373710615458151222nteger
% 8.69/4.97                  @ ( groups7713935264441627589nteger
% 8.69/4.97                    @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7337_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 8.69/4.97        ( ! [I4: nat] :
% 8.69/4.97            ( ( member_nat @ I4 @ I6 )
% 8.69/4.97           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 8.69/4.97            = one_one_Code_integer )
% 8.69/4.97         => ( ! [I4: nat] :
% 8.69/4.97                ( ( member_nat @ I4 @ I6 )
% 8.69/4.97               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_le3102999989581377725nteger
% 8.69/4.97              @ ( abs_abs_Code_integer
% 8.69/4.97                @ ( minus_8373710615458151222nteger
% 8.69/4.97                  @ ( groups7501900531339628137nteger
% 8.69/4.97                    @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7338_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 8.69/4.97        ( ! [I4: int] :
% 8.69/4.97            ( ( member_int @ I4 @ I6 )
% 8.69/4.97           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 8.69/4.97            = one_one_Code_integer )
% 8.69/4.97         => ( ! [I4: int] :
% 8.69/4.97                ( ( member_int @ I4 @ I6 )
% 8.69/4.97               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_le3102999989581377725nteger
% 8.69/4.97              @ ( abs_abs_Code_integer
% 8.69/4.97                @ ( minus_8373710615458151222nteger
% 8.69/4.97                  @ ( groups7873554091576472773nteger
% 8.69/4.97                    @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7339_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 8.69/4.97        ( ! [I4: complex] :
% 8.69/4.97            ( ( member_complex @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 8.69/4.97            = one_one_real )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_real
% 8.69/4.97              @ ( abs_abs_real
% 8.69/4.97                @ ( minus_minus_real
% 8.69/4.97                  @ ( groups5808333547571424918x_real
% 8.69/4.97                    @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7340_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 8.69/4.97        ( ! [I4: real] :
% 8.69/4.97            ( ( member_real @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 8.69/4.97            = one_one_real )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_real
% 8.69/4.97              @ ( abs_abs_real
% 8.69/4.97                @ ( minus_minus_real
% 8.69/4.97                  @ ( groups8097168146408367636l_real
% 8.69/4.97                    @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7341_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 8.69/4.97        ( ! [I4: int] :
% 8.69/4.97            ( ( member_int @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 8.69/4.97            = one_one_real )
% 8.69/4.97         => ( ! [I4: int] :
% 8.69/4.97                ( ( member_int @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_real
% 8.69/4.97              @ ( abs_abs_real
% 8.69/4.97                @ ( minus_minus_real
% 8.69/4.97                  @ ( groups8778361861064173332t_real
% 8.69/4.97                    @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7342_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 8.69/4.97        ( ! [I4: complex] :
% 8.69/4.97            ( ( member_complex @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 8.69/4.97            = one_one_rat )
% 8.69/4.97         => ( ! [I4: complex] :
% 8.69/4.97                ( ( member_complex @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_rat
% 8.69/4.97              @ ( abs_abs_rat
% 8.69/4.97                @ ( minus_minus_rat
% 8.69/4.97                  @ ( groups5058264527183730370ex_rat
% 8.69/4.97                    @ ^ [I5: complex] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7343_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 8.69/4.97        ( ! [I4: real] :
% 8.69/4.97            ( ( member_real @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 8.69/4.97            = one_one_rat )
% 8.69/4.97         => ( ! [I4: real] :
% 8.69/4.97                ( ( member_real @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_rat
% 8.69/4.97              @ ( abs_abs_rat
% 8.69/4.97                @ ( minus_minus_rat
% 8.69/4.97                  @ ( groups1300246762558778688al_rat
% 8.69/4.97                    @ ^ [I5: real] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7344_convex__sum__bound__le,axiom,
% 8.69/4.97      ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 8.69/4.97        ( ! [I4: nat] :
% 8.69/4.97            ( ( member_nat @ I4 @ I6 )
% 8.69/4.97           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 8.69/4.97       => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 8.69/4.97            = one_one_rat )
% 8.69/4.97         => ( ! [I4: nat] :
% 8.69/4.97                ( ( member_nat @ I4 @ I6 )
% 8.69/4.97               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 8.69/4.97           => ( ord_less_eq_rat
% 8.69/4.97              @ ( abs_abs_rat
% 8.69/4.97                @ ( minus_minus_rat
% 8.69/4.97                  @ ( groups2906978787729119204at_rat
% 8.69/4.97                    @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 8.69/4.97                    @ I6 )
% 8.69/4.97                  @ B ) )
% 8.69/4.97              @ Delta ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7345_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 8.69/4.97        = ( N = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7346_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.69/4.97        = ( N = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7347_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 8.69/4.97        = ( N = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7348_mask__nat__def,axiom,
% 8.69/4.97      ( bit_se2002935070580805687sk_nat
% 8.69/4.97      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7349_mask__half__int,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.97        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7350_mask__int__def,axiom,
% 8.69/4.97      ( bit_se2000444600071755411sk_int
% 8.69/4.97      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7351_mask__eq__exp__minus__1,axiom,
% 8.69/4.97      ( bit_se2002935070580805687sk_nat
% 8.69/4.97      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7352_mask__eq__exp__minus__1,axiom,
% 8.69/4.97      ( bit_se2000444600071755411sk_int
% 8.69/4.97      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7353_divmod__step__nat__def,axiom,
% 8.69/4.97      ( unique5026877609467782581ep_nat
% 8.69/4.97      = ( ^ [L: num] :
% 8.69/4.97            ( produc2626176000494625587at_nat
% 8.69/4.97            @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7354_divmod__step__int__def,axiom,
% 8.69/4.97      ( unique5024387138958732305ep_int
% 8.69/4.97      = ( ^ [L: num] :
% 8.69/4.97            ( produc4245557441103728435nt_int
% 8.69/4.97            @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7355_divmod__nat__if,axiom,
% 8.69/4.97      ( divmod_nat
% 8.69/4.97      = ( ^ [M3: nat,N2: nat] :
% 8.69/4.97            ( if_Pro6206227464963214023at_nat
% 8.69/4.97            @ ( ( N2 = zero_zero_nat )
% 8.69/4.97              | ( ord_less_nat @ M3 @ N2 ) )
% 8.69/4.97            @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 8.69/4.97            @ ( produc2626176000494625587at_nat
% 8.69/4.97              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 8.69/4.97              @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7356_num_Osize__gen_I3_J,axiom,
% 8.69/4.97      ! [X32: num] :
% 8.69/4.97        ( ( size_num @ ( bit1 @ X32 ) )
% 8.69/4.97        = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7357_take__bit__rec,axiom,
% 8.69/4.97      ( bit_se1745604003318907178nteger
% 8.69/4.97      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7358_take__bit__rec,axiom,
% 8.69/4.97      ( bit_se2923211474154528505it_int
% 8.69/4.97      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7359_take__bit__rec,axiom,
% 8.69/4.97      ( bit_se2925701944663578781it_nat
% 8.69/4.97      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7360_num_Osize__gen_I2_J,axiom,
% 8.69/4.97      ! [X22: num] :
% 8.69/4.97        ( ( size_num @ ( bit0 @ X22 ) )
% 8.69/4.97        = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7361_tanh__real__altdef,axiom,
% 8.69/4.97      ( tanh_real
% 8.69/4.97      = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7362_and__int__unfold,axiom,
% 8.69/4.97      ( bit_se725231765392027082nd_int
% 8.69/4.97      = ( ^ [K2: int,L: int] :
% 8.69/4.97            ( if_int
% 8.69/4.97            @ ( ( K2 = zero_zero_int )
% 8.69/4.97              | ( L = zero_zero_int ) )
% 8.69/4.97            @ zero_zero_int
% 8.69/4.97            @ ( if_int
% 8.69/4.97              @ ( K2
% 8.69/4.97                = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97              @ L
% 8.69/4.97              @ ( if_int
% 8.69/4.97                @ ( L
% 8.69/4.97                  = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97                @ K2
% 8.69/4.97                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7363_and_Oidem,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ A @ A )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7364_and_Oidem,axiom,
% 8.69/4.97      ! [A: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ A @ A )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7365_and_Oleft__idem,axiom,
% 8.69/4.97      ! [A: int,B: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7366_and_Oleft__idem,axiom,
% 8.69/4.97      ! [A: nat,B: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 8.69/4.97        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7367_and_Oright__idem,axiom,
% 8.69/4.97      ! [A: int,B: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7368_and_Oright__idem,axiom,
% 8.69/4.97      ! [A: nat,B: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 8.69/4.97        = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7369_case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc8763457246119570046nteger,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 8.69/4.97        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( C @ A5 @ B5 ) )
% 8.69/4.97       => ( produc127349428274296955eger_o @ C @ P5 ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7370_case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 8.69/4.97        ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( C @ A5 @ B5 ) )
% 8.69/4.97       => ( produc6253627499356882019eger_o @ C @ P5 ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7371_case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 8.69/4.97        ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 8.69/4.97           => ( C @ A5 @ B5 ) )
% 8.69/4.97       => ( produc1573362020775583542_int_o @ C @ P5 ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7372_case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 8.69/4.97        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 8.69/4.97           => ( C @ A5 @ B5 ) )
% 8.69/4.97       => ( produc2558449545302689196_int_o @ C @ P5 ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7373_case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,C: int > int > $o] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( C @ A5 @ B5 ) )
% 8.69/4.97       => ( produc4947309494688390418_int_o @ C @ P5 ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7374_case__prodI,axiom,
% 8.69/4.97      ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( F @ A @ B )
% 8.69/4.97       => ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7375_case__prodI,axiom,
% 8.69/4.97      ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( F @ A @ B )
% 8.69/4.97       => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7376_case__prodI,axiom,
% 8.69/4.97      ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 8.69/4.97        ( ( F @ A @ B )
% 8.69/4.97       => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7377_case__prodI,axiom,
% 8.69/4.97      ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 8.69/4.97        ( ( F @ A @ B )
% 8.69/4.97       => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7378_case__prodI,axiom,
% 8.69/4.97      ! [F: int > int > $o,A: int,B: int] :
% 8.69/4.97        ( ( F @ A @ B )
% 8.69/4.97       => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7379_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,Z: complex,C: int > int > set_complex] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7380_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,Z: real,C: int > int > set_real] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7381_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,Z: nat,C: int > int > set_nat] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7382_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,Z: int,C: int > int > set_int] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7383_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: product_prod_int_int,Z: set_nat,C: int > int > set_set_nat] :
% 8.69/4.97        ( ! [A5: int,B5: int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( product_Pair_int_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_set_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7384_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc8763457246119570046nteger,Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex] :
% 8.69/4.97        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7385_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc8763457246119570046nteger,Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real] :
% 8.69/4.97        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7386_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc8763457246119570046nteger,Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 8.69/4.97        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7387_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc8763457246119570046nteger,Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 8.69/4.97        ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 8.69/4.97           => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7388_mem__case__prodI2,axiom,
% 8.69/4.97      ! [P5: produc7773217078559923341nt_int,Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex] :
% 8.69/4.97        ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 8.69/4.97            ( ( P5
% 8.69/4.97              = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 8.69/4.97           => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7389_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: complex,C: int > int > set_complex,A: int,B: int] :
% 8.69/4.97        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7390_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: real,C: int > int > set_real,A: int,B: int] :
% 8.69/4.97        ( ( member_real @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7391_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: nat,C: int > int > set_nat,A: int,B: int] :
% 8.69/4.97        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7392_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: int,C: int > int > set_int,A: int,B: int] :
% 8.69/4.97        ( ( member_int @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7393_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: set_nat,C: int > int > set_set_nat,A: int,B: int] :
% 8.69/4.97        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7394_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7395_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( member_real @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7396_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7397_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( member_int @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7398_mem__case__prodI,axiom,
% 8.69/4.97      ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 8.69/4.97        ( ( member_complex @ Z @ ( C @ A @ B ) )
% 8.69/4.97       => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7399_case__prodI2_H,axiom,
% 8.69/4.97      ! [P5: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 8.69/4.97        ( ! [A5: nat,B5: nat] :
% 8.69/4.97            ( ( ( product_Pair_nat_nat @ A5 @ B5 )
% 8.69/4.97              = P5 )
% 8.69/4.97           => ( C @ A5 @ B5 @ X ) )
% 8.69/4.97       => ( produc8739625826339149834_nat_o @ C @ P5 @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7400_take__bit__of__0,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7401_take__bit__of__0,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7402_and__zero__eq,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7403_and__zero__eq,axiom,
% 8.69/4.97      ! [A: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7404_zero__and__eq,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7405_zero__and__eq,axiom,
% 8.69/4.97      ! [A: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7406_bit_Oconj__zero__left,axiom,
% 8.69/4.97      ! [X: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7407_bit_Oconj__zero__right,axiom,
% 8.69/4.97      ! [X: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7408_take__bit__and,axiom,
% 8.69/4.97      ! [N: nat,A: int,B: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7409_take__bit__and,axiom,
% 8.69/4.97      ! [N: nat,A: nat,B: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 8.69/4.97        = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7410_exp__le__cancel__iff,axiom,
% 8.69/4.97      ! [X: real,Y: real] :
% 8.69/4.97        ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 8.69/4.97        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7411_concat__bit__of__zero__2,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 8.69/4.97        = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7412_take__bit__0,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7413_take__bit__0,axiom,
% 8.69/4.97      ! [A: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7414_exp__zero,axiom,
% 8.69/4.97      ( ( exp_complex @ zero_zero_complex )
% 8.69/4.97      = one_one_complex ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7415_exp__zero,axiom,
% 8.69/4.97      ( ( exp_real @ zero_zero_real )
% 8.69/4.97      = one_one_real ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7416_take__bit__Suc__1,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7417_take__bit__Suc__1,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 8.69/4.97        = one_one_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7418_and_Oleft__neutral,axiom,
% 8.69/4.97      ! [A: code_integer] :
% 8.69/4.97        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7419_and_Oleft__neutral,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7420_and_Oright__neutral,axiom,
% 8.69/4.97      ! [A: code_integer] :
% 8.69/4.97        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7421_and_Oright__neutral,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97        = A ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7422_bit_Oconj__one__right,axiom,
% 8.69/4.97      ! [X: code_integer] :
% 8.69/4.97        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.97        = X ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7423_bit_Oconj__one__right,axiom,
% 8.69/4.97      ! [X: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97        = X ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7424_take__bit__numeral__1,axiom,
% 8.69/4.97      ! [L2: num] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7425_take__bit__numeral__1,axiom,
% 8.69/4.97      ! [L2: num] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 8.69/4.97        = one_one_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7426_exp__eq__one__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ( exp_real @ X )
% 8.69/4.97          = one_one_real )
% 8.69/4.97        = ( X = zero_zero_real ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7427_and__nonnegative__int__iff,axiom,
% 8.69/4.97      ! [K: int,L2: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 8.69/4.97        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/4.97          | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7428_and__negative__int__iff,axiom,
% 8.69/4.97      ! [K: int,L2: int] :
% 8.69/4.97        ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 8.69/4.97        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.69/4.97          & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7429_take__bit__of__1__eq__0__iff,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 8.69/4.97          = zero_zero_int )
% 8.69/4.97        = ( N = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7430_take__bit__of__1__eq__0__iff,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 8.69/4.97          = zero_zero_nat )
% 8.69/4.97        = ( N = zero_zero_nat ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7431_and__numerals_I2_J,axiom,
% 8.69/4.97      ! [Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7432_and__numerals_I2_J,axiom,
% 8.69/4.97      ! [Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/4.97        = one_one_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7433_and__numerals_I8_J,axiom,
% 8.69/4.97      ! [X: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7434_and__numerals_I8_J,axiom,
% 8.69/4.97      ! [X: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 8.69/4.97        = one_one_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7435_one__less__exp__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 8.69/4.97        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7436_exp__less__one__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 8.69/4.97        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7437_exp__le__one__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 8.69/4.97        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7438_one__le__exp__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 8.69/4.97        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7439_take__bit__minus__one__eq__mask,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.97        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7440_take__bit__minus__one__eq__mask,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7441_exp__ln,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.97       => ( ( exp_real @ ( ln_ln_real @ X ) )
% 8.69/4.97          = X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7442_exp__ln__iff,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 8.69/4.97          = X )
% 8.69/4.97        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7443_take__bit__of__Suc__0,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/4.97        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7444_and__numerals_I1_J,axiom,
% 8.69/4.97      ! [Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7445_and__numerals_I1_J,axiom,
% 8.69/4.97      ! [Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7446_and__numerals_I5_J,axiom,
% 8.69/4.97      ! [X: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7447_and__numerals_I5_J,axiom,
% 8.69/4.97      ! [X: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 8.69/4.97        = zero_zero_nat ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7448_and__numerals_I3_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.69/4.97        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7449_and__numerals_I3_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/4.97        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7450_sum_Ocl__ivl__Suc,axiom,
% 8.69/4.97      ! [N: nat,M: nat,G: nat > complex] :
% 8.69/4.97        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = zero_zero_complex ) )
% 8.69/4.97        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7451_sum_Ocl__ivl__Suc,axiom,
% 8.69/4.97      ! [N: nat,M: nat,G: nat > rat] :
% 8.69/4.97        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = zero_zero_rat ) )
% 8.69/4.97        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7452_sum_Ocl__ivl__Suc,axiom,
% 8.69/4.97      ! [N: nat,M: nat,G: nat > int] :
% 8.69/4.97        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = zero_zero_int ) )
% 8.69/4.97        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7453_sum_Ocl__ivl__Suc,axiom,
% 8.69/4.97      ! [N: nat,M: nat,G: nat > nat] :
% 8.69/4.97        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = zero_zero_nat ) )
% 8.69/4.97        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7454_sum_Ocl__ivl__Suc,axiom,
% 8.69/4.97      ! [N: nat,M: nat,G: nat > real] :
% 8.69/4.97        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = zero_zero_real ) )
% 8.69/4.97        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 8.69/4.97         => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97            = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7455_take__bit__of__1,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 8.69/4.97        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7456_take__bit__of__1,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 8.69/4.97        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7457_take__bit__of__1,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 8.69/4.97        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7458_and__minus__numerals_I6_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7459_and__minus__numerals_I2_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/4.97        = one_one_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7460_sum__zero__power,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > complex] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2073611262835488442omplex
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( C @ zero_zero_nat ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2073611262835488442omplex
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_complex ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7461_sum__zero__power,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > rat] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( C @ zero_zero_nat ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_rat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7462_sum__zero__power,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > real] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups6591440286371151544t_real
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( C @ zero_zero_nat ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups6591440286371151544t_real
% 8.69/4.97              @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_real ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7463_and__numerals_I4_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 8.69/4.97        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7464_and__numerals_I4_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/4.97        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7465_and__numerals_I6_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.69/4.97        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7466_and__numerals_I6_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/4.97        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7467_even__take__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,A: code_integer] :
% 8.69/4.97        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 8.69/4.97        = ( ( N = zero_zero_nat )
% 8.69/4.97          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7468_even__take__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,A: int] :
% 8.69/4.97        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 8.69/4.97        = ( ( N = zero_zero_nat )
% 8.69/4.97          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7469_even__take__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,A: nat] :
% 8.69/4.97        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 8.69/4.97        = ( ( N = zero_zero_nat )
% 8.69/4.97          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7470_and__minus__numerals_I1_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7471_and__minus__numerals_I5_J,axiom,
% 8.69/4.97      ! [N: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 8.69/4.97        = zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7472_sum__zero__power_H,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2073611262835488442omplex
% 8.69/4.97              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2073611262835488442omplex
% 8.69/4.97              @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_complex ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7473_sum__zero__power_H,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat
% 8.69/4.97              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups2906978787729119204at_rat
% 8.69/4.97              @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_rat ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7474_sum__zero__power_H,axiom,
% 8.69/4.97      ! [A2: set_nat,C: nat > real,D: nat > real] :
% 8.69/4.97        ( ( ( ( finite_finite_nat @ A2 )
% 8.69/4.97            & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups6591440286371151544t_real
% 8.69/4.97              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.69/4.97        & ( ~ ( ( finite_finite_nat @ A2 )
% 8.69/4.97              & ( member_nat @ zero_zero_nat @ A2 ) )
% 8.69/4.97         => ( ( groups6591440286371151544t_real
% 8.69/4.97              @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 8.69/4.97              @ A2 )
% 8.69/4.97            = zero_zero_real ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7475_take__bit__Suc__0,axiom,
% 8.69/4.97      ! [A: code_integer] :
% 8.69/4.97        ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 8.69/4.97        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7476_take__bit__Suc__0,axiom,
% 8.69/4.97      ! [A: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 8.69/4.97        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7477_take__bit__Suc__0,axiom,
% 8.69/4.97      ! [A: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 8.69/4.97        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7478_and__numerals_I7_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 8.69/4.97        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7479_and__numerals_I7_J,axiom,
% 8.69/4.97      ! [X: num,Y: num] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/4.97        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7480_take__bit__of__exp,axiom,
% 8.69/4.97      ! [M: nat,N: nat] :
% 8.69/4.97        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.97        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7481_take__bit__of__exp,axiom,
% 8.69/4.97      ! [M: nat,N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.97        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7482_take__bit__of__exp,axiom,
% 8.69/4.97      ! [M: nat,N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.97        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7483_take__bit__of__2,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.97        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7484_take__bit__of__2,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.97        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7485_take__bit__of__2,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.97        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7486_take__bit__eq__mask,axiom,
% 8.69/4.97      ( bit_se2923211474154528505it_int
% 8.69/4.97      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7487_take__bit__eq__mask,axiom,
% 8.69/4.97      ( bit_se2925701944663578781it_nat
% 8.69/4.97      = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7488_of__int__and__eq,axiom,
% 8.69/4.97      ! [K: int,L2: int] :
% 8.69/4.97        ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7489_take__bit__of__int,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 8.69/4.97        = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7490_and_Oassoc,axiom,
% 8.69/4.97      ! [A: int,B: int,C: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7491_and_Oassoc,axiom,
% 8.69/4.97      ! [A: nat,B: nat,C: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 8.69/4.97        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7492_and_Ocommute,axiom,
% 8.69/4.97      ( bit_se725231765392027082nd_int
% 8.69/4.97      = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7493_and_Ocommute,axiom,
% 8.69/4.97      ( bit_se727722235901077358nd_nat
% 8.69/4.97      = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7494_and_Oleft__commute,axiom,
% 8.69/4.97      ! [B: int,A: int,C: int] :
% 8.69/4.97        ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 8.69/4.97        = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7495_and_Oleft__commute,axiom,
% 8.69/4.97      ! [B: nat,A: nat,C: nat] :
% 8.69/4.97        ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 8.69/4.97        = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7496_take__bit__add,axiom,
% 8.69/4.97      ! [N: nat,A: int,B: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 8.69/4.97        = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7497_take__bit__add,axiom,
% 8.69/4.97      ! [N: nat,A: nat,B: nat] :
% 8.69/4.97        ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 8.69/4.97        = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7498_take__bit__tightened,axiom,
% 8.69/4.97      ! [N: nat,A: int,B: int,M: nat] :
% 8.69/4.97        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 8.69/4.97          = ( bit_se2923211474154528505it_int @ N @ B ) )
% 8.69/4.97       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ M @ A )
% 8.69/4.97            = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7499_take__bit__tightened,axiom,
% 8.69/4.97      ! [N: nat,A: nat,B: nat,M: nat] :
% 8.69/4.97        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 8.69/4.97          = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 8.69/4.97       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 8.69/4.97            = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7500_take__bit__tightened__less__eq__nat,axiom,
% 8.69/4.97      ! [M: nat,N: nat,Q2: nat] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7501_take__bit__nat__less__eq__self,axiom,
% 8.69/4.97      ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7502_exp__not__eq__zero,axiom,
% 8.69/4.97      ! [X: complex] :
% 8.69/4.97        ( ( exp_complex @ X )
% 8.69/4.97       != zero_zero_complex ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7503_exp__not__eq__zero,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( exp_real @ X )
% 8.69/4.97       != zero_zero_real ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7504_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: complex,C: int > int > set_complex,P5: product_prod_int_int] :
% 8.69/4.97        ( ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7505_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: real,C: int > int > set_real,P5: product_prod_int_int] :
% 8.69/4.97        ( ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7506_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: nat,C: int > int > set_nat,P5: product_prod_int_int] :
% 8.69/4.97        ( ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7507_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: int,C: int > int > set_int,P5: product_prod_int_int] :
% 8.69/4.97        ( ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7508_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: set_nat,C: int > int > set_set_nat,P5: product_prod_int_int] :
% 8.69/4.97        ( ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_set_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7509_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,P5: produc8763457246119570046nteger] :
% 8.69/4.97        ( ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7510_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,P5: produc8763457246119570046nteger] :
% 8.69/4.97        ( ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7511_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P5: produc8763457246119570046nteger] :
% 8.69/4.97        ( ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7512_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P5: produc8763457246119570046nteger] :
% 8.69/4.97        ( ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7513_mem__case__prodE,axiom,
% 8.69/4.97      ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,P5: produc7773217078559923341nt_int] :
% 8.69/4.97        ( ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) )
% 8.69/4.97       => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7514_take__bit__minus,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 8.69/4.97        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7515_exp__times__arg__commute,axiom,
% 8.69/4.97      ! [A2: complex] :
% 8.69/4.97        ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 8.69/4.97        = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7516_exp__times__arg__commute,axiom,
% 8.69/4.97      ! [A2: real] :
% 8.69/4.97        ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 8.69/4.97        = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7517_take__bit__mult,axiom,
% 8.69/4.97      ! [N: nat,K: int,L2: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 8.69/4.97        = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7518_take__bit__diff,axiom,
% 8.69/4.97      ! [N: nat,K: int,L2: int] :
% 8.69/4.97        ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 8.69/4.97        = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7519_concat__bit__eq__iff,axiom,
% 8.69/4.97      ! [N: nat,K: int,L2: int,R: int,S: int] :
% 8.69/4.97        ( ( ( bit_concat_bit @ N @ K @ L2 )
% 8.69/4.97          = ( bit_concat_bit @ N @ R @ S ) )
% 8.69/4.97        = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.97            = ( bit_se2923211474154528505it_int @ N @ R ) )
% 8.69/4.97          & ( L2 = S ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7520_concat__bit__take__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,B: int] :
% 8.69/4.97        ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 8.69/4.97        = ( bit_concat_bit @ N @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7521_case__prodE,axiom,
% 8.69/4.97      ! [C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc8763457246119570046nteger] :
% 8.69/4.97        ( ( produc127349428274296955eger_o @ C @ P5 )
% 8.69/4.97       => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7522_case__prodE,axiom,
% 8.69/4.97      ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc1908205239877642774nteger] :
% 8.69/4.97        ( ( produc6253627499356882019eger_o @ C @ P5 )
% 8.69/4.97       => ~ ! [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc8603105652947943368nteger @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7523_case__prodE,axiom,
% 8.69/4.97      ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc2285326912895808259nt_int] :
% 8.69/4.97        ( ( produc1573362020775583542_int_o @ C @ P5 )
% 8.69/4.97       => ~ ! [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc5700946648718959541nt_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7524_case__prodE,axiom,
% 8.69/4.97      ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc7773217078559923341nt_int] :
% 8.69/4.97        ( ( produc2558449545302689196_int_o @ C @ P5 )
% 8.69/4.97       => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7525_case__prodE,axiom,
% 8.69/4.97      ! [C: int > int > $o,P5: product_prod_int_int] :
% 8.69/4.97        ( ( produc4947309494688390418_int_o @ C @ P5 )
% 8.69/4.97       => ~ ! [X6: int,Y5: int] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_int_int @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7526_case__prodD,axiom,
% 8.69/4.97      ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) )
% 8.69/4.97       => ( F @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7527_case__prodD,axiom,
% 8.69/4.97      ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 8.69/4.97        ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 8.69/4.97       => ( F @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7528_case__prodD,axiom,
% 8.69/4.97      ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 8.69/4.97        ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 8.69/4.97       => ( F @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7529_case__prodD,axiom,
% 8.69/4.97      ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 8.69/4.97        ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 8.69/4.97       => ( F @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7530_case__prodD,axiom,
% 8.69/4.97      ! [F: int > int > $o,A: int,B: int] :
% 8.69/4.97        ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 8.69/4.97       => ( F @ A @ B ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7531_case__prodE_H,axiom,
% 8.69/4.97      ! [C: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 8.69/4.97        ( ( produc8739625826339149834_nat_o @ C @ P5 @ Z )
% 8.69/4.97       => ~ ! [X6: nat,Y5: nat] :
% 8.69/4.97              ( ( P5
% 8.69/4.97                = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 8.69/4.97             => ~ ( C @ X6 @ Y5 @ Z ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7532_case__prodD_H,axiom,
% 8.69/4.97      ! [R4: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 8.69/4.97        ( ( produc8739625826339149834_nat_o @ R4 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 8.69/4.97       => ( R4 @ A @ B @ C ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7533_and__eq__minus__1__iff,axiom,
% 8.69/4.97      ! [A: code_integer,B: code_integer] :
% 8.69/4.97        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 8.69/4.97          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.97        = ( ( A
% 8.69/4.97            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.97          & ( B
% 8.69/4.97            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7534_and__eq__minus__1__iff,axiom,
% 8.69/4.97      ! [A: int,B: int] :
% 8.69/4.97        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 8.69/4.97          = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97        = ( ( A
% 8.69/4.97            = ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.97          & ( B
% 8.69/4.97            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7535_not__exp__less__zero,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7536_exp__gt__zero,axiom,
% 8.69/4.97      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7537_exp__total,axiom,
% 8.69/4.97      ! [Y: real] :
% 8.69/4.97        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.97       => ? [X6: real] :
% 8.69/4.97            ( ( exp_real @ X6 )
% 8.69/4.97            = Y ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7538_exp__ge__zero,axiom,
% 8.69/4.97      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7539_not__exp__le__zero,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7540_sum__cong__Suc,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 8.69/4.97        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 8.69/4.97       => ( ! [X6: nat] :
% 8.69/4.97              ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 8.69/4.97             => ( ( F @ ( suc @ X6 ) )
% 8.69/4.97                = ( G @ ( suc @ X6 ) ) ) )
% 8.69/4.97         => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 8.69/4.97            = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7541_sum__cong__Suc,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > real,G: nat > real] :
% 8.69/4.97        ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 8.69/4.97       => ( ! [X6: nat] :
% 8.69/4.97              ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 8.69/4.97             => ( ( F @ ( suc @ X6 ) )
% 8.69/4.97                = ( G @ ( suc @ X6 ) ) ) )
% 8.69/4.97         => ( ( groups6591440286371151544t_real @ F @ A2 )
% 8.69/4.97            = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7542_take__bit__tightened__less__eq__int,axiom,
% 8.69/4.97      ! [M: nat,N: nat,K: int] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7543_AND__upper2_H,axiom,
% 8.69/4.97      ! [Y: int,Z: int,X: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.97       => ( ( ord_less_eq_int @ Y @ Z )
% 8.69/4.97         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7544_AND__upper1_H,axiom,
% 8.69/4.97      ! [Y: int,Z: int,Ya: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.97       => ( ( ord_less_eq_int @ Y @ Z )
% 8.69/4.97         => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7545_AND__upper2,axiom,
% 8.69/4.97      ! [Y: int,X: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.97       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7546_AND__upper1,axiom,
% 8.69/4.97      ! [X: int,Y: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/4.97       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7547_AND__lower,axiom,
% 8.69/4.97      ! [X: int,Y: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/4.97       => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7548_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,A: int,B: int] :
% 8.69/4.97        ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 8.69/4.97          = ( bit_ri631733984087533419it_int @ N @ B ) )
% 8.69/4.97        = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 8.69/4.97          = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7549_take__bit__int__less__eq__self__iff,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 8.69/4.97        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7550_take__bit__nonnegative,axiom,
% 8.69/4.97      ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7551_not__take__bit__negative,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7552_take__bit__int__greater__self__iff,axiom,
% 8.69/4.97      ! [K: int,N: nat] :
% 8.69/4.97        ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.69/4.97        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7553_signed__take__bit__take__bit,axiom,
% 8.69/4.97      ! [M: nat,N: nat,A: int] :
% 8.69/4.97        ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 8.69/4.97        = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7554_mult__exp__exp,axiom,
% 8.69/4.97      ! [X: complex,Y: complex] :
% 8.69/4.97        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 8.69/4.97        = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7555_mult__exp__exp,axiom,
% 8.69/4.97      ! [X: real,Y: real] :
% 8.69/4.97        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 8.69/4.97        = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7556_exp__add__commuting,axiom,
% 8.69/4.97      ! [X: complex,Y: complex] :
% 8.69/4.97        ( ( ( times_times_complex @ X @ Y )
% 8.69/4.97          = ( times_times_complex @ Y @ X ) )
% 8.69/4.97       => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 8.69/4.97          = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7557_exp__add__commuting,axiom,
% 8.69/4.97      ! [X: real,Y: real] :
% 8.69/4.97        ( ( ( times_times_real @ X @ Y )
% 8.69/4.97          = ( times_times_real @ Y @ X ) )
% 8.69/4.97       => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 8.69/4.97          = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7558_exp__diff,axiom,
% 8.69/4.97      ! [X: complex,Y: complex] :
% 8.69/4.97        ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 8.69/4.97        = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7559_exp__diff,axiom,
% 8.69/4.97      ! [X: real,Y: real] :
% 8.69/4.97        ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 8.69/4.97        = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7560_take__bit__unset__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: int] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7561_take__bit__unset__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: nat] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7562_take__bit__set__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: int] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7563_take__bit__set__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: nat] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7564_take__bit__flip__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: int] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 8.69/4.97            = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7565_take__bit__flip__bit__eq,axiom,
% 8.69/4.97      ! [N: nat,M: nat,A: nat] :
% 8.69/4.97        ( ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 8.69/4.97        & ( ~ ( ord_less_eq_nat @ N @ M )
% 8.69/4.97         => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 8.69/4.97            = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7566_sum__subtractf__nat,axiom,
% 8.69/4.97      ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 8.69/4.97        ( ! [X6: complex] :
% 8.69/4.97            ( ( member_complex @ X6 @ A2 )
% 8.69/4.97           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 8.69/4.97       => ( ( groups5693394587270226106ex_nat
% 8.69/4.97            @ ^ [X3: complex] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.97            @ A2 )
% 8.69/4.97          = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7567_sum__subtractf__nat,axiom,
% 8.69/4.97      ! [A2: set_real,G: real > nat,F: real > nat] :
% 8.69/4.97        ( ! [X6: real] :
% 8.69/4.97            ( ( member_real @ X6 @ A2 )
% 8.69/4.97           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 8.69/4.97       => ( ( groups1935376822645274424al_nat
% 8.69/4.97            @ ^ [X3: real] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.97            @ A2 )
% 8.69/4.97          = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7568_sum__subtractf__nat,axiom,
% 8.69/4.97      ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 8.69/4.97        ( ! [X6: set_nat] :
% 8.69/4.97            ( ( member_set_nat @ X6 @ A2 )
% 8.69/4.97           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 8.69/4.97       => ( ( groups8294997508430121362at_nat
% 8.69/4.97            @ ^ [X3: set_nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.97            @ A2 )
% 8.69/4.97          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7569_sum__subtractf__nat,axiom,
% 8.69/4.97      ! [A2: set_int,G: int > nat,F: int > nat] :
% 8.69/4.97        ( ! [X6: int] :
% 8.69/4.97            ( ( member_int @ X6 @ A2 )
% 8.69/4.97           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 8.69/4.97       => ( ( groups4541462559716669496nt_nat
% 8.69/4.97            @ ^ [X3: int] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.97            @ A2 )
% 8.69/4.97          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7570_sum__subtractf__nat,axiom,
% 8.69/4.97      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 8.69/4.97        ( ! [X6: nat] :
% 8.69/4.97            ( ( member_nat @ X6 @ A2 )
% 8.69/4.97           => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 8.69/4.97       => ( ( groups3542108847815614940at_nat
% 8.69/4.97            @ ^ [X3: nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/4.97            @ A2 )
% 8.69/4.97          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7571_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.69/4.97      ! [G: nat > nat,M: nat,N: nat] :
% 8.69/4.97        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 8.69/4.97        = ( groups3542108847815614940at_nat
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7572_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.69/4.97      ! [G: nat > real,M: nat,N: nat] :
% 8.69/4.97        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 8.69/4.97        = ( groups6591440286371151544t_real
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7573_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 8.69/4.97      ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 8.69/4.97        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 8.69/4.97        = ( groups3542108847815614940at_nat
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7574_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 8.69/4.97      ! [G: nat > real,M: nat,K: nat,N: nat] :
% 8.69/4.97        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 8.69/4.97        = ( groups6591440286371151544t_real
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7575_sum__eq__Suc0__iff,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 8.69/4.97            = ( suc @ zero_zero_nat ) )
% 8.69/4.97          = ( ? [X3: int] :
% 8.69/4.97                ( ( member_int @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = ( suc @ zero_zero_nat ) )
% 8.69/4.97                & ! [Y3: int] :
% 8.69/4.97                    ( ( member_int @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7576_sum__eq__Suc0__iff,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 8.69/4.97            = ( suc @ zero_zero_nat ) )
% 8.69/4.97          = ( ? [X3: complex] :
% 8.69/4.97                ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = ( suc @ zero_zero_nat ) )
% 8.69/4.97                & ! [Y3: complex] :
% 8.69/4.97                    ( ( member_complex @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7577_sum__eq__Suc0__iff,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > nat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 8.69/4.97            = ( suc @ zero_zero_nat ) )
% 8.69/4.97          = ( ? [X3: nat] :
% 8.69/4.97                ( ( member_nat @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = ( suc @ zero_zero_nat ) )
% 8.69/4.97                & ! [Y3: nat] :
% 8.69/4.97                    ( ( member_nat @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7578_sum__SucD,axiom,
% 8.69/4.97      ! [F: nat > nat,A2: set_nat,N: nat] :
% 8.69/4.97        ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 8.69/4.97          = ( suc @ N ) )
% 8.69/4.97       => ? [X6: nat] :
% 8.69/4.97            ( ( member_nat @ X6 @ A2 )
% 8.69/4.97            & ( ord_less_nat @ zero_zero_nat @ ( F @ X6 ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7579_exp__gt__one,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.97       => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7580_sum__eq__1__iff,axiom,
% 8.69/4.97      ! [A2: set_int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ A2 )
% 8.69/4.97       => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 8.69/4.97            = one_one_nat )
% 8.69/4.97          = ( ? [X3: int] :
% 8.69/4.97                ( ( member_int @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = one_one_nat )
% 8.69/4.97                & ! [Y3: int] :
% 8.69/4.97                    ( ( member_int @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7581_sum__eq__1__iff,axiom,
% 8.69/4.97      ! [A2: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.97       => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 8.69/4.97            = one_one_nat )
% 8.69/4.97          = ( ? [X3: complex] :
% 8.69/4.97                ( ( member_complex @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = one_one_nat )
% 8.69/4.97                & ! [Y3: complex] :
% 8.69/4.97                    ( ( member_complex @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7582_sum__eq__1__iff,axiom,
% 8.69/4.97      ! [A2: set_nat,F: nat > nat] :
% 8.69/4.97        ( ( finite_finite_nat @ A2 )
% 8.69/4.97       => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 8.69/4.97            = one_one_nat )
% 8.69/4.97          = ( ? [X3: nat] :
% 8.69/4.97                ( ( member_nat @ X3 @ A2 )
% 8.69/4.97                & ( ( F @ X3 )
% 8.69/4.97                  = one_one_nat )
% 8.69/4.97                & ! [Y3: nat] :
% 8.69/4.97                    ( ( member_nat @ Y3 @ A2 )
% 8.69/4.97                   => ( ( X3 != Y3 )
% 8.69/4.97                     => ( ( F @ Y3 )
% 8.69/4.97                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7583_take__bit__signed__take__bit,axiom,
% 8.69/4.97      ! [M: nat,N: nat,A: int] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.97       => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 8.69/4.97          = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7584_exp__ge__add__one__self,axiom,
% 8.69/4.97      ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7585_and__less__eq,axiom,
% 8.69/4.97      ! [L2: int,K: int] :
% 8.69/4.97        ( ( ord_less_int @ L2 @ zero_zero_int )
% 8.69/4.97       => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7586_AND__upper1_H_H,axiom,
% 8.69/4.97      ! [Y: int,Z: int,Ya: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.97       => ( ( ord_less_int @ Y @ Z )
% 8.69/4.97         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7587_AND__upper2_H_H,axiom,
% 8.69/4.97      ! [Y: int,Z: int,X: int] :
% 8.69/4.97        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/4.97       => ( ( ord_less_int @ Y @ Z )
% 8.69/4.97         => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7588_take__bit__eq__mask__iff,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.97          = ( bit_se2000444600071755411sk_int @ N ) )
% 8.69/4.97        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 8.69/4.97          = zero_zero_int ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7589_exp__minus__inverse,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 8.69/4.97        = one_one_real ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7590_exp__minus__inverse,axiom,
% 8.69/4.97      ! [X: complex] :
% 8.69/4.97        ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 8.69/4.97        = one_one_complex ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7591_take__bit__decr__eq,axiom,
% 8.69/4.97      ! [N: nat,K: int] :
% 8.69/4.97        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.97         != zero_zero_int )
% 8.69/4.97       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 8.69/4.97          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7592_sum__power__add,axiom,
% 8.69/4.97      ! [X: complex,M: nat,I6: set_nat] :
% 8.69/4.97        ( ( groups2073611262835488442omplex
% 8.69/4.97          @ ^ [I5: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I5 ) )
% 8.69/4.97          @ I6 )
% 8.69/4.97        = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7593_sum__power__add,axiom,
% 8.69/4.97      ! [X: rat,M: nat,I6: set_nat] :
% 8.69/4.97        ( ( groups2906978787729119204at_rat
% 8.69/4.97          @ ^ [I5: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I5 ) )
% 8.69/4.97          @ I6 )
% 8.69/4.97        = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I6 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7594_sum__power__add,axiom,
% 8.69/4.97      ! [X: int,M: nat,I6: set_nat] :
% 8.69/4.97        ( ( groups3539618377306564664at_int
% 8.69/4.97          @ ^ [I5: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I5 ) )
% 8.69/4.97          @ I6 )
% 8.69/4.97        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7595_sum__power__add,axiom,
% 8.69/4.97      ! [X: real,M: nat,I6: set_nat] :
% 8.69/4.97        ( ( groups6591440286371151544t_real
% 8.69/4.97          @ ^ [I5: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I5 ) )
% 8.69/4.97          @ I6 )
% 8.69/4.97        = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7596_sum_OatLeastAtMost__rev,axiom,
% 8.69/4.97      ! [G: nat > nat,N: nat,M: nat] :
% 8.69/4.97        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 8.69/4.97        = ( groups3542108847815614940at_nat
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7597_sum_OatLeastAtMost__rev,axiom,
% 8.69/4.97      ! [G: nat > real,N: nat,M: nat] :
% 8.69/4.97        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 8.69/4.97        = ( groups6591440286371151544t_real
% 8.69/4.97          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 8.69/4.97          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7598_sum__nth__roots,axiom,
% 8.69/4.97      ! [N: nat,C: complex] :
% 8.69/4.97        ( ( ord_less_nat @ one_one_nat @ N )
% 8.69/4.97       => ( ( groups7754918857620584856omplex
% 8.69/4.97            @ ^ [X3: complex] : X3
% 8.69/4.97            @ ( collect_complex
% 8.69/4.97              @ ^ [Z3: complex] :
% 8.69/4.97                  ( ( power_power_complex @ Z3 @ N )
% 8.69/4.97                  = C ) ) )
% 8.69/4.97          = zero_zero_complex ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7599_sum__roots__unity,axiom,
% 8.69/4.97      ! [N: nat] :
% 8.69/4.97        ( ( ord_less_nat @ one_one_nat @ N )
% 8.69/4.97       => ( ( groups7754918857620584856omplex
% 8.69/4.97            @ ^ [X3: complex] : X3
% 8.69/4.97            @ ( collect_complex
% 8.69/4.97              @ ^ [Z3: complex] :
% 8.69/4.97                  ( ( power_power_complex @ Z3 @ N )
% 8.69/4.97                  = one_one_complex ) ) )
% 8.69/4.97          = zero_zero_complex ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7600_even__and__iff,axiom,
% 8.69/4.97      ! [A: code_integer,B: code_integer] :
% 8.69/4.97        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 8.69/4.97        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.97          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7601_even__and__iff,axiom,
% 8.69/4.97      ! [A: int,B: int] :
% 8.69/4.97        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 8.69/4.97        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.97          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7602_even__and__iff,axiom,
% 8.69/4.97      ! [A: nat,B: nat] :
% 8.69/4.97        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 8.69/4.97        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.97          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7603_sum__diff__nat,axiom,
% 8.69/4.97      ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 8.69/4.97        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.97       => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 8.69/4.97         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7604_sum__diff__nat,axiom,
% 8.69/4.97      ! [B3: set_int,A2: set_int,F: int > nat] :
% 8.69/4.97        ( ( finite_finite_int @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 8.69/4.97         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7605_sum__diff__nat,axiom,
% 8.69/4.97      ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 8.69/4.97        ( ( finite_finite_nat @ B3 )
% 8.69/4.97       => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 8.69/4.97         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 8.69/4.97            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7606_exp__ge__add__one__self__aux,axiom,
% 8.69/4.97      ! [X: real] :
% 8.69/4.97        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.97       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7607_sum__shift__lb__Suc0__0,axiom,
% 8.69/4.97      ! [F: nat > complex,K: nat] :
% 8.69/4.97        ( ( ( F @ zero_zero_nat )
% 8.69/4.97          = zero_zero_complex )
% 8.69/4.97       => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 8.69/4.97          = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7608_sum__shift__lb__Suc0__0,axiom,
% 8.69/4.97      ! [F: nat > rat,K: nat] :
% 8.69/4.97        ( ( ( F @ zero_zero_nat )
% 8.69/4.97          = zero_zero_rat )
% 8.69/4.97       => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 8.69/4.97          = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7609_sum__shift__lb__Suc0__0,axiom,
% 8.69/4.97      ! [F: nat > int,K: nat] :
% 8.69/4.97        ( ( ( F @ zero_zero_nat )
% 8.69/4.97          = zero_zero_int )
% 8.69/4.97       => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 8.69/4.97          = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7610_sum__shift__lb__Suc0__0,axiom,
% 8.69/4.97      ! [F: nat > nat,K: nat] :
% 8.69/4.97        ( ( ( F @ zero_zero_nat )
% 8.69/4.97          = zero_zero_nat )
% 8.69/4.97       => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 8.69/4.97          = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7611_sum__shift__lb__Suc0__0,axiom,
% 8.69/4.97      ! [F: nat > real,K: nat] :
% 8.69/4.97        ( ( ( F @ zero_zero_nat )
% 8.69/4.97          = zero_zero_real )
% 8.69/4.97       => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 8.69/4.97          = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7612_even__and__iff__int,axiom,
% 8.69/4.97      ! [K: int,L2: int] :
% 8.69/4.97        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 8.69/4.97        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 8.69/4.97          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7613_sum_OatLeast0__atMost__Suc,axiom,
% 8.69/4.97      ! [G: nat > rat,N: nat] :
% 8.69/4.97        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.69/4.97        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7614_sum_OatLeast0__atMost__Suc,axiom,
% 8.69/4.97      ! [G: nat > int,N: nat] :
% 8.69/4.97        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.69/4.97        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7615_sum_OatLeast0__atMost__Suc,axiom,
% 8.69/4.97      ! [G: nat > nat,N: nat] :
% 8.69/4.97        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.69/4.97        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7616_sum_OatLeast0__atMost__Suc,axiom,
% 8.69/4.97      ! [G: nat > real,N: nat] :
% 8.69/4.97        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.69/4.97        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7617_lemma__exp__total,axiom,
% 8.69/4.97      ! [Y: real] :
% 8.69/4.97        ( ( ord_less_eq_real @ one_one_real @ Y )
% 8.69/4.97       => ? [X6: real] :
% 8.69/4.97            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 8.69/4.97            & ( ord_less_eq_real @ X6 @ ( minus_minus_real @ Y @ one_one_real ) )
% 8.69/4.97            & ( ( exp_real @ X6 )
% 8.69/4.97              = Y ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7618_sum_OatLeast__Suc__atMost,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > rat] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.97          = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7619_sum_OatLeast__Suc__atMost,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > int] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.97          = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7620_sum_OatLeast__Suc__atMost,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > nat] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.97          = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7621_sum_OatLeast__Suc__atMost,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > real] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.97       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.97          = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7622_sum_Onat__ivl__Suc_H,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > rat] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.97       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97          = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7623_sum_Onat__ivl__Suc_H,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > int] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.97       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97          = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.97  
% 8.69/4.97  thf(fact_7624_sum_Onat__ivl__Suc_H,axiom,
% 8.69/4.97      ! [M: nat,N: nat,G: nat > nat] :
% 8.69/4.97        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.97       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.97          = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7625_sum_Onat__ivl__Suc_H,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > real] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.98       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 8.69/4.98          = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7626_ln__ge__iff,axiom,
% 8.69/4.98      ! [X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 8.69/4.98          = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7627_ln__x__over__x__mono,axiom,
% 8.69/4.98      ! [X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 8.69/4.98       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.98         => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7628_sum_OSuc__reindex__ivl,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > rat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 8.69/4.98          = ( plus_plus_rat @ ( G @ M )
% 8.69/4.98            @ ( groups2906978787729119204at_rat
% 8.69/4.98              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7629_sum_OSuc__reindex__ivl,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > int] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 8.69/4.98          = ( plus_plus_int @ ( G @ M )
% 8.69/4.98            @ ( groups3539618377306564664at_int
% 8.69/4.98              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7630_sum_OSuc__reindex__ivl,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 8.69/4.98          = ( plus_plus_nat @ ( G @ M )
% 8.69/4.98            @ ( groups3542108847815614940at_nat
% 8.69/4.98              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7631_sum_OSuc__reindex__ivl,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > real] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 8.69/4.98          = ( plus_plus_real @ ( G @ M )
% 8.69/4.98            @ ( groups6591440286371151544t_real
% 8.69/4.98              @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7632_sum__Suc__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > rat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.98       => ( ( groups2906978787729119204at_rat
% 8.69/4.98            @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7633_sum__Suc__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > int] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.98       => ( ( groups3539618377306564664at_int
% 8.69/4.98            @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7634_sum__Suc__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > real] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.98       => ( ( groups6591440286371151544t_real
% 8.69/4.98            @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7635_take__bit__Suc__bit0,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 8.69/4.98        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7636_take__bit__Suc__bit0,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.98        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7637_take__bit__eq__mod,axiom,
% 8.69/4.98      ( bit_se1745604003318907178nteger
% 8.69/4.98      = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7638_take__bit__eq__mod,axiom,
% 8.69/4.98      ( bit_se2923211474154528505it_int
% 8.69/4.98      = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7639_take__bit__eq__mod,axiom,
% 8.69/4.98      ( bit_se2925701944663578781it_nat
% 8.69/4.98      = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7640_one__and__eq,axiom,
% 8.69/4.98      ! [A: code_integer] :
% 8.69/4.98        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 8.69/4.98        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7641_one__and__eq,axiom,
% 8.69/4.98      ! [A: int] :
% 8.69/4.98        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 8.69/4.98        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7642_one__and__eq,axiom,
% 8.69/4.98      ! [A: nat] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 8.69/4.98        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7643_and__one__eq,axiom,
% 8.69/4.98      ! [A: code_integer] :
% 8.69/4.98        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 8.69/4.98        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7644_and__one__eq,axiom,
% 8.69/4.98      ! [A: int] :
% 8.69/4.98        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 8.69/4.98        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7645_and__one__eq,axiom,
% 8.69/4.98      ! [A: nat] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 8.69/4.98        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7646_take__bit__nat__eq__self__iff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 8.69/4.98          = M )
% 8.69/4.98        = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7647_take__bit__nat__less__exp,axiom,
% 8.69/4.98      ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7648_take__bit__nat__eq__self,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98       => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 8.69/4.98          = M ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7649_take__bit__nat__def,axiom,
% 8.69/4.98      ( bit_se2925701944663578781it_nat
% 8.69/4.98      = ( ^ [N2: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7650_exp__le,axiom,
% 8.69/4.98      ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7651_take__bit__int__less__exp,axiom,
% 8.69/4.98      ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7652_sum_Oub__add__nat,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > rat,P5: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.69/4.98       => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 8.69/4.98          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7653_sum_Oub__add__nat,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > int,P5: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.69/4.98       => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 8.69/4.98          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7654_sum_Oub__add__nat,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > nat,P5: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.69/4.98       => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 8.69/4.98          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7655_sum_Oub__add__nat,axiom,
% 8.69/4.98      ! [M: nat,N: nat,G: nat > real,P5: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.69/4.98       => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 8.69/4.98          = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7656_take__bit__int__def,axiom,
% 8.69/4.98      ( bit_se2923211474154528505it_int
% 8.69/4.98      = ( ^ [N2: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7657_set__encode__def,axiom,
% 8.69/4.98      ( nat_set_encode
% 8.69/4.98      = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7658_tanh__altdef,axiom,
% 8.69/4.98      ( tanh_real
% 8.69/4.98      = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7659_tanh__altdef,axiom,
% 8.69/4.98      ( tanh_complex
% 8.69/4.98      = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7660_num_Osize__gen_I1_J,axiom,
% 8.69/4.98      ( ( size_num @ one )
% 8.69/4.98      = zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7661_take__bit__eq__0__iff,axiom,
% 8.69/4.98      ! [N: nat,A: code_integer] :
% 8.69/4.98        ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 8.69/4.98          = zero_z3403309356797280102nteger )
% 8.69/4.98        = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7662_take__bit__eq__0__iff,axiom,
% 8.69/4.98      ! [N: nat,A: int] :
% 8.69/4.98        ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 8.69/4.98          = zero_zero_int )
% 8.69/4.98        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7663_take__bit__eq__0__iff,axiom,
% 8.69/4.98      ! [N: nat,A: nat] :
% 8.69/4.98        ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 8.69/4.98          = zero_zero_nat )
% 8.69/4.98        = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7664_Divides_Oadjust__div__def,axiom,
% 8.69/4.98      ( adjust_div
% 8.69/4.98      = ( produc8211389475949308722nt_int
% 8.69/4.98        @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7665_take__bit__numeral__bit0,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 8.69/4.98        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7666_take__bit__numeral__bit0,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 8.69/4.98        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7667_take__bit__nat__less__self__iff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7668_exp__half__le2,axiom,
% 8.69/4.98      ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7669_take__bit__Suc__minus__bit0,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/4.98        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7670_take__bit__int__less__self__iff,axiom,
% 8.69/4.98      ! [N: nat,K: int] :
% 8.69/4.98        ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 8.69/4.98        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7671_take__bit__int__greater__eq__self__iff,axiom,
% 8.69/4.98      ! [K: int,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.69/4.98        = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7672_exp__double,axiom,
% 8.69/4.98      ! [Z: complex] :
% 8.69/4.98        ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 8.69/4.98        = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7673_exp__double,axiom,
% 8.69/4.98      ! [Z: real] :
% 8.69/4.98        ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 8.69/4.98        = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7674_sum__natinterval__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > complex] :
% 8.69/4.98        ( ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups2073611262835488442omplex
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.69/4.98        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups2073611262835488442omplex
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_complex ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7675_sum__natinterval__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > rat] :
% 8.69/4.98        ( ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.69/4.98        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_rat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7676_sum__natinterval__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > int] :
% 8.69/4.98        ( ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups3539618377306564664at_int
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.69/4.98        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups3539618377306564664at_int
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7677_sum__natinterval__diff,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > real] :
% 8.69/4.98        ( ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups6591440286371151544t_real
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.69/4.98        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.69/4.98         => ( ( groups6591440286371151544t_real
% 8.69/4.98              @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7678_sum__telescope_H_H,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > rat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( groups2906978787729119204at_rat
% 8.69/4.98            @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 8.69/4.98          = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7679_sum__telescope_H_H,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > int] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( groups3539618377306564664at_int
% 8.69/4.98            @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 8.69/4.98          = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7680_sum__telescope_H_H,axiom,
% 8.69/4.98      ! [M: nat,N: nat,F: nat > real] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( groups6591440286371151544t_real
% 8.69/4.98            @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 8.69/4.98          = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7681_take__bit__int__eq__self__iff,axiom,
% 8.69/4.98      ! [N: nat,K: int] :
% 8.69/4.98        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.98          = K )
% 8.69/4.98        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/4.98          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7682_take__bit__int__eq__self,axiom,
% 8.69/4.98      ! [K: int,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/4.98       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98         => ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.98            = K ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7683_take__bit__numeral__minus__bit0,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/4.98        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7684_take__bit__incr__eq,axiom,
% 8.69/4.98      ! [N: nat,K: int] :
% 8.69/4.98        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.98         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 8.69/4.98       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 8.69/4.98          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7685_divmod__nat__def,axiom,
% 8.69/4.98      ( divmod_nat
% 8.69/4.98      = ( ^ [M3: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N2 ) @ ( modulo_modulo_nat @ M3 @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7686_take__bit__eq__mask__iff__exp__dvd,axiom,
% 8.69/4.98      ! [N: nat,K: int] :
% 8.69/4.98        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.69/4.98          = ( bit_se2000444600071755411sk_int @ N ) )
% 8.69/4.98        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7687_mask__eq__sum__exp,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 8.69/4.98        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.98          @ ( collect_nat
% 8.69/4.98            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7688_mask__eq__sum__exp,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 8.69/4.98        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.98          @ ( collect_nat
% 8.69/4.98            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7689_sum__gp__multiplied,axiom,
% 8.69/4.98      ! [M: nat,N: nat,X: complex] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 8.69/4.98          = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7690_sum__gp__multiplied,axiom,
% 8.69/4.98      ! [M: nat,N: nat,X: rat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 8.69/4.98          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7691_sum__gp__multiplied,axiom,
% 8.69/4.98      ! [M: nat,N: nat,X: int] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 8.69/4.98          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7692_sum__gp__multiplied,axiom,
% 8.69/4.98      ! [M: nat,N: nat,X: real] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.98       => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 8.69/4.98          = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7693_sum_Oin__pairs,axiom,
% 8.69/4.98      ! [G: nat > rat,M: nat,N: nat] :
% 8.69/4.98        ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.69/4.98        = ( groups2906978787729119204at_rat
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7694_sum_Oin__pairs,axiom,
% 8.69/4.98      ! [G: nat > int,M: nat,N: nat] :
% 8.69/4.98        ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.69/4.98        = ( groups3539618377306564664at_int
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7695_sum_Oin__pairs,axiom,
% 8.69/4.98      ! [G: nat > nat,M: nat,N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.69/4.98        = ( groups3542108847815614940at_nat
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7696_sum_Oin__pairs,axiom,
% 8.69/4.98      ! [G: nat > real,M: nat,N: nat] :
% 8.69/4.98        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.69/4.98        = ( groups6591440286371151544t_real
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7697_take__bit__Suc__minus__1__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.98        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7698_take__bit__Suc__minus__1__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.98        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7699_take__bit__Suc__bit1,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7700_take__bit__Suc__bit1,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.98        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7701_take__bit__numeral__minus__1__eq,axiom,
% 8.69/4.98      ! [K: num] :
% 8.69/4.98        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.98        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7702_take__bit__numeral__minus__1__eq,axiom,
% 8.69/4.98      ! [K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.98        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7703_take__bit__Suc,axiom,
% 8.69/4.98      ! [N: nat,A: code_integer] :
% 8.69/4.98        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 8.69/4.98        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7704_take__bit__Suc,axiom,
% 8.69/4.98      ! [N: nat,A: int] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7705_take__bit__Suc,axiom,
% 8.69/4.98      ! [N: nat,A: nat] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 8.69/4.98        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7706_exp__bound,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.98         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7707_take__bit__int__less__eq,axiom,
% 8.69/4.98      ! [N: nat,K: int] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.98         => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7708_take__bit__int__greater__eq,axiom,
% 8.69/4.98      ! [K: int,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ K @ zero_zero_int )
% 8.69/4.98       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7709_signed__take__bit__eq__take__bit__shift,axiom,
% 8.69/4.98      ( bit_ri631733984087533419it_int
% 8.69/4.98      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7710_mask__eq__sum__exp__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 8.69/4.98        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.98          @ ( collect_nat
% 8.69/4.98            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7711_and__int__rec,axiom,
% 8.69/4.98      ( bit_se725231765392027082nd_int
% 8.69/4.98      = ( ^ [K2: int,L: int] :
% 8.69/4.98            ( plus_plus_int
% 8.69/4.98            @ ( zero_n2684676970156552555ol_int
% 8.69/4.98              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.69/4.98                & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 8.69/4.98            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7712_stable__imp__take__bit__eq,axiom,
% 8.69/4.98      ! [A: code_integer,N: nat] :
% 8.69/4.98        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/4.98          = A )
% 8.69/4.98       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 8.69/4.98              = zero_z3403309356797280102nteger ) )
% 8.69/4.98          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 8.69/4.98              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7713_stable__imp__take__bit__eq,axiom,
% 8.69/4.98      ! [A: int,N: nat] :
% 8.69/4.98        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/4.98          = A )
% 8.69/4.98       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 8.69/4.98              = zero_zero_int ) )
% 8.69/4.98          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 8.69/4.98              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7714_stable__imp__take__bit__eq,axiom,
% 8.69/4.98      ! [A: nat,N: nat] :
% 8.69/4.98        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.98          = A )
% 8.69/4.98       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 8.69/4.98              = zero_zero_nat ) )
% 8.69/4.98          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.69/4.98           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 8.69/4.98              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7715_gauss__sum__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat
% 8.69/4.98          @ ^ [X3: nat] : X3
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7716_take__bit__numeral__bit1,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7717_take__bit__numeral__bit1,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 8.69/4.98        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7718_real__exp__bound__lemma,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.98         => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7719_take__bit__minus__small__eq,axiom,
% 8.69/4.98      ! [K: int,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ zero_zero_int @ K )
% 8.69/4.98       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 8.69/4.98            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7720_arith__series__nat,axiom,
% 8.69/4.98      ! [A: nat,D: nat,N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7721_Sum__Icc__nat,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat
% 8.69/4.98          @ ^ [X3: nat] : X3
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7722_exp__lower__Taylor__quadratic,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7723_take__bit__numeral__minus__bit1,axiom,
% 8.69/4.98      ! [L2: num,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7724_and__int_Oelims,axiom,
% 8.69/4.98      ! [X: int,Xa2: int,Y: int] :
% 8.69/4.98        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 8.69/4.98          = Y )
% 8.69/4.98       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.98              & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.98           => ( Y
% 8.69/4.98              = ( uminus_uminus_int
% 8.69/4.98                @ ( zero_n2684676970156552555ol_int
% 8.69/4.98                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.69/4.98                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.98                & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.98           => ( Y
% 8.69/4.98              = ( plus_plus_int
% 8.69/4.98                @ ( zero_n2684676970156552555ol_int
% 8.69/4.98                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.69/4.98                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 8.69/4.98                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7725_and__int_Osimps,axiom,
% 8.69/4.98      ( bit_se725231765392027082nd_int
% 8.69/4.98      = ( ^ [K2: int,L: int] :
% 8.69/4.98            ( if_int
% 8.69/4.98            @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.98              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.98            @ ( uminus_uminus_int
% 8.69/4.98              @ ( zero_n2684676970156552555ol_int
% 8.69/4.98                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.69/4.98                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 8.69/4.98            @ ( plus_plus_int
% 8.69/4.98              @ ( zero_n2684676970156552555ol_int
% 8.69/4.98                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.69/4.98                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 8.69/4.98              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7726_take__bit__Suc__minus__bit1,axiom,
% 8.69/4.98      ! [N: nat,K: num] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7727_sum__gp,axiom,
% 8.69/4.98      ! [N: nat,M: nat,X: complex] :
% 8.69/4.98        ( ( ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_complex ) )
% 8.69/4.98        & ( ~ ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( ( X = one_one_complex )
% 8.69/4.98             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 8.69/4.98            & ( ( X != one_one_complex )
% 8.69/4.98             => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7728_sum__gp,axiom,
% 8.69/4.98      ! [N: nat,M: nat,X: rat] :
% 8.69/4.98        ( ( ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_rat ) )
% 8.69/4.98        & ( ~ ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( ( X = one_one_rat )
% 8.69/4.98             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 8.69/4.98            & ( ( X != one_one_rat )
% 8.69/4.98             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7729_sum__gp,axiom,
% 8.69/4.98      ! [N: nat,M: nat,X: real] :
% 8.69/4.98        ( ( ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98            = zero_zero_real ) )
% 8.69/4.98        & ( ~ ( ord_less_nat @ N @ M )
% 8.69/4.98         => ( ( ( X = one_one_real )
% 8.69/4.98             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 8.69/4.98            & ( ( X != one_one_real )
% 8.69/4.98             => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 8.69/4.98                = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7730_log__base__10__eq1,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.98          = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7731_of__nat__eq__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ( semiri8010041392384452111omplex @ M )
% 8.69/4.98          = ( semiri8010041392384452111omplex @ N ) )
% 8.69/4.98        = ( M = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7732_of__nat__eq__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ M )
% 8.69/4.98          = ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( M = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7733_of__nat__eq__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ( semiri681578069525770553at_rat @ M )
% 8.69/4.98          = ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( M = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7734_of__nat__eq__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ( semiri1316708129612266289at_nat @ M )
% 8.69/4.98          = ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( M = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7735_of__nat__eq__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ M )
% 8.69/4.98          = ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( M = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7736_insert__subset,axiom,
% 8.69/4.98      ! [X: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.98        ( ( ord_le211207098394363844omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 8.69/4.98        = ( ( member_complex @ X @ B3 )
% 8.69/4.98          & ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7737_insert__subset,axiom,
% 8.69/4.98      ! [X: real,A2: set_real,B3: set_real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 8.69/4.98        = ( ( member_real @ X @ B3 )
% 8.69/4.98          & ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7738_insert__subset,axiom,
% 8.69/4.98      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.98        ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 8.69/4.98        = ( ( member_set_nat @ X @ B3 )
% 8.69/4.98          & ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7739_insert__subset,axiom,
% 8.69/4.98      ! [X: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 8.69/4.98        = ( ( member_nat @ X @ B3 )
% 8.69/4.98          & ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7740_insert__subset,axiom,
% 8.69/4.98      ! [X: int,A2: set_int,B3: set_int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 8.69/4.98        = ( ( member_int @ X @ B3 )
% 8.69/4.98          & ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7741_int__eq__iff__numeral,axiom,
% 8.69/4.98      ! [M: nat,V: num] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ M )
% 8.69/4.98          = ( numeral_numeral_int @ V ) )
% 8.69/4.98        = ( M
% 8.69/4.98          = ( numeral_numeral_nat @ V ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7742_abs__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 8.69/4.98        = ( semiri4939895301339042750nteger @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7743_abs__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( semiri5074537144036343181t_real @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7744_abs__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( semiri681578069525770553at_rat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7745_abs__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7746_negative__eq__positive,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98          = ( semiri1314217659103216013at_int @ M ) )
% 8.69/4.98        = ( ( N = zero_zero_nat )
% 8.69/4.98          & ( M = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7747_Diff__insert0,axiom,
% 8.69/4.98      ! [X: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.98        ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98       => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 8.69/4.98          = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7748_Diff__insert0,axiom,
% 8.69/4.98      ! [X: real,A2: set_real,B3: set_real] :
% 8.69/4.98        ( ~ ( member_real @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 8.69/4.98          = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7749_Diff__insert0,axiom,
% 8.69/4.98      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.98        ( ~ ( member_set_nat @ X @ A2 )
% 8.69/4.98       => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 8.69/4.98          = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7750_Diff__insert0,axiom,
% 8.69/4.98      ! [X: int,A2: set_int,B3: set_int] :
% 8.69/4.98        ( ~ ( member_int @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 8.69/4.98          = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7751_Diff__insert0,axiom,
% 8.69/4.98      ! [X: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.98        ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 8.69/4.98          = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7752_insert__Diff1,axiom,
% 8.69/4.98      ! [X: complex,B3: set_complex,A2: set_complex] :
% 8.69/4.98        ( ( member_complex @ X @ B3 )
% 8.69/4.98       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 8.69/4.98          = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7753_insert__Diff1,axiom,
% 8.69/4.98      ! [X: real,B3: set_real,A2: set_real] :
% 8.69/4.98        ( ( member_real @ X @ B3 )
% 8.69/4.98       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 8.69/4.98          = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7754_insert__Diff1,axiom,
% 8.69/4.98      ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 8.69/4.98        ( ( member_set_nat @ X @ B3 )
% 8.69/4.98       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 8.69/4.98          = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7755_insert__Diff1,axiom,
% 8.69/4.98      ! [X: int,B3: set_int,A2: set_int] :
% 8.69/4.98        ( ( member_int @ X @ B3 )
% 8.69/4.98       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 8.69/4.98          = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7756_insert__Diff1,axiom,
% 8.69/4.98      ! [X: nat,B3: set_nat,A2: set_nat] :
% 8.69/4.98        ( ( member_nat @ X @ B3 )
% 8.69/4.98       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 8.69/4.98          = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7757_negative__zle,axiom,
% 8.69/4.98      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7758_of__nat__eq__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ( semiri8010041392384452111omplex @ M )
% 8.69/4.98          = zero_zero_complex )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7759_of__nat__eq__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ M )
% 8.69/4.98          = zero_zero_real )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7760_of__nat__eq__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ( semiri681578069525770553at_rat @ M )
% 8.69/4.98          = zero_zero_rat )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7761_of__nat__eq__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ( semiri1316708129612266289at_nat @ M )
% 8.69/4.98          = zero_zero_nat )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7762_of__nat__eq__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ M )
% 8.69/4.98          = zero_zero_int )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7763_of__nat__0__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( zero_zero_complex
% 8.69/4.98          = ( semiri8010041392384452111omplex @ N ) )
% 8.69/4.98        = ( zero_zero_nat = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7764_of__nat__0__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( zero_zero_real
% 8.69/4.98          = ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( zero_zero_nat = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7765_of__nat__0__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( zero_zero_rat
% 8.69/4.98          = ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( zero_zero_nat = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7766_of__nat__0__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( zero_zero_nat
% 8.69/4.98          = ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( zero_zero_nat = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7767_of__nat__0__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( zero_zero_int
% 8.69/4.98          = ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( zero_zero_nat = N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7768_of__nat__0,axiom,
% 8.69/4.98      ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 8.69/4.98      = zero_zero_complex ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7769_of__nat__0,axiom,
% 8.69/4.98      ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 8.69/4.98      = zero_zero_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7770_of__nat__0,axiom,
% 8.69/4.98      ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 8.69/4.98      = zero_zero_rat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7771_of__nat__0,axiom,
% 8.69/4.98      ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 8.69/4.98      = zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7772_of__nat__0,axiom,
% 8.69/4.98      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.69/4.98      = zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7773_of__nat__less__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7774_of__nat__less__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7775_of__nat__less__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7776_of__nat__less__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7777_of__nat__numeral,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numera6690914467698888265omplex @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7778_of__nat__numeral,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numeral_numeral_real @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7779_of__nat__numeral,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numeral_numeral_rat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7780_of__nat__numeral,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numeral_numeral_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7781_of__nat__numeral,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7782_of__nat__le__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7783_of__nat__le__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7784_of__nat__le__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7785_of__nat__le__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7786_singleton__insert__inj__eq,axiom,
% 8.69/4.98      ! [B: nat,A: nat,A2: set_nat] :
% 8.69/4.98        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 8.69/4.98          = ( insert_nat @ A @ A2 ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7787_singleton__insert__inj__eq,axiom,
% 8.69/4.98      ! [B: real,A: real,A2: set_real] :
% 8.69/4.98        ( ( ( insert_real @ B @ bot_bot_set_real )
% 8.69/4.98          = ( insert_real @ A @ A2 ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7788_singleton__insert__inj__eq,axiom,
% 8.69/4.98      ! [B: int,A: int,A2: set_int] :
% 8.69/4.98        ( ( ( insert_int @ B @ bot_bot_set_int )
% 8.69/4.98          = ( insert_int @ A @ A2 ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7789_singleton__insert__inj__eq_H,axiom,
% 8.69/4.98      ! [A: nat,A2: set_nat,B: nat] :
% 8.69/4.98        ( ( ( insert_nat @ A @ A2 )
% 8.69/4.98          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7790_singleton__insert__inj__eq_H,axiom,
% 8.69/4.98      ! [A: real,A2: set_real,B: real] :
% 8.69/4.98        ( ( ( insert_real @ A @ A2 )
% 8.69/4.98          = ( insert_real @ B @ bot_bot_set_real ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7791_singleton__insert__inj__eq_H,axiom,
% 8.69/4.98      ! [A: int,A2: set_int,B: int] :
% 8.69/4.98        ( ( ( insert_int @ A @ A2 )
% 8.69/4.98          = ( insert_int @ B @ bot_bot_set_int ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7792_of__nat__add,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 8.69/4.98        = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7793_of__nat__add,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 8.69/4.98        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7794_of__nat__add,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 8.69/4.98        = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7795_of__nat__add,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 8.69/4.98        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7796_of__nat__add,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7797_of__nat__mult,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 8.69/4.98        = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7798_of__nat__mult,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 8.69/4.98        = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7799_of__nat__mult,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 8.69/4.98        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7800_of__nat__mult,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 8.69/4.98        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7801_of__nat__mult,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 8.69/4.98        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7802_of__nat__1,axiom,
% 8.69/4.98      ( ( semiri8010041392384452111omplex @ one_one_nat )
% 8.69/4.98      = one_one_complex ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7803_of__nat__1,axiom,
% 8.69/4.98      ( ( semiri5074537144036343181t_real @ one_one_nat )
% 8.69/4.98      = one_one_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7804_of__nat__1,axiom,
% 8.69/4.98      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 8.69/4.98      = one_one_rat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7805_of__nat__1,axiom,
% 8.69/4.98      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 8.69/4.98      = one_one_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7806_of__nat__1,axiom,
% 8.69/4.98      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 8.69/4.98      = one_one_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7807_of__nat__1__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( one_one_complex
% 8.69/4.98          = ( semiri8010041392384452111omplex @ N ) )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7808_of__nat__1__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( one_one_real
% 8.69/4.98          = ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7809_of__nat__1__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( one_one_rat
% 8.69/4.98          = ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7810_of__nat__1__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( one_one_nat
% 8.69/4.98          = ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7811_of__nat__1__eq__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( one_one_int
% 8.69/4.98          = ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7812_of__nat__eq__1__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ( semiri8010041392384452111omplex @ N )
% 8.69/4.98          = one_one_complex )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7813_of__nat__eq__1__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ N )
% 8.69/4.98          = one_one_real )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7814_of__nat__eq__1__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ( semiri681578069525770553at_rat @ N )
% 8.69/4.98          = one_one_rat )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7815_of__nat__eq__1__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ( semiri1316708129612266289at_nat @ N )
% 8.69/4.98          = one_one_nat )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7816_of__nat__eq__1__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ N )
% 8.69/4.98          = one_one_int )
% 8.69/4.98        = ( N = one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7817_atLeastAtMost__singleton,axiom,
% 8.69/4.98      ! [A: nat] :
% 8.69/4.98        ( ( set_or1269000886237332187st_nat @ A @ A )
% 8.69/4.98        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7818_atLeastAtMost__singleton,axiom,
% 8.69/4.98      ! [A: int] :
% 8.69/4.98        ( ( set_or1266510415728281911st_int @ A @ A )
% 8.69/4.98        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7819_atLeastAtMost__singleton,axiom,
% 8.69/4.98      ! [A: real] :
% 8.69/4.98        ( ( set_or1222579329274155063t_real @ A @ A )
% 8.69/4.98        = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7820_atLeastAtMost__singleton__iff,axiom,
% 8.69/4.98      ! [A: nat,B: nat,C: nat] :
% 8.69/4.98        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.69/4.98          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( B = C ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7821_atLeastAtMost__singleton__iff,axiom,
% 8.69/4.98      ! [A: int,B: int,C: int] :
% 8.69/4.98        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 8.69/4.98          = ( insert_int @ C @ bot_bot_set_int ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( B = C ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7822_atLeastAtMost__singleton__iff,axiom,
% 8.69/4.98      ! [A: real,B: real,C: real] :
% 8.69/4.98        ( ( ( set_or1222579329274155063t_real @ A @ B )
% 8.69/4.98          = ( insert_real @ C @ bot_bot_set_real ) )
% 8.69/4.98        = ( ( A = B )
% 8.69/4.98          & ( B = C ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7823_insert__Diff__single,axiom,
% 8.69/4.98      ! [A: int,A2: set_int] :
% 8.69/4.98        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98        = ( insert_int @ A @ A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7824_insert__Diff__single,axiom,
% 8.69/4.98      ! [A: real,A2: set_real] :
% 8.69/4.98        ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98        = ( insert_real @ A @ A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7825_insert__Diff__single,axiom,
% 8.69/4.98      ! [A: nat,A2: set_nat] :
% 8.69/4.98        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98        = ( insert_nat @ A @ A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7826_finite__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,B3: set_real] :
% 8.69/4.98        ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) ) )
% 8.69/4.98        = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7827_finite__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_int,A: int,B3: set_int] :
% 8.69/4.98        ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) ) )
% 8.69/4.98        = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7828_finite__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_complex,A: complex,B3: set_complex] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B3 ) ) )
% 8.69/4.98        = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7829_finite__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_nat,A: nat,B3: set_nat] :
% 8.69/4.98        ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) ) )
% 8.69/4.98        = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7830_of__nat__power,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 8.69/4.98        = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7831_of__nat__power,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 8.69/4.98        = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7832_of__nat__power,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 8.69/4.98        = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7833_of__nat__power,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 8.69/4.98        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7834_of__nat__power,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 8.69/4.98        = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7835_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 8.69/4.98          = ( semiri8010041392384452111omplex @ X ) )
% 8.69/4.98        = ( ( power_power_nat @ B @ W )
% 8.69/4.98          = X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7836_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 8.69/4.98          = ( semiri5074537144036343181t_real @ X ) )
% 8.69/4.98        = ( ( power_power_nat @ B @ W )
% 8.69/4.98          = X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7837_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 8.69/4.98          = ( semiri681578069525770553at_rat @ X ) )
% 8.69/4.98        = ( ( power_power_nat @ B @ W )
% 8.69/4.98          = X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7838_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 8.69/4.98          = ( semiri1316708129612266289at_nat @ X ) )
% 8.69/4.98        = ( ( power_power_nat @ B @ W )
% 8.69/4.98          = X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7839_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 8.69/4.98          = ( semiri1314217659103216013at_int @ X ) )
% 8.69/4.98        = ( ( power_power_nat @ B @ W )
% 8.69/4.98          = X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7840_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ( semiri8010041392384452111omplex @ X )
% 8.69/4.98          = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 8.69/4.98        = ( X
% 8.69/4.98          = ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7841_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ X )
% 8.69/4.98          = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 8.69/4.98        = ( X
% 8.69/4.98          = ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7842_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ( semiri681578069525770553at_rat @ X )
% 8.69/4.98          = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 8.69/4.98        = ( X
% 8.69/4.98          = ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7843_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ( semiri1316708129612266289at_nat @ X )
% 8.69/4.98          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 8.69/4.98        = ( X
% 8.69/4.98          = ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7844_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ X )
% 8.69/4.98          = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 8.69/4.98        = ( X
% 8.69/4.98          = ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7845_log__one,axiom,
% 8.69/4.98      ! [A: real] :
% 8.69/4.98        ( ( log @ A @ one_one_real )
% 8.69/4.98        = zero_zero_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7846_pred__numeral__inc,axiom,
% 8.69/4.98      ! [K: num] :
% 8.69/4.98        ( ( pred_numeral @ ( inc @ K ) )
% 8.69/4.98        = ( numeral_numeral_nat @ K ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7847_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n1201886186963655149omplex @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7848_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n3304061248610475627l_real @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7849_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7850_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7851_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7852_of__nat__of__bool,axiom,
% 8.69/4.98      ! [P: $o] :
% 8.69/4.98        ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.69/4.98        = ( zero_n356916108424825756nteger @ P ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7853_of__nat__le__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7854_of__nat__le__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7855_of__nat__le__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7856_of__nat__le__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 8.69/4.98        = ( M = zero_zero_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7857_and__nat__numerals_I3_J,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/4.98        = zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7858_and__nat__numerals_I1_J,axiom,
% 8.69/4.98      ! [Y: num] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/4.98        = zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7859_of__nat__Suc,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 8.69/4.98        = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7860_of__nat__Suc,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 8.69/4.98        = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7861_of__nat__Suc,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 8.69/4.98        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7862_of__nat__Suc,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 8.69/4.98        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7863_of__nat__Suc,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 8.69/4.98        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7864_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ~ ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7865_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > real] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ~ ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7866_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > real] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7867_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ~ ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7868_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat,G: nat > rat] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7869_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ~ ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7870_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7871_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > nat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ~ ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7872_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > nat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ~ ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7873_sum_Oinsert,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > nat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7874_numeral__less__real__of__nat__iff,axiom,
% 8.69/4.98      ! [W: num,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7875_real__of__nat__less__numeral__iff,axiom,
% 8.69/4.98      ! [N: nat,W: num] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 8.69/4.98        = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7876_numeral__le__real__of__nat__iff,axiom,
% 8.69/4.98      ! [N: num,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7877_subset__Compl__singleton,axiom,
% 8.69/4.98      ! [A2: set_complex,B: complex] :
% 8.69/4.98        ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 8.69/4.98        = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7878_subset__Compl__singleton,axiom,
% 8.69/4.98      ! [A2: set_set_nat,B: set_nat] :
% 8.69/4.98        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 8.69/4.98        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7879_subset__Compl__singleton,axiom,
% 8.69/4.98      ! [A2: set_nat,B: nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 8.69/4.98        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7880_subset__Compl__singleton,axiom,
% 8.69/4.98      ! [A2: set_real,B: real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 8.69/4.98        = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7881_subset__Compl__singleton,axiom,
% 8.69/4.98      ! [A2: set_int,B: int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 8.69/4.98        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7882_log__eq__one,axiom,
% 8.69/4.98      ! [A: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( log @ A @ A )
% 8.69/4.98            = one_one_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7883_log__less__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.98           => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 8.69/4.98              = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7884_log__less__one__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 8.69/4.98            = ( ord_less_real @ X @ A ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7885_one__less__log__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 8.69/4.98            = ( ord_less_real @ A @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7886_log__less__zero__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 8.69/4.98            = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7887_zero__less__log__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 8.69/4.98            = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7888_of__nat__0__less__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7889_of__nat__0__less__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7890_of__nat__0__less__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7891_of__nat__0__less__iff,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7892_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7893_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7894_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7895_of__nat__less__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7896_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7897_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7898_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7899_of__nat__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7900_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: num,N: nat,Y: nat] :
% 8.69/4.98        ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 8.69/4.98          = ( semiri8010041392384452111omplex @ Y ) )
% 8.69/4.98        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = Y ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7901_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: num,N: nat,Y: nat] :
% 8.69/4.98        ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 8.69/4.98          = ( semiri5074537144036343181t_real @ Y ) )
% 8.69/4.98        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = Y ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7902_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: num,N: nat,Y: nat] :
% 8.69/4.98        ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 8.69/4.98          = ( semiri681578069525770553at_rat @ Y ) )
% 8.69/4.98        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = Y ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7903_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: num,N: nat,Y: nat] :
% 8.69/4.98        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = ( semiri1316708129612266289at_nat @ Y ) )
% 8.69/4.98        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = Y ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7904_numeral__power__eq__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: num,N: nat,Y: nat] :
% 8.69/4.98        ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/4.98          = ( semiri1314217659103216013at_int @ Y ) )
% 8.69/4.98        = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/4.98          = Y ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7905_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [Y: nat,X: num,N: nat] :
% 8.69/4.98        ( ( ( semiri8010041392384452111omplex @ Y )
% 8.69/4.98          = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 8.69/4.98        = ( Y
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7906_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [Y: nat,X: num,N: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ Y )
% 8.69/4.98          = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 8.69/4.98        = ( Y
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7907_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [Y: nat,X: num,N: nat] :
% 8.69/4.98        ( ( ( semiri681578069525770553at_rat @ Y )
% 8.69/4.98          = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 8.69/4.98        = ( Y
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7908_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [Y: nat,X: num,N: nat] :
% 8.69/4.98        ( ( ( semiri1316708129612266289at_nat @ Y )
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 8.69/4.98        = ( Y
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7909_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [Y: nat,X: num,N: nat] :
% 8.69/4.98        ( ( ( semiri1314217659103216013at_int @ Y )
% 8.69/4.98          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 8.69/4.98        = ( Y
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7910_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7911_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7912_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7913_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.69/4.98      ! [B: nat,W: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7914_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7915_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7916_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7917_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,B: nat,W: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7918_and__nat__numerals_I4_J,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/4.98        = one_one_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7919_and__nat__numerals_I2_J,axiom,
% 8.69/4.98      ! [Y: num] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/4.98        = one_one_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7920_set__replicate,axiom,
% 8.69/4.98      ! [N: nat,X: vEBT_VEBT] :
% 8.69/4.98        ( ( N != zero_zero_nat )
% 8.69/4.98       => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.69/4.98          = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7921_set__replicate,axiom,
% 8.69/4.98      ! [N: nat,X: nat] :
% 8.69/4.98        ( ( N != zero_zero_nat )
% 8.69/4.98       => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.69/4.98          = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7922_set__replicate,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( N != zero_zero_nat )
% 8.69/4.98       => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.69/4.98          = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7923_set__replicate,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( N != zero_zero_nat )
% 8.69/4.98       => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.69/4.98          = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7924_log__le__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.98           => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 8.69/4.98              = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7925_log__le__one__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 8.69/4.98            = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7926_one__le__log__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 8.69/4.98            = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7927_log__le__zero__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 8.69/4.98            = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7928_zero__le__log__cancel__iff,axiom,
% 8.69/4.98      ! [A: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.98       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98         => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 8.69/4.98            = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7929_add__neg__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.98        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7930_add__neg__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/4.98        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7931_add__neg__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.69/4.98        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7932_add__neg__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.69/4.98        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7933_add__neg__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.69/4.98        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7934_add__neg__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.98        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7935_add__neg__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.98        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7936_add__neg__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.98        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7937_add__neg__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.98        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7938_add__neg__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.98        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7939_diff__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.98        = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7940_diff__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/4.98        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7941_diff__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.98        = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7942_diff__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.69/4.98        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7943_diff__numeral__special_I6_J,axiom,
% 8.69/4.98      ! [M: num] :
% 8.69/4.98        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/4.98        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7944_diff__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.98        = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7945_diff__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.69/4.98        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7946_diff__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 8.69/4.98        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7947_diff__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 8.69/4.98        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7948_diff__numeral__special_I5_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 8.69/4.98        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7949_log__pow__cancel,axiom,
% 8.69/4.98      ! [A: real,B: nat] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 8.69/4.98            = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7950_of__nat__zero__less__power__iff,axiom,
% 8.69/4.98      ! [X: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 8.69/4.98        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.69/4.98          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7951_of__nat__zero__less__power__iff,axiom,
% 8.69/4.98      ! [X: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 8.69/4.98        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.69/4.98          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7952_of__nat__zero__less__power__iff,axiom,
% 8.69/4.98      ! [X: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 8.69/4.98        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.69/4.98          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7953_of__nat__zero__less__power__iff,axiom,
% 8.69/4.98      ! [X: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 8.69/4.98        = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.69/4.98          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7954_Suc__0__and__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/4.98        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7955_and__Suc__0__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/4.98        = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7956_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7957_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7958_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7959_numeral__power__less__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.69/4.98        = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7960_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7961_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7962_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7963_of__nat__less__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7964_even__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7965_even__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7966_even__of__nat,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7967_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7968_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7969_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7970_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.69/4.98      ! [I: num,N: nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.69/4.98        = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7971_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7972_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7973_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7974_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.69/4.98      ! [X: nat,I: num,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7975_Collect__case__prod__mono,axiom,
% 8.69/4.98      ! [A2: int > int > $o,B3: int > int > $o] :
% 8.69/4.98        ( ( ord_le6741204236512500942_int_o @ A2 @ B3 )
% 8.69/4.98       => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7976_real__arch__simple,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98      ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7977_real__arch__simple,axiom,
% 8.69/4.98      ! [X: rat] :
% 8.69/4.98      ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7978_reals__Archimedean2,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98      ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7979_reals__Archimedean2,axiom,
% 8.69/4.98      ! [X: rat] :
% 8.69/4.98      ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7980_mult__of__nat__commute,axiom,
% 8.69/4.98      ! [X: nat,Y: complex] :
% 8.69/4.98        ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 8.69/4.98        = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7981_mult__of__nat__commute,axiom,
% 8.69/4.98      ! [X: nat,Y: real] :
% 8.69/4.98        ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 8.69/4.98        = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7982_mult__of__nat__commute,axiom,
% 8.69/4.98      ! [X: nat,Y: rat] :
% 8.69/4.98        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 8.69/4.98        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7983_mult__of__nat__commute,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 8.69/4.98        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7984_mult__of__nat__commute,axiom,
% 8.69/4.98      ! [X: nat,Y: int] :
% 8.69/4.98        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 8.69/4.98        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7985_insert__mono,axiom,
% 8.69/4.98      ! [C4: set_nat,D4: set_nat,A: nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ C4 @ D4 )
% 8.69/4.98       => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7986_insert__mono,axiom,
% 8.69/4.98      ! [C4: set_real,D4: set_real,A: real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ C4 @ D4 )
% 8.69/4.98       => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7987_insert__mono,axiom,
% 8.69/4.98      ! [C4: set_int,D4: set_int,A: int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ C4 @ D4 )
% 8.69/4.98       => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7988_subset__insert,axiom,
% 8.69/4.98      ! [X: complex,A2: set_complex,B3: set_complex] :
% 8.69/4.98        ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98       => ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 8.69/4.98          = ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7989_subset__insert,axiom,
% 8.69/4.98      ! [X: real,A2: set_real,B3: set_real] :
% 8.69/4.98        ( ~ ( member_real @ X @ A2 )
% 8.69/4.98       => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 8.69/4.98          = ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7990_subset__insert,axiom,
% 8.69/4.98      ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 8.69/4.98        ( ~ ( member_set_nat @ X @ A2 )
% 8.69/4.98       => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 8.69/4.98          = ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7991_subset__insert,axiom,
% 8.69/4.98      ! [X: nat,A2: set_nat,B3: set_nat] :
% 8.69/4.98        ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98       => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 8.69/4.98          = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7992_subset__insert,axiom,
% 8.69/4.98      ! [X: int,A2: set_int,B3: set_int] :
% 8.69/4.98        ( ~ ( member_int @ X @ A2 )
% 8.69/4.98       => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 8.69/4.98          = ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7993_subset__insertI,axiom,
% 8.69/4.98      ! [B3: set_nat,A: nat] : ( ord_less_eq_set_nat @ B3 @ ( insert_nat @ A @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7994_subset__insertI,axiom,
% 8.69/4.98      ! [B3: set_real,A: real] : ( ord_less_eq_set_real @ B3 @ ( insert_real @ A @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7995_subset__insertI,axiom,
% 8.69/4.98      ! [B3: set_int,A: int] : ( ord_less_eq_set_int @ B3 @ ( insert_int @ A @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7996_subset__insertI2,axiom,
% 8.69/4.98      ! [A2: set_nat,B3: set_nat,B: nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7997_subset__insertI2,axiom,
% 8.69/4.98      ! [A2: set_real,B3: set_real,B: real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7998_subset__insertI2,axiom,
% 8.69/4.98      ! [A2: set_int,B3: set_int,B: int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_7999_take__bit__of__nat,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 8.69/4.98        = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8000_take__bit__of__nat,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 8.69/4.98        = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8001_of__nat__and__eq,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 8.69/4.98        = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8002_of__nat__and__eq,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 8.69/4.98        = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8003_insert__Diff__if,axiom,
% 8.69/4.98      ! [X: complex,B3: set_complex,A2: set_complex] :
% 8.69/4.98        ( ( ( member_complex @ X @ B3 )
% 8.69/4.98         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( minus_811609699411566653omplex @ A2 @ B3 ) ) )
% 8.69/4.98        & ( ~ ( member_complex @ X @ B3 )
% 8.69/4.98         => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8004_insert__Diff__if,axiom,
% 8.69/4.98      ! [X: real,B3: set_real,A2: set_real] :
% 8.69/4.98        ( ( ( member_real @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( minus_minus_set_real @ A2 @ B3 ) ) )
% 8.69/4.98        & ( ~ ( member_real @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8005_insert__Diff__if,axiom,
% 8.69/4.98      ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 8.69/4.98        ( ( ( member_set_nat @ X @ B3 )
% 8.69/4.98         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) )
% 8.69/4.98        & ( ~ ( member_set_nat @ X @ B3 )
% 8.69/4.98         => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8006_insert__Diff__if,axiom,
% 8.69/4.98      ! [X: int,B3: set_int,A2: set_int] :
% 8.69/4.98        ( ( ( member_int @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( minus_minus_set_int @ A2 @ B3 ) ) )
% 8.69/4.98        & ( ~ ( member_int @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8007_insert__Diff__if,axiom,
% 8.69/4.98      ! [X: nat,B3: set_nat,A2: set_nat] :
% 8.69/4.98        ( ( ( member_nat @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( minus_minus_set_nat @ A2 @ B3 ) ) )
% 8.69/4.98        & ( ~ ( member_nat @ X @ B3 )
% 8.69/4.98         => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 8.69/4.98            = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8008_int__diff__cases,axiom,
% 8.69/4.98      ! [Z: int] :
% 8.69/4.98        ~ ! [M4: nat,N3: nat] :
% 8.69/4.98            ( Z
% 8.69/4.98           != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8009_log__of__power__eq,axiom,
% 8.69/4.98      ! [M: nat,B: real,N: nat] :
% 8.69/4.98        ( ( ( semiri5074537144036343181t_real @ M )
% 8.69/4.98          = ( power_power_real @ B @ N ) )
% 8.69/4.98       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.98         => ( ( semiri5074537144036343181t_real @ N )
% 8.69/4.98            = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8010_less__log__of__power,axiom,
% 8.69/4.98      ! [B: real,N: nat,M: real] :
% 8.69/4.98        ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 8.69/4.98       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.98         => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8011_of__nat__less__of__int__iff,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 8.69/4.98        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8012_of__nat__less__of__int__iff,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 8.69/4.98        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8013_of__nat__less__of__int__iff,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 8.69/4.98        = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8014_num__induct,axiom,
% 8.69/4.98      ! [P: num > $o,X: num] :
% 8.69/4.98        ( ( P @ one )
% 8.69/4.98       => ( ! [X6: num] :
% 8.69/4.98              ( ( P @ X6 )
% 8.69/4.98             => ( P @ ( inc @ X6 ) ) )
% 8.69/4.98         => ( P @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8015_add__inc,axiom,
% 8.69/4.98      ! [X: num,Y: num] :
% 8.69/4.98        ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 8.69/4.98        = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8016_le__log__of__power,axiom,
% 8.69/4.98      ! [B: real,N: nat,M: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 8.69/4.98       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.98         => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8017_log__base__pow,axiom,
% 8.69/4.98      ! [A: real,N: nat,X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 8.69/4.98          = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8018_log__nat__power,axiom,
% 8.69/4.98      ! [X: real,B: real,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 8.69/4.98          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8019_of__nat__0__le__iff,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8020_of__nat__0__le__iff,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8021_of__nat__0__le__iff,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8022_of__nat__0__le__iff,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8023_of__nat__less__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8024_of__nat__less__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8025_of__nat__less__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8026_of__nat__less__0__iff,axiom,
% 8.69/4.98      ! [M: nat] :
% 8.69/4.98        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8027_of__nat__neq__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 8.69/4.98       != zero_zero_complex ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8028_of__nat__neq__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 8.69/4.98       != zero_zero_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8029_of__nat__neq__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 8.69/4.98       != zero_zero_rat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8030_of__nat__neq__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 8.69/4.98       != zero_zero_nat ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8031_of__nat__neq__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.69/4.98       != zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8032_div__mult2__eq_H,axiom,
% 8.69/4.98      ! [A: nat,M: nat,N: nat] :
% 8.69/4.98        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.69/4.98        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8033_div__mult2__eq_H,axiom,
% 8.69/4.98      ! [A: int,M: nat,N: nat] :
% 8.69/4.98        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/4.98        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8034_less__imp__of__nat__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ N )
% 8.69/4.98       => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8035_less__imp__of__nat__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ N )
% 8.69/4.98       => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8036_less__imp__of__nat__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ N )
% 8.69/4.98       => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8037_less__imp__of__nat__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ N )
% 8.69/4.98       => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8038_of__nat__less__imp__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98       => ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8039_of__nat__less__imp__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.69/4.98       => ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8040_of__nat__less__imp__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98       => ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8041_of__nat__less__imp__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98       => ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8042_of__nat__mono,axiom,
% 8.69/4.98      ! [I: nat,J: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ I @ J )
% 8.69/4.98       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8043_of__nat__mono,axiom,
% 8.69/4.98      ! [I: nat,J: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ I @ J )
% 8.69/4.98       => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8044_of__nat__mono,axiom,
% 8.69/4.98      ! [I: nat,J: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ I @ J )
% 8.69/4.98       => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8045_of__nat__mono,axiom,
% 8.69/4.98      ! [I: nat,J: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ I @ J )
% 8.69/4.98       => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8046_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8047_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 8.69/4.98        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8048_of__nat__dvd__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8049_of__nat__dvd__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8050_of__nat__dvd__iff,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( dvd_dvd_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8051_subset__singletonD,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.69/4.98       => ( ( A2 = bot_bot_set_nat )
% 8.69/4.98          | ( A2
% 8.69/4.98            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8052_subset__singletonD,axiom,
% 8.69/4.98      ! [A2: set_real,X: real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 8.69/4.98       => ( ( A2 = bot_bot_set_real )
% 8.69/4.98          | ( A2
% 8.69/4.98            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8053_subset__singletonD,axiom,
% 8.69/4.98      ! [A2: set_int,X: int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 8.69/4.98       => ( ( A2 = bot_bot_set_int )
% 8.69/4.98          | ( A2
% 8.69/4.98            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8054_subset__singleton__iff,axiom,
% 8.69/4.98      ! [X8: set_nat,A: nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 8.69/4.98        = ( ( X8 = bot_bot_set_nat )
% 8.69/4.98          | ( X8
% 8.69/4.98            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8055_subset__singleton__iff,axiom,
% 8.69/4.98      ! [X8: set_real,A: real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 8.69/4.98        = ( ( X8 = bot_bot_set_real )
% 8.69/4.98          | ( X8
% 8.69/4.98            = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8056_subset__singleton__iff,axiom,
% 8.69/4.98      ! [X8: set_int,A: int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 8.69/4.98        = ( ( X8 = bot_bot_set_int )
% 8.69/4.98          | ( X8
% 8.69/4.98            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8057_int__ops_I1_J,axiom,
% 8.69/4.98      ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.69/4.98      = zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8058_int__ops_I3_J,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 8.69/4.98        = ( numeral_numeral_int @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8059_nat__int__comparison_I2_J,axiom,
% 8.69/4.98      ( ord_less_nat
% 8.69/4.98      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8060_atLeastAtMost__singleton_H,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( A = B )
% 8.69/4.98       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.69/4.98          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8061_atLeastAtMost__singleton_H,axiom,
% 8.69/4.98      ! [A: int,B: int] :
% 8.69/4.98        ( ( A = B )
% 8.69/4.98       => ( ( set_or1266510415728281911st_int @ A @ B )
% 8.69/4.98          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8062_atLeastAtMost__singleton_H,axiom,
% 8.69/4.98      ! [A: real,B: real] :
% 8.69/4.98        ( ( A = B )
% 8.69/4.98       => ( ( set_or1222579329274155063t_real @ A @ B )
% 8.69/4.98          = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8063_Diff__insert__absorb,axiom,
% 8.69/4.98      ! [X: complex,A2: set_complex] :
% 8.69/4.98        ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98       => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8064_Diff__insert__absorb,axiom,
% 8.69/4.98      ! [X: set_nat,A2: set_set_nat] :
% 8.69/4.98        ( ~ ( member_set_nat @ X @ A2 )
% 8.69/4.98       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8065_Diff__insert__absorb,axiom,
% 8.69/4.98      ! [X: int,A2: set_int] :
% 8.69/4.98        ( ~ ( member_int @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8066_Diff__insert__absorb,axiom,
% 8.69/4.98      ! [X: real,A2: set_real] :
% 8.69/4.98        ( ~ ( member_real @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8067_Diff__insert__absorb,axiom,
% 8.69/4.98      ! [X: nat,A2: set_nat] :
% 8.69/4.98        ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8068_Diff__insert2,axiom,
% 8.69/4.98      ! [A2: set_int,A: int,B3: set_int] :
% 8.69/4.98        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8069_Diff__insert2,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,B3: set_real] :
% 8.69/4.98        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8070_Diff__insert2,axiom,
% 8.69/4.98      ! [A2: set_nat,A: nat,B3: set_nat] :
% 8.69/4.98        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B3 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8071_insert__Diff,axiom,
% 8.69/4.98      ! [A: complex,A2: set_complex] :
% 8.69/4.98        ( ( member_complex @ A @ A2 )
% 8.69/4.98       => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8072_insert__Diff,axiom,
% 8.69/4.98      ! [A: set_nat,A2: set_set_nat] :
% 8.69/4.98        ( ( member_set_nat @ A @ A2 )
% 8.69/4.98       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8073_insert__Diff,axiom,
% 8.69/4.98      ! [A: int,A2: set_int] :
% 8.69/4.98        ( ( member_int @ A @ A2 )
% 8.69/4.98       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8074_insert__Diff,axiom,
% 8.69/4.98      ! [A: real,A2: set_real] :
% 8.69/4.98        ( ( member_real @ A @ A2 )
% 8.69/4.98       => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8075_insert__Diff,axiom,
% 8.69/4.98      ! [A: nat,A2: set_nat] :
% 8.69/4.98        ( ( member_nat @ A @ A2 )
% 8.69/4.98       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98          = A2 ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8076_Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_int,A: int,B3: set_int] :
% 8.69/4.98        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8077_Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,B3: set_real] :
% 8.69/4.98        ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B3 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8078_Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_nat,A: nat,B3: set_nat] :
% 8.69/4.98        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 8.69/4.98        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8079_zle__int,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.98        = ( ord_less_eq_nat @ M @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8080_nat__int__comparison_I3_J,axiom,
% 8.69/4.98      ( ord_less_eq_nat
% 8.69/4.98      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8081_subset__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_complex,B3: set_complex,X: complex,C4: set_complex] :
% 8.69/4.98        ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ ( insert_complex @ X @ C4 ) ) )
% 8.69/4.98        = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ C4 ) )
% 8.69/4.98          & ~ ( member_complex @ X @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8082_subset__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_real,B3: set_real,X: real,C4: set_real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ ( insert_real @ X @ C4 ) ) )
% 8.69/4.98        = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ C4 ) )
% 8.69/4.98          & ~ ( member_real @ X @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8083_subset__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_set_nat,B3: set_set_nat,X: set_nat,C4: set_set_nat] :
% 8.69/4.98        ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ ( insert_set_nat @ X @ C4 ) ) )
% 8.69/4.98        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ C4 ) )
% 8.69/4.98          & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8084_subset__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_nat,B3: set_nat,X: nat,C4: set_nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ ( insert_nat @ X @ C4 ) ) )
% 8.69/4.98        = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ C4 ) )
% 8.69/4.98          & ~ ( member_nat @ X @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8085_subset__Diff__insert,axiom,
% 8.69/4.98      ! [A2: set_int,B3: set_int,X: int,C4: set_int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ ( insert_int @ X @ C4 ) ) )
% 8.69/4.98        = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ C4 ) )
% 8.69/4.98          & ~ ( member_int @ X @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8086_nonneg__int__cases,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ( K
% 8.69/4.98             != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8087_zero__le__imp__eq__int,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/4.98       => ? [N3: nat] :
% 8.69/4.98            ( K
% 8.69/4.98            = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8088_of__nat__mod,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 8.69/4.98        = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8089_of__nat__mod,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 8.69/4.98        = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8090_of__nat__mod,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 8.69/4.98        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8091_zadd__int__left,axiom,
% 8.69/4.98      ! [M: nat,N: nat,Z: int] :
% 8.69/4.98        ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8092_int__plus,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8093_int__ops_I5_J,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8094_int__ops_I7_J,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 8.69/4.98        = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8095_int__ops_I2_J,axiom,
% 8.69/4.98      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 8.69/4.98      = one_one_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8096_zle__iff__zadd,axiom,
% 8.69/4.98      ( ord_less_eq_int
% 8.69/4.98      = ( ^ [W3: int,Z3: int] :
% 8.69/4.98          ? [N2: nat] :
% 8.69/4.98            ( Z3
% 8.69/4.98            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8097_zdiv__int,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 8.69/4.98        = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8098_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8099_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8100_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8101_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8102_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8103_of__nat__max,axiom,
% 8.69/4.98      ! [X: nat,Y: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 8.69/4.98        = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8104_zmod__int,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 8.69/4.98        = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8105_log2__of__power__eq,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( M
% 8.69/4.98          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98       => ( ( semiri5074537144036343181t_real @ N )
% 8.69/4.98          = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8106_log__of__power__less,axiom,
% 8.69/4.98      ! [M: nat,B: real,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 8.69/4.98       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.98         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.98           => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8107_nat__less__as__int,axiom,
% 8.69/4.98      ( ord_less_nat
% 8.69/4.98      = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8108_nat__leq__as__int,axiom,
% 8.69/4.98      ( ord_less_eq_nat
% 8.69/4.98      = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8109_of__nat__mask__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.69/4.98        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8110_of__nat__mask__eq,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.69/4.98        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8111_inc_Osimps_I1_J,axiom,
% 8.69/4.98      ( ( inc @ one )
% 8.69/4.98      = ( bit0 @ one ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8112_inc_Osimps_I3_J,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( inc @ ( bit1 @ X ) )
% 8.69/4.98        = ( bit0 @ ( inc @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8113_inc_Osimps_I2_J,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( inc @ ( bit0 @ X ) )
% 8.69/4.98        = ( bit1 @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8114_log__of__power__le,axiom,
% 8.69/4.98      ! [M: nat,B: real,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 8.69/4.98       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.98         => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.98           => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8115_ex__less__of__nat__mult,axiom,
% 8.69/4.98      ! [X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8116_ex__less__of__nat__mult,axiom,
% 8.69/4.98      ! [X: rat,Y: rat] :
% 8.69/4.98        ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.69/4.98       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8117_add__One,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( plus_plus_num @ X @ one )
% 8.69/4.98        = ( inc @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8118_inc__BitM__eq,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( inc @ ( bitM @ N ) )
% 8.69/4.98        = ( bit0 @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8119_of__nat__diff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8120_of__nat__diff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8121_of__nat__diff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8122_of__nat__diff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8123_of__nat__diff,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 8.69/4.98          = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8124_BitM__inc__eq,axiom,
% 8.69/4.98      ! [N: num] :
% 8.69/4.98        ( ( bitM @ ( inc @ N ) )
% 8.69/4.98        = ( bit1 @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8125_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_complex )
% 8.69/4.98         => ( ! [X6: complex,S5: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ S5 )
% 8.69/4.98               => ( ! [Y2: complex] :
% 8.69/4.98                      ( ( member_complex @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8126_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 8.69/4.98        ( ( finite_finite_nat @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [X6: nat,S5: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ S5 )
% 8.69/4.98               => ( ! [Y2: nat] :
% 8.69/4.98                      ( ( member_nat @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8127_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [X6: int,S5: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ S5 )
% 8.69/4.98               => ( ! [Y2: int] :
% 8.69/4.98                      ( ( member_int @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8128_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [X6: real,S5: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ S5 )
% 8.69/4.98               => ( ! [Y2: real] :
% 8.69/4.98                      ( ( member_real @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8129_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_complex )
% 8.69/4.98         => ( ! [X6: complex,S5: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ S5 )
% 8.69/4.98               => ( ! [Y2: complex] :
% 8.69/4.98                      ( ( member_complex @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8130_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 8.69/4.98        ( ( finite_finite_nat @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [X6: nat,S5: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ S5 )
% 8.69/4.98               => ( ! [Y2: nat] :
% 8.69/4.98                      ( ( member_nat @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8131_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_int,P: set_int > $o,F: int > num] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [X6: int,S5: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ S5 )
% 8.69/4.98               => ( ! [Y2: int] :
% 8.69/4.98                      ( ( member_int @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8132_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_real,P: set_real > $o,F: real > num] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [X6: real,S5: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ S5 )
% 8.69/4.98               => ( ! [Y2: real] :
% 8.69/4.98                      ( ( member_real @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8133_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_complex )
% 8.69/4.98         => ( ! [X6: complex,S5: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ S5 )
% 8.69/4.98               => ( ! [Y2: complex] :
% 8.69/4.98                      ( ( member_complex @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8134_finite__ranking__induct,axiom,
% 8.69/4.98      ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 8.69/4.98        ( ( finite_finite_nat @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [X6: nat,S5: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ S5 )
% 8.69/4.98               => ( ! [Y2: nat] :
% 8.69/4.98                      ( ( member_nat @ Y2 @ S5 )
% 8.69/4.98                     => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 8.69/4.98                 => ( ( P @ S5 )
% 8.69/4.98                   => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8135_finite__linorder__max__induct,axiom,
% 8.69/4.98      ! [A2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [B5: real,A7: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ A7 )
% 8.69/4.98               => ( ! [X4: real] :
% 8.69/4.98                      ( ( member_real @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_real @ X4 @ B5 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8136_finite__linorder__max__induct,axiom,
% 8.69/4.98      ! [A2: set_rat,P: set_rat > $o] :
% 8.69/4.98        ( ( finite_finite_rat @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_rat )
% 8.69/4.98         => ( ! [B5: rat,A7: set_rat] :
% 8.69/4.98                ( ( finite_finite_rat @ A7 )
% 8.69/4.98               => ( ! [X4: rat] :
% 8.69/4.98                      ( ( member_rat @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_rat @ X4 @ B5 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8137_finite__linorder__max__induct,axiom,
% 8.69/4.98      ! [A2: set_num,P: set_num > $o] :
% 8.69/4.98        ( ( finite_finite_num @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_num )
% 8.69/4.98         => ( ! [B5: num,A7: set_num] :
% 8.69/4.98                ( ( finite_finite_num @ A7 )
% 8.69/4.98               => ( ! [X4: num] :
% 8.69/4.98                      ( ( member_num @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_num @ X4 @ B5 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8138_finite__linorder__max__induct,axiom,
% 8.69/4.98      ! [A2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [B5: nat,A7: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ A7 )
% 8.69/4.98               => ( ! [X4: nat] :
% 8.69/4.98                      ( ( member_nat @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_nat @ X4 @ B5 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8139_finite__linorder__max__induct,axiom,
% 8.69/4.98      ! [A2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [B5: int,A7: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ A7 )
% 8.69/4.98               => ( ! [X4: int] :
% 8.69/4.98                      ( ( member_int @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_int @ X4 @ B5 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8140_finite__linorder__min__induct,axiom,
% 8.69/4.98      ! [A2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [B5: real,A7: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ A7 )
% 8.69/4.98               => ( ! [X4: real] :
% 8.69/4.98                      ( ( member_real @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_real @ B5 @ X4 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8141_finite__linorder__min__induct,axiom,
% 8.69/4.98      ! [A2: set_rat,P: set_rat > $o] :
% 8.69/4.98        ( ( finite_finite_rat @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_rat )
% 8.69/4.98         => ( ! [B5: rat,A7: set_rat] :
% 8.69/4.98                ( ( finite_finite_rat @ A7 )
% 8.69/4.98               => ( ! [X4: rat] :
% 8.69/4.98                      ( ( member_rat @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_rat @ B5 @ X4 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8142_finite__linorder__min__induct,axiom,
% 8.69/4.98      ! [A2: set_num,P: set_num > $o] :
% 8.69/4.98        ( ( finite_finite_num @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_num )
% 8.69/4.98         => ( ! [B5: num,A7: set_num] :
% 8.69/4.98                ( ( finite_finite_num @ A7 )
% 8.69/4.98               => ( ! [X4: num] :
% 8.69/4.98                      ( ( member_num @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_num @ B5 @ X4 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8143_finite__linorder__min__induct,axiom,
% 8.69/4.98      ! [A2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [B5: nat,A7: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ A7 )
% 8.69/4.98               => ( ! [X4: nat] :
% 8.69/4.98                      ( ( member_nat @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_nat @ B5 @ X4 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8144_finite__linorder__min__induct,axiom,
% 8.69/4.98      ! [A2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [B5: int,A7: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ A7 )
% 8.69/4.98               => ( ! [X4: int] :
% 8.69/4.98                      ( ( member_int @ X4 @ A7 )
% 8.69/4.98                     => ( ord_less_int @ B5 @ X4 ) )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8145_exp__of__nat2__mult,axiom,
% 8.69/4.98      ! [X: complex,N: nat] :
% 8.69/4.98        ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 8.69/4.98        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8146_exp__of__nat2__mult,axiom,
% 8.69/4.98      ! [X: real,N: nat] :
% 8.69/4.98        ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.98        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8147_exp__of__nat__mult,axiom,
% 8.69/4.98      ! [N: nat,X: complex] :
% 8.69/4.98        ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 8.69/4.98        = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8148_exp__of__nat__mult,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 8.69/4.98        = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8149_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8150_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > real] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8151_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > real] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8152_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8153_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat,G: nat > rat] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( ( member_nat @ X @ A2 )
% 8.69/4.98           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 8.69/4.98              = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98           => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8154_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8155_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8156_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > nat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( groups1935376822645274424al_nat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_real @ X @ A2 )
% 8.69/4.98           => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8157_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > nat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_int @ X @ A2 )
% 8.69/4.98           => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8158_sum_Oinsert__if,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > nat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( groups5693394587270226106ex_nat @ G @ A2 ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98              = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8159_finite__subset__induct,axiom,
% 8.69/4.98      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 8.69/4.98        ( ( finite1152437895449049373et_nat @ F3 )
% 8.69/4.98       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_set_nat )
% 8.69/4.98           => ( ! [A5: set_nat,F4: set_set_nat] :
% 8.69/4.98                  ( ( finite1152437895449049373et_nat @ F4 )
% 8.69/4.98                 => ( ( member_set_nat @ A5 @ A2 )
% 8.69/4.98                   => ( ~ ( member_set_nat @ A5 @ F4 )
% 8.69/4.98                     => ( ( P @ F4 )
% 8.69/4.98                       => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8160_finite__subset__induct,axiom,
% 8.69/4.98      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ F3 )
% 8.69/4.98       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_complex )
% 8.69/4.98           => ( ! [A5: complex,F4: set_complex] :
% 8.69/4.98                  ( ( finite3207457112153483333omplex @ F4 )
% 8.69/4.98                 => ( ( member_complex @ A5 @ A2 )
% 8.69/4.98                   => ( ~ ( member_complex @ A5 @ F4 )
% 8.69/4.98                     => ( ( P @ F4 )
% 8.69/4.98                       => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8161_finite__subset__induct,axiom,
% 8.69/4.98      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_nat )
% 8.69/4.98           => ( ! [A5: nat,F4: set_nat] :
% 8.69/4.98                  ( ( finite_finite_nat @ F4 )
% 8.69/4.98                 => ( ( member_nat @ A5 @ A2 )
% 8.69/4.98                   => ( ~ ( member_nat @ A5 @ F4 )
% 8.69/4.98                     => ( ( P @ F4 )
% 8.69/4.98                       => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8162_finite__subset__induct,axiom,
% 8.69/4.98      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_real )
% 8.69/4.98           => ( ! [A5: real,F4: set_real] :
% 8.69/4.98                  ( ( finite_finite_real @ F4 )
% 8.69/4.98                 => ( ( member_real @ A5 @ A2 )
% 8.69/4.98                   => ( ~ ( member_real @ A5 @ F4 )
% 8.69/4.98                     => ( ( P @ F4 )
% 8.69/4.98                       => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8163_finite__subset__induct,axiom,
% 8.69/4.98      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_int )
% 8.69/4.98           => ( ! [A5: int,F4: set_int] :
% 8.69/4.98                  ( ( finite_finite_int @ F4 )
% 8.69/4.98                 => ( ( member_int @ A5 @ A2 )
% 8.69/4.98                   => ( ~ ( member_int @ A5 @ F4 )
% 8.69/4.98                     => ( ( P @ F4 )
% 8.69/4.98                       => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8164_finite__subset__induct_H,axiom,
% 8.69/4.98      ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 8.69/4.98        ( ( finite1152437895449049373et_nat @ F3 )
% 8.69/4.98       => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_set_nat )
% 8.69/4.98           => ( ! [A5: set_nat,F4: set_set_nat] :
% 8.69/4.98                  ( ( finite1152437895449049373et_nat @ F4 )
% 8.69/4.98                 => ( ( member_set_nat @ A5 @ A2 )
% 8.69/4.98                   => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 8.69/4.98                     => ( ~ ( member_set_nat @ A5 @ F4 )
% 8.69/4.98                       => ( ( P @ F4 )
% 8.69/4.98                         => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8165_finite__subset__induct_H,axiom,
% 8.69/4.98      ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ F3 )
% 8.69/4.98       => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_complex )
% 8.69/4.98           => ( ! [A5: complex,F4: set_complex] :
% 8.69/4.98                  ( ( finite3207457112153483333omplex @ F4 )
% 8.69/4.98                 => ( ( member_complex @ A5 @ A2 )
% 8.69/4.98                   => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 8.69/4.98                     => ( ~ ( member_complex @ A5 @ F4 )
% 8.69/4.98                       => ( ( P @ F4 )
% 8.69/4.98                         => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8166_finite__subset__induct_H,axiom,
% 8.69/4.98      ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_nat )
% 8.69/4.98           => ( ! [A5: nat,F4: set_nat] :
% 8.69/4.98                  ( ( finite_finite_nat @ F4 )
% 8.69/4.98                 => ( ( member_nat @ A5 @ A2 )
% 8.69/4.98                   => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 8.69/4.98                     => ( ~ ( member_nat @ A5 @ F4 )
% 8.69/4.98                       => ( ( P @ F4 )
% 8.69/4.98                         => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8167_finite__subset__induct_H,axiom,
% 8.69/4.98      ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_real )
% 8.69/4.98           => ( ! [A5: real,F4: set_real] :
% 8.69/4.98                  ( ( finite_finite_real @ F4 )
% 8.69/4.98                 => ( ( member_real @ A5 @ A2 )
% 8.69/4.98                   => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 8.69/4.98                     => ( ~ ( member_real @ A5 @ F4 )
% 8.69/4.98                       => ( ( P @ F4 )
% 8.69/4.98                         => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8168_finite__subset__induct_H,axiom,
% 8.69/4.98      ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ F3 )
% 8.69/4.98       => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 8.69/4.98         => ( ( P @ bot_bot_set_int )
% 8.69/4.98           => ( ! [A5: int,F4: set_int] :
% 8.69/4.98                  ( ( finite_finite_int @ F4 )
% 8.69/4.98                 => ( ( member_int @ A5 @ A2 )
% 8.69/4.98                   => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 8.69/4.98                     => ( ~ ( member_int @ A5 @ F4 )
% 8.69/4.98                       => ( ( P @ F4 )
% 8.69/4.98                         => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) ) )
% 8.69/4.98             => ( P @ F3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8169_reals__Archimedean3,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ! [Y2: real] :
% 8.69/4.98          ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8170_log__ln,axiom,
% 8.69/4.98      ( ln_ln_real
% 8.69/4.98      = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8171_int__cases4,axiom,
% 8.69/4.98      ! [M: int] :
% 8.69/4.98        ( ! [N3: nat] :
% 8.69/4.98            ( M
% 8.69/4.98           != ( semiri1314217659103216013at_int @ N3 ) )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.69/4.98             => ( M
% 8.69/4.98               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8172_infinite__remove,axiom,
% 8.69/4.98      ! [S2: set_complex,A: complex] :
% 8.69/4.98        ( ~ ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8173_infinite__remove,axiom,
% 8.69/4.98      ! [S2: set_int,A: int] :
% 8.69/4.98        ( ~ ( finite_finite_int @ S2 )
% 8.69/4.98       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8174_infinite__remove,axiom,
% 8.69/4.98      ! [S2: set_real,A: real] :
% 8.69/4.98        ( ~ ( finite_finite_real @ S2 )
% 8.69/4.98       => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8175_infinite__remove,axiom,
% 8.69/4.98      ! [S2: set_nat,A: nat] :
% 8.69/4.98        ( ~ ( finite_finite_nat @ S2 )
% 8.69/4.98       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8176_infinite__coinduct,axiom,
% 8.69/4.98      ! [X8: set_complex > $o,A2: set_complex] :
% 8.69/4.98        ( ( X8 @ A2 )
% 8.69/4.98       => ( ! [A7: set_complex] :
% 8.69/4.98              ( ( X8 @ A7 )
% 8.69/4.98             => ? [X4: complex] :
% 8.69/4.98                  ( ( member_complex @ X4 @ A7 )
% 8.69/4.98                  & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) )
% 8.69/4.98                    | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98         => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8177_infinite__coinduct,axiom,
% 8.69/4.98      ! [X8: set_int > $o,A2: set_int] :
% 8.69/4.98        ( ( X8 @ A2 )
% 8.69/4.98       => ( ! [A7: set_int] :
% 8.69/4.98              ( ( X8 @ A7 )
% 8.69/4.98             => ? [X4: int] :
% 8.69/4.98                  ( ( member_int @ X4 @ A7 )
% 8.69/4.98                  & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) )
% 8.69/4.98                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ) )
% 8.69/4.98         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8178_infinite__coinduct,axiom,
% 8.69/4.98      ! [X8: set_real > $o,A2: set_real] :
% 8.69/4.98        ( ( X8 @ A2 )
% 8.69/4.98       => ( ! [A7: set_real] :
% 8.69/4.98              ( ( X8 @ A7 )
% 8.69/4.98             => ? [X4: real] :
% 8.69/4.98                  ( ( member_real @ X4 @ A7 )
% 8.69/4.98                  & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) )
% 8.69/4.98                    | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ) )
% 8.69/4.98         => ~ ( finite_finite_real @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8179_infinite__coinduct,axiom,
% 8.69/4.98      ! [X8: set_nat > $o,A2: set_nat] :
% 8.69/4.98        ( ( X8 @ A2 )
% 8.69/4.98       => ( ! [A7: set_nat] :
% 8.69/4.98              ( ( X8 @ A7 )
% 8.69/4.98             => ? [X4: nat] :
% 8.69/4.98                  ( ( member_nat @ X4 @ A7 )
% 8.69/4.98                  & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
% 8.69/4.98                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
% 8.69/4.98         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8180_finite__empty__induct,axiom,
% 8.69/4.98      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 8.69/4.98        ( ( finite1152437895449049373et_nat @ A2 )
% 8.69/4.98       => ( ( P @ A2 )
% 8.69/4.98         => ( ! [A5: set_nat,A7: set_set_nat] :
% 8.69/4.98                ( ( finite1152437895449049373et_nat @ A7 )
% 8.69/4.98               => ( ( member_set_nat @ A5 @ A7 )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ A5 @ bot_bot_set_set_nat ) ) ) ) ) )
% 8.69/4.98           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8181_finite__empty__induct,axiom,
% 8.69/4.98      ! [A2: set_complex,P: set_complex > $o] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( P @ A2 )
% 8.69/4.98         => ( ! [A5: complex,A7: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ A7 )
% 8.69/4.98               => ( ( member_complex @ A5 @ A7 )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A5 @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98           => ( P @ bot_bot_set_complex ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8182_finite__empty__induct,axiom,
% 8.69/4.98      ! [A2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( P @ A2 )
% 8.69/4.98         => ( ! [A5: int,A7: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ A7 )
% 8.69/4.98               => ( ( member_int @ A5 @ A7 )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ) )
% 8.69/4.98           => ( P @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8183_finite__empty__induct,axiom,
% 8.69/4.98      ! [A2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( P @ A2 )
% 8.69/4.98         => ( ! [A5: real,A7: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ A7 )
% 8.69/4.98               => ( ( member_real @ A5 @ A7 )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A5 @ bot_bot_set_real ) ) ) ) ) )
% 8.69/4.98           => ( P @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8184_finite__empty__induct,axiom,
% 8.69/4.98      ! [A2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( P @ A2 )
% 8.69/4.98         => ( ! [A5: nat,A7: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ A7 )
% 8.69/4.98               => ( ( member_nat @ A5 @ A7 )
% 8.69/4.98                 => ( ( P @ A7 )
% 8.69/4.98                   => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ) )
% 8.69/4.98           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8185_Diff__single__insert,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,B3: set_real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8186_Diff__single__insert,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat,B3: set_nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8187_Diff__single__insert,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,B3: set_int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 )
% 8.69/4.98       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8188_subset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,B3: set_complex] :
% 8.69/4.98        ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 8.69/4.98          & ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98           => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8189_subset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 8.69/4.98        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_set_nat @ X @ A2 )
% 8.69/4.98           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 8.69/4.98          & ( ~ ( member_set_nat @ X @ A2 )
% 8.69/4.98           => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8190_subset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,B3: set_real] :
% 8.69/4.98        ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_real @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 8.69/4.98          & ( ~ ( member_real @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8191_subset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat,B3: set_nat] :
% 8.69/4.98        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_nat @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 8.69/4.98          & ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8192_subset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,B3: set_int] :
% 8.69/4.98        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_int @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 8.69/4.98          & ( ~ ( member_int @ X @ A2 )
% 8.69/4.98           => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8193_real__of__nat__div4,axiom,
% 8.69/4.98      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8194_sum__diff1__nat,axiom,
% 8.69/4.98      ! [A: complex,A2: set_complex,F: complex > nat] :
% 8.69/4.98        ( ( ( member_complex @ A @ A2 )
% 8.69/4.98         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98            = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98        & ( ~ ( member_complex @ A @ A2 )
% 8.69/4.98         => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98            = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8195_sum__diff1__nat,axiom,
% 8.69/4.98      ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 8.69/4.98        ( ( ( member_set_nat @ A @ A2 )
% 8.69/4.98         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 8.69/4.98            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98        & ( ~ ( member_set_nat @ A @ A2 )
% 8.69/4.98         => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 8.69/4.98            = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8196_sum__diff1__nat,axiom,
% 8.69/4.98      ! [A: int,A2: set_int,F: int > nat] :
% 8.69/4.98        ( ( ( member_int @ A @ A2 )
% 8.69/4.98         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98        & ( ~ ( member_int @ A @ A2 )
% 8.69/4.98         => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98            = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8197_sum__diff1__nat,axiom,
% 8.69/4.98      ! [A: real,A2: set_real,F: real > nat] :
% 8.69/4.98        ( ( ( member_real @ A @ A2 )
% 8.69/4.98         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98            = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98        & ( ~ ( member_real @ A @ A2 )
% 8.69/4.98         => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98            = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8198_sum__diff1__nat,axiom,
% 8.69/4.98      ! [A: nat,A2: set_nat,F: nat > nat] :
% 8.69/4.98        ( ( ( member_nat @ A @ A2 )
% 8.69/4.98         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98        & ( ~ ( member_nat @ A @ A2 )
% 8.69/4.98         => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98            = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8199_int__ops_I4_J,axiom,
% 8.69/4.98      ! [A: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8200_int__Suc,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.69/4.98        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8201_zless__iff__Suc__zadd,axiom,
% 8.69/4.98      ( ord_less_int
% 8.69/4.98      = ( ^ [W3: int,Z3: int] :
% 8.69/4.98          ? [N2: nat] :
% 8.69/4.98            ( Z3
% 8.69/4.98            = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8202_int__zle__neg,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 8.69/4.98        = ( ( N = zero_zero_nat )
% 8.69/4.98          & ( M = zero_zero_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8203_real__of__nat__div,axiom,
% 8.69/4.98      ! [D: nat,N: nat] :
% 8.69/4.98        ( ( dvd_dvd_nat @ D @ N )
% 8.69/4.98       => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 8.69/4.98          = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8204_negative__zle__0,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8205_nonpos__int__cases,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ( K
% 8.69/4.98             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8206_mult__inc,axiom,
% 8.69/4.98      ! [X: num,Y: num] :
% 8.69/4.98        ( ( times_times_num @ X @ ( inc @ Y ) )
% 8.69/4.98        = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8207_set__update__subset__insert,axiom,
% 8.69/4.98      ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8208_set__update__subset__insert,axiom,
% 8.69/4.98      ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8209_set__update__subset__insert,axiom,
% 8.69/4.98      ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8210_set__update__subset__insert,axiom,
% 8.69/4.98      ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8211_Compl__insert,axiom,
% 8.69/4.98      ! [X: int,A2: set_int] :
% 8.69/4.98        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 8.69/4.98        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8212_Compl__insert,axiom,
% 8.69/4.98      ! [X: real,A2: set_real] :
% 8.69/4.98        ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 8.69/4.98        = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8213_Compl__insert,axiom,
% 8.69/4.98      ! [X: nat,A2: set_nat] :
% 8.69/4.98        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 8.69/4.98        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8214_less__log2__of__power,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 8.69/4.98       => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8215_le__log2__of__power,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 8.69/4.98       => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8216_log2__of__power__less,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.98         => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8217_log__base__change,axiom,
% 8.69/4.98      ! [A: real,B: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( log @ B @ X )
% 8.69/4.98            = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8218_numeral__inc,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 8.69/4.98        = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8219_numeral__inc,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( numeral_numeral_real @ ( inc @ X ) )
% 8.69/4.98        = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8220_numeral__inc,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 8.69/4.98        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8221_numeral__inc,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 8.69/4.98        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8222_numeral__inc,axiom,
% 8.69/4.98      ! [X: num] :
% 8.69/4.98        ( ( numeral_numeral_int @ ( inc @ X ) )
% 8.69/4.98        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8223_mod__mult2__eq_H,axiom,
% 8.69/4.98      ! [A: code_integer,M: nat,N: nat] :
% 8.69/4.98        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 8.69/4.98        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8224_mod__mult2__eq_H,axiom,
% 8.69/4.98      ! [A: nat,M: nat,N: nat] :
% 8.69/4.98        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.69/4.98        = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8225_mod__mult2__eq_H,axiom,
% 8.69/4.98      ! [A: int,M: nat,N: nat] :
% 8.69/4.98        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/4.98        = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8226_field__char__0__class_Oof__nat__div,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 8.69/4.98        = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8227_field__char__0__class_Oof__nat__div,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 8.69/4.98        = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8228_field__char__0__class_Oof__nat__div,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 8.69/4.98        = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8229_remove__induct,axiom,
% 8.69/4.98      ! [P: set_set_nat > $o,B3: set_set_nat] :
% 8.69/4.98        ( ( P @ bot_bot_set_set_nat )
% 8.69/4.98       => ( ( ~ ( finite1152437895449049373et_nat @ B3 )
% 8.69/4.98           => ( P @ B3 ) )
% 8.69/4.98         => ( ! [A7: set_set_nat] :
% 8.69/4.98                ( ( finite1152437895449049373et_nat @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_set_nat )
% 8.69/4.98                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: set_nat] :
% 8.69/4.98                          ( ( member_set_nat @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8230_remove__induct,axiom,
% 8.69/4.98      ! [P: set_complex > $o,B3: set_complex] :
% 8.69/4.98        ( ( P @ bot_bot_set_complex )
% 8.69/4.98       => ( ( ~ ( finite3207457112153483333omplex @ B3 )
% 8.69/4.98           => ( P @ B3 ) )
% 8.69/4.98         => ( ! [A7: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_complex )
% 8.69/4.98                 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: complex] :
% 8.69/4.98                          ( ( member_complex @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8231_remove__induct,axiom,
% 8.69/4.98      ! [P: set_real > $o,B3: set_real] :
% 8.69/4.98        ( ( P @ bot_bot_set_real )
% 8.69/4.98       => ( ( ~ ( finite_finite_real @ B3 )
% 8.69/4.98           => ( P @ B3 ) )
% 8.69/4.98         => ( ! [A7: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_real )
% 8.69/4.98                 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: real] :
% 8.69/4.98                          ( ( member_real @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8232_remove__induct,axiom,
% 8.69/4.98      ! [P: set_nat > $o,B3: set_nat] :
% 8.69/4.98        ( ( P @ bot_bot_set_nat )
% 8.69/4.98       => ( ( ~ ( finite_finite_nat @ B3 )
% 8.69/4.98           => ( P @ B3 ) )
% 8.69/4.98         => ( ! [A7: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_nat )
% 8.69/4.98                 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: nat] :
% 8.69/4.98                          ( ( member_nat @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8233_remove__induct,axiom,
% 8.69/4.98      ! [P: set_int > $o,B3: set_int] :
% 8.69/4.98        ( ( P @ bot_bot_set_int )
% 8.69/4.98       => ( ( ~ ( finite_finite_int @ B3 )
% 8.69/4.98           => ( P @ B3 ) )
% 8.69/4.98         => ( ! [A7: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_int )
% 8.69/4.98                 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: int] :
% 8.69/4.98                          ( ( member_int @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8234_finite__remove__induct,axiom,
% 8.69/4.98      ! [B3: set_set_nat,P: set_set_nat > $o] :
% 8.69/4.98        ( ( finite1152437895449049373et_nat @ B3 )
% 8.69/4.98       => ( ( P @ bot_bot_set_set_nat )
% 8.69/4.98         => ( ! [A7: set_set_nat] :
% 8.69/4.98                ( ( finite1152437895449049373et_nat @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_set_nat )
% 8.69/4.98                 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: set_nat] :
% 8.69/4.98                          ( ( member_set_nat @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8235_finite__remove__induct,axiom,
% 8.69/4.98      ! [B3: set_complex,P: set_complex > $o] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ B3 )
% 8.69/4.98       => ( ( P @ bot_bot_set_complex )
% 8.69/4.98         => ( ! [A7: set_complex] :
% 8.69/4.98                ( ( finite3207457112153483333omplex @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_complex )
% 8.69/4.98                 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: complex] :
% 8.69/4.98                          ( ( member_complex @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8236_finite__remove__induct,axiom,
% 8.69/4.98      ! [B3: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ B3 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [A7: set_real] :
% 8.69/4.98                ( ( finite_finite_real @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_real )
% 8.69/4.98                 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: real] :
% 8.69/4.98                          ( ( member_real @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8237_finite__remove__induct,axiom,
% 8.69/4.98      ! [B3: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ B3 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [A7: set_nat] :
% 8.69/4.98                ( ( finite_finite_nat @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_nat )
% 8.69/4.98                 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: nat] :
% 8.69/4.98                          ( ( member_nat @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8238_finite__remove__induct,axiom,
% 8.69/4.98      ! [B3: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ B3 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [A7: set_int] :
% 8.69/4.98                ( ( finite_finite_int @ A7 )
% 8.69/4.98               => ( ( A7 != bot_bot_set_int )
% 8.69/4.98                 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 8.69/4.98                   => ( ! [X4: int] :
% 8.69/4.98                          ( ( member_int @ X4 @ A7 )
% 8.69/4.98                         => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 8.69/4.98                     => ( P @ A7 ) ) ) ) )
% 8.69/4.98           => ( P @ B3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8239_zero__less__imp__eq__int,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_int @ zero_zero_int @ K )
% 8.69/4.98       => ? [N3: nat] :
% 8.69/4.98            ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.69/4.98            & ( K
% 8.69/4.98              = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8240_pos__int__cases,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_int @ zero_zero_int @ K )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ( ( K
% 8.69/4.98                = ( semiri1314217659103216013at_int @ N3 ) )
% 8.69/4.98             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8241_int__cases3,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( K != zero_zero_int )
% 8.69/4.98       => ( ! [N3: nat] :
% 8.69/4.98              ( ( K
% 8.69/4.98                = ( semiri1314217659103216013at_int @ N3 ) )
% 8.69/4.98             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 8.69/4.98         => ~ ! [N3: nat] :
% 8.69/4.98                ( ( K
% 8.69/4.98                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 8.69/4.98               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8242_nat__less__real__le,axiom,
% 8.69/4.98      ( ord_less_nat
% 8.69/4.98      = ( ^ [N2: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8243_nat__le__real__less,axiom,
% 8.69/4.98      ( ord_less_eq_nat
% 8.69/4.98      = ( ^ [N2: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8244_zmult__zless__mono2__lemma,axiom,
% 8.69/4.98      ! [I: int,J: int,K: nat] :
% 8.69/4.98        ( ( ord_less_int @ I @ J )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.98         => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8245_not__zle__0__negative,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8246_negative__zless__0,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8247_negD,axiom,
% 8.69/4.98      ! [X: int] :
% 8.69/4.98        ( ( ord_less_int @ X @ zero_zero_int )
% 8.69/4.98       => ? [N3: nat] :
% 8.69/4.98            ( X
% 8.69/4.98            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8248_finite__induct__select,axiom,
% 8.69/4.98      ! [S2: set_complex,P: set_complex > $o] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_complex )
% 8.69/4.98         => ( ! [T5: set_complex] :
% 8.69/4.98                ( ( ord_less_set_complex @ T5 @ S2 )
% 8.69/4.98               => ( ( P @ T5 )
% 8.69/4.98                 => ? [X4: complex] :
% 8.69/4.98                      ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ S2 @ T5 ) )
% 8.69/4.98                      & ( P @ ( insert_complex @ X4 @ T5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8249_finite__induct__select,axiom,
% 8.69/4.98      ! [S2: set_int,P: set_int > $o] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_int )
% 8.69/4.98         => ( ! [T5: set_int] :
% 8.69/4.98                ( ( ord_less_set_int @ T5 @ S2 )
% 8.69/4.98               => ( ( P @ T5 )
% 8.69/4.98                 => ? [X4: int] :
% 8.69/4.98                      ( ( member_int @ X4 @ ( minus_minus_set_int @ S2 @ T5 ) )
% 8.69/4.98                      & ( P @ ( insert_int @ X4 @ T5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8250_finite__induct__select,axiom,
% 8.69/4.98      ! [S2: set_real,P: set_real > $o] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_real )
% 8.69/4.98         => ( ! [T5: set_real] :
% 8.69/4.98                ( ( ord_less_set_real @ T5 @ S2 )
% 8.69/4.98               => ( ( P @ T5 )
% 8.69/4.98                 => ? [X4: real] :
% 8.69/4.98                      ( ( member_real @ X4 @ ( minus_minus_set_real @ S2 @ T5 ) )
% 8.69/4.98                      & ( P @ ( insert_real @ X4 @ T5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8251_finite__induct__select,axiom,
% 8.69/4.98      ! [S2: set_nat,P: set_nat > $o] :
% 8.69/4.98        ( ( finite_finite_nat @ S2 )
% 8.69/4.98       => ( ( P @ bot_bot_set_nat )
% 8.69/4.98         => ( ! [T5: set_nat] :
% 8.69/4.98                ( ( ord_less_set_nat @ T5 @ S2 )
% 8.69/4.98               => ( ( P @ T5 )
% 8.69/4.98                 => ? [X4: nat] :
% 8.69/4.98                      ( ( member_nat @ X4 @ ( minus_minus_set_nat @ S2 @ T5 ) )
% 8.69/4.98                      & ( P @ ( insert_nat @ X4 @ T5 ) ) ) ) )
% 8.69/4.98           => ( P @ S2 ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8252_psubset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,B3: set_complex] :
% 8.69/4.98        ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_complex @ X @ B3 )
% 8.69/4.98           => ( ord_less_set_complex @ A2 @ B3 ) )
% 8.69/4.98          & ( ~ ( member_complex @ X @ B3 )
% 8.69/4.98           => ( ( ( member_complex @ X @ A2 )
% 8.69/4.98               => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 8.69/4.98              & ( ~ ( member_complex @ X @ A2 )
% 8.69/4.98               => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8253_psubset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 8.69/4.98        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_set_nat @ X @ B3 )
% 8.69/4.98           => ( ord_less_set_set_nat @ A2 @ B3 ) )
% 8.69/4.98          & ( ~ ( member_set_nat @ X @ B3 )
% 8.69/4.98           => ( ( ( member_set_nat @ X @ A2 )
% 8.69/4.98               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 8.69/4.98              & ( ~ ( member_set_nat @ X @ A2 )
% 8.69/4.98               => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8254_psubset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,B3: set_real] :
% 8.69/4.98        ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_real @ X @ B3 )
% 8.69/4.98           => ( ord_less_set_real @ A2 @ B3 ) )
% 8.69/4.98          & ( ~ ( member_real @ X @ B3 )
% 8.69/4.98           => ( ( ( member_real @ X @ A2 )
% 8.69/4.98               => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 8.69/4.98              & ( ~ ( member_real @ X @ A2 )
% 8.69/4.98               => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8255_psubset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_nat,X: nat,B3: set_nat] :
% 8.69/4.98        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_nat @ X @ B3 )
% 8.69/4.98           => ( ord_less_set_nat @ A2 @ B3 ) )
% 8.69/4.98          & ( ~ ( member_nat @ X @ B3 )
% 8.69/4.98           => ( ( ( member_nat @ X @ A2 )
% 8.69/4.98               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 8.69/4.98              & ( ~ ( member_nat @ X @ A2 )
% 8.69/4.98               => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8256_psubset__insert__iff,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,B3: set_int] :
% 8.69/4.98        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 8.69/4.98        = ( ( ( member_int @ X @ B3 )
% 8.69/4.98           => ( ord_less_set_int @ A2 @ B3 ) )
% 8.69/4.98          & ( ~ ( member_int @ X @ B3 )
% 8.69/4.98           => ( ( ( member_int @ X @ A2 )
% 8.69/4.98               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 8.69/4.98              & ( ~ ( member_int @ X @ A2 )
% 8.69/4.98               => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8257_set__replicate__Suc,axiom,
% 8.69/4.98      ! [N: nat,X: vEBT_VEBT] :
% 8.69/4.98        ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 8.69/4.98        = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8258_set__replicate__Suc,axiom,
% 8.69/4.98      ! [N: nat,X: nat] :
% 8.69/4.98        ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 8.69/4.98        = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8259_set__replicate__Suc,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 8.69/4.98        = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8260_set__replicate__Suc,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 8.69/4.98        = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8261_log2__of__power__le,axiom,
% 8.69/4.98      ! [M: nat,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.98         => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8262_set__replicate__conv__if,axiom,
% 8.69/4.98      ! [N: nat,X: vEBT_VEBT] :
% 8.69/4.98        ( ( ( N = zero_zero_nat )
% 8.69/4.98         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.69/4.98            = bot_bo8194388402131092736T_VEBT ) )
% 8.69/4.98        & ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.69/4.98            = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8263_set__replicate__conv__if,axiom,
% 8.69/4.98      ! [N: nat,X: nat] :
% 8.69/4.98        ( ( ( N = zero_zero_nat )
% 8.69/4.98         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.69/4.98            = bot_bot_set_nat ) )
% 8.69/4.98        & ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.69/4.98            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8264_set__replicate__conv__if,axiom,
% 8.69/4.98      ! [N: nat,X: int] :
% 8.69/4.98        ( ( ( N = zero_zero_nat )
% 8.69/4.98         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.69/4.98            = bot_bot_set_int ) )
% 8.69/4.98        & ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.69/4.98            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8265_set__replicate__conv__if,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( ( N = zero_zero_nat )
% 8.69/4.98         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.69/4.98            = bot_bot_set_real ) )
% 8.69/4.98        & ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.69/4.98            = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8266_int__ops_I6_J,axiom,
% 8.69/4.98      ! [A: nat,B: nat] :
% 8.69/4.98        ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 8.69/4.98         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 8.69/4.98            = zero_zero_int ) )
% 8.69/4.98        & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 8.69/4.98         => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 8.69/4.98            = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8267_real__of__nat__div__aux,axiom,
% 8.69/4.98      ! [X: nat,D: nat] :
% 8.69/4.98        ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 8.69/4.98        = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8268_atLeastAtMostPlus1__int__conv,axiom,
% 8.69/4.98      ! [M: int,N: int] :
% 8.69/4.98        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 8.69/4.98       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 8.69/4.98          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8269_simp__from__to,axiom,
% 8.69/4.98      ( set_or1266510415728281911st_int
% 8.69/4.98      = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8270_nat__approx__posE,axiom,
% 8.69/4.98      ! [E: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ E )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8271_nat__approx__posE,axiom,
% 8.69/4.98      ! [E: rat] :
% 8.69/4.98        ( ( ord_less_rat @ zero_zero_rat @ E )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8272_log__mult,axiom,
% 8.69/4.98      ! [A: real,X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98           => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.98             => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 8.69/4.98                = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8273_of__nat__less__two__power,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8274_of__nat__less__two__power,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8275_of__nat__less__two__power,axiom,
% 8.69/4.98      ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8276_log__divide,axiom,
% 8.69/4.98      ! [A: real,X: real,Y: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98           => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.98             => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 8.69/4.98                = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8277_inverse__of__nat__le,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8278_inverse__of__nat__le,axiom,
% 8.69/4.98      ! [N: nat,M: nat] :
% 8.69/4.98        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.98       => ( ( N != zero_zero_nat )
% 8.69/4.98         => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8279_exp__divide__power__eq,axiom,
% 8.69/4.98      ! [N: nat,X: complex] :
% 8.69/4.98        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.98       => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 8.69/4.98          = ( exp_complex @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8280_exp__divide__power__eq,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.98       => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 8.69/4.98          = ( exp_real @ X ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8281_real__archimedian__rdiv__eq__0,axiom,
% 8.69/4.98      ! [X: real,C: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 8.69/4.98         => ( ! [M4: nat] :
% 8.69/4.98                ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 8.69/4.98               => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 8.69/4.98           => ( X = zero_zero_real ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8282_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > real] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5808333547571424918x_real @ G @ A2 )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8283_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8284_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > nat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8285_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_complex,X: complex,G: complex > int] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( member_complex @ X @ A2 )
% 8.69/4.98         => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 8.69/4.98            = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8286_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > real] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups8778361861064173332t_real @ G @ A2 )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8287_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8288_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_int,X: int,G: int > nat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( member_int @ X @ A2 )
% 8.69/4.98         => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8289_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups8097168146408367636l_real @ G @ A2 )
% 8.69/4.98            = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8290_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8291_sum_Oremove,axiom,
% 8.69/4.98      ! [A2: set_real,X: real,G: real > nat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( member_real @ X @ A2 )
% 8.69/4.98         => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 8.69/4.98            = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8292_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_complex,G: complex > real,X: complex] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8293_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_complex,G: complex > rat,X: complex] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8294_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_complex,G: complex > nat,X: complex] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8295_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_complex,G: complex > int,X: complex] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8296_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_int,G: int > real,X: int] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8297_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_int,G: int > rat,X: int] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8298_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_int,G: int > nat,X: int] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8299_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_real,G: real > real,X: real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8300_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_real,G: real > rat,X: real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8301_sum_Oinsert__remove,axiom,
% 8.69/4.98      ! [A2: set_real,G: real > nat,X: real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 8.69/4.98          = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8302_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_complex,A: complex,F: complex > real] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8303_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_int,A: int,F: int > real] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( ( member_int @ A @ A2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98              = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_int @ A @ A2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98              = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8304_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,F: real > real] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8305_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_complex,A: complex,F: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8306_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_int,A: int,F: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ A2 )
% 8.69/4.98       => ( ( ( member_int @ A @ A2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_int @ A @ A2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.69/4.98              = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8307_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,F: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8308_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_complex,A: complex,F: complex > int] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ A2 )
% 8.69/4.98           => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.69/4.98              = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8309_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_real,A: real,F: real > int] :
% 8.69/4.98        ( ( finite_finite_real @ A2 )
% 8.69/4.98       => ( ( ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ A2 )
% 8.69/4.98           => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.69/4.98              = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8310_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_nat,A: nat,F: nat > rat] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( ( member_nat @ A @ A2 )
% 8.69/4.98           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_nat @ A @ A2 )
% 8.69/4.98           => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98              = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8311_sum__diff1,axiom,
% 8.69/4.98      ! [A2: set_nat,A: nat,F: nat > int] :
% 8.69/4.98        ( ( finite_finite_nat @ A2 )
% 8.69/4.98       => ( ( ( member_nat @ A @ A2 )
% 8.69/4.98           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 8.69/4.98          & ( ~ ( member_nat @ A @ A2 )
% 8.69/4.98           => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.69/4.98              = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8312_neg__int__cases,axiom,
% 8.69/4.98      ! [K: int] :
% 8.69/4.98        ( ( ord_less_int @ K @ zero_zero_int )
% 8.69/4.98       => ~ ! [N3: nat] :
% 8.69/4.98              ( ( K
% 8.69/4.98                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 8.69/4.98             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8313_zdiff__int__split,axiom,
% 8.69/4.98      ! [P: int > $o,X: nat,Y: nat] :
% 8.69/4.98        ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 8.69/4.98        = ( ( ( ord_less_eq_nat @ Y @ X )
% 8.69/4.98           => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 8.69/4.98          & ( ( ord_less_nat @ X @ Y )
% 8.69/4.98           => ( P @ zero_zero_int ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8314_real__of__nat__div2,axiom,
% 8.69/4.98      ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8315_real__of__nat__div3,axiom,
% 8.69/4.98      ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8316_ln__realpow,axiom,
% 8.69/4.98      ! [X: real,N: nat] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 8.69/4.98          = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8317_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real
% 8.69/4.98                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5808333547571424918x_real
% 8.69/4.98                @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8318_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat
% 8.69/4.98                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5058264527183730370ex_rat
% 8.69/4.98                @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8319_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5693394587270226106ex_nat
% 8.69/4.98                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5693394587270226106ex_nat
% 8.69/4.98                @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8320_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 8.69/4.98        ( ( finite3207457112153483333omplex @ S2 )
% 8.69/4.98       => ( ( ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5690904116761175830ex_int
% 8.69/4.98                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_complex @ A @ S2 )
% 8.69/4.98           => ( ( groups5690904116761175830ex_int
% 8.69/4.98                @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8321_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real
% 8.69/4.98                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups8778361861064173332t_real
% 8.69/4.98                @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8322_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat
% 8.69/4.98                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups3906332499630173760nt_rat
% 8.69/4.98                @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8323_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_int,A: int,B: int > nat,C: int > nat] :
% 8.69/4.98        ( ( finite_finite_int @ S2 )
% 8.69/4.98       => ( ( ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups4541462559716669496nt_nat
% 8.69/4.98                @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_int @ A @ S2 )
% 8.69/4.98           => ( ( groups4541462559716669496nt_nat
% 8.69/4.98                @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8324_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real
% 8.69/4.98                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups8097168146408367636l_real
% 8.69/4.98                @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8325_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat
% 8.69/4.98                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups1300246762558778688al_rat
% 8.69/4.98                @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8326_sum_Odelta__remove,axiom,
% 8.69/4.98      ! [S2: set_real,A: real,B: real > nat,C: real > nat] :
% 8.69/4.98        ( ( finite_finite_real @ S2 )
% 8.69/4.98       => ( ( ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups1935376822645274424al_nat
% 8.69/4.98                @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 8.69/4.98          & ( ~ ( member_real @ A @ S2 )
% 8.69/4.98           => ( ( groups1935376822645274424al_nat
% 8.69/4.98                @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 8.69/4.98                @ S2 )
% 8.69/4.98              = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8327_log__eq__div__ln__mult__log,axiom,
% 8.69/4.98      ! [A: real,B: real,X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.98       => ( ( A != one_one_real )
% 8.69/4.98         => ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/4.98           => ( ( B != one_one_real )
% 8.69/4.98             => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98               => ( ( log @ A @ X )
% 8.69/4.98                  = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8328_member__le__sum,axiom,
% 8.69/4.98      ! [I: complex,A2: set_complex,F: complex > real] :
% 8.69/4.98        ( ( member_complex @ I @ A2 )
% 8.69/4.98       => ( ! [X6: complex] :
% 8.69/4.98              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 8.69/4.98             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98           => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8329_member__le__sum,axiom,
% 8.69/4.98      ! [I: int,A2: set_int,F: int > real] :
% 8.69/4.98        ( ( member_int @ I @ A2 )
% 8.69/4.98       => ( ! [X6: int] :
% 8.69/4.98              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 8.69/4.98             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_int @ A2 )
% 8.69/4.98           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8330_member__le__sum,axiom,
% 8.69/4.98      ! [I: real,A2: set_real,F: real > real] :
% 8.69/4.98        ( ( member_real @ I @ A2 )
% 8.69/4.98       => ( ! [X6: real] :
% 8.69/4.98              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 8.69/4.98             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_real @ A2 )
% 8.69/4.98           => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8331_member__le__sum,axiom,
% 8.69/4.98      ! [I: complex,A2: set_complex,F: complex > rat] :
% 8.69/4.98        ( ( member_complex @ I @ A2 )
% 8.69/4.98       => ( ! [X6: complex] :
% 8.69/4.98              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 8.69/4.98             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8332_member__le__sum,axiom,
% 8.69/4.98      ! [I: int,A2: set_int,F: int > rat] :
% 8.69/4.98        ( ( member_int @ I @ A2 )
% 8.69/4.98       => ( ! [X6: int] :
% 8.69/4.98              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 8.69/4.98             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_int @ A2 )
% 8.69/4.98           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8333_member__le__sum,axiom,
% 8.69/4.98      ! [I: real,A2: set_real,F: real > rat] :
% 8.69/4.98        ( ( member_real @ I @ A2 )
% 8.69/4.98       => ( ! [X6: real] :
% 8.69/4.98              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 8.69/4.98             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_real @ A2 )
% 8.69/4.98           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8334_member__le__sum,axiom,
% 8.69/4.98      ! [I: nat,A2: set_nat,F: nat > rat] :
% 8.69/4.98        ( ( member_nat @ I @ A2 )
% 8.69/4.98       => ( ! [X6: nat] :
% 8.69/4.98              ( ( member_nat @ X6 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 8.69/4.98             => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_nat @ A2 )
% 8.69/4.98           => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8335_member__le__sum,axiom,
% 8.69/4.98      ! [I: complex,A2: set_complex,F: complex > nat] :
% 8.69/4.98        ( ( member_complex @ I @ A2 )
% 8.69/4.98       => ( ! [X6: complex] :
% 8.69/4.98              ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 8.69/4.98             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite3207457112153483333omplex @ A2 )
% 8.69/4.98           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8336_member__le__sum,axiom,
% 8.69/4.98      ! [I: int,A2: set_int,F: int > nat] :
% 8.69/4.98        ( ( member_int @ I @ A2 )
% 8.69/4.98       => ( ! [X6: int] :
% 8.69/4.98              ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 8.69/4.98             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_int @ A2 )
% 8.69/4.98           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8337_member__le__sum,axiom,
% 8.69/4.98      ! [I: real,A2: set_real,F: real > nat] :
% 8.69/4.98        ( ( member_real @ I @ A2 )
% 8.69/4.98       => ( ! [X6: real] :
% 8.69/4.98              ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 8.69/4.98             => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 8.69/4.98         => ( ( finite_finite_real @ A2 )
% 8.69/4.98           => ( ord_less_eq_nat @ ( F @ I ) @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8338_linear__plus__1__le__power,axiom,
% 8.69/4.98      ! [X: real,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8339_Bernoulli__inequality,axiom,
% 8.69/4.98      ! [X: real,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.98       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8340_and__nat__unfold,axiom,
% 8.69/4.98      ( bit_se727722235901077358nd_nat
% 8.69/4.98      = ( ^ [M3: nat,N2: nat] :
% 8.69/4.98            ( if_nat
% 8.69/4.98            @ ( ( M3 = zero_zero_nat )
% 8.69/4.98              | ( N2 = zero_zero_nat ) )
% 8.69/4.98            @ zero_zero_nat
% 8.69/4.98            @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8341_and__nat__rec,axiom,
% 8.69/4.98      ( bit_se727722235901077358nd_nat
% 8.69/4.98      = ( ^ [M3: nat,N2: nat] :
% 8.69/4.98            ( plus_plus_nat
% 8.69/4.98            @ ( zero_n2687167440665602831ol_nat
% 8.69/4.98              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 8.69/4.98                & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/4.98            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8342_double__gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8343_double__gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8344_double__gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8345_double__gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8346_double__gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8347_double__arith__series,axiom,
% 8.69/4.98      ! [A: complex,D: complex,N: nat] :
% 8.69/4.98        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 8.69/4.98          @ ( groups2073611262835488442omplex
% 8.69/4.98            @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8348_double__arith__series,axiom,
% 8.69/4.98      ! [A: rat,D: rat,N: nat] :
% 8.69/4.98        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 8.69/4.98          @ ( groups2906978787729119204at_rat
% 8.69/4.98            @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8349_double__arith__series,axiom,
% 8.69/4.98      ! [A: int,D: int,N: nat] :
% 8.69/4.98        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.69/4.98          @ ( groups3539618377306564664at_int
% 8.69/4.98            @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8350_double__arith__series,axiom,
% 8.69/4.98      ! [A: nat,D: nat,N: nat] :
% 8.69/4.98        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 8.69/4.98          @ ( groups3542108847815614940at_nat
% 8.69/4.98            @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8351_double__arith__series,axiom,
% 8.69/4.98      ! [A: real,D: real,N: nat] :
% 8.69/4.98        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.69/4.98          @ ( groups6591440286371151544t_real
% 8.69/4.98            @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 8.69/4.98            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.69/4.98        = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8352_gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8353_gauss__sum,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8354_arith__series,axiom,
% 8.69/4.98      ! [A: int,D: int,N: nat] :
% 8.69/4.98        ( ( groups3539618377306564664at_int
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8355_arith__series,axiom,
% 8.69/4.98      ! [A: nat,D: nat,N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat
% 8.69/4.98          @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 8.69/4.98          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8356_double__gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.69/4.98        = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8357_double__gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.69/4.98        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8358_double__gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.69/4.98        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8359_double__gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.69/4.98        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8360_double__gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.69/4.98        = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8361_Bernoulli__inequality__even,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.98       => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8362_sum__gp__offset,axiom,
% 8.69/4.98      ! [X: complex,M: nat,N: nat] :
% 8.69/4.98        ( ( ( X = one_one_complex )
% 8.69/4.98         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 8.69/4.98        & ( ( X != one_one_complex )
% 8.69/4.98         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8363_sum__gp__offset,axiom,
% 8.69/4.98      ! [X: rat,M: nat,N: nat] :
% 8.69/4.98        ( ( ( X = one_one_rat )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 8.69/4.98        & ( ( X != one_one_rat )
% 8.69/4.98         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8364_sum__gp__offset,axiom,
% 8.69/4.98      ! [X: real,M: nat,N: nat] :
% 8.69/4.98        ( ( ( X = one_one_real )
% 8.69/4.98         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 8.69/4.98        & ( ( X != one_one_real )
% 8.69/4.98         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 8.69/4.98            = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8365_exp__ge__one__plus__x__over__n__power__n,axiom,
% 8.69/4.98      ! [N: nat,X: real] :
% 8.69/4.98        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.98         => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8366_exp__ge__one__minus__x__over__n__power__n,axiom,
% 8.69/4.98      ! [X: real,N: nat] :
% 8.69/4.98        ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.98       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.98         => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8367_log__base__10__eq2,axiom,
% 8.69/4.98      ! [X: real] :
% 8.69/4.98        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.98       => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.98          = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8368_gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.69/4.98        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8369_gauss__sum__from__Suc__0,axiom,
% 8.69/4.98      ! [N: nat] :
% 8.69/4.98        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.69/4.98        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8370_of__nat__code__if,axiom,
% 8.69/4.98      ( semiri8010041392384452111omplex
% 8.69/4.98      = ( ^ [N2: nat] :
% 8.69/4.98            ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 8.69/4.98            @ ( produc1917071388513777916omplex
% 8.69/4.98              @ ^ [M3: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 8.69/4.98              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.98  
% 8.69/4.98  thf(fact_8371_of__nat__code__if,axiom,
% 8.69/4.99      ( semiri5074537144036343181t_real
% 8.69/4.99      = ( ^ [N2: nat] :
% 8.69/4.99            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 8.69/4.99            @ ( produc1703576794950452218t_real
% 8.69/4.99              @ ^ [M3: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 8.69/4.99              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8372_of__nat__code__if,axiom,
% 8.69/4.99      ( semiri681578069525770553at_rat
% 8.69/4.99      = ( ^ [N2: nat] :
% 8.69/4.99            ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 8.69/4.99            @ ( produc6207742614233964070at_rat
% 8.69/4.99              @ ^ [M3: nat,Q5: nat] : ( if_rat @ ( Q5 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 8.69/4.99              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8373_of__nat__code__if,axiom,
% 8.69/4.99      ( semiri1316708129612266289at_nat
% 8.69/4.99      = ( ^ [N2: nat] :
% 8.69/4.99            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 8.69/4.99            @ ( produc6842872674320459806at_nat
% 8.69/4.99              @ ^ [M3: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 8.69/4.99              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8374_of__nat__code__if,axiom,
% 8.69/4.99      ( semiri1314217659103216013at_int
% 8.69/4.99      = ( ^ [N2: nat] :
% 8.69/4.99            ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 8.69/4.99            @ ( produc6840382203811409530at_int
% 8.69/4.99              @ ^ [M3: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 8.69/4.99              @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8375_monoseq__arctan__series,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( topolo6980174941875973593q_real
% 8.69/4.99          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8376_lemma__termdiff3,axiom,
% 8.69/4.99      ! [H2: real,Z: real,K5: real,N: nat] :
% 8.69/4.99        ( ( H2 != zero_zero_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8377_lemma__termdiff3,axiom,
% 8.69/4.99      ! [H2: complex,Z: complex,K5: real,N: nat] :
% 8.69/4.99        ( ( H2 != zero_zero_complex )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8378_ln__series,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99         => ( ( ln_ln_real @ X )
% 8.69/4.99            = ( suminf_real
% 8.69/4.99              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8379_lemma__termdiff2,axiom,
% 8.69/4.99      ! [H2: complex,Z: complex,N: nat] :
% 8.69/4.99        ( ( H2 != zero_zero_complex )
% 8.69/4.99       => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.69/4.99          = ( times_times_complex @ H2
% 8.69/4.99            @ ( groups2073611262835488442omplex
% 8.69/4.99              @ ^ [P2: nat] :
% 8.69/4.99                  ( groups2073611262835488442omplex
% 8.69/4.99                  @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.69/4.99                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8380_lemma__termdiff2,axiom,
% 8.69/4.99      ! [H2: rat,Z: rat,N: nat] :
% 8.69/4.99        ( ( H2 != zero_zero_rat )
% 8.69/4.99       => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.69/4.99          = ( times_times_rat @ H2
% 8.69/4.99            @ ( groups2906978787729119204at_rat
% 8.69/4.99              @ ^ [P2: nat] :
% 8.69/4.99                  ( groups2906978787729119204at_rat
% 8.69/4.99                  @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.69/4.99                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8381_lemma__termdiff2,axiom,
% 8.69/4.99      ! [H2: real,Z: real,N: nat] :
% 8.69/4.99        ( ( H2 != zero_zero_real )
% 8.69/4.99       => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.69/4.99          = ( times_times_real @ H2
% 8.69/4.99            @ ( groups6591440286371151544t_real
% 8.69/4.99              @ ^ [P2: nat] :
% 8.69/4.99                  ( groups6591440286371151544t_real
% 8.69/4.99                  @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.69/4.99                  @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8382_lessThan__eq__iff,axiom,
% 8.69/4.99      ! [X: nat,Y: nat] :
% 8.69/4.99        ( ( ( set_ord_lessThan_nat @ X )
% 8.69/4.99          = ( set_ord_lessThan_nat @ Y ) )
% 8.69/4.99        = ( X = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8383_lessThan__eq__iff,axiom,
% 8.69/4.99      ! [X: int,Y: int] :
% 8.69/4.99        ( ( ( set_ord_lessThan_int @ X )
% 8.69/4.99          = ( set_ord_lessThan_int @ Y ) )
% 8.69/4.99        = ( X = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8384_lessThan__eq__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( set_or5984915006950818249n_real @ X )
% 8.69/4.99          = ( set_or5984915006950818249n_real @ Y ) )
% 8.69/4.99        = ( X = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8385_lessThan__iff,axiom,
% 8.69/4.99      ! [I: set_nat,K: set_nat] :
% 8.69/4.99        ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 8.69/4.99        = ( ord_less_set_nat @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8386_lessThan__iff,axiom,
% 8.69/4.99      ! [I: rat,K: rat] :
% 8.69/4.99        ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 8.69/4.99        = ( ord_less_rat @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8387_lessThan__iff,axiom,
% 8.69/4.99      ! [I: num,K: num] :
% 8.69/4.99        ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 8.69/4.99        = ( ord_less_num @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8388_lessThan__iff,axiom,
% 8.69/4.99      ! [I: nat,K: nat] :
% 8.69/4.99        ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 8.69/4.99        = ( ord_less_nat @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8389_lessThan__iff,axiom,
% 8.69/4.99      ! [I: int,K: int] :
% 8.69/4.99        ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 8.69/4.99        = ( ord_less_int @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8390_lessThan__iff,axiom,
% 8.69/4.99      ! [I: real,K: real] :
% 8.69/4.99        ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 8.69/4.99        = ( ord_less_real @ I @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8391_finite__lessThan,axiom,
% 8.69/4.99      ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8392_lessThan__subset__iff,axiom,
% 8.69/4.99      ! [X: rat,Y: rat] :
% 8.69/4.99        ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 8.69/4.99        = ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8393_lessThan__subset__iff,axiom,
% 8.69/4.99      ! [X: num,Y: num] :
% 8.69/4.99        ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 8.69/4.99        = ( ord_less_eq_num @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8394_lessThan__subset__iff,axiom,
% 8.69/4.99      ! [X: nat,Y: nat] :
% 8.69/4.99        ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 8.69/4.99        = ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8395_lessThan__subset__iff,axiom,
% 8.69/4.99      ! [X: int,Y: int] :
% 8.69/4.99        ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 8.69/4.99        = ( ord_less_eq_int @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8396_lessThan__subset__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 8.69/4.99        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8397_lessThan__0,axiom,
% 8.69/4.99      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 8.69/4.99      = bot_bot_set_nat ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8398_sum_OlessThan__Suc,axiom,
% 8.69/4.99      ! [G: nat > rat,N: nat] :
% 8.69/4.99        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8399_sum_OlessThan__Suc,axiom,
% 8.69/4.99      ! [G: nat > int,N: nat] :
% 8.69/4.99        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8400_sum_OlessThan__Suc,axiom,
% 8.69/4.99      ! [G: nat > nat,N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8401_sum_OlessThan__Suc,axiom,
% 8.69/4.99      ! [G: nat > real,N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8402_single__Diff__lessThan,axiom,
% 8.69/4.99      ! [K: nat] :
% 8.69/4.99        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 8.69/4.99        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8403_single__Diff__lessThan,axiom,
% 8.69/4.99      ! [K: int] :
% 8.69/4.99        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 8.69/4.99        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8404_single__Diff__lessThan,axiom,
% 8.69/4.99      ! [K: real] :
% 8.69/4.99        ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 8.69/4.99        = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8405_powser__zero,axiom,
% 8.69/4.99      ! [F: nat > complex] :
% 8.69/4.99        ( ( suminf_complex
% 8.69/4.99          @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 8.69/4.99        = ( F @ zero_zero_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8406_powser__zero,axiom,
% 8.69/4.99      ! [F: nat > real] :
% 8.69/4.99        ( ( suminf_real
% 8.69/4.99          @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 8.69/4.99        = ( F @ zero_zero_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8407_set__encode__insert,axiom,
% 8.69/4.99      ! [A2: set_nat,N: nat] :
% 8.69/4.99        ( ( finite_finite_nat @ A2 )
% 8.69/4.99       => ( ~ ( member_nat @ N @ A2 )
% 8.69/4.99         => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 8.69/4.99            = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8408_lessThan__nat__numeral,axiom,
% 8.69/4.99      ! [K: num] :
% 8.69/4.99        ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 8.69/4.99        = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8409_lessThan__Suc,axiom,
% 8.69/4.99      ! [K: nat] :
% 8.69/4.99        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 8.69/4.99        = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8410_lessThan__non__empty,axiom,
% 8.69/4.99      ! [X: int] :
% 8.69/4.99        ( ( set_ord_lessThan_int @ X )
% 8.69/4.99       != bot_bot_set_int ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8411_lessThan__non__empty,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( set_or5984915006950818249n_real @ X )
% 8.69/4.99       != bot_bot_set_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8412_infinite__Iio,axiom,
% 8.69/4.99      ! [A: int] :
% 8.69/4.99        ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8413_infinite__Iio,axiom,
% 8.69/4.99      ! [A: real] :
% 8.69/4.99        ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8414_lessThan__def,axiom,
% 8.69/4.99      ( set_or890127255671739683et_nat
% 8.69/4.99      = ( ^ [U2: set_nat] :
% 8.69/4.99            ( collect_set_nat
% 8.69/4.99            @ ^ [X3: set_nat] : ( ord_less_set_nat @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8415_lessThan__def,axiom,
% 8.69/4.99      ( set_ord_lessThan_rat
% 8.69/4.99      = ( ^ [U2: rat] :
% 8.69/4.99            ( collect_rat
% 8.69/4.99            @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8416_lessThan__def,axiom,
% 8.69/4.99      ( set_ord_lessThan_num
% 8.69/4.99      = ( ^ [U2: num] :
% 8.69/4.99            ( collect_num
% 8.69/4.99            @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8417_lessThan__def,axiom,
% 8.69/4.99      ( set_ord_lessThan_nat
% 8.69/4.99      = ( ^ [U2: nat] :
% 8.69/4.99            ( collect_nat
% 8.69/4.99            @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8418_lessThan__def,axiom,
% 8.69/4.99      ( set_ord_lessThan_int
% 8.69/4.99      = ( ^ [U2: int] :
% 8.69/4.99            ( collect_int
% 8.69/4.99            @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8419_lessThan__def,axiom,
% 8.69/4.99      ( set_or5984915006950818249n_real
% 8.69/4.99      = ( ^ [U2: real] :
% 8.69/4.99            ( collect_real
% 8.69/4.99            @ ^ [X3: real] : ( ord_less_real @ X3 @ U2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8420_Iio__eq__empty__iff,axiom,
% 8.69/4.99      ! [N: extended_enat] :
% 8.69/4.99        ( ( ( set_or8419480210114673929d_enat @ N )
% 8.69/4.99          = bot_bo7653980558646680370d_enat )
% 8.69/4.99        = ( N = bot_bo4199563552545308370d_enat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8421_Iio__eq__empty__iff,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ( set_ord_lessThan_nat @ N )
% 8.69/4.99          = bot_bot_set_nat )
% 8.69/4.99        = ( N = bot_bot_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8422_lessThan__strict__subset__iff,axiom,
% 8.69/4.99      ! [M: rat,N: rat] :
% 8.69/4.99        ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 8.69/4.99        = ( ord_less_rat @ M @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8423_lessThan__strict__subset__iff,axiom,
% 8.69/4.99      ! [M: num,N: num] :
% 8.69/4.99        ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 8.69/4.99        = ( ord_less_num @ M @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8424_lessThan__strict__subset__iff,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99        = ( ord_less_nat @ M @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8425_lessThan__strict__subset__iff,axiom,
% 8.69/4.99      ! [M: int,N: int] :
% 8.69/4.99        ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 8.69/4.99        = ( ord_less_int @ M @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8426_lessThan__strict__subset__iff,axiom,
% 8.69/4.99      ! [M: real,N: real] :
% 8.69/4.99        ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 8.69/4.99        = ( ord_less_real @ M @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8427_complex__mod__minus__le__complex__mod,axiom,
% 8.69/4.99      ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8428_complex__mod__triangle__ineq2,axiom,
% 8.69/4.99      ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8429_lessThan__empty__iff,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ( set_ord_lessThan_nat @ N )
% 8.69/4.99          = bot_bot_set_nat )
% 8.69/4.99        = ( N = zero_zero_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8430_finite__nat__bounded,axiom,
% 8.69/4.99      ! [S2: set_nat] :
% 8.69/4.99        ( ( finite_finite_nat @ S2 )
% 8.69/4.99       => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8431_finite__nat__iff__bounded,axiom,
% 8.69/4.99      ( finite_finite_nat
% 8.69/4.99      = ( ^ [S6: set_nat] :
% 8.69/4.99          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8432_atLeast0__atMost__Suc,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.69/4.99        = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8433_Icc__eq__insert__lb__nat,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99       => ( ( set_or1269000886237332187st_nat @ M @ N )
% 8.69/4.99          = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8434_atLeastAtMostSuc__conv,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 8.69/4.99       => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 8.69/4.99          = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8435_atLeastAtMost__insertL,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99       => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 8.69/4.99          = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8436_norm__exp,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8437_norm__exp,axiom,
% 8.69/4.99      ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8438_sum_Onat__diff__reindex,axiom,
% 8.69/4.99      ! [G: nat > nat,N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99        = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8439_sum_Onat__diff__reindex,axiom,
% 8.69/4.99      ! [G: nat > real,N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99        = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8440_sum__diff__distrib,axiom,
% 8.69/4.99      ! [Q: int > nat,P: int > nat,N: int] :
% 8.69/4.99        ( ! [X6: int] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 8.69/4.99       => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 8.69/4.99          = ( groups4541462559716669496nt_nat
% 8.69/4.99            @ ^ [X3: int] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 8.69/4.99            @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8441_sum__diff__distrib,axiom,
% 8.69/4.99      ! [Q: real > nat,P: real > nat,N: real] :
% 8.69/4.99        ( ! [X6: real] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 8.69/4.99       => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 8.69/4.99          = ( groups1935376822645274424al_nat
% 8.69/4.99            @ ^ [X3: real] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 8.69/4.99            @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8442_sum__diff__distrib,axiom,
% 8.69/4.99      ! [Q: nat > nat,P: nat > nat,N: nat] :
% 8.69/4.99        ( ! [X6: nat] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 8.69/4.99       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 8.69/4.99          = ( groups3542108847815614940at_nat
% 8.69/4.99            @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8443_sum_OlessThan__Suc__shift,axiom,
% 8.69/4.99      ! [G: nat > rat,N: nat] :
% 8.69/4.99        ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 8.69/4.99          @ ( groups2906978787729119204at_rat
% 8.69/4.99            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8444_sum_OlessThan__Suc__shift,axiom,
% 8.69/4.99      ! [G: nat > int,N: nat] :
% 8.69/4.99        ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_int @ ( G @ zero_zero_nat )
% 8.69/4.99          @ ( groups3539618377306564664at_int
% 8.69/4.99            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8445_sum_OlessThan__Suc__shift,axiom,
% 8.69/4.99      ! [G: nat > nat,N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 8.69/4.99          @ ( groups3542108847815614940at_nat
% 8.69/4.99            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8446_sum_OlessThan__Suc__shift,axiom,
% 8.69/4.99      ! [G: nat > real,N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = ( plus_plus_real @ ( G @ zero_zero_nat )
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8447_sum__lessThan__telescope,axiom,
% 8.69/4.99      ! [F: nat > rat,M: nat] :
% 8.69/4.99        ( ( groups2906978787729119204at_rat
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8448_sum__lessThan__telescope,axiom,
% 8.69/4.99      ! [F: nat > int,M: nat] :
% 8.69/4.99        ( ( groups3539618377306564664at_int
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8449_sum__lessThan__telescope,axiom,
% 8.69/4.99      ! [F: nat > real,M: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8450_sum__lessThan__telescope_H,axiom,
% 8.69/4.99      ! [F: nat > rat,M: nat] :
% 8.69/4.99        ( ( groups2906978787729119204at_rat
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8451_sum__lessThan__telescope_H,axiom,
% 8.69/4.99      ! [F: nat > int,M: nat] :
% 8.69/4.99        ( ( groups3539618377306564664at_int
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8452_sum__lessThan__telescope_H,axiom,
% 8.69/4.99      ! [F: nat > real,M: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8453_sumr__diff__mult__const2,axiom,
% 8.69/4.99      ! [F: nat > complex,N: nat,R: complex] :
% 8.69/4.99        ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 8.69/4.99        = ( groups2073611262835488442omplex
% 8.69/4.99          @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ I5 ) @ R )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8454_sumr__diff__mult__const2,axiom,
% 8.69/4.99      ! [F: nat > rat,N: nat,R: rat] :
% 8.69/4.99        ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 8.69/4.99        = ( groups2906978787729119204at_rat
% 8.69/4.99          @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ R )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8455_sumr__diff__mult__const2,axiom,
% 8.69/4.99      ! [F: nat > int,N: nat,R: int] :
% 8.69/4.99        ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 8.69/4.99        = ( groups3539618377306564664at_int
% 8.69/4.99          @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8456_sumr__diff__mult__const2,axiom,
% 8.69/4.99      ! [F: nat > real,N: nat,R: real] :
% 8.69/4.99        ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 8.69/4.99        = ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8457_sum_OatLeast1__atMost__eq,axiom,
% 8.69/4.99      ! [G: nat > nat,N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.69/4.99        = ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8458_sum_OatLeast1__atMost__eq,axiom,
% 8.69/4.99      ! [G: nat > real,N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.69/4.99        = ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8459_power__diff__1__eq,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 8.69/4.99        = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8460_power__diff__1__eq,axiom,
% 8.69/4.99      ! [X: rat,N: nat] :
% 8.69/4.99        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 8.69/4.99        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8461_power__diff__1__eq,axiom,
% 8.69/4.99      ! [X: int,N: nat] :
% 8.69/4.99        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 8.69/4.99        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8462_power__diff__1__eq,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 8.69/4.99        = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8463_one__diff__power__eq,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 8.69/4.99        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8464_one__diff__power__eq,axiom,
% 8.69/4.99      ! [X: rat,N: nat] :
% 8.69/4.99        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 8.69/4.99        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8465_one__diff__power__eq,axiom,
% 8.69/4.99      ! [X: int,N: nat] :
% 8.69/4.99        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 8.69/4.99        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8466_one__diff__power__eq,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 8.69/4.99        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8467_geometric__sum,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( X != one_one_complex )
% 8.69/4.99       => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99          = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8468_geometric__sum,axiom,
% 8.69/4.99      ! [X: rat,N: nat] :
% 8.69/4.99        ( ( X != one_one_rat )
% 8.69/4.99       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8469_geometric__sum,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( X != one_one_real )
% 8.69/4.99       => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99          = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8470_monoseq__realpow,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8471_sum__gp__strict,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( ( X = one_one_complex )
% 8.69/4.99         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( semiri8010041392384452111omplex @ N ) ) )
% 8.69/4.99        & ( ( X != one_one_complex )
% 8.69/4.99         => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8472_sum__gp__strict,axiom,
% 8.69/4.99      ! [X: rat,N: nat] :
% 8.69/4.99        ( ( ( X = one_one_rat )
% 8.69/4.99         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( semiri681578069525770553at_rat @ N ) ) )
% 8.69/4.99        & ( ( X != one_one_rat )
% 8.69/4.99         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8473_sum__gp__strict,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( ( X = one_one_real )
% 8.69/4.99         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99        & ( ( X != one_one_real )
% 8.69/4.99         => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8474_lemma__termdiff1,axiom,
% 8.69/4.99      ! [Z: complex,H2: complex,M: nat] :
% 8.69/4.99        ( ( groups2073611262835488442omplex
% 8.69/4.99          @ ^ [P2: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ P2 ) ) @ ( power_power_complex @ Z @ M ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( groups2073611262835488442omplex
% 8.69/4.99          @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P2 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8475_lemma__termdiff1,axiom,
% 8.69/4.99      ! [Z: rat,H2: rat,M: nat] :
% 8.69/4.99        ( ( groups2906978787729119204at_rat
% 8.69/4.99          @ ^ [P2: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ P2 ) ) @ ( power_power_rat @ Z @ M ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( groups2906978787729119204at_rat
% 8.69/4.99          @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P2 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8476_lemma__termdiff1,axiom,
% 8.69/4.99      ! [Z: int,H2: int,M: nat] :
% 8.69/4.99        ( ( groups3539618377306564664at_int
% 8.69/4.99          @ ^ [P2: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ P2 ) ) @ ( power_power_int @ Z @ M ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( groups3539618377306564664at_int
% 8.69/4.99          @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ Z @ P2 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8477_lemma__termdiff1,axiom,
% 8.69/4.99      ! [Z: real,H2: real,M: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [P2: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ P2 ) ) @ ( power_power_real @ Z @ M ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) )
% 8.69/4.99        = ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ Z @ P2 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8478_power__diff__sumr2,axiom,
% 8.69/4.99      ! [X: complex,N: nat,Y: complex] :
% 8.69/4.99        ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 8.69/4.99        = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.69/4.99          @ ( groups2073611262835488442omplex
% 8.69/4.99            @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8479_power__diff__sumr2,axiom,
% 8.69/4.99      ! [X: rat,N: nat,Y: rat] :
% 8.69/4.99        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 8.69/4.99        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.69/4.99          @ ( groups2906978787729119204at_rat
% 8.69/4.99            @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8480_power__diff__sumr2,axiom,
% 8.69/4.99      ! [X: int,N: nat,Y: int] :
% 8.69/4.99        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 8.69/4.99        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.69/4.99          @ ( groups3539618377306564664at_int
% 8.69/4.99            @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_int @ X @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8481_power__diff__sumr2,axiom,
% 8.69/4.99      ! [X: real,N: nat,Y: real] :
% 8.69/4.99        ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 8.69/4.99        = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_real @ X @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8482_diff__power__eq__sum,axiom,
% 8.69/4.99      ! [X: complex,N: nat,Y: complex] :
% 8.69/4.99        ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 8.69/4.99        = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.69/4.99          @ ( groups2073611262835488442omplex
% 8.69/4.99            @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ X @ P2 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8483_diff__power__eq__sum,axiom,
% 8.69/4.99      ! [X: rat,N: nat,Y: rat] :
% 8.69/4.99        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 8.69/4.99        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.69/4.99          @ ( groups2906978787729119204at_rat
% 8.69/4.99            @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ X @ P2 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8484_diff__power__eq__sum,axiom,
% 8.69/4.99      ! [X: int,N: nat,Y: int] :
% 8.69/4.99        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 8.69/4.99        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.69/4.99          @ ( groups3539618377306564664at_int
% 8.69/4.99            @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ X @ P2 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8485_diff__power__eq__sum,axiom,
% 8.69/4.99      ! [X: real,N: nat,Y: real] :
% 8.69/4.99        ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 8.69/4.99        = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ X @ P2 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8486_set__decode__plus__power__2,axiom,
% 8.69/4.99      ! [N: nat,Z: nat] :
% 8.69/4.99        ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 8.69/4.99       => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 8.69/4.99          = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8487_real__sum__nat__ivl__bounded2,axiom,
% 8.69/4.99      ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 8.69/4.99        ( ! [P7: nat] :
% 8.69/4.99            ( ( ord_less_nat @ P7 @ N )
% 8.69/4.99           => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 8.69/4.99       => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 8.69/4.99         => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8488_real__sum__nat__ivl__bounded2,axiom,
% 8.69/4.99      ! [N: nat,F: nat > int,K5: int,K: nat] :
% 8.69/4.99        ( ! [P7: nat] :
% 8.69/4.99            ( ( ord_less_nat @ P7 @ N )
% 8.69/4.99           => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 8.69/4.99       => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 8.69/4.99         => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8489_real__sum__nat__ivl__bounded2,axiom,
% 8.69/4.99      ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 8.69/4.99        ( ! [P7: nat] :
% 8.69/4.99            ( ( ord_less_nat @ P7 @ N )
% 8.69/4.99           => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 8.69/4.99       => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 8.69/4.99         => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8490_real__sum__nat__ivl__bounded2,axiom,
% 8.69/4.99      ! [N: nat,F: nat > real,K5: real,K: nat] :
% 8.69/4.99        ( ! [P7: nat] :
% 8.69/4.99            ( ( ord_less_nat @ P7 @ N )
% 8.69/4.99           => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 8.69/4.99         => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8491_exp__bound__half,axiom,
% 8.69/4.99      ! [Z: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8492_exp__bound__half,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8493_one__diff__power__eq_H,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 8.69/4.99        = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 8.69/4.99          @ ( groups2073611262835488442omplex
% 8.69/4.99            @ ^ [I5: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8494_one__diff__power__eq_H,axiom,
% 8.69/4.99      ! [X: rat,N: nat] :
% 8.69/4.99        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 8.69/4.99        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 8.69/4.99          @ ( groups2906978787729119204at_rat
% 8.69/4.99            @ ^ [I5: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8495_one__diff__power__eq_H,axiom,
% 8.69/4.99      ! [X: int,N: nat] :
% 8.69/4.99        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 8.69/4.99        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 8.69/4.99          @ ( groups3539618377306564664at_int
% 8.69/4.99            @ ^ [I5: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8496_one__diff__power__eq_H,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 8.69/4.99        = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [I5: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8497_sum__split__even__odd,axiom,
% 8.69/4.99      ! [F: nat > real,G: nat > real,N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/4.99        = ( plus_plus_real
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8498_exp__bound__lemma,axiom,
% 8.69/4.99      ! [Z: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( 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 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8499_exp__bound__lemma,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( 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 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8500_arctan__series,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( arctan @ X )
% 8.69/4.99          = ( suminf_real
% 8.69/4.99            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8501_norm__divide__numeral,axiom,
% 8.69/4.99      ! [A: real,W: num] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.99        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8502_norm__divide__numeral,axiom,
% 8.69/4.99      ! [A: complex,W: num] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.99        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8503_norm__mult__numeral2,axiom,
% 8.69/4.99      ! [A: real,W: num] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.99        = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8504_norm__mult__numeral2,axiom,
% 8.69/4.99      ! [A: complex,W: num] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.99        = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8505_norm__mult__numeral1,axiom,
% 8.69/4.99      ! [W: num,A: real] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 8.69/4.99        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8506_norm__mult__numeral1,axiom,
% 8.69/4.99      ! [W: num,A: complex] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 8.69/4.99        = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8507_norm__neg__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.99        = ( numeral_numeral_real @ W ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8508_norm__neg__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.99        = ( numeral_numeral_real @ W ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8509_norm__le__zero__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8510_norm__le__zero__iff,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8511_norm__zero,axiom,
% 8.69/4.99      ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8512_norm__zero,axiom,
% 8.69/4.99      ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8513_norm__eq__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( real_V7735802525324610683m_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8514_norm__eq__zero,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( ( real_V1022390504157884413omplex @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8515_norm__one,axiom,
% 8.69/4.99      ( ( real_V7735802525324610683m_real @ one_one_real )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8516_norm__one,axiom,
% 8.69/4.99      ( ( real_V1022390504157884413omplex @ one_one_complex )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8517_norm__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 8.69/4.99        = ( numeral_numeral_real @ W ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8518_norm__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 8.69/4.99        = ( numeral_numeral_real @ W ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8519_zero__less__norm__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 8.69/4.99        = ( X != zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8520_zero__less__norm__iff,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 8.69/4.99        = ( X != zero_zero_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8521_norm__minus__commute,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 8.69/4.99        = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8522_norm__minus__commute,axiom,
% 8.69/4.99      ! [A: complex,B: complex] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 8.69/4.99        = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8523_norm__not__less__zero,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8524_norm__ge__zero,axiom,
% 8.69/4.99      ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8525_norm__mult,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 8.69/4.99        = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8526_norm__mult,axiom,
% 8.69/4.99      ! [X: complex,Y: complex] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 8.69/4.99        = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8527_norm__divide,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.99        = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8528_norm__divide,axiom,
% 8.69/4.99      ! [A: complex,B: complex] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.99        = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8529_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_real,F: real > complex,G: real > real] :
% 8.69/4.99        ( ! [X6: real] :
% 8.69/4.99            ( ( member_real @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8530_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 8.69/4.99        ( ! [X6: set_nat] :
% 8.69/4.99            ( ( member_set_nat @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8531_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_int,F: int > complex,G: int > real] :
% 8.69/4.99        ( ! [X6: int] :
% 8.69/4.99            ( ( member_int @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8532_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 8.69/4.99        ( ! [X6: nat] :
% 8.69/4.99            ( ( member_nat @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8533_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 8.69/4.99        ( ! [X6: complex] :
% 8.69/4.99            ( ( member_complex @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8534_sum__norm__le,axiom,
% 8.69/4.99      ! [S2: set_nat,F: nat > real,G: nat > real] :
% 8.69/4.99        ( ! [X6: nat] :
% 8.69/4.99            ( ( member_nat @ X6 @ S2 )
% 8.69/4.99           => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8535_norm__power,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 8.69/4.99        = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8536_norm__power,axiom,
% 8.69/4.99      ! [X: complex,N: nat] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 8.69/4.99        = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8537_norm__sum,axiom,
% 8.69/4.99      ! [F: nat > complex,A2: set_nat] :
% 8.69/4.99        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 8.69/4.99        @ ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 8.69/4.99          @ A2 ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8538_norm__sum,axiom,
% 8.69/4.99      ! [F: complex > complex,A2: set_complex] :
% 8.69/4.99        ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 8.69/4.99        @ ( groups5808333547571424918x_real
% 8.69/4.99          @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 8.69/4.99          @ A2 ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8539_norm__sum,axiom,
% 8.69/4.99      ! [F: nat > real,A2: set_nat] :
% 8.69/4.99        ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 8.69/4.99        @ ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( F @ I5 ) )
% 8.69/4.99          @ A2 ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8540_norm__uminus__minus,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 8.69/4.99        = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8541_norm__uminus__minus,axiom,
% 8.69/4.99      ! [X: complex,Y: complex] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 8.69/4.99        = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8542_nonzero__norm__divide,axiom,
% 8.69/4.99      ! [B: real,A: real] :
% 8.69/4.99        ( ( B != zero_zero_real )
% 8.69/4.99       => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 8.69/4.99          = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8543_nonzero__norm__divide,axiom,
% 8.69/4.99      ! [B: complex,A: complex] :
% 8.69/4.99        ( ( B != zero_zero_complex )
% 8.69/4.99       => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/4.99          = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8544_power__eq__imp__eq__norm,axiom,
% 8.69/4.99      ! [W: real,N: nat,Z: real] :
% 8.69/4.99        ( ( ( power_power_real @ W @ N )
% 8.69/4.99          = ( power_power_real @ Z @ N ) )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99         => ( ( real_V7735802525324610683m_real @ W )
% 8.69/4.99            = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8545_power__eq__imp__eq__norm,axiom,
% 8.69/4.99      ! [W: complex,N: nat,Z: complex] :
% 8.69/4.99        ( ( ( power_power_complex @ W @ N )
% 8.69/4.99          = ( power_power_complex @ Z @ N ) )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99         => ( ( real_V1022390504157884413omplex @ W )
% 8.69/4.99            = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8546_norm__mult__less,axiom,
% 8.69/4.99      ! [X: real,R: real,Y: real,S: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 8.69/4.99         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8547_norm__mult__less,axiom,
% 8.69/4.99      ! [X: complex,R: real,Y: complex,S: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 8.69/4.99         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8548_norm__mult__ineq,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8549_norm__mult__ineq,axiom,
% 8.69/4.99      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8550_norm__triangle__lt,axiom,
% 8.69/4.99      ! [X: real,Y: real,E: real] :
% 8.69/4.99        ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8551_norm__triangle__lt,axiom,
% 8.69/4.99      ! [X: complex,Y: complex,E: real] :
% 8.69/4.99        ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8552_norm__add__less,axiom,
% 8.69/4.99      ! [X: real,R: real,Y: real,S: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 8.69/4.99         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8553_norm__add__less,axiom,
% 8.69/4.99      ! [X: complex,R: real,Y: complex,S: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 8.69/4.99         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8554_norm__power__ineq,axiom,
% 8.69/4.99      ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8555_norm__power__ineq,axiom,
% 8.69/4.99      ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8556_norm__triangle__mono,axiom,
% 8.69/4.99      ! [A: real,R: real,B: real,S: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 8.69/4.99         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8557_norm__triangle__mono,axiom,
% 8.69/4.99      ! [A: complex,R: real,B: complex,S: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 8.69/4.99         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8558_norm__triangle__ineq,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8559_norm__triangle__ineq,axiom,
% 8.69/4.99      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8560_norm__triangle__le,axiom,
% 8.69/4.99      ! [X: real,Y: real,E: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8561_norm__triangle__le,axiom,
% 8.69/4.99      ! [X: complex,Y: complex,E: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8562_norm__add__leD,axiom,
% 8.69/4.99      ! [A: real,B: real,C: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8563_norm__add__leD,axiom,
% 8.69/4.99      ! [A: complex,B: complex,C: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8564_norm__diff__triangle__less,axiom,
% 8.69/4.99      ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 8.69/4.99         => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8565_norm__diff__triangle__less,axiom,
% 8.69/4.99      ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 8.69/4.99        ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 8.69/4.99       => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 8.69/4.99         => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8566_norm__triangle__le__diff,axiom,
% 8.69/4.99      ! [X: real,Y: real,E: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8567_norm__triangle__le__diff,axiom,
% 8.69/4.99      ! [X: complex,Y: complex,E: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 8.69/4.99       => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8568_norm__diff__triangle__le,axiom,
% 8.69/4.99      ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 8.69/4.99         => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8569_norm__diff__triangle__le,axiom,
% 8.69/4.99      ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 8.69/4.99         => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8570_norm__triangle__ineq4,axiom,
% 8.69/4.99      ! [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 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8571_norm__triangle__ineq4,axiom,
% 8.69/4.99      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8572_norm__triangle__sub,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8573_norm__triangle__sub,axiom,
% 8.69/4.99      ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8574_norm__diff__ineq,axiom,
% 8.69/4.99      ! [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 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8575_norm__diff__ineq,axiom,
% 8.69/4.99      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8576_norm__triangle__ineq2,axiom,
% 8.69/4.99      ! [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 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8577_norm__triangle__ineq2,axiom,
% 8.69/4.99      ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8578_power__eq__1__iff,axiom,
% 8.69/4.99      ! [W: real,N: nat] :
% 8.69/4.99        ( ( ( power_power_real @ W @ N )
% 8.69/4.99          = one_one_real )
% 8.69/4.99       => ( ( ( real_V7735802525324610683m_real @ W )
% 8.69/4.99            = one_one_real )
% 8.69/4.99          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8579_power__eq__1__iff,axiom,
% 8.69/4.99      ! [W: complex,N: nat] :
% 8.69/4.99        ( ( ( power_power_complex @ W @ N )
% 8.69/4.99          = one_one_complex )
% 8.69/4.99       => ( ( ( real_V1022390504157884413omplex @ W )
% 8.69/4.99            = one_one_real )
% 8.69/4.99          | ( N = zero_zero_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8580_norm__diff__triangle__ineq,axiom,
% 8.69/4.99      ! [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 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8581_norm__diff__triangle__ineq,axiom,
% 8.69/4.99      ! [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 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8582_norm__triangle__ineq3,axiom,
% 8.69/4.99      ! [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 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8583_norm__triangle__ineq3,axiom,
% 8.69/4.99      ! [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 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8584_square__norm__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = one_one_real )
% 8.69/4.99       => ( ( real_V7735802525324610683m_real @ X )
% 8.69/4.99          = one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8585_square__norm__one,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = one_one_complex )
% 8.69/4.99       => ( ( real_V1022390504157884413omplex @ X )
% 8.69/4.99          = one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8586_norm__power__diff,axiom,
% 8.69/4.99      ! [Z: complex,W: complex,M: nat] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 8.69/4.99         => ( 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 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8587_sumr__cos__zero__one,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( groups6591440286371151544t_real
% 8.69/4.99          @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8588_cos__coeff__0,axiom,
% 8.69/4.99      ( ( cos_coeff @ zero_zero_nat )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8589_pi__series,axiom,
% 8.69/4.99      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = ( suminf_real
% 8.69/4.99        @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8590_ceiling__log__nat__eq__powr__iff,axiom,
% 8.69/4.99      ! [B: nat,K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.99         => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 8.69/4.99              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 8.69/4.99            = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 8.69/4.99              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8591_summable__arctan__series,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( summable_real
% 8.69/4.99          @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8592_ceiling__log__nat__eq__if,axiom,
% 8.69/4.99      ! [B: nat,N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 8.69/4.99       => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 8.69/4.99         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.69/4.99           => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 8.69/4.99              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8593_ceiling__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [A: num,B: num] :
% 8.69/4.99        ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 8.69/4.99        = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8594_ceiling__minus__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [A: num,B: num] :
% 8.69/4.99        ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 8.69/4.99        = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8595_pi__neq__zero,axiom,
% 8.69/4.99      pi != zero_zero_real ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8596_pi__gt__zero,axiom,
% 8.69/4.99      ord_less_real @ zero_zero_real @ pi ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8597_pi__not__less__zero,axiom,
% 8.69/4.99      ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8598_pi__ge__zero,axiom,
% 8.69/4.99      ord_less_eq_real @ zero_zero_real @ pi ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8599_summable__rabs__comparison__test,axiom,
% 8.69/4.99      ! [F: nat > real,G: nat > real] :
% 8.69/4.99        ( ? [N8: nat] :
% 8.69/4.99          ! [N3: nat] :
% 8.69/4.99            ( ( ord_less_eq_nat @ N8 @ N3 )
% 8.69/4.99           => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 8.69/4.99       => ( ( summable_real @ G )
% 8.69/4.99         => ( summable_real
% 8.69/4.99            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8600_summable__rabs,axiom,
% 8.69/4.99      ! [F: nat > real] :
% 8.69/4.99        ( ( summable_real
% 8.69/4.99          @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 8.69/4.99          @ ( suminf_real
% 8.69/4.99            @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8601_pi__less__4,axiom,
% 8.69/4.99      ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8602_pi__ge__two,axiom,
% 8.69/4.99      ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8603_pi__half__neq__two,axiom,
% 8.69/4.99      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99     != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8604_pi__half__neq__zero,axiom,
% 8.69/4.99      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99     != zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8605_pi__half__less__two,axiom,
% 8.69/4.99      ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8606_pi__half__le__two,axiom,
% 8.69/4.99      ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8607_summable__power__series,axiom,
% 8.69/4.99      ! [F: nat > real,Z: real] :
% 8.69/4.99        ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 8.69/4.99       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 8.69/4.99           => ( ( ord_less_real @ Z @ one_one_real )
% 8.69/4.99             => ( summable_real
% 8.69/4.99                @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8608_pi__half__gt__zero,axiom,
% 8.69/4.99      ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8609_pi__half__ge__zero,axiom,
% 8.69/4.99      ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8610_m2pi__less__pi,axiom,
% 8.69/4.99      ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8611_arctan__ubound,axiom,
% 8.69/4.99      ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8612_arctan__one,axiom,
% 8.69/4.99      ( ( arctan @ one_one_real )
% 8.69/4.99      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8613_minus__pi__half__less__zero,axiom,
% 8.69/4.99      ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8614_arctan__lbound,axiom,
% 8.69/4.99      ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8615_arctan__bounded,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 8.69/4.99        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8616_machin__Euler,axiom,
% 8.69/4.99      ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8617_machin,axiom,
% 8.69/4.99      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8618_sum__pos__lt__pair,axiom,
% 8.69/4.99      ! [F: nat > real,K: nat] :
% 8.69/4.99        ( ( summable_real @ F )
% 8.69/4.99       => ( ! [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 ) ) ) ) )
% 8.69/4.99         => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8619_ceiling__log2__div2,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99          = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8620_sin__cos__npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8621_cos__pi__eq__zero,axiom,
% 8.69/4.99      ! [M: nat] :
% 8.69/4.99        ( ( 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 ) ) ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8622_and__int_Opsimps,axiom,
% 8.69/4.99      ! [K: int,L2: int] :
% 8.69/4.99        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 8.69/4.99       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.99              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.99           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 8.69/4.99              = ( uminus_uminus_int
% 8.69/4.99                @ ( zero_n2684676970156552555ol_int
% 8.69/4.99                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 8.69/4.99                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 8.69/4.99          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.99                & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.99           => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 8.69/4.99              = ( plus_plus_int
% 8.69/4.99                @ ( zero_n2684676970156552555ol_int
% 8.69/4.99                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 8.69/4.99                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.69/4.99                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8623_and__int_Opelims,axiom,
% 8.69/4.99      ! [X: int,Xa2: int,Y: int] :
% 8.69/4.99        ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 8.69/4.99          = Y )
% 8.69/4.99       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 8.69/4.99         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.99                    & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.99                 => ( Y
% 8.69/4.99                    = ( uminus_uminus_int
% 8.69/4.99                      @ ( zero_n2684676970156552555ol_int
% 8.69/4.99                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.69/4.99                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 8.69/4.99                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.99                      & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.99                 => ( Y
% 8.69/4.99                    = ( plus_plus_int
% 8.69/4.99                      @ ( zero_n2684676970156552555ol_int
% 8.69/4.99                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.69/4.99                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 8.69/4.99                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 8.69/4.99             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8624_Maclaurin__exp__lt,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( X != zero_zero_real )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99         => ? [T6: real] :
% 8.69/4.99              ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 8.69/4.99              & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/4.99              & ( ( exp_real @ X )
% 8.69/4.99                = ( plus_plus_real
% 8.69/4.99                  @ ( groups6591440286371151544t_real
% 8.69/4.99                    @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 8.69/4.99                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99                  @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8625_sin__pi,axiom,
% 8.69/4.99      ( ( sin_real @ pi )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8626_sin__pi__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 8.69/4.99        = ( sin_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8627_cos__pi,axiom,
% 8.69/4.99      ( ( cos_real @ pi )
% 8.69/4.99      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8628_cos__periodic__pi2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8629_cos__periodic__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8630_sin__periodic__pi2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8631_sin__periodic__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8632_cos__minus__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8633_cos__pi__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8634_sin__minus__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8635_sin__npi2,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8636_sin__npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8637_sin__npi__int,axiom,
% 8.69/4.99      ! [N: int] :
% 8.69/4.99        ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8638_cos__pi__half,axiom,
% 8.69/4.99      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8639_sin__two__pi,axiom,
% 8.69/4.99      ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8640_sin__pi__half,axiom,
% 8.69/4.99      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8641_cos__two__pi,axiom,
% 8.69/4.99      ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8642_cos__periodic,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/4.99        = ( cos_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8643_sin__periodic,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/4.99        = ( sin_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8644_cos__2pi__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 8.69/4.99        = ( cos_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8645_cos__npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.69/4.99        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8646_cos__npi2,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99        = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8647_sin__2npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8648_cos__2npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8649_sin__2pi__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8650_sin__int__2pin,axiom,
% 8.69/4.99      ! [N: int] :
% 8.69/4.99        ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8651_cos__int__2pin,axiom,
% 8.69/4.99      ! [N: int] :
% 8.69/4.99        ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8652_cos__3over2__pi,axiom,
% 8.69/4.99      ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8653_sin__3over2__pi,axiom,
% 8.69/4.99      ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.69/4.99      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8654_cos__npi__int,axiom,
% 8.69/4.99      ! [N: int] :
% 8.69/4.99        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.69/4.99         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.69/4.99            = one_one_real ) )
% 8.69/4.99        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.69/4.99         => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.69/4.99            = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8655_polar__Ex,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99      ? [R2: real,A5: real] :
% 8.69/4.99        ( ( X
% 8.69/4.99          = ( times_times_real @ R2 @ ( cos_real @ A5 ) ) )
% 8.69/4.99        & ( Y
% 8.69/4.99          = ( times_times_real @ R2 @ ( sin_real @ A5 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8656_sin__zero__abs__cos__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sin_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99       => ( ( abs_abs_real @ ( cos_real @ X ) )
% 8.69/4.99          = one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8657_sincos__principal__value,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99      ? [Y5: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y5 )
% 8.69/4.99        & ( ord_less_eq_real @ Y5 @ pi )
% 8.69/4.99        & ( ( sin_real @ Y5 )
% 8.69/4.99          = ( sin_real @ X ) )
% 8.69/4.99        & ( ( cos_real @ Y5 )
% 8.69/4.99          = ( cos_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8658_sin__x__le__x,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8659_sin__le__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8660_cos__le__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8661_abs__sin__x__le__abs__x,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8662_cos__arctan__not__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( arctan @ X ) )
% 8.69/4.99       != zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8663_sin__cos__le1,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8664_sin__gt__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ pi )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8665_sin__x__ge__neg__x,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8666_sin__ge__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99         => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8667_sin__ge__minus__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8668_cos__inj__pi,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ pi )
% 8.69/4.99             => ( ( ( cos_real @ X )
% 8.69/4.99                  = ( cos_real @ Y ) )
% 8.69/4.99               => ( X = Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8669_cos__mono__le__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ pi )
% 8.69/4.99             => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 8.69/4.99                = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8670_cos__monotone__0__pi__le,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99           => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8671_cos__ge__minus__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8672_abs__sin__le__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8673_abs__cos__le__one,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8674_cos__two__neq__zero,axiom,
% 8.69/4.99      ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99     != zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8675_cos__mono__less__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ pi )
% 8.69/4.99             => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 8.69/4.99                = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8676_cos__monotone__0__pi,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99           => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8677_sin__eq__0__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ pi )
% 8.69/4.99         => ( ( ( sin_real @ X )
% 8.69/4.99              = zero_zero_real )
% 8.69/4.99           => ( X = zero_zero_real ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8678_sin__zero__pi__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 8.69/4.99       => ( ( ( sin_real @ X )
% 8.69/4.99            = zero_zero_real )
% 8.69/4.99          = ( X = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8679_cos__monotone__minus__pi__0_H,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.99           => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8680_sin__zero__iff__int2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sin_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( ? [I5: int] :
% 8.69/4.99              ( X
% 8.69/4.99              = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8681_sincos__total__pi,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99            = one_one_real )
% 8.69/4.99         => ? [T6: real] :
% 8.69/4.99              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/4.99              & ( ord_less_eq_real @ T6 @ pi )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( cos_real @ T6 ) )
% 8.69/4.99              & ( Y
% 8.69/4.99                = ( sin_real @ T6 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8682_sin__expansion__lemma,axiom,
% 8.69/4.99      ! [X: real,M: nat] :
% 8.69/4.99        ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99        = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8683_cos__expansion__lemma,axiom,
% 8.69/4.99      ! [X: real,M: nat] :
% 8.69/4.99        ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8684_sin__gt__zero__02,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8685_cos__two__less__zero,axiom,
% 8.69/4.99      ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8686_cos__is__zero,axiom,
% 8.69/4.99      ? [X6: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 8.69/4.99        & ( ord_less_eq_real @ X6 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99        & ( ( cos_real @ X6 )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        & ! [Y2: real] :
% 8.69/4.99            ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 8.69/4.99              & ( ord_less_eq_real @ Y2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99              & ( ( cos_real @ Y2 )
% 8.69/4.99                = zero_zero_real ) )
% 8.69/4.99           => ( Y2 = X6 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8687_cos__two__le__zero,axiom,
% 8.69/4.99      ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8688_cos__monotone__minus__pi__0,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.99           => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8689_cos__total,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ? [X6: real] :
% 8.69/4.99              ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 8.69/4.99              & ( ord_less_eq_real @ X6 @ pi )
% 8.69/4.99              & ( ( cos_real @ X6 )
% 8.69/4.99                = Y )
% 8.69/4.99              & ! [Y2: real] :
% 8.69/4.99                  ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 8.69/4.99                    & ( ord_less_eq_real @ Y2 @ pi )
% 8.69/4.99                    & ( ( cos_real @ Y2 )
% 8.69/4.99                      = Y ) )
% 8.69/4.99                 => ( Y2 = X6 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8690_sincos__total__pi__half,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99              = one_one_real )
% 8.69/4.99           => ? [T6: real] :
% 8.69/4.99                ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/4.99                & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99                & ( X
% 8.69/4.99                  = ( cos_real @ T6 ) )
% 8.69/4.99                & ( Y
% 8.69/4.99                  = ( sin_real @ T6 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8691_sincos__total__2pi__le,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99          = one_one_real )
% 8.69/4.99       => ? [T6: real] :
% 8.69/4.99            ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/4.99            & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99            & ( X
% 8.69/4.99              = ( cos_real @ T6 ) )
% 8.69/4.99            & ( Y
% 8.69/4.99              = ( sin_real @ T6 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8692_square__fact__le__2__fact,axiom,
% 8.69/4.99      ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8693_sincos__total__2pi,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99          = one_one_real )
% 8.69/4.99       => ~ ! [T6: real] :
% 8.69/4.99              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/4.99             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99               => ( ( X
% 8.69/4.99                    = ( cos_real @ T6 ) )
% 8.69/4.99                 => ( Y
% 8.69/4.99                   != ( sin_real @ T6 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8694_sin__pi__divide__n__ge__0,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( N != zero_zero_nat )
% 8.69/4.99       => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8695_sin__gt__zero2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8696_sin__lt__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ pi @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8697_cos__double__less__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/4.99         => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8698_sin__30,axiom,
% 8.69/4.99      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8699_cos__gt__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8700_sin__monotone__2pi__le,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8701_sin__mono__le__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 8.69/4.99                = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8702_sin__inj__pi,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ( sin_real @ X )
% 8.69/4.99                  = ( sin_real @ Y ) )
% 8.69/4.99               => ( X = Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8703_cos__60,axiom,
% 8.69/4.99      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8704_cos__one__2pi__int,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( cos_real @ X )
% 8.69/4.99          = one_one_real )
% 8.69/4.99        = ( ? [X3: int] :
% 8.69/4.99              ( X
% 8.69/4.99              = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8705_Maclaurin__cos__expansion,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99      ? [T6: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/4.99        & ( ( cos_real @ X )
% 8.69/4.99          = ( plus_plus_real
% 8.69/4.99            @ ( groups6591440286371151544t_real
% 8.69/4.99              @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8706_sin__le__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ pi @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99         => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8707_sin__less__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/4.99         => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8708_sin__monotone__2pi,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8709_sin__mono__less__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 8.69/4.99                = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8710_sin__total,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ? [X6: real] :
% 8.69/4.99              ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 8.69/4.99              & ( ord_less_eq_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99              & ( ( sin_real @ X6 )
% 8.69/4.99                = Y )
% 8.69/4.99              & ! [Y2: real] :
% 8.69/4.99                  ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 8.69/4.99                    & ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99                    & ( ( sin_real @ Y2 )
% 8.69/4.99                      = Y ) )
% 8.69/4.99                 => ( Y2 = X6 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8711_cos__gt__zero__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8712_cos__ge__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8713_cos__one__2pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( cos_real @ X )
% 8.69/4.99          = one_one_real )
% 8.69/4.99        = ( ? [X3: nat] :
% 8.69/4.99              ( X
% 8.69/4.99              = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.69/4.99          | ? [X3: nat] :
% 8.69/4.99              ( X
% 8.69/4.99              = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8714_and__int_Opinduct,axiom,
% 8.69/4.99      ! [A0: int,A12: int,P: int > int > $o] :
% 8.69/4.99        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 8.69/4.99       => ( ! [K3: int,L4: int] :
% 8.69/4.99              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 8.69/4.99             => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.69/4.99                      & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.69/4.99                 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99               => ( P @ K3 @ L4 ) ) )
% 8.69/4.99         => ( P @ A0 @ A12 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8715_Maclaurin__lemma,axiom,
% 8.69/4.99      ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ H2 )
% 8.69/4.99       => ? [B8: real] :
% 8.69/4.99            ( ( F @ H2 )
% 8.69/4.99            = ( plus_plus_real
% 8.69/4.99              @ ( groups6591440286371151544t_real
% 8.69/4.99                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 8.69/4.99                @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99              @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8716_Maclaurin__minus__cos__expansion,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/4.99         => ? [T6: real] :
% 8.69/4.99              ( ( ord_less_real @ X @ T6 )
% 8.69/4.99              & ( ord_less_real @ T6 @ zero_zero_real )
% 8.69/4.99              & ( ( cos_real @ X )
% 8.69/4.99                = ( plus_plus_real
% 8.69/4.99                  @ ( groups6591440286371151544t_real
% 8.69/4.99                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8717_Maclaurin__cos__expansion2,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99         => ? [T6: real] :
% 8.69/4.99              ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.69/4.99              & ( ord_less_real @ T6 @ X )
% 8.69/4.99              & ( ( cos_real @ X )
% 8.69/4.99                = ( plus_plus_real
% 8.69/4.99                  @ ( groups6591440286371151544t_real
% 8.69/4.99                    @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99                  @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8718_sin__pi__divide__n__gt__0,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8719_Maclaurin__exp__le,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99      ? [T6: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/4.99        & ( ( exp_real @ X )
% 8.69/4.99          = ( plus_plus_real
% 8.69/4.99            @ ( groups6591440286371151544t_real
% 8.69/4.99              @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8720_sin__zero__iff__int,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sin_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( ? [I5: int] :
% 8.69/4.99              ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8721_cos__zero__iff__int,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( cos_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( ? [I5: int] :
% 8.69/4.99              ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8722_sin__zero__lemma,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ( sin_real @ X )
% 8.69/4.99            = zero_zero_real )
% 8.69/4.99         => ? [N3: nat] :
% 8.69/4.99              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8723_sin__zero__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sin_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( ? [N2: nat] :
% 8.69/4.99              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.99          | ? [N2: nat] :
% 8.69/4.99              ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8724_cos__coeff__def,axiom,
% 8.69/4.99      ( cos_coeff
% 8.69/4.99      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8725_cos__zero__lemma,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ( cos_real @ X )
% 8.69/4.99            = zero_zero_real )
% 8.69/4.99         => ? [N3: nat] :
% 8.69/4.99              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8726_cos__zero__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( cos_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( ? [N2: nat] :
% 8.69/4.99              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.99          | ? [N2: nat] :
% 8.69/4.99              ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 8.69/4.99              & ( X
% 8.69/4.99                = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8727_Maclaurin__sin__expansion3,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ? [T6: real] :
% 8.69/4.99              ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.69/4.99              & ( ord_less_real @ T6 @ X )
% 8.69/4.99              & ( ( sin_real @ X )
% 8.69/4.99                = ( plus_plus_real
% 8.69/4.99                  @ ( groups6591440286371151544t_real
% 8.69/4.99                    @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99                  @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8728_Maclaurin__sin__expansion4,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ? [T6: real] :
% 8.69/4.99            ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.69/4.99            & ( ord_less_eq_real @ T6 @ X )
% 8.69/4.99            & ( ( sin_real @ X )
% 8.69/4.99              = ( plus_plus_real
% 8.69/4.99                @ ( groups6591440286371151544t_real
% 8.69/4.99                  @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99                  @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99                @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8729_Maclaurin__sin__expansion2,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99      ? [T6: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/4.99        & ( ( sin_real @ X )
% 8.69/4.99          = ( plus_plus_real
% 8.69/4.99            @ ( groups6591440286371151544t_real
% 8.69/4.99              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99            @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8730_Maclaurin__sin__expansion,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99      ? [T6: real] :
% 8.69/4.99        ( ( sin_real @ X )
% 8.69/4.99        = ( plus_plus_real
% 8.69/4.99          @ ( groups6591440286371151544t_real
% 8.69/4.99            @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99            @ ( set_ord_lessThan_nat @ N ) )
% 8.69/4.99          @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8731_sin__coeff__def,axiom,
% 8.69/4.99      ( sin_coeff
% 8.69/4.99      = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8732_sin__coeff__0,axiom,
% 8.69/4.99      ( ( sin_coeff @ zero_zero_nat )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8733_fact__ge__self,axiom,
% 8.69/4.99      ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8734_fact__mono__nat,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99       => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8735_fact__less__mono__nat,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/4.99       => ( ( ord_less_nat @ M @ N )
% 8.69/4.99         => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8736_fact__ge__Suc__0__nat,axiom,
% 8.69/4.99      ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8737_dvd__fact,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 8.69/4.99       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8738_fact__diff__Suc,axiom,
% 8.69/4.99      ! [N: nat,M: nat] :
% 8.69/4.99        ( ( ord_less_nat @ N @ ( suc @ M ) )
% 8.69/4.99       => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 8.69/4.99          = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8739_fact__div__fact__le__pow,axiom,
% 8.69/4.99      ! [R: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ R @ N )
% 8.69/4.99       => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8740_upto_Opinduct,axiom,
% 8.69/4.99      ! [A0: int,A12: int,P: int > int > $o] :
% 8.69/4.99        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 8.69/4.99       => ( ! [I4: int,J2: int] :
% 8.69/4.99              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 8.69/4.99             => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 8.69/4.99                 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 8.69/4.99               => ( P @ I4 @ J2 ) ) )
% 8.69/4.99         => ( P @ A0 @ A12 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8741_complex__unimodular__polar,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ( real_V1022390504157884413omplex @ Z )
% 8.69/4.99          = one_one_real )
% 8.69/4.99       => ~ ! [T6: real] :
% 8.69/4.99              ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/4.99             => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99               => ( Z
% 8.69/4.99                 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8742_sin__paired,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( sums_real
% 8.69/4.99        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 8.69/4.99        @ ( sin_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8743_tan__pi,axiom,
% 8.69/4.99      ( ( tan_real @ pi )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8744_tan__periodic__pi,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 8.69/4.99        = ( tan_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8745_tan__npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8746_tan__periodic__n,axiom,
% 8.69/4.99      ! [X: real,N: num] :
% 8.69/4.99        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 8.69/4.99        = ( tan_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8747_tan__periodic__nat,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 8.69/4.99        = ( tan_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8748_tan__periodic__int,axiom,
% 8.69/4.99      ! [X: real,I: int] :
% 8.69/4.99        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 8.69/4.99        = ( tan_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8749_norm__cos__sin,axiom,
% 8.69/4.99      ! [T: real] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8750_tan__periodic,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/4.99        = ( tan_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8751_complex__diff,axiom,
% 8.69/4.99      ! [A: real,B: real,C: real,D: real] :
% 8.69/4.99        ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 8.69/4.99        = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8752_Complex__eq__numeral,axiom,
% 8.69/4.99      ! [A: real,B: real,W: num] :
% 8.69/4.99        ( ( ( complex2 @ A @ B )
% 8.69/4.99          = ( numera6690914467698888265omplex @ W ) )
% 8.69/4.99        = ( ( A
% 8.69/4.99            = ( numeral_numeral_real @ W ) )
% 8.69/4.99          & ( B = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8753_Complex__eq__0,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( ( complex2 @ A @ B )
% 8.69/4.99          = zero_zero_complex )
% 8.69/4.99        = ( ( A = zero_zero_real )
% 8.69/4.99          & ( B = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8754_zero__complex_Ocode,axiom,
% 8.69/4.99      ( zero_zero_complex
% 8.69/4.99      = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8755_complex__add,axiom,
% 8.69/4.99      ! [A: real,B: real,C: real,D: real] :
% 8.69/4.99        ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 8.69/4.99        = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8756_Complex__eq__neg__numeral,axiom,
% 8.69/4.99      ! [A: real,B: real,W: num] :
% 8.69/4.99        ( ( ( complex2 @ A @ B )
% 8.69/4.99          = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/4.99        = ( ( A
% 8.69/4.99            = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 8.69/4.99          & ( B = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8757_complex__mult,axiom,
% 8.69/4.99      ! [A: real,B: real,C: real,D: real] :
% 8.69/4.99        ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 8.69/4.99        = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8758_Complex__eq__1,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( ( complex2 @ A @ B )
% 8.69/4.99          = one_one_complex )
% 8.69/4.99        = ( ( A = one_one_real )
% 8.69/4.99          & ( B = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8759_one__complex_Ocode,axiom,
% 8.69/4.99      ( one_one_complex
% 8.69/4.99      = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8760_Complex__eq__neg__1,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( ( complex2 @ A @ B )
% 8.69/4.99          = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.69/4.99        = ( ( A
% 8.69/4.99            = ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.99          & ( B = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8761_tan__45,axiom,
% 8.69/4.99      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8762_power__half__series,axiom,
% 8.69/4.99      ( sums_real
% 8.69/4.99      @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 8.69/4.99      @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8763_lemma__tan__total,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.99       => ? [X6: real] :
% 8.69/4.99            ( ( ord_less_real @ zero_zero_real @ X6 )
% 8.69/4.99            & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99            & ( ord_less_real @ Y @ ( tan_real @ X6 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8764_tan__gt__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8765_lemma__tan__total1,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99      ? [X6: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 8.69/4.99        & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99        & ( ( tan_real @ X6 )
% 8.69/4.99          = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8766_tan__mono__lt__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 8.69/4.99                = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8767_tan__monotone_H,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99           => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_real @ Y @ X )
% 8.69/4.99                = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8768_tan__monotone,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ X )
% 8.69/4.99         => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8769_tan__total,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99      ? [X6: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 8.69/4.99        & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99        & ( ( tan_real @ X6 )
% 8.69/4.99          = Y )
% 8.69/4.99        & ! [Y2: real] :
% 8.69/4.99            ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 8.69/4.99              & ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99              & ( ( tan_real @ Y2 )
% 8.69/4.99                = Y ) )
% 8.69/4.99           => ( Y2 = X6 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8770_tan__minus__45,axiom,
% 8.69/4.99      ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 8.69/4.99      = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8771_tan__inverse,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 8.69/4.99        = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8772_sums__if_H,axiom,
% 8.69/4.99      ! [G: nat > real,X: real] :
% 8.69/4.99        ( ( sums_real @ G @ X )
% 8.69/4.99       => ( sums_real
% 8.69/4.99          @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99          @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8773_sums__if,axiom,
% 8.69/4.99      ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 8.69/4.99        ( ( sums_real @ G @ X )
% 8.69/4.99       => ( ( sums_real @ F @ Y )
% 8.69/4.99         => ( sums_real
% 8.69/4.99            @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99            @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8774_tan__pos__pi2__le,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8775_tan__total__pos,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ? [X6: real] :
% 8.69/4.99            ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 8.69/4.99            & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99            & ( ( tan_real @ X6 )
% 8.69/4.99              = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8776_tan__less__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/4.99         => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8777_tan__mono__le__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 8.69/4.99                = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8778_tan__mono__le,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99         => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8779_tan__bound__pi2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99       => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8780_arctan__unique,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ( tan_real @ X )
% 8.69/4.99              = Y )
% 8.69/4.99           => ( ( arctan @ Y )
% 8.69/4.99              = X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8781_arctan__tan,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( arctan @ ( tan_real @ X ) )
% 8.69/4.99            = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8782_arctan,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 8.69/4.99        & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99        & ( ( tan_real @ ( arctan @ Y ) )
% 8.69/4.99          = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8783_tan__total__pi4,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ? [Z5: real] :
% 8.69/4.99            ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z5 )
% 8.69/4.99            & ( ord_less_real @ Z5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99            & ( ( tan_real @ Z5 )
% 8.69/4.99              = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8784_cos__paired,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( sums_real
% 8.69/4.99        @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/4.99        @ ( cos_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8785_ceiling__log__eq__powr__iff,axiom,
% 8.69/4.99      ! [X: real,B: real,K: nat] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99         => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 8.69/4.99              = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 8.69/4.99            = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 8.69/4.99              & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8786_sin__tan,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ( sin_real @ X )
% 8.69/4.99          = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8787_real__sqrt__eq__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( sqrt @ X )
% 8.69/4.99          = ( sqrt @ Y ) )
% 8.69/4.99        = ( X = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8788_real__sqrt__eq__zero__cancel__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sqrt @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8789_real__sqrt__zero,axiom,
% 8.69/4.99      ( ( sqrt @ zero_zero_real )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8790_real__sqrt__less__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_real @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8791_real__sqrt__le__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8792_real__sqrt__eq__1__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sqrt @ X )
% 8.69/4.99          = one_one_real )
% 8.69/4.99        = ( X = one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8793_real__sqrt__one,axiom,
% 8.69/4.99      ( ( sqrt @ one_one_real )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8794_real__sqrt__lt__0__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 8.69/4.99        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8795_real__sqrt__gt__0__iff,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8796_real__sqrt__le__0__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 8.69/4.99        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8797_real__sqrt__ge__0__iff,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8798_powr__gt__zero,axiom,
% 8.69/4.99      ! [X: real,A: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 8.69/4.99        = ( X != zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8799_powr__nonneg__iff,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 8.69/4.99        = ( A = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8800_real__sqrt__gt__1__iff,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_real @ one_one_real @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8801_real__sqrt__lt__1__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 8.69/4.99        = ( ord_less_real @ X @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8802_real__sqrt__le__1__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 8.69/4.99        = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8803_real__sqrt__ge__1__iff,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 8.69/4.99        = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8804_powr__less__cancel__iff,axiom,
% 8.69/4.99      ! [X: real,A: real,B: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 8.69/4.99          = ( ord_less_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8805_real__sqrt__mult__self,axiom,
% 8.69/4.99      ! [A: real] :
% 8.69/4.99        ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 8.69/4.99        = ( abs_abs_real @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8806_real__sqrt__abs2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sqrt @ ( times_times_real @ X @ X ) )
% 8.69/4.99        = ( abs_abs_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8807_real__sqrt__four,axiom,
% 8.69/4.99      ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8808_powr__eq__one__iff,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ A )
% 8.69/4.99       => ( ( ( powr_real @ A @ X )
% 8.69/4.99            = one_one_real )
% 8.69/4.99          = ( X = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8809_powr__one__gt__zero__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( powr_real @ X @ one_one_real )
% 8.69/4.99          = X )
% 8.69/4.99        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8810_powr__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ one_one_real )
% 8.69/4.99          = X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8811_powr__le__cancel__iff,axiom,
% 8.69/4.99      ! [X: real,A: real,B: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 8.69/4.99          = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8812_numeral__powr__numeral__real,axiom,
% 8.69/4.99      ! [M: num,N: num] :
% 8.69/4.99        ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 8.69/4.99        = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8813_powr__log__cancel,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( A != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( powr_real @ A @ ( log @ A @ X ) )
% 8.69/4.99              = X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8814_log__powr__cancel,axiom,
% 8.69/4.99      ! [A: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( A != one_one_real )
% 8.69/4.99         => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 8.69/4.99            = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8815_real__sqrt__abs,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99        = ( abs_abs_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8816_powr__numeral,axiom,
% 8.69/4.99      ! [X: real,N: num] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 8.69/4.99          = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8817_real__sqrt__pow2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8818_real__sqrt__pow2__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = X )
% 8.69/4.99        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8819_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 8.69/4.99      ! [X: real,Y: real,Xa2: real,Ya: real] :
% 8.69/4.99        ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99        = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8820_square__powr__half,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99        = ( abs_abs_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8821_real__sqrt__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8822_real__sqrt__le__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99       => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8823_real__sqrt__power,axiom,
% 8.69/4.99      ! [X: real,K: nat] :
% 8.69/4.99        ( ( sqrt @ ( power_power_real @ X @ K ) )
% 8.69/4.99        = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8824_real__sqrt__mult,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 8.69/4.99        = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8825_real__sqrt__divide,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 8.69/4.99        = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8826_powr__powr,axiom,
% 8.69/4.99      ! [X: real,A: real,B: real] :
% 8.69/4.99        ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 8.69/4.99        = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8827_real__sqrt__less__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ X @ Y )
% 8.69/4.99       => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8828_powr__non__neg,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8829_powr__less__mono2__neg,axiom,
% 8.69/4.99      ! [A: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ A @ zero_zero_real )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ X @ Y )
% 8.69/4.99           => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8830_powr__ge__pzero,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8831_powr__mono2,axiom,
% 8.69/4.99      ! [A: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8832_real__sqrt__gt__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8833_real__sqrt__eq__zero__cancel,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ( sqrt @ X )
% 8.69/4.99            = zero_zero_real )
% 8.69/4.99         => ( X = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8834_real__sqrt__ge__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8835_powr__less__mono,axiom,
% 8.69/4.99      ! [A: real,B: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ A @ B )
% 8.69/4.99       => ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99         => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8836_powr__less__cancel,axiom,
% 8.69/4.99      ! [X: real,A: real,B: real] :
% 8.69/4.99        ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 8.69/4.99       => ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99         => ( ord_less_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8837_powr__mono,axiom,
% 8.69/4.99      ! [A: real,B: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ A @ B )
% 8.69/4.99       => ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99         => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8838_real__sqrt__ge__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8839_powr__mono2_H,axiom,
% 8.69/4.99      ! [A: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99           => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8840_powr__less__mono2,axiom,
% 8.69/4.99      ! [A: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ X @ Y )
% 8.69/4.99           => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8841_powr__inj,axiom,
% 8.69/4.99      ! [A: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( A != one_one_real )
% 8.69/4.99         => ( ( ( powr_real @ A @ X )
% 8.69/4.99              = ( powr_real @ A @ Y ) )
% 8.69/4.99            = ( X = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8842_gr__one__powr,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8843_ge__one__powr__ge__zero,axiom,
% 8.69/4.99      ! [X: real,A: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.99         => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8844_powr__mono__both,axiom,
% 8.69/4.99      ! [A: real,B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( ord_less_eq_real @ A @ B )
% 8.69/4.99         => ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99           => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99             => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8845_powr__le1,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99           => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8846_powr__divide,axiom,
% 8.69/4.99      ! [X: real,Y: real,A: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 8.69/4.99            = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8847_powr__mult,axiom,
% 8.69/4.99      ! [X: real,Y: real,A: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 8.69/4.99            = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8848_real__div__sqrt,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 8.69/4.99          = ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8849_sqrt__add__le__add__sqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8850_le__real__sqrt__sumsq,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8851_divide__powr__uminus,axiom,
% 8.69/4.99      ! [A: real,B: real,C: real] :
% 8.69/4.99        ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 8.69/4.99        = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8852_log__base__powr,axiom,
% 8.69/4.99      ! [A: real,B: real,X: real] :
% 8.69/4.99        ( ( A != zero_zero_real )
% 8.69/4.99       => ( ( log @ ( powr_real @ A @ B ) @ X )
% 8.69/4.99          = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8853_ln__powr,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( X != zero_zero_real )
% 8.69/4.99       => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 8.69/4.99          = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8854_log__powr,axiom,
% 8.69/4.99      ! [X: real,B: real,Y: real] :
% 8.69/4.99        ( ( X != zero_zero_real )
% 8.69/4.99       => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 8.69/4.99          = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8855_powr__half__sqrt,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99          = ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8856_sqrt2__less__2,axiom,
% 8.69/4.99      ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8857_powr__realpow,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 8.69/4.99          = ( power_power_real @ X @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8858_powr__less__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 8.69/4.99            = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8859_less__powr__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 8.69/4.99            = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8860_log__less__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 8.69/4.99            = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8861_less__log__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 8.69/4.99            = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8862_real__less__rsqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 8.69/4.99       => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8863_sqrt__le__D,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 8.69/4.99       => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8864_real__le__rsqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 8.69/4.99       => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8865_powr__neg__one,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.99          = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8866_powr__mult__base,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 8.69/4.99          = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8867_tan__60,axiom,
% 8.69/4.99      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 8.69/4.99      = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8868_le__log__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 8.69/4.99            = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8869_log__le__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 8.69/4.99            = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8870_le__powr__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 8.69/4.99            = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8871_powr__le__iff,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 8.69/4.99            = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8872_real__le__lsqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8873_real__sqrt__unique,axiom,
% 8.69/4.99      ! [Y: real,X: real] :
% 8.69/4.99        ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( sqrt @ X )
% 8.69/4.99            = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8874_lemma__real__divide__sqrt__less,axiom,
% 8.69/4.99      ! [U: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ U )
% 8.69/4.99       => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8875_real__sqrt__sum__squares__eq__cancel,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99          = X )
% 8.69/4.99       => ( Y = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8876_real__sqrt__sum__squares__eq__cancel2,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99          = Y )
% 8.69/4.99       => ( X = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8877_real__sqrt__sum__squares__ge1,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8878_real__sqrt__sum__squares__ge2,axiom,
% 8.69/4.99      ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8879_real__sqrt__sum__squares__triangle__ineq,axiom,
% 8.69/4.99      ! [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 ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8880_sqrt__ge__absD,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 8.69/4.99       => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8881_ln__powr__bound,axiom,
% 8.69/4.99      ! [X: real,A: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99         => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8882_ln__powr__bound2,axiom,
% 8.69/4.99      ! [X: real,A: real] :
% 8.69/4.99        ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99         => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8883_cos__45,axiom,
% 8.69/4.99      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8884_sin__45,axiom,
% 8.69/4.99      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8885_add__log__eq__powr,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/4.99       => ( ( B != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 8.69/4.99              = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8886_log__add__eq__powr,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/4.99       => ( ( B != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 8.69/4.99              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8887_minus__log__eq__powr,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/4.99       => ( ( B != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 8.69/4.99              = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8888_real__less__lsqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99           => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8889_sqrt__sum__squares__le__sum,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8890_sqrt__even__pow2,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 8.69/4.99          = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8891_tan__30,axiom,
% 8.69/4.99      ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8892_real__sqrt__ge__abs1,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8893_real__sqrt__ge__abs2,axiom,
% 8.69/4.99      ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8894_sqrt__sum__squares__le__sum__abs,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8895_ln__sqrt,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ln_ln_real @ ( sqrt @ X ) )
% 8.69/4.99          = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8896_arsinh__real__def,axiom,
% 8.69/4.99      ( arsinh_real
% 8.69/4.99      = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8897_cos__30,axiom,
% 8.69/4.99      ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8898_sin__60,axiom,
% 8.69/4.99      ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 8.69/4.99      = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8899_log__minus__eq__powr,axiom,
% 8.69/4.99      ! [B: real,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/4.99       => ( ( B != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 8.69/4.99              = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8900_complex__norm,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 8.69/4.99        = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8901_arsinh__real__aux,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8902_real__sqrt__power__even,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 8.69/4.99            = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8903_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 8.69/4.99      ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8904_arith__geo__mean__sqrt,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8905_powr__neg__numeral,axiom,
% 8.69/4.99      ! [X: real,N: num] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.69/4.99          = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8906_cos__x__y__le__one,axiom,
% 8.69/4.99      ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8907_real__sqrt__sum__squares__less,axiom,
% 8.69/4.99      ! [X: real,U: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99       => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99         => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8908_arcosh__real__def,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99       => ( ( arcosh_real @ X )
% 8.69/4.99          = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8909_cos__arctan,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cos_real @ ( arctan @ X ) )
% 8.69/4.99        = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8910_sin__arctan,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sin_real @ ( arctan @ X ) )
% 8.69/4.99        = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8911_sqrt__sum__squares__half__less,axiom,
% 8.69/4.99      ! [X: real,U: real,Y: real] :
% 8.69/4.99        ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99             => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8912_sin__cos__sqrt,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 8.69/4.99       => ( ( sin_real @ X )
% 8.69/4.99          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8913_arctan__half,axiom,
% 8.69/4.99      ( arctan
% 8.69/4.99      = ( ^ [X3: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X3 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8914_cos__tan,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ( cos_real @ X )
% 8.69/4.99          = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8915_vebt__mint_Opelims,axiom,
% 8.69/4.99      ! [X: vEBT_VEBT,Y: option_nat] :
% 8.69/4.99        ( ( ( vEBT_vebt_mint @ X )
% 8.69/4.99          = Y )
% 8.69/4.99       => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 8.69/4.99         => ( ! [A5: $o,B5: $o] :
% 8.69/4.99                ( ( X
% 8.69/4.99                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.99               => ( ( ( A5
% 8.69/4.99                     => ( Y
% 8.69/4.99                        = ( some_nat @ zero_zero_nat ) ) )
% 8.69/4.99                    & ( ~ A5
% 8.69/4.99                     => ( ( B5
% 8.69/4.99                         => ( Y
% 8.69/4.99                            = ( some_nat @ one_one_nat ) ) )
% 8.69/4.99                        & ( ~ B5
% 8.69/4.99                         => ( Y = none_nat ) ) ) ) )
% 8.69/4.99                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 8.69/4.99           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.99                  ( ( X
% 8.69/4.99                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.69/4.99                 => ( ( Y = none_nat )
% 8.69/4.99                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 8.69/4.99             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.69/4.99                    ( ( X
% 8.69/4.99                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 8.69/4.99                   => ( ( Y
% 8.69/4.99                        = ( some_nat @ Mi2 ) )
% 8.69/4.99                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8916_vebt__maxt_Opelims,axiom,
% 8.69/4.99      ! [X: vEBT_VEBT,Y: option_nat] :
% 8.69/4.99        ( ( ( vEBT_vebt_maxt @ X )
% 8.69/4.99          = Y )
% 8.69/4.99       => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 8.69/4.99         => ( ! [A5: $o,B5: $o] :
% 8.69/4.99                ( ( X
% 8.69/4.99                  = ( vEBT_Leaf @ A5 @ B5 ) )
% 8.69/4.99               => ( ( ( B5
% 8.69/4.99                     => ( Y
% 8.69/4.99                        = ( some_nat @ one_one_nat ) ) )
% 8.69/4.99                    & ( ~ B5
% 8.69/4.99                     => ( ( A5
% 8.69/4.99                         => ( Y
% 8.69/4.99                            = ( some_nat @ zero_zero_nat ) ) )
% 8.69/4.99                        & ( ~ A5
% 8.69/4.99                         => ( Y = none_nat ) ) ) ) )
% 8.69/4.99                 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 8.69/4.99           => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 8.69/4.99                  ( ( X
% 8.69/4.99                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 8.69/4.99                 => ( ( Y = none_nat )
% 8.69/4.99                   => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 8.69/4.99             => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.69/4.99                    ( ( X
% 8.69/4.99                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 8.69/4.99                   => ( ( Y
% 8.69/4.99                        = ( some_nat @ Ma2 ) )
% 8.69/4.99                     => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8917_complex__exp__exists,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99      ? [A5: complex,R2: real] :
% 8.69/4.99        ( Z
% 8.69/4.99        = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( exp_complex @ A5 ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8918_complex__of__real__def,axiom,
% 8.69/4.99      ( real_V4546457046886955230omplex
% 8.69/4.99      = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8919_complex__of__real__code,axiom,
% 8.69/4.99      ( real_V4546457046886955230omplex
% 8.69/4.99      = ( ^ [X3: real] : ( complex2 @ X3 @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8920_complex__eq__cancel__iff2,axiom,
% 8.69/4.99      ! [X: real,Y: real,Xa2: real] :
% 8.69/4.99        ( ( ( complex2 @ X @ Y )
% 8.69/4.99          = ( real_V4546457046886955230omplex @ Xa2 ) )
% 8.69/4.99        = ( ( X = Xa2 )
% 8.69/4.99          & ( Y = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8921_complex__of__real__mult__Complex,axiom,
% 8.69/4.99      ! [R: real,X: real,Y: real] :
% 8.69/4.99        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 8.69/4.99        = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8922_Complex__mult__complex__of__real,axiom,
% 8.69/4.99      ! [X: real,Y: real,R: real] :
% 8.69/4.99        ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 8.69/4.99        = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y @ R ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8923_complex__of__real__add__Complex,axiom,
% 8.69/4.99      ! [R: real,X: real,Y: real] :
% 8.69/4.99        ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 8.69/4.99        = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8924_Complex__add__complex__of__real,axiom,
% 8.69/4.99      ! [X: real,Y: real,R: real] :
% 8.69/4.99        ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 8.69/4.99        = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8925_cos__arcsin,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( cos_real @ ( arcsin @ X ) )
% 8.69/4.99            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8926_sin__arccos__abs,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99       => ( ( sin_real @ ( arccos @ Y ) )
% 8.69/4.99          = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8927_sin__arccos,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( sin_real @ ( arccos @ X ) )
% 8.69/4.99            = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8928_arcsin__0,axiom,
% 8.69/4.99      ( ( arcsin @ zero_zero_real )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8929_arccos__1,axiom,
% 8.69/4.99      ( ( arccos @ one_one_real )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8930_arccos__minus__1,axiom,
% 8.69/4.99      ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.99      = pi ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8931_cos__arccos,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( cos_real @ ( arccos @ Y ) )
% 8.69/4.99            = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8932_sin__arcsin,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( sin_real @ ( arcsin @ Y ) )
% 8.69/4.99            = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8933_arccos__0,axiom,
% 8.69/4.99      ( ( arccos @ zero_zero_real )
% 8.69/4.99      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8934_arcsin__1,axiom,
% 8.69/4.99      ( ( arcsin @ one_one_real )
% 8.69/4.99      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8935_arcsin__minus__1,axiom,
% 8.69/4.99      ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 8.69/4.99      = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8936_arccos__le__arccos,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99           => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8937_arccos__eq__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99          & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 8.69/4.99       => ( ( ( arccos @ X )
% 8.69/4.99            = ( arccos @ Y ) )
% 8.69/4.99          = ( X = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8938_arccos__le__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 8.69/4.99            = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8939_arcsin__le__arcsin,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99           => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8940_arcsin__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 8.69/4.99            = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8941_arcsin__eq__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99         => ( ( ( arcsin @ X )
% 8.69/4.99              = ( arcsin @ Y ) )
% 8.69/4.99            = ( X = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8942_arcsin__le__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 8.69/4.99            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8943_arccos__lbound,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8944_arccos__less__arccos,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99           => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8945_arccos__less__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 8.69/4.99            = ( ord_less_real @ Y @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8946_arccos__ubound,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8947_arccos__cos,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ pi )
% 8.69/4.99         => ( ( arccos @ ( cos_real @ X ) )
% 8.69/4.99            = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8948_arcsin__less__arcsin,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99           => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8949_arcsin__less__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 8.69/4.99            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8950_cos__arccos__abs,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.69/4.99       => ( ( cos_real @ ( arccos @ Y ) )
% 8.69/4.99          = Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8951_arccos__cos__eq__abs,axiom,
% 8.69/4.99      ! [Theta: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 8.69/4.99       => ( ( arccos @ ( cos_real @ Theta ) )
% 8.69/4.99          = ( abs_abs_real @ Theta ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8952_arccos__lt__bounded,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 8.69/4.99            & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8953_arccos__bounded,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 8.69/4.99            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8954_sin__arccos__nonzero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/4.99         => ( ( sin_real @ ( arccos @ X ) )
% 8.69/4.99           != zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8955_arccos__cos2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 8.69/4.99         => ( ( arccos @ ( cos_real @ X ) )
% 8.69/4.99            = ( uminus_uminus_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8956_arccos__minus,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 8.69/4.99            = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8957_cos__arcsin__nonzero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/4.99         => ( ( cos_real @ ( arcsin @ X ) )
% 8.69/4.99           != zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8958_arccos,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 8.69/4.99            & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 8.69/4.99            & ( ( cos_real @ ( arccos @ Y ) )
% 8.69/4.99              = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8959_arccos__minus__abs,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/4.99       => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 8.69/4.99          = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8960_arccos__le__pi2,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8961_arcsin__lt__bounded,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 8.69/4.99            & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8962_arcsin__bounded,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 8.69/4.99            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8963_arcsin__ubound,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8964_arcsin__lbound,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8965_arcsin__sin,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99         => ( ( arcsin @ ( sin_real @ X ) )
% 8.69/4.99            = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8966_le__arcsin__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 8.69/4.99                = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8967_arcsin__le__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 8.69/4.99           => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99             => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 8.69/4.99                = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8968_arcsin__pi,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 8.69/4.99            & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 8.69/4.99            & ( ( sin_real @ ( arcsin @ Y ) )
% 8.69/4.99              = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8969_arcsin,axiom,
% 8.69/4.99      ! [Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 8.69/4.99            & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99            & ( ( sin_real @ ( arcsin @ Y ) )
% 8.69/4.99              = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8970_arccos__cos__eq__abs__2pi,axiom,
% 8.69/4.99      ! [Theta: real] :
% 8.69/4.99        ~ ! [K3: int] :
% 8.69/4.99            ( ( arccos @ ( cos_real @ Theta ) )
% 8.69/4.99           != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8971_exp__two__pi__i_H,axiom,
% 8.69/4.99      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99      = one_one_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8972_exp__two__pi__i,axiom,
% 8.69/4.99      ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 8.69/4.99      = one_one_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8973_binomial__code,axiom,
% 8.69/4.99      ( binomial
% 8.69/4.99      = ( ^ [N2: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K2 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8974_binomial__n__n,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( binomial @ N @ N )
% 8.69/4.99        = one_one_nat ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8975_binomial__1,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 8.69/4.99        = N ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8976_binomial__0__Suc,axiom,
% 8.69/4.99      ! [K: nat] :
% 8.69/4.99        ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 8.69/4.99        = zero_zero_nat ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8977_binomial__eq__0__iff,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( ( binomial @ N @ K )
% 8.69/4.99          = zero_zero_nat )
% 8.69/4.99        = ( ord_less_nat @ N @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8978_binomial__Suc__Suc,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 8.69/4.99        = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8979_binomial__n__0,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( binomial @ N @ zero_zero_nat )
% 8.69/4.99        = one_one_nat ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8980_norm__ii,axiom,
% 8.69/4.99      ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 8.69/4.99      = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8981_complex__i__mult__minus,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 8.69/4.99        = ( uminus1482373934393186551omplex @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8982_divide__i,axiom,
% 8.69/4.99      ! [X: complex] :
% 8.69/4.99        ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 8.69/4.99        = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8983_zero__less__binomial__iff,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 8.69/4.99        = ( ord_less_eq_nat @ K @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8984_i__squared,axiom,
% 8.69/4.99      ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8985_divide__numeral__i,axiom,
% 8.69/4.99      ! [Z: complex,N: num] :
% 8.69/4.99        ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 8.69/4.99        = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8986_power2__i,axiom,
% 8.69/4.99      ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8987_exp__pi__i,axiom,
% 8.69/4.99      ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8988_exp__pi__i_H,axiom,
% 8.69/4.99      ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8989_i__even__power,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99        = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8990_choose__one,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( binomial @ N @ one_one_nat )
% 8.69/4.99        = N ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8991_complex__i__not__zero,axiom,
% 8.69/4.99      imaginary_unit != zero_zero_complex ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8992_complex__i__not__one,axiom,
% 8.69/4.99      imaginary_unit != one_one_complex ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8993_complex__i__not__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( imaginary_unit
% 8.69/4.99       != ( numera6690914467698888265omplex @ W ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8994_binomial__eq__0,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ N @ K )
% 8.69/4.99       => ( ( binomial @ N @ K )
% 8.69/4.99          = zero_zero_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8995_Suc__times__binomial,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 8.69/4.99        = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8996_Suc__times__binomial__eq,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 8.69/4.99        = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8997_binomial__symmetric,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.99       => ( ( binomial @ N @ K )
% 8.69/4.99          = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8998_choose__mult__lemma,axiom,
% 8.69/4.99      ! [M: nat,R: nat,K: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 8.69/4.99        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_8999_binomial__le__pow,axiom,
% 8.69/4.99      ! [R: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ R @ N )
% 8.69/4.99       => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9000_i__times__eq__iff,axiom,
% 8.69/4.99      ! [W: complex,Z: complex] :
% 8.69/4.99        ( ( ( times_times_complex @ imaginary_unit @ W )
% 8.69/4.99          = Z )
% 8.69/4.99        = ( W
% 8.69/4.99          = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9001_zero__less__binomial,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.99       => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9002_Suc__times__binomial__add,axiom,
% 8.69/4.99      ! [A: nat,B: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 8.69/4.99        = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9003_binomial__Suc__Suc__eq__times,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 8.69/4.99        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9004_choose__mult,axiom,
% 8.69/4.99      ! [K: nat,M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ M )
% 8.69/4.99       => ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99         => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 8.69/4.99            = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9005_binomial__absorb__comp,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 8.69/4.99        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9006_complex__i__not__neg__numeral,axiom,
% 8.69/4.99      ! [W: num] :
% 8.69/4.99        ( imaginary_unit
% 8.69/4.99       != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9007_imaginary__unit_Ocode,axiom,
% 8.69/4.99      ( imaginary_unit
% 8.69/4.99      = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9008_Complex__eq__i,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ( complex2 @ X @ Y )
% 8.69/4.99          = imaginary_unit )
% 8.69/4.99        = ( ( X = zero_zero_real )
% 8.69/4.99          & ( Y = one_one_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9009_binomial__absorption,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 8.69/4.99        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9010_i__mult__Complex,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 8.69/4.99        = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9011_Complex__mult__i,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 8.69/4.99        = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9012_binomial__fact__lemma,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.99       => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 8.69/4.99          = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9013_binomial__mono,axiom,
% 8.69/4.99      ! [K: nat,K6: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ K6 )
% 8.69/4.99       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 8.69/4.99         => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9014_binomial__maximum_H,axiom,
% 8.69/4.99      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9015_binomial__maximum,axiom,
% 8.69/4.99      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9016_binomial__antimono,axiom,
% 8.69/4.99      ! [K: nat,K6: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ K6 )
% 8.69/4.99       => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 8.69/4.99         => ( ( ord_less_eq_nat @ K6 @ N )
% 8.69/4.99           => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9017_binomial__le__pow2,axiom,
% 8.69/4.99      ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9018_choose__reduce__nat,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.99         => ( ( binomial @ N @ K )
% 8.69/4.99            = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9019_times__binomial__minus1__eq,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.99       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 8.69/4.99          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9020_binomial__altdef__nat,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ K @ N )
% 8.69/4.99       => ( ( binomial @ N @ K )
% 8.69/4.99          = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9021_i__complex__of__real,axiom,
% 8.69/4.99      ! [R: real] :
% 8.69/4.99        ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R ) )
% 8.69/4.99        = ( complex2 @ zero_zero_real @ R ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9022_complex__of__real__i,axiom,
% 8.69/4.99      ! [R: real] :
% 8.69/4.99        ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ imaginary_unit )
% 8.69/4.99        = ( complex2 @ zero_zero_real @ R ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9023_Complex__eq,axiom,
% 8.69/4.99      ( complex2
% 8.69/4.99      = ( ^ [A3: real,B2: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9024_binomial__less__binomial__Suc,axiom,
% 8.69/4.99      ! [K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/4.99       => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9025_binomial__strict__mono,axiom,
% 8.69/4.99      ! [K: nat,K6: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ K @ K6 )
% 8.69/4.99       => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 8.69/4.99         => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9026_binomial__strict__antimono,axiom,
% 8.69/4.99      ! [K: nat,K6: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ K @ K6 )
% 8.69/4.99       => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 8.69/4.99         => ( ( ord_less_eq_nat @ K6 @ N )
% 8.69/4.99           => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9027_central__binomial__odd,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99          = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9028_binomial__addition__formula,axiom,
% 8.69/4.99      ! [N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( binomial @ N @ ( suc @ K ) )
% 8.69/4.99          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9029_choose__two,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9030_complex__split__polar,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99      ? [R2: real,A5: real] :
% 8.69/4.99        ( Z
% 8.69/4.99        = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9031_cmod__unit__one,axiom,
% 8.69/4.99      ! [A: real] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9032_cmod__complex__polar,axiom,
% 8.69/4.99      ! [R: real,A: real] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 8.69/4.99        = ( abs_abs_real @ R ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9033_central__binomial__lower__bound,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9034_Arg__minus__ii,axiom,
% 8.69/4.99      ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 8.69/4.99      = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9035_csqrt__ii,axiom,
% 8.69/4.99      ( ( csqrt @ imaginary_unit )
% 8.69/4.99      = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9036_Arg__ii,axiom,
% 8.69/4.99      ( ( arg @ imaginary_unit )
% 8.69/4.99      = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9037_finite__atMost,axiom,
% 8.69/4.99      ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9038_csqrt__0,axiom,
% 8.69/4.99      ( ( csqrt @ zero_zero_complex )
% 8.69/4.99      = zero_zero_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9039_csqrt__eq__0,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ( csqrt @ Z )
% 8.69/4.99          = zero_zero_complex )
% 8.69/4.99        = ( Z = zero_zero_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9040_csqrt__eq__1,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ( csqrt @ Z )
% 8.69/4.99          = one_one_complex )
% 8.69/4.99        = ( Z = one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9041_csqrt__1,axiom,
% 8.69/4.99      ( ( csqrt @ one_one_complex )
% 8.69/4.99      = one_one_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9042_atMost__0,axiom,
% 8.69/4.99      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 8.69/4.99      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9043_power2__csqrt,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99        = Z ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9044_atMost__atLeast0,axiom,
% 8.69/4.99      ( set_ord_atMost_nat
% 8.69/4.99      = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9045_lessThan__Suc__atMost,axiom,
% 8.69/4.99      ! [K: nat] :
% 8.69/4.99        ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 8.69/4.99        = ( set_ord_atMost_nat @ K ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9046_atMost__Suc,axiom,
% 8.69/4.99      ! [K: nat] :
% 8.69/4.99        ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 8.69/4.99        = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9047_finite__nat__iff__bounded__le,axiom,
% 8.69/4.99      ( finite_finite_nat
% 8.69/4.99      = ( ^ [S6: set_nat] :
% 8.69/4.99          ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9048_atMost__nat__numeral,axiom,
% 8.69/4.99      ! [K: num] :
% 8.69/4.99        ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 8.69/4.99        = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9049_Arg__zero,axiom,
% 8.69/4.99      ( ( arg @ zero_zero_complex )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9050_sum__choose__lower,axiom,
% 8.69/4.99      ! [R: nat,N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 8.69/4.99          @ ( set_ord_atMost_nat @ N ) )
% 8.69/4.99        = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9051_choose__rising__sum_I2_J,axiom,
% 8.69/4.99      ! [N: nat,M: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 8.69/4.99          @ ( set_ord_atMost_nat @ M ) )
% 8.69/4.99        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9052_choose__rising__sum_I1_J,axiom,
% 8.69/4.99      ! [N: nat,M: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 8.69/4.99          @ ( set_ord_atMost_nat @ M ) )
% 8.69/4.99        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9053_atLeast1__atMost__eq__remove0,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/4.99        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9054_sum__choose__diagonal,axiom,
% 8.69/4.99      ! [M: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ M @ N )
% 8.69/4.99       => ( ( groups3542108847815614940at_nat
% 8.69/4.99            @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 8.69/4.99            @ ( set_ord_atMost_nat @ M ) )
% 8.69/4.99          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9055_vandermonde,axiom,
% 8.69/4.99      ! [M: nat,N: nat,R: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 8.69/4.99          @ ( set_ord_atMost_nat @ R ) )
% 8.69/4.99        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9056_of__real__sqrt,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 8.69/4.99          = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9057_choose__row__sum,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 8.69/4.99        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9058_Arg__bounded,axiom,
% 8.69/4.99      ! [Z: complex] :
% 8.69/4.99        ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 8.69/4.99        & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9059_binomial,axiom,
% 8.69/4.99      ! [A: nat,B: nat,N: nat] :
% 8.69/4.99        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 8.69/4.99        = ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 8.69/4.99          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9060_polynomial__product__nat,axiom,
% 8.69/4.99      ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 8.69/4.99        ( ! [I4: nat] :
% 8.69/4.99            ( ( ord_less_nat @ M @ I4 )
% 8.69/4.99           => ( ( A @ I4 )
% 8.69/4.99              = zero_zero_nat ) )
% 8.69/4.99       => ( ! [J2: nat] :
% 8.69/4.99              ( ( ord_less_nat @ N @ J2 )
% 8.69/4.99             => ( ( B @ J2 )
% 8.69/4.99                = zero_zero_nat ) )
% 8.69/4.99         => ( ( times_times_nat
% 8.69/4.99              @ ( groups3542108847815614940at_nat
% 8.69/4.99                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X @ I5 ) )
% 8.69/4.99                @ ( set_ord_atMost_nat @ M ) )
% 8.69/4.99              @ ( groups3542108847815614940at_nat
% 8.69/4.99                @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 8.69/4.99                @ ( set_ord_atMost_nat @ N ) ) )
% 8.69/4.99            = ( groups3542108847815614940at_nat
% 8.69/4.99              @ ^ [R5: nat] :
% 8.69/4.99                  ( times_times_nat
% 8.69/4.99                  @ ( groups3542108847815614940at_nat
% 8.69/4.99                    @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 8.69/4.99                    @ ( set_ord_atMost_nat @ R5 ) )
% 8.69/4.99                  @ ( power_power_nat @ X @ R5 ) )
% 8.69/4.99              @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9061_choose__square__sum,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          @ ( set_ord_atMost_nat @ N ) )
% 8.69/4.99        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9062_binomial__r__part__sum,axiom,
% 8.69/4.99      ! [M: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 8.69/4.99        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9063_choose__linear__sum,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( groups3542108847815614940at_nat
% 8.69/4.99          @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N @ I5 ) )
% 8.69/4.99          @ ( set_ord_atMost_nat @ N ) )
% 8.69/4.99        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9064_of__nat__id,axiom,
% 8.69/4.99      ( semiri1316708129612266289at_nat
% 8.69/4.99      = ( ^ [N2: nat] : N2 ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9065_real__scaleR__def,axiom,
% 8.69/4.99      real_V1485227260804924795R_real = times_times_real ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9066_complex__scaleR,axiom,
% 8.69/4.99      ! [R: real,A: real,B: real] :
% 8.69/4.99        ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 8.69/4.99        = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9067_cis__minus__pi__half,axiom,
% 8.69/4.99      ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9068_floor__log__nat__eq__powr__iff,axiom,
% 8.69/4.99      ! [B: nat,K: nat,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.69/4.99         => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 8.69/4.99              = ( semiri1314217659103216013at_int @ N ) )
% 8.69/4.99            = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 8.69/4.99              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9069_norm__cis,axiom,
% 8.69/4.99      ! [A: real] :
% 8.69/4.99        ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 8.69/4.99        = one_one_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9070_cis__zero,axiom,
% 8.69/4.99      ( ( cis @ zero_zero_real )
% 8.69/4.99      = one_one_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9071_cis__pi,axiom,
% 8.69/4.99      ( ( cis @ pi )
% 8.69/4.99      = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9072_floor__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [A: num,B: num] :
% 8.69/4.99        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 8.69/4.99        = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9073_cis__pi__half,axiom,
% 8.69/4.99      ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/4.99      = imaginary_unit ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9074_floor__one__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [B: num] :
% 8.69/4.99        ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 8.69/4.99        = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9075_cis__2pi,axiom,
% 8.69/4.99      ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.69/4.99      = one_one_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9076_floor__minus__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [A: num,B: num] :
% 8.69/4.99        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 8.69/4.99        = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9077_floor__minus__one__divide__eq__div__numeral,axiom,
% 8.69/4.99      ! [B: num] :
% 8.69/4.99        ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 8.69/4.99        = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9078_real__sqrt__inverse,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 8.69/4.99        = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9079_cis__neq__zero,axiom,
% 8.69/4.99      ! [A: real] :
% 8.69/4.99        ( ( cis @ A )
% 8.69/4.99       != zero_zero_complex ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9080_divide__real__def,axiom,
% 8.69/4.99      ( divide_divide_real
% 8.69/4.99      = ( ^ [X3: real,Y3: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y3 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9081_cis__mult,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 8.69/4.99        = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9082_cis__divide,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 8.69/4.99        = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9083_inverse__powr,axiom,
% 8.69/4.99      ! [Y: real,A: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99       => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 8.69/4.99          = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9084_real__of__int__floor__add__one__gt,axiom,
% 8.69/4.99      ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9085_floor__eq,axiom,
% 8.69/4.99      ! [N: int,X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 8.69/4.99         => ( ( archim6058952711729229775r_real @ X )
% 8.69/4.99            = N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9086_real__of__int__floor__add__one__ge,axiom,
% 8.69/4.99      ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9087_real__of__int__floor__gt__diff__one,axiom,
% 8.69/4.99      ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9088_real__of__int__floor__ge__diff__one,axiom,
% 8.69/4.99      ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9089_forall__pos__mono__1,axiom,
% 8.69/4.99      ! [P: real > $o,E: real] :
% 8.69/4.99        ( ! [D3: real,E2: real] :
% 8.69/4.99            ( ( ord_less_real @ D3 @ E2 )
% 8.69/4.99           => ( ( P @ D3 )
% 8.69/4.99             => ( P @ E2 ) ) )
% 8.69/4.99       => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ E )
% 8.69/4.99           => ( P @ E ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9090_DeMoivre,axiom,
% 8.69/4.99      ! [A: real,N: nat] :
% 8.69/4.99        ( ( power_power_complex @ ( cis @ A ) @ N )
% 8.69/4.99        = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9091_forall__pos__mono,axiom,
% 8.69/4.99      ! [P: real > $o,E: real] :
% 8.69/4.99        ( ! [D3: real,E2: real] :
% 8.69/4.99            ( ( ord_less_real @ D3 @ E2 )
% 8.69/4.99           => ( ( P @ D3 )
% 8.69/4.99             => ( P @ E2 ) ) )
% 8.69/4.99       => ( ! [N3: nat] :
% 8.69/4.99              ( ( N3 != zero_zero_nat )
% 8.69/4.99             => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ E )
% 8.69/4.99           => ( P @ E ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9092_real__arch__inverse,axiom,
% 8.69/4.99      ! [E: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ E )
% 8.69/4.99        = ( ? [N2: nat] :
% 8.69/4.99              ( ( N2 != zero_zero_nat )
% 8.69/4.99              & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 8.69/4.99              & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9093_sqrt__divide__self__eq,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 8.69/4.99          = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9094_ln__inverse,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 8.69/4.99          = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9095_floor__eq2,axiom,
% 8.69/4.99      ! [N: int,X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 8.69/4.99         => ( ( archim6058952711729229775r_real @ X )
% 8.69/4.99            = N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9096_floor__divide__real__eq__div,axiom,
% 8.69/4.99      ! [B: int,A: real] :
% 8.69/4.99        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.69/4.99       => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 8.69/4.99          = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9097_log__inverse,axiom,
% 8.69/4.99      ! [A: real,X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/4.99       => ( ( A != one_one_real )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 8.69/4.99              = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9098_cis__conv__exp,axiom,
% 8.69/4.99      ( cis
% 8.69/4.99      = ( ^ [B2: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9099_exp__plus__inverse__exp,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9100_plus__inverse__ge__2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9101_real__inv__sqrt__pow2,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/4.99          = ( inverse_inverse_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9102_tan__cot,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 8.69/4.99        = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9103_real__le__x__sinh,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9104_real__le__abs__sinh,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9105_floor__log__eq__powr__iff,axiom,
% 8.69/4.99      ! [X: real,B: real,K: int] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ one_one_real @ B )
% 8.69/4.99         => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 8.69/4.99              = K )
% 8.69/4.99            = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 8.69/4.99              & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9106_floor__log2__div2,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/4.99       => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99          = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9107_floor__log__nat__eq__if,axiom,
% 8.69/4.99      ! [B: nat,N: nat,K: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 8.69/4.99       => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 8.69/4.99         => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.69/4.99           => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 8.69/4.99              = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9108_Maclaurin__sin__bound,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ord_less_eq_real
% 8.69/4.99        @ ( abs_abs_real
% 8.69/4.99          @ ( minus_minus_real @ ( sin_real @ X )
% 8.69/4.99            @ ( groups6591440286371151544t_real
% 8.69/4.99              @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 8.69/4.99              @ ( set_ord_lessThan_nat @ N ) ) ) )
% 8.69/4.99        @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9109_bij__betw__roots__unity,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( bij_betw_nat_complex
% 8.69/4.99          @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.69/4.99          @ ( set_ord_lessThan_nat @ N )
% 8.69/4.99          @ ( collect_complex
% 8.69/4.99            @ ^ [Z3: complex] :
% 8.69/4.99                ( ( power_power_complex @ Z3 @ N )
% 8.69/4.99                = one_one_complex ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9110_sinh__real__zero__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ( sinh_real @ X )
% 8.69/4.99          = zero_zero_real )
% 8.69/4.99        = ( X = zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9111_sinh__real__le__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 8.69/4.99        = ( ord_less_eq_real @ X @ Y ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9112_sinh__real__neg__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 8.69/4.99        = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9113_sinh__real__pos__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 8.69/4.99        = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9114_sinh__real__nonpos__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 8.69/4.99        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9115_sinh__real__nonneg__iff,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 8.69/4.99        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9116_divide__complex__def,axiom,
% 8.69/4.99      ( divide1717551699836669952omplex
% 8.69/4.99      = ( ^ [X3: complex,Y3: complex] : ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ Y3 ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9117_fact__eq__fact__times,axiom,
% 8.69/4.99      ! [N: nat,M: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.99       => ( ( semiri1408675320244567234ct_nat @ M )
% 8.69/4.99          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 8.69/4.99            @ ( groups708209901874060359at_nat
% 8.69/4.99              @ ^ [X3: nat] : X3
% 8.69/4.99              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9118_fact__div__fact,axiom,
% 8.69/4.99      ! [N: nat,M: nat] :
% 8.69/4.99        ( ( ord_less_eq_nat @ N @ M )
% 8.69/4.99       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.69/4.99          = ( groups708209901874060359at_nat
% 8.69/4.99            @ ^ [X3: nat] : X3
% 8.69/4.99            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9119_complex__inverse,axiom,
% 8.69/4.99      ! [A: real,B: real] :
% 8.69/4.99        ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 8.69/4.99        = ( 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 ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9120_sinh__ln__real,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 8.69/4.99          = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9121_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 8.69/4.99      ! [X: vEBT_VEBT,Y: $o] :
% 8.69/4.99        ( ( ( vEBT_VEBT_minNull @ X )
% 8.69/4.99          = Y )
% 8.69/4.99       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.69/4.99         => ( ( ( X
% 8.69/4.99                = ( vEBT_Leaf @ $false @ $false ) )
% 8.69/4.99             => ( Y
% 8.69/4.99               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 8.69/4.99           => ( ! [Uv2: $o] :
% 8.69/4.99                  ( ( X
% 8.69/4.99                    = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.69/4.99                 => ( ~ Y
% 8.69/4.99                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 8.69/4.99             => ( ! [Uu2: $o] :
% 8.69/4.99                    ( ( X
% 8.69/4.99                      = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.69/4.99                   => ( ~ Y
% 8.69/4.99                     => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 8.69/4.99               => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.69/4.99                      ( ( X
% 8.69/4.99                        = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 8.69/4.99                     => ( Y
% 8.69/4.99                       => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 8.69/4.99                 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.99                        ( ( X
% 8.69/4.99                          = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 8.69/4.99                       => ( ~ Y
% 8.69/4.99                         => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9122_sinh__le__cosh__real,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9123_cosh__real__nonzero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cosh_real @ X )
% 8.69/4.99       != zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9124_cosh__real__pos,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9125_cosh__real__nonneg,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9126_cosh__real__nonneg__le__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 8.69/4.99            = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9127_cosh__real__nonpos__le__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.69/4.99         => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 8.69/4.99            = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9128_cosh__real__ge__1,axiom,
% 8.69/4.99      ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9129_cosh__real__nonpos__less__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/4.99       => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.69/4.99         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 8.69/4.99            = ( ord_less_real @ Y @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9130_cosh__real__nonneg__less__iff,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 8.69/4.99            = ( ord_less_real @ X @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9131_cosh__real__strict__mono,axiom,
% 8.69/4.99      ! [X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ Y )
% 8.69/4.99         => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9132_prod__int__eq,axiom,
% 8.69/4.99      ! [I: nat,J: nat] :
% 8.69/4.99        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 8.69/4.99        = ( groups1705073143266064639nt_int
% 8.69/4.99          @ ^ [X3: int] : X3
% 8.69/4.99          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9133_arcosh__cosh__real,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( arcosh_real @ ( cosh_real @ X ) )
% 8.69/4.99          = X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9134_prod__int__plus__eq,axiom,
% 8.69/4.99      ! [I: nat,J: nat] :
% 8.69/4.99        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 8.69/4.99        = ( groups1705073143266064639nt_int
% 8.69/4.99          @ ^ [X3: int] : X3
% 8.69/4.99          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9135_cosh__ln__real,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 8.69/4.99          = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9136_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 8.69/4.99      ! [X: vEBT_VEBT] :
% 8.69/4.99        ( ~ ( vEBT_VEBT_minNull @ X )
% 8.69/4.99       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.69/4.99         => ( ! [Uv2: $o] :
% 8.69/4.99                ( ( X
% 8.69/4.99                  = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.69/4.99               => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 8.69/4.99           => ( ! [Uu2: $o] :
% 8.69/4.99                  ( ( X
% 8.69/4.99                    = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.69/4.99                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 8.69/4.99             => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.69/4.99                    ( ( X
% 8.69/4.99                      = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 8.69/4.99                   => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9137_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 8.69/4.99      ! [X: vEBT_VEBT] :
% 8.69/4.99        ( ( vEBT_VEBT_minNull @ X )
% 8.69/4.99       => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.69/4.99         => ( ( ( X
% 8.69/4.99                = ( vEBT_Leaf @ $false @ $false ) )
% 8.69/4.99             => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 8.69/4.99           => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 8.69/4.99                  ( ( X
% 8.69/4.99                    = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 8.69/4.99                 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9138_bij__betw__nth__root__unity,axiom,
% 8.69/4.99      ! [C: complex,N: nat] :
% 8.69/4.99        ( ( C != zero_zero_complex )
% 8.69/4.99       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99         => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 8.69/4.99            @ ( collect_complex
% 8.69/4.99              @ ^ [Z3: complex] :
% 8.69/4.99                  ( ( power_power_complex @ Z3 @ N )
% 8.69/4.99                  = one_one_complex ) )
% 8.69/4.99            @ ( collect_complex
% 8.69/4.99              @ ^ [Z3: complex] :
% 8.69/4.99                  ( ( power_power_complex @ Z3 @ N )
% 8.69/4.99                  = C ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9139_cot__less__zero,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 8.69/4.99       => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/4.99         => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9140_int__ge__less__than__def,axiom,
% 8.69/4.99      ( int_ge_less_than
% 8.69/4.99      = ( ^ [D2: int] :
% 8.69/4.99            ( collec213857154873943460nt_int
% 8.69/4.99            @ ( produc4947309494688390418_int_o
% 8.69/4.99              @ ^ [Z6: int,Z3: int] :
% 8.69/4.99                  ( ( ord_less_eq_int @ D2 @ Z6 )
% 8.69/4.99                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9141_int__ge__less__than2__def,axiom,
% 8.69/4.99      ( int_ge_less_than2
% 8.69/4.99      = ( ^ [D2: int] :
% 8.69/4.99            ( collec213857154873943460nt_int
% 8.69/4.99            @ ( produc4947309494688390418_int_o
% 8.69/4.99              @ ^ [Z6: int,Z3: int] :
% 8.69/4.99                  ( ( ord_less_eq_int @ D2 @ Z3 )
% 8.69/4.99                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9142_real__root__zero,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( root @ N @ zero_zero_real )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9143_real__root__Suc__0,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 8.69/4.99        = X ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9144_real__root__eq__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ( root @ N @ X )
% 8.69/4.99            = ( root @ N @ Y ) )
% 8.69/4.99          = ( X = Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9145_root__0,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( root @ zero_zero_nat @ X )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9146_cot__pi,axiom,
% 8.69/4.99      ( ( cot_real @ pi )
% 8.69/4.99      = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9147_real__root__eq__0__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ( root @ N @ X )
% 8.69/4.99            = zero_zero_real )
% 8.69/4.99          = ( X = zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9148_real__root__less__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_real @ X @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9149_real__root__le__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9150_real__root__eq__1__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ( root @ N @ X )
% 8.69/4.99            = one_one_real )
% 8.69/4.99          = ( X = one_one_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9151_real__root__one,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( root @ N @ one_one_real )
% 8.69/4.99          = one_one_real ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9152_real__root__gt__0__iff,axiom,
% 8.69/4.99      ! [N: nat,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9153_real__root__lt__0__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 8.69/4.99          = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9154_real__root__ge__0__iff,axiom,
% 8.69/4.99      ! [N: nat,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9155_real__root__le__0__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 8.69/4.99          = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9156_real__root__lt__1__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 8.69/4.99          = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9157_real__root__gt__1__iff,axiom,
% 8.69/4.99      ! [N: nat,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9158_real__root__le__1__iff,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 8.69/4.99          = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9159_real__root__ge__1__iff,axiom,
% 8.69/4.99      ! [N: nat,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 8.69/4.99          = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9160_cot__npi,axiom,
% 8.69/4.99      ! [N: nat] :
% 8.69/4.99        ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.69/4.99        = zero_zero_real ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9161_real__root__pow__pos2,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 8.69/4.99            = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9162_cot__periodic,axiom,
% 8.69/4.99      ! [X: real] :
% 8.69/4.99        ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/4.99        = ( cot_real @ X ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9163_real__root__inverse,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 8.69/4.99        = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9164_real__root__divide,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( root @ N @ ( divide_divide_real @ X @ Y ) )
% 8.69/4.99        = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9165_real__root__commute,axiom,
% 8.69/4.99      ! [M: nat,N: nat,X: real] :
% 8.69/4.99        ( ( root @ M @ ( root @ N @ X ) )
% 8.69/4.99        = ( root @ N @ ( root @ M @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9166_real__root__mult__exp,axiom,
% 8.69/4.99      ! [M: nat,N: nat,X: real] :
% 8.69/4.99        ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 8.69/4.99        = ( root @ M @ ( root @ N @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9167_real__root__mult,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 8.69/4.99        = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9168_real__root__minus,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 8.69/4.99        = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9169_real__root__pos__pos__le,axiom,
% 8.69/4.99      ! [X: real,N: nat] :
% 8.69/4.99        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/4.99       => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9170_real__root__less__mono,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ X @ Y )
% 8.69/4.99         => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9171_real__root__le__mono,axiom,
% 8.69/4.99      ! [N: nat,X: real,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ X @ Y )
% 8.69/4.99         => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9172_real__root__power,axiom,
% 8.69/4.99      ! [N: nat,X: real,K: nat] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 8.69/4.99          = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9173_real__root__abs,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( root @ N @ ( abs_abs_real @ X ) )
% 8.69/4.99          = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9174_real__root__gt__zero,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9175_real__root__strict__decreasing,axiom,
% 8.69/4.99      ! [N: nat,N4: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_nat @ N @ N4 )
% 8.69/4.99         => ( ( ord_less_real @ one_one_real @ X )
% 8.69/4.99           => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9176_sqrt__def,axiom,
% 8.69/4.99      ( sqrt
% 8.69/4.99      = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9177_root__abs__power,axiom,
% 8.69/4.99      ! [N: nat,Y: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 8.69/4.99          = ( abs_abs_real @ Y ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9178_real__root__pos__pos,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9179_real__root__strict__increasing,axiom,
% 8.69/4.99      ! [N: nat,N4: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_nat @ N @ N4 )
% 8.69/4.99         => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99           => ( ( ord_less_real @ X @ one_one_real )
% 8.69/4.99             => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9180_real__root__decreasing,axiom,
% 8.69/4.99      ! [N: nat,N4: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_nat @ N @ N4 )
% 8.69/4.99         => ( ( ord_less_eq_real @ one_one_real @ X )
% 8.69/4.99           => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9181_real__root__pow__pos,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/4.99         => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 8.69/4.99            = X ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9182_real__root__pos__unique,axiom,
% 8.69/4.99      ! [N: nat,Y: real,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/4.99       => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.69/4.99         => ( ( ( power_power_real @ Y @ N )
% 8.69/4.99              = X )
% 8.69/4.99           => ( ( root @ N @ X )
% 8.69/4.99              = Y ) ) ) ) ).
% 8.69/4.99  
% 8.69/4.99  thf(fact_9183_real__root__power__cancel,axiom,
% 8.69/4.99      ! [N: nat,X: real] :
% 8.69/4.99        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/5.00         => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 8.69/5.00            = X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9184_odd__real__root__pow,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00       => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 8.69/5.00          = X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9185_odd__real__root__unique,axiom,
% 8.69/5.00      ! [N: nat,Y: real,X: real] :
% 8.69/5.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00       => ( ( ( power_power_real @ Y @ N )
% 8.69/5.00            = X )
% 8.69/5.00         => ( ( root @ N @ X )
% 8.69/5.00            = Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9186_odd__real__root__power__cancel,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00       => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 8.69/5.00          = X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9187_real__root__increasing,axiom,
% 8.69/5.00      ! [N: nat,N4: nat,X: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_eq_nat @ N @ N4 )
% 8.69/5.00         => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/5.00           => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/5.00             => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9188_ln__root,axiom,
% 8.69/5.00      ! [N: nat,B: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/5.00         => ( ( ln_ln_real @ ( root @ N @ B ) )
% 8.69/5.00            = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9189_log__root,axiom,
% 8.69/5.00      ! [N: nat,A: real,B: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ A )
% 8.69/5.00         => ( ( log @ B @ ( root @ N @ A ) )
% 8.69/5.00            = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9190_log__base__root,axiom,
% 8.69/5.00      ! [N: nat,B: real,X: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ B )
% 8.69/5.00         => ( ( log @ ( root @ N @ B ) @ X )
% 8.69/5.00            = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9191_root__powr__inverse,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00         => ( ( root @ N @ X )
% 8.69/5.00            = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9192_cot__gt__zero,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00       => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/5.00         => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9193_tan__cot_H,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 8.69/5.00        = ( cot_real @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9194_arctan__def,axiom,
% 8.69/5.00      ( arctan
% 8.69/5.00      = ( ^ [Y3: real] :
% 8.69/5.00            ( the_real
% 8.69/5.00            @ ^ [X3: real] :
% 8.69/5.00                ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 8.69/5.00                & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/5.00                & ( ( tan_real @ X3 )
% 8.69/5.00                  = Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9195_arcsin__def,axiom,
% 8.69/5.00      ( arcsin
% 8.69/5.00      = ( ^ [Y3: real] :
% 8.69/5.00            ( the_real
% 8.69/5.00            @ ^ [X3: real] :
% 8.69/5.00                ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 8.69/5.00                & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/5.00                & ( ( sin_real @ X3 )
% 8.69/5.00                  = Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9196_signed__take__bit__eq__take__bit__minus,axiom,
% 8.69/5.00      ( bit_ri631733984087533419it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9197_modulo__int__unfold,axiom,
% 8.69/5.00      ! [L2: int,K: int,N: nat,M: nat] :
% 8.69/5.00        ( ( ( ( ( sgn_sgn_int @ L2 )
% 8.69/5.00              = zero_zero_int )
% 8.69/5.00            | ( ( sgn_sgn_int @ K )
% 8.69/5.00              = zero_zero_int )
% 8.69/5.00            | ( N = zero_zero_nat ) )
% 8.69/5.00         => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00            = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 8.69/5.00        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 8.69/5.00                = zero_zero_int )
% 8.69/5.00              | ( ( sgn_sgn_int @ K )
% 8.69/5.00                = zero_zero_int )
% 8.69/5.00              | ( N = zero_zero_nat ) )
% 8.69/5.00         => ( ( ( ( sgn_sgn_int @ K )
% 8.69/5.00                = ( sgn_sgn_int @ L2 ) )
% 8.69/5.00             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00                = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 8.69/5.00            & ( ( ( sgn_sgn_int @ K )
% 8.69/5.00               != ( sgn_sgn_int @ L2 ) )
% 8.69/5.00             => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00                = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 8.69/5.00                  @ ( minus_minus_int
% 8.69/5.00                    @ ( semiri1314217659103216013at_int
% 8.69/5.00                      @ ( times_times_nat @ N
% 8.69/5.00                        @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00                          @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 8.69/5.00                    @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9198_dvd__mult__sgn__iff,axiom,
% 8.69/5.00      ! [L2: int,K: int,R: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 8.69/5.00        = ( ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00          | ( R = zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9199_dvd__sgn__mult__iff,axiom,
% 8.69/5.00      ! [L2: int,R: int,K: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 8.69/5.00        = ( ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00          | ( R = zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9200_mult__sgn__dvd__iff,axiom,
% 8.69/5.00      ! [L2: int,R: int,K: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R ) ) @ K )
% 8.69/5.00        = ( ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00          & ( ( R = zero_zero_int )
% 8.69/5.00           => ( K = zero_zero_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9201_sgn__mult__dvd__iff,axiom,
% 8.69/5.00      ! [R: int,L2: int,K: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L2 ) @ K )
% 8.69/5.00        = ( ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00          & ( ( R = zero_zero_int )
% 8.69/5.00           => ( K = zero_zero_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9202_signed__take__bit__nonnegative__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 8.69/5.00        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9203_signed__take__bit__negative__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 8.69/5.00        = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9204_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 8.69/5.00      ! [W: num,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 8.69/5.00        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9205_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 8.69/5.00      ! [W: num,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 8.69/5.00        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9206_bit__minus__numeral__int_I1_J,axiom,
% 8.69/5.00      ! [W: num,N: num] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.00        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9207_bit__minus__numeral__int_I2_J,axiom,
% 8.69/5.00      ! [W: num,N: num] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.00        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9208_bit__and__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 8.69/5.00        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 8.69/5.00          & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9209_int__sgnE,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ~ ! [N3: nat,L4: int] :
% 8.69/5.00            ( K
% 8.69/5.00           != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9210_div__eq__sgn__abs,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( ( sgn_sgn_int @ K )
% 8.69/5.00          = ( sgn_sgn_int @ L2 ) )
% 8.69/5.00       => ( ( divide_divide_int @ K @ L2 )
% 8.69/5.00          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9211_bit__not__int__iff_H,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 8.69/5.00        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9212_sgn__mod,axiom,
% 8.69/5.00      ! [L2: int,K: int] :
% 8.69/5.00        ( ( L2 != zero_zero_int )
% 8.69/5.00       => ( ~ ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00         => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 8.69/5.00            = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9213_ln__neg__is__const,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/5.00       => ( ( ln_ln_real @ X )
% 8.69/5.00          = ( the_real
% 8.69/5.00            @ ^ [X3: real] : $false ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9214_zsgn__def,axiom,
% 8.69/5.00      ( sgn_sgn_int
% 8.69/5.00      = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9215_div__sgn__abs__cancel,axiom,
% 8.69/5.00      ! [V: int,K: int,L2: int] :
% 8.69/5.00        ( ( V != zero_zero_int )
% 8.69/5.00       => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 8.69/5.00          = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9216_bit__imp__take__bit__positive,axiom,
% 8.69/5.00      ! [N: nat,M: nat,K: int] :
% 8.69/5.00        ( ( ord_less_nat @ N @ M )
% 8.69/5.00       => ( ( bit_se1146084159140164899it_int @ K @ N )
% 8.69/5.00         => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9217_div__dvd__sgn__abs,axiom,
% 8.69/5.00      ! [L2: int,K: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ L2 @ K )
% 8.69/5.00       => ( ( divide_divide_int @ K @ L2 )
% 8.69/5.00          = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9218_bit__concat__bit__iff,axiom,
% 8.69/5.00      ! [M: nat,K: int,L2: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 8.69/5.00        = ( ( ( ord_less_nat @ N @ M )
% 8.69/5.00            & ( bit_se1146084159140164899it_int @ K @ N ) )
% 8.69/5.00          | ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.00            & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9219_signed__take__bit__eq__concat__bit,axiom,
% 8.69/5.00      ( bit_ri631733984087533419it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( bit_concat_bit @ N2 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9220_int__bit__bound,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ~ ! [N3: nat] :
% 8.69/5.00            ( ! [M2: nat] :
% 8.69/5.00                ( ( ord_less_eq_nat @ N3 @ M2 )
% 8.69/5.00               => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 8.69/5.00                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 8.69/5.00           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.69/5.00               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 8.69/5.00                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9221_bit__int__def,axiom,
% 8.69/5.00      ( bit_se1146084159140164899it_int
% 8.69/5.00      = ( ^ [K2: int,N2: nat] :
% 8.69/5.00            ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9222_arccos__def,axiom,
% 8.69/5.00      ( arccos
% 8.69/5.00      = ( ^ [Y3: real] :
% 8.69/5.00            ( the_real
% 8.69/5.00            @ ^ [X3: real] :
% 8.69/5.00                ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 8.69/5.00                & ( ord_less_eq_real @ X3 @ pi )
% 8.69/5.00                & ( ( cos_real @ X3 )
% 8.69/5.00                  = Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9223_eucl__rel__int__remainderI,axiom,
% 8.69/5.00      ! [R: int,L2: int,K: int,Q2: int] :
% 8.69/5.00        ( ( ( sgn_sgn_int @ R )
% 8.69/5.00          = ( sgn_sgn_int @ L2 ) )
% 8.69/5.00       => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 8.69/5.00         => ( ( K
% 8.69/5.00              = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 8.69/5.00           => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9224_eucl__rel__int_Ocases,axiom,
% 8.69/5.00      ! [A12: int,A23: int,A32: product_prod_int_int] :
% 8.69/5.00        ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 8.69/5.00       => ( ( ( A23 = zero_zero_int )
% 8.69/5.00           => ( A32
% 8.69/5.00             != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 8.69/5.00         => ( ! [Q3: int] :
% 8.69/5.00                ( ( A32
% 8.69/5.00                  = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 8.69/5.00               => ( ( A23 != zero_zero_int )
% 8.69/5.00                 => ( A12
% 8.69/5.00                   != ( times_times_int @ Q3 @ A23 ) ) ) )
% 8.69/5.00           => ~ ! [R2: int,Q3: int] :
% 8.69/5.00                  ( ( A32
% 8.69/5.00                    = ( product_Pair_int_int @ Q3 @ R2 ) )
% 8.69/5.00                 => ( ( ( sgn_sgn_int @ R2 )
% 8.69/5.00                      = ( sgn_sgn_int @ A23 ) )
% 8.69/5.00                   => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 8.69/5.00                     => ( A12
% 8.69/5.00                       != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9225_eucl__rel__int_Osimps,axiom,
% 8.69/5.00      ( eucl_rel_int
% 8.69/5.00      = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 8.69/5.00            ( ? [K2: int] :
% 8.69/5.00                ( ( A1 = K2 )
% 8.69/5.00                & ( A22 = zero_zero_int )
% 8.69/5.00                & ( A33
% 8.69/5.00                  = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 8.69/5.00            | ? [L: int,K2: int,Q5: int] :
% 8.69/5.00                ( ( A1 = K2 )
% 8.69/5.00                & ( A22 = L )
% 8.69/5.00                & ( A33
% 8.69/5.00                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 8.69/5.00                & ( L != zero_zero_int )
% 8.69/5.00                & ( K2
% 8.69/5.00                  = ( times_times_int @ Q5 @ L ) ) )
% 8.69/5.00            | ? [R5: int,L: int,K2: int,Q5: int] :
% 8.69/5.00                ( ( A1 = K2 )
% 8.69/5.00                & ( A22 = L )
% 8.69/5.00                & ( A33
% 8.69/5.00                  = ( product_Pair_int_int @ Q5 @ R5 ) )
% 8.69/5.00                & ( ( sgn_sgn_int @ R5 )
% 8.69/5.00                  = ( sgn_sgn_int @ L ) )
% 8.69/5.00                & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 8.69/5.00                & ( K2
% 8.69/5.00                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L ) @ R5 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9226_div__noneq__sgn__abs,axiom,
% 8.69/5.00      ! [L2: int,K: int] :
% 8.69/5.00        ( ( L2 != zero_zero_int )
% 8.69/5.00       => ( ( ( sgn_sgn_int @ K )
% 8.69/5.00           != ( sgn_sgn_int @ L2 ) )
% 8.69/5.00         => ( ( divide_divide_int @ K @ L2 )
% 8.69/5.00            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 8.69/5.00              @ ( zero_n2684676970156552555ol_int
% 8.69/5.00                @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9227_set__bit__eq,axiom,
% 8.69/5.00      ( bit_se7879613467334960850it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] :
% 8.69/5.00            ( plus_plus_int @ K2
% 8.69/5.00            @ ( times_times_int
% 8.69/5.00              @ ( zero_n2684676970156552555ol_int
% 8.69/5.00                @ ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 8.69/5.00              @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9228_unset__bit__eq,axiom,
% 8.69/5.00      ( bit_se4203085406695923979it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9229_pi__half,axiom,
% 8.69/5.00      ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/5.00      = ( the_real
% 8.69/5.00        @ ^ [X3: real] :
% 8.69/5.00            ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 8.69/5.00            & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/5.00            & ( ( cos_real @ X3 )
% 8.69/5.00              = zero_zero_real ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9230_pi__def,axiom,
% 8.69/5.00      ( pi
% 8.69/5.00      = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.69/5.00        @ ( the_real
% 8.69/5.00          @ ^ [X3: real] :
% 8.69/5.00              ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 8.69/5.00              & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.69/5.00              & ( ( cos_real @ X3 )
% 8.69/5.00                = zero_zero_real ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9231_take__bit__Suc__from__most,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 8.69/5.00        = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9232_divide__int__unfold,axiom,
% 8.69/5.00      ! [L2: int,K: int,N: nat,M: nat] :
% 8.69/5.00        ( ( ( ( ( sgn_sgn_int @ L2 )
% 8.69/5.00              = zero_zero_int )
% 8.69/5.00            | ( ( sgn_sgn_int @ K )
% 8.69/5.00              = zero_zero_int )
% 8.69/5.00            | ( N = zero_zero_nat ) )
% 8.69/5.00         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00            = zero_zero_int ) )
% 8.69/5.00        & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 8.69/5.00                = zero_zero_int )
% 8.69/5.00              | ( ( sgn_sgn_int @ K )
% 8.69/5.00                = zero_zero_int )
% 8.69/5.00              | ( N = zero_zero_nat ) )
% 8.69/5.00         => ( ( ( ( sgn_sgn_int @ K )
% 8.69/5.00                = ( sgn_sgn_int @ L2 ) )
% 8.69/5.00             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 8.69/5.00            & ( ( ( sgn_sgn_int @ K )
% 8.69/5.00               != ( sgn_sgn_int @ L2 ) )
% 8.69/5.00             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00                = ( uminus_uminus_int
% 8.69/5.00                  @ ( semiri1314217659103216013at_int
% 8.69/5.00                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 8.69/5.00                      @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9233_modulo__int__def,axiom,
% 8.69/5.00      ( modulo_modulo_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( if_int @ ( L = zero_zero_int ) @ K2
% 8.69/5.00            @ ( if_int
% 8.69/5.00              @ ( ( sgn_sgn_int @ K2 )
% 8.69/5.00                = ( sgn_sgn_int @ L ) )
% 8.69/5.00              @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 8.69/5.00              @ ( times_times_int @ ( sgn_sgn_int @ L )
% 8.69/5.00                @ ( minus_minus_int
% 8.69/5.00                  @ ( times_times_int @ ( abs_abs_int @ L )
% 8.69/5.00                    @ ( zero_n2684676970156552555ol_int
% 8.69/5.00                      @ ~ ( dvd_dvd_int @ L @ K2 ) ) )
% 8.69/5.00                  @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9234_divide__int__def,axiom,
% 8.69/5.00      ( divide_divide_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 8.69/5.00            @ ( if_int
% 8.69/5.00              @ ( ( sgn_sgn_int @ K2 )
% 8.69/5.00                = ( sgn_sgn_int @ L ) )
% 8.69/5.00              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 8.69/5.00              @ ( uminus_uminus_int
% 8.69/5.00                @ ( semiri1314217659103216013at_int
% 8.69/5.00                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 8.69/5.00                    @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00                      @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9235_powr__int,axiom,
% 8.69/5.00      ! [X: real,I: int] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00       => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 8.69/5.00           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 8.69/5.00              = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 8.69/5.00           => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 8.69/5.00              = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9236_zero__le__sgn__iff,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 8.69/5.00        = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9237_sgn__le__0__iff,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 8.69/5.00        = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9238_nat__numeral,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 8.69/5.00        = ( numeral_numeral_nat @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9239_nat__1,axiom,
% 8.69/5.00      ( ( nat2 @ one_one_int )
% 8.69/5.00      = ( suc @ zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9240_nat__le__0,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 8.69/5.00       => ( ( nat2 @ Z )
% 8.69/5.00          = zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9241_nat__0__iff,axiom,
% 8.69/5.00      ! [I: int] :
% 8.69/5.00        ( ( ( nat2 @ I )
% 8.69/5.00          = zero_zero_nat )
% 8.69/5.00        = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9242_zless__nat__conj,axiom,
% 8.69/5.00      ! [W: int,Z: int] :
% 8.69/5.00        ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 8.69/5.00        = ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/5.00          & ( ord_less_int @ W @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9243_nat__neg__numeral,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/5.00        = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9244_nat__zminus__int,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.69/5.00        = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9245_int__nat__eq,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 8.69/5.00            = Z ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00         => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 8.69/5.00            = zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9246_zero__less__nat__eq,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 8.69/5.00        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9247_diff__nat__numeral,axiom,
% 8.69/5.00      ! [V: num,V3: num] :
% 8.69/5.00        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 8.69/5.00        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9248_nat__eq__numeral__power__cancel__iff,axiom,
% 8.69/5.00      ! [Y: int,X: num,N: nat] :
% 8.69/5.00        ( ( ( nat2 @ Y )
% 8.69/5.00          = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 8.69/5.00        = ( Y
% 8.69/5.00          = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9249_numeral__power__eq__nat__cancel__iff,axiom,
% 8.69/5.00      ! [X: num,N: nat,Y: int] :
% 8.69/5.00        ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 8.69/5.00          = ( nat2 @ Y ) )
% 8.69/5.00        = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 8.69/5.00          = Y ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9250_nat__ceiling__le__eq,axiom,
% 8.69/5.00      ! [X: real,A: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 8.69/5.00        = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9251_one__less__nat__eq,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 8.69/5.00        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9252_nat__numeral__diff__1,axiom,
% 8.69/5.00      ! [V: num] :
% 8.69/5.00        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 8.69/5.00        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9253_nat__less__numeral__power__cancel__iff,axiom,
% 8.69/5.00      ! [A: int,X: num,N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 8.69/5.00        = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9254_numeral__power__less__nat__cancel__iff,axiom,
% 8.69/5.00      ! [X: num,N: nat,A: int] :
% 8.69/5.00        ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 8.69/5.00        = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9255_numeral__power__le__nat__cancel__iff,axiom,
% 8.69/5.00      ! [X: num,N: nat,A: int] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 8.69/5.00        = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9256_nat__le__numeral__power__cancel__iff,axiom,
% 8.69/5.00      ! [A: int,X: num,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 8.69/5.00        = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9257_bit__nat__iff,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 8.69/5.00        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00          & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9258_not__bit__Suc__0__Suc,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9259_bit__Suc__0__iff,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/5.00        = ( N = zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9260_nat__zero__as__int,axiom,
% 8.69/5.00      ( zero_zero_nat
% 8.69/5.00      = ( nat2 @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9261_nat__numeral__as__int,axiom,
% 8.69/5.00      ( numeral_numeral_nat
% 8.69/5.00      = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9262_nat__mono,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ X @ Y )
% 8.69/5.00       => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9263_ex__nat,axiom,
% 8.69/5.00      ( ( ^ [P3: nat > $o] :
% 8.69/5.00          ? [X7: nat] : ( P3 @ X7 ) )
% 8.69/5.00      = ( ^ [P4: nat > $o] :
% 8.69/5.00          ? [X3: int] :
% 8.69/5.00            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 8.69/5.00            & ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9264_all__nat,axiom,
% 8.69/5.00      ( ( ^ [P3: nat > $o] :
% 8.69/5.00          ! [X7: nat] : ( P3 @ X7 ) )
% 8.69/5.00      = ( ^ [P4: nat > $o] :
% 8.69/5.00          ! [X3: int] :
% 8.69/5.00            ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 8.69/5.00           => ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9265_eq__nat__nat__iff,axiom,
% 8.69/5.00      ! [Z: int,Z7: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 8.69/5.00         => ( ( ( nat2 @ Z )
% 8.69/5.00              = ( nat2 @ Z7 ) )
% 8.69/5.00            = ( Z = Z7 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9266_nat__one__as__int,axiom,
% 8.69/5.00      ( one_one_nat
% 8.69/5.00      = ( nat2 @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9267_unset__bit__nat__def,axiom,
% 8.69/5.00      ( bit_se4205575877204974255it_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9268_nat__mask__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 8.69/5.00        = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9269_not__bit__Suc__0__numeral,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9270_sgn__root,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 8.69/5.00          = ( sgn_sgn_real @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9271_nat__mono__iff,axiom,
% 8.69/5.00      ! [Z: int,W: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 8.69/5.00          = ( ord_less_int @ W @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9272_zless__nat__eq__int__zless,axiom,
% 8.69/5.00      ! [M: nat,Z: int] :
% 8.69/5.00        ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 8.69/5.00        = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9273_nat__le__iff,axiom,
% 8.69/5.00      ! [X: int,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 8.69/5.00        = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9274_int__eq__iff,axiom,
% 8.69/5.00      ! [M: nat,Z: int] :
% 8.69/5.00        ( ( ( semiri1314217659103216013at_int @ M )
% 8.69/5.00          = Z )
% 8.69/5.00        = ( ( M
% 8.69/5.00            = ( nat2 @ Z ) )
% 8.69/5.00          & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9275_nat__0__le,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 8.69/5.00          = Z ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9276_nat__int__add,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 8.69/5.00        = ( plus_plus_nat @ A @ B ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9277_int__minus,axiom,
% 8.69/5.00      ! [N: nat,M: nat] :
% 8.69/5.00        ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 8.69/5.00        = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9278_nat__abs__mult__distrib,axiom,
% 8.69/5.00      ! [W: int,Z: int] :
% 8.69/5.00        ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 8.69/5.00        = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9279_and__nat__def,axiom,
% 8.69/5.00      ( bit_se727722235901077358nd_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9280_nat__plus__as__int,axiom,
% 8.69/5.00      ( plus_plus_nat
% 8.69/5.00      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9281_nat__times__as__int,axiom,
% 8.69/5.00      ( times_times_nat
% 8.69/5.00      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9282_real__nat__ceiling__ge,axiom,
% 8.69/5.00      ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9283_nat__minus__as__int,axiom,
% 8.69/5.00      ( minus_minus_nat
% 8.69/5.00      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9284_nat__div__as__int,axiom,
% 8.69/5.00      ( divide_divide_nat
% 8.69/5.00      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9285_nat__mod__as__int,axiom,
% 8.69/5.00      ( modulo_modulo_nat
% 8.69/5.00      = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9286_cis__Arg,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( Z != zero_zero_complex )
% 8.69/5.00       => ( ( cis @ ( arg @ Z ) )
% 8.69/5.00          = ( sgn_sgn_complex @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9287_sgn__real__def,axiom,
% 8.69/5.00      ( sgn_sgn_real
% 8.69/5.00      = ( ^ [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 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9288_nat__less__eq__zless,axiom,
% 8.69/5.00      ! [W: int,Z: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00       => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 8.69/5.00          = ( ord_less_int @ W @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9289_nat__le__eq__zle,axiom,
% 8.69/5.00      ! [W: int,Z: int] :
% 8.69/5.00        ( ( ( ord_less_int @ zero_zero_int @ W )
% 8.69/5.00          | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 8.69/5.00       => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 8.69/5.00          = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9290_nat__eq__iff,axiom,
% 8.69/5.00      ! [W: int,M: nat] :
% 8.69/5.00        ( ( ( nat2 @ W )
% 8.69/5.00          = M )
% 8.69/5.00        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00           => ( W
% 8.69/5.00              = ( semiri1314217659103216013at_int @ M ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00           => ( M = zero_zero_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9291_nat__eq__iff2,axiom,
% 8.69/5.00      ! [M: nat,W: int] :
% 8.69/5.00        ( ( M
% 8.69/5.00          = ( nat2 @ W ) )
% 8.69/5.00        = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00           => ( W
% 8.69/5.00              = ( semiri1314217659103216013at_int @ M ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00           => ( M = zero_zero_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9292_split__nat,axiom,
% 8.69/5.00      ! [P: nat > $o,I: int] :
% 8.69/5.00        ( ( P @ ( nat2 @ I ) )
% 8.69/5.00        = ( ! [N2: nat] :
% 8.69/5.00              ( ( I
% 8.69/5.00                = ( semiri1314217659103216013at_int @ N2 ) )
% 8.69/5.00             => ( P @ N2 ) )
% 8.69/5.00          & ( ( ord_less_int @ I @ zero_zero_int )
% 8.69/5.00           => ( P @ zero_zero_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9293_le__nat__iff,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00       => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 8.69/5.00          = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9294_nat__add__distrib,axiom,
% 8.69/5.00      ! [Z: int,Z7: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 8.69/5.00         => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 8.69/5.00            = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9295_nat__mult__distrib,axiom,
% 8.69/5.00      ! [Z: int,Z7: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 8.69/5.00          = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9296_Suc__as__int,axiom,
% 8.69/5.00      ( suc
% 8.69/5.00      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9297_nat__diff__distrib,axiom,
% 8.69/5.00      ! [Z7: int,Z: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 8.69/5.00       => ( ( ord_less_eq_int @ Z7 @ Z )
% 8.69/5.00         => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 8.69/5.00            = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9298_nat__diff__distrib_H,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00         => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 8.69/5.00            = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9299_nat__abs__triangle__ineq,axiom,
% 8.69/5.00      ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9300_nat__div__distrib,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 8.69/5.00          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9301_nat__div__distrib_H,axiom,
% 8.69/5.00      ! [Y: int,X: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00       => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 8.69/5.00          = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9302_nat__power__eq,axiom,
% 8.69/5.00      ! [Z: int,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 8.69/5.00          = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9303_nat__floor__neg,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.69/5.00       => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.69/5.00          = zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9304_nat__mod__distrib,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00         => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 8.69/5.00            = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9305_div__abs__eq__div__nat,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 8.69/5.00        = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9306_floor__eq3,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 8.69/5.00       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 8.69/5.00         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.69/5.00            = N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9307_le__nat__floor,axiom,
% 8.69/5.00      ! [X: nat,A: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 8.69/5.00       => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9308_mod__abs__eq__div__nat,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 8.69/5.00        = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9309_nat__take__bit__eq,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00       => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 8.69/5.00          = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9310_take__bit__nat__eq,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00       => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 8.69/5.00          = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9311_nat__2,axiom,
% 8.69/5.00      ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/5.00      = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9312_sgn__power__injE,axiom,
% 8.69/5.00      ! [A: real,N: nat,X: real,B: real] :
% 8.69/5.00        ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 8.69/5.00          = X )
% 8.69/5.00       => ( ( X
% 8.69/5.00            = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 8.69/5.00         => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00           => ( A = B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9313_Suc__nat__eq__nat__zadd1,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00       => ( ( suc @ ( nat2 @ Z ) )
% 8.69/5.00          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9314_nat__less__iff,axiom,
% 8.69/5.00      ! [W: int,M: nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ W )
% 8.69/5.00       => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 8.69/5.00          = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9315_nat__mult__distrib__neg,axiom,
% 8.69/5.00      ! [Z: int,Z7: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 8.69/5.00       => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 8.69/5.00          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9316_nat__abs__int__diff,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( ( ord_less_eq_nat @ A @ B )
% 8.69/5.00         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.69/5.00            = ( minus_minus_nat @ B @ A ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_nat @ A @ B )
% 8.69/5.00         => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.69/5.00            = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9317_floor__eq4,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 8.69/5.00       => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 8.69/5.00         => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.69/5.00            = N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9318_diff__nat__eq__if,axiom,
% 8.69/5.00      ! [Z7: int,Z: int] :
% 8.69/5.00        ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 8.69/5.00         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 8.69/5.00            = ( nat2 @ Z ) ) )
% 8.69/5.00        & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 8.69/5.00         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 8.69/5.00            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9319_bit__nat__def,axiom,
% 8.69/5.00      ( bit_se1148574629649215175it_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] :
% 8.69/5.00            ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9320_root__sgn__power,axiom,
% 8.69/5.00      ! [N: nat,Y: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 8.69/5.00          = Y ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9321_sgn__power__root,axiom,
% 8.69/5.00      ! [N: nat,X: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 8.69/5.00          = X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9322_nat__dvd__iff,axiom,
% 8.69/5.00      ! [Z: int,M: nat] :
% 8.69/5.00        ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 8.69/5.00        = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00           => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 8.69/5.00           => ( M = zero_zero_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9323_cis__Arg__unique,axiom,
% 8.69/5.00      ! [Z: complex,X: real] :
% 8.69/5.00        ( ( ( sgn_sgn_complex @ Z )
% 8.69/5.00          = ( cis @ X ) )
% 8.69/5.00       => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 8.69/5.00         => ( ( ord_less_eq_real @ X @ pi )
% 8.69/5.00           => ( ( arg @ Z )
% 8.69/5.00              = X ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9324_split__root,axiom,
% 8.69/5.00      ! [P: real > $o,N: nat,X: real] :
% 8.69/5.00        ( ( P @ ( root @ N @ X ) )
% 8.69/5.00        = ( ( ( N = zero_zero_nat )
% 8.69/5.00           => ( P @ zero_zero_real ) )
% 8.69/5.00          & ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00           => ! [Y3: real] :
% 8.69/5.00                ( ( ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) )
% 8.69/5.00                  = X )
% 8.69/5.00               => ( P @ Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9325_Arg__correct,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( Z != zero_zero_complex )
% 8.69/5.00       => ( ( ( sgn_sgn_complex @ Z )
% 8.69/5.00            = ( cis @ ( arg @ Z ) ) )
% 8.69/5.00          & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 8.69/5.00          & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9326_even__nat__iff,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 8.69/5.00          = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9327_powr__real__of__int,axiom,
% 8.69/5.00      ! [X: real,N: int] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00       => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 8.69/5.00           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 8.69/5.00              = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 8.69/5.00           => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 8.69/5.00              = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9328_arctan__inverse,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( X != zero_zero_real )
% 8.69/5.00       => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 8.69/5.00          = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9329_Arg__def,axiom,
% 8.69/5.00      ( arg
% 8.69/5.00      = ( ^ [Z3: complex] :
% 8.69/5.00            ( if_real @ ( Z3 = zero_zero_complex ) @ zero_zero_real
% 8.69/5.00            @ ( fChoice_real
% 8.69/5.00              @ ^ [A3: real] :
% 8.69/5.00                  ( ( ( sgn_sgn_complex @ Z3 )
% 8.69/5.00                    = ( cis @ A3 ) )
% 8.69/5.00                  & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 8.69/5.00                  & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9330_or__int__unfold,axiom,
% 8.69/5.00      ( bit_se1409905431419307370or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( if_int
% 8.69/5.00            @ ( ( K2
% 8.69/5.00                = ( uminus_uminus_int @ one_one_int ) )
% 8.69/5.00              | ( L
% 8.69/5.00                = ( uminus_uminus_int @ one_one_int ) ) )
% 8.69/5.00            @ ( uminus_uminus_int @ one_one_int )
% 8.69/5.00            @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9331_or__nonnegative__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 8.69/5.00        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00          & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9332_or__negative__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 8.69/5.00        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.69/5.00          | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9333_or__minus__numerals_I6_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9334_or__minus__numerals_I2_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9335_bit__or__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 8.69/5.00        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 8.69/5.00          | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9336_or__greater__eq,axiom,
% 8.69/5.00      ! [L2: int,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 8.69/5.00       => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9337_OR__lower,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9338_plus__and__or,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_int @ X @ Y ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9339_OR__upper,axiom,
% 8.69/5.00      ! [X: int,N: nat,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/5.00         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/5.00           => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9340_or__int__rec,axiom,
% 8.69/5.00      ( bit_se1409905431419307370or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( plus_plus_int
% 8.69/5.00            @ ( zero_n2684676970156552555ol_int
% 8.69/5.00              @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.69/5.00                | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 8.69/5.00            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9341_or__minus__numerals_I5_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9342_or__minus__numerals_I1_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9343_cis__multiple__2pi,axiom,
% 8.69/5.00      ! [N: real] :
% 8.69/5.00        ( ( member_real @ N @ ring_1_Ints_real )
% 8.69/5.00       => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.69/5.00          = one_one_complex ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9344_or__nat__numerals_I2_J,axiom,
% 8.69/5.00      ! [Y: num] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9345_or__nat__numerals_I4_J,axiom,
% 8.69/5.00      ! [X: num] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9346_or__nat__numerals_I3_J,axiom,
% 8.69/5.00      ! [X: num] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9347_or__nat__numerals_I1_J,axiom,
% 8.69/5.00      ! [Y: num] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9348_or__minus__numerals_I8_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9349_or__minus__numerals_I4_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9350_or__minus__numerals_I7_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9351_or__minus__numerals_I3_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9352_or__not__num__neg_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( bit_or_not_num_neg @ one @ one )
% 8.69/5.00      = one ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9353_or__not__num__neg_Osimps_I4_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 8.69/5.00        = ( bit0 @ one ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9354_or__not__num__neg_Osimps_I6_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 8.69/5.00        = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9355_or__not__num__neg_Osimps_I7_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 8.69/5.00        = one ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9356_or__not__num__neg_Osimps_I3_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 8.69/5.00        = ( bit1 @ M ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9357_or__not__num__neg_Osimps_I5_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 8.69/5.00        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9358_or__not__num__neg_Osimps_I9_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 8.69/5.00        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9359_or__nat__def,axiom,
% 8.69/5.00      ( bit_se1412395901928357646or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9360_or__not__num__neg_Osimps_I2_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 8.69/5.00        = ( bit1 @ M ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9361_or__not__num__neg_Osimps_I8_J,axiom,
% 8.69/5.00      ! [N: num,M: num] :
% 8.69/5.00        ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 8.69/5.00        = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9362_sin__times__pi__eq__0,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00        = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9363_or__not__num__neg_Oelims,axiom,
% 8.69/5.00      ! [X: num,Xa2: num,Y: num] :
% 8.69/5.00        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( X = one )
% 8.69/5.00           => ( ( Xa2 = one )
% 8.69/5.00             => ( Y != one ) ) )
% 8.69/5.00         => ( ( ( X = one )
% 8.69/5.00             => ! [M4: num] :
% 8.69/5.00                  ( ( Xa2
% 8.69/5.00                    = ( bit0 @ M4 ) )
% 8.69/5.00                 => ( Y
% 8.69/5.00                   != ( bit1 @ M4 ) ) ) )
% 8.69/5.00           => ( ( ( X = one )
% 8.69/5.00               => ! [M4: num] :
% 8.69/5.00                    ( ( Xa2
% 8.69/5.00                      = ( bit1 @ M4 ) )
% 8.69/5.00                   => ( Y
% 8.69/5.00                     != ( bit1 @ M4 ) ) ) )
% 8.69/5.00             => ( ( ? [N3: num] :
% 8.69/5.00                      ( X
% 8.69/5.00                      = ( bit0 @ N3 ) )
% 8.69/5.00                 => ( ( Xa2 = one )
% 8.69/5.00                   => ( Y
% 8.69/5.00                     != ( bit0 @ one ) ) ) )
% 8.69/5.00               => ( ! [N3: num] :
% 8.69/5.00                      ( ( X
% 8.69/5.00                        = ( bit0 @ N3 ) )
% 8.69/5.00                     => ! [M4: num] :
% 8.69/5.00                          ( ( Xa2
% 8.69/5.00                            = ( bit0 @ M4 ) )
% 8.69/5.00                         => ( Y
% 8.69/5.00                           != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 8.69/5.00                 => ( ! [N3: num] :
% 8.69/5.00                        ( ( X
% 8.69/5.00                          = ( bit0 @ N3 ) )
% 8.69/5.00                       => ! [M4: num] :
% 8.69/5.00                            ( ( Xa2
% 8.69/5.00                              = ( bit1 @ M4 ) )
% 8.69/5.00                           => ( Y
% 8.69/5.00                             != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 8.69/5.00                   => ( ( ? [N3: num] :
% 8.69/5.00                            ( X
% 8.69/5.00                            = ( bit1 @ N3 ) )
% 8.69/5.00                       => ( ( Xa2 = one )
% 8.69/5.00                         => ( Y != one ) ) )
% 8.69/5.00                     => ( ! [N3: num] :
% 8.69/5.00                            ( ( X
% 8.69/5.00                              = ( bit1 @ N3 ) )
% 8.69/5.00                           => ! [M4: num] :
% 8.69/5.00                                ( ( Xa2
% 8.69/5.00                                  = ( bit0 @ M4 ) )
% 8.69/5.00                               => ( Y
% 8.69/5.00                                 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 8.69/5.00                       => ~ ! [N3: num] :
% 8.69/5.00                              ( ( X
% 8.69/5.00                                = ( bit1 @ N3 ) )
% 8.69/5.00                             => ! [M4: num] :
% 8.69/5.00                                  ( ( Xa2
% 8.69/5.00                                    = ( bit1 @ M4 ) )
% 8.69/5.00                                 => ( Y
% 8.69/5.00                                   != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9364_sin__integer__2pi,axiom,
% 8.69/5.00      ! [N: real] :
% 8.69/5.00        ( ( member_real @ N @ ring_1_Ints_real )
% 8.69/5.00       => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9365_cos__integer__2pi,axiom,
% 8.69/5.00      ! [N: real] :
% 8.69/5.00        ( ( member_real @ N @ ring_1_Ints_real )
% 8.69/5.00       => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.69/5.00          = one_one_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9366_or__Suc__0__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9367_Suc__0__or__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/5.00        = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9368_or__nat__rec,axiom,
% 8.69/5.00      ( bit_se1412395901928357646or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] :
% 8.69/5.00            ( plus_plus_nat
% 8.69/5.00            @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00              @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 8.69/5.00                | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/5.00            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9369_or__nat__unfold,axiom,
% 8.69/5.00      ( bit_se1412395901928357646or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9370_or__not__num__neg_Opelims,axiom,
% 8.69/5.00      ! [X: num,Xa2: num,Y: num] :
% 8.69/5.00        ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 8.69/5.00         => ( ( ( X = one )
% 8.69/5.00             => ( ( Xa2 = one )
% 8.69/5.00               => ( ( Y = one )
% 8.69/5.00                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 8.69/5.00           => ( ( ( X = one )
% 8.69/5.00               => ! [M4: num] :
% 8.69/5.00                    ( ( Xa2
% 8.69/5.00                      = ( bit0 @ M4 ) )
% 8.69/5.00                   => ( ( Y
% 8.69/5.00                        = ( bit1 @ M4 ) )
% 8.69/5.00                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 8.69/5.00             => ( ( ( X = one )
% 8.69/5.00                 => ! [M4: num] :
% 8.69/5.00                      ( ( Xa2
% 8.69/5.00                        = ( bit1 @ M4 ) )
% 8.69/5.00                     => ( ( Y
% 8.69/5.00                          = ( bit1 @ M4 ) )
% 8.69/5.00                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 8.69/5.00               => ( ! [N3: num] :
% 8.69/5.00                      ( ( X
% 8.69/5.00                        = ( bit0 @ N3 ) )
% 8.69/5.00                     => ( ( Xa2 = one )
% 8.69/5.00                       => ( ( Y
% 8.69/5.00                            = ( bit0 @ one ) )
% 8.69/5.00                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 8.69/5.00                 => ( ! [N3: num] :
% 8.69/5.00                        ( ( X
% 8.69/5.00                          = ( bit0 @ N3 ) )
% 8.69/5.00                       => ! [M4: num] :
% 8.69/5.00                            ( ( Xa2
% 8.69/5.00                              = ( bit0 @ M4 ) )
% 8.69/5.00                           => ( ( Y
% 8.69/5.00                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 8.69/5.00                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 8.69/5.00                   => ( ! [N3: num] :
% 8.69/5.00                          ( ( X
% 8.69/5.00                            = ( bit0 @ N3 ) )
% 8.69/5.00                         => ! [M4: num] :
% 8.69/5.00                              ( ( Xa2
% 8.69/5.00                                = ( bit1 @ M4 ) )
% 8.69/5.00                             => ( ( Y
% 8.69/5.00                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 8.69/5.00                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 8.69/5.00                     => ( ! [N3: num] :
% 8.69/5.00                            ( ( X
% 8.69/5.00                              = ( bit1 @ N3 ) )
% 8.69/5.00                           => ( ( Xa2 = one )
% 8.69/5.00                             => ( ( Y = one )
% 8.69/5.00                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 8.69/5.00                       => ( ! [N3: num] :
% 8.69/5.00                              ( ( X
% 8.69/5.00                                = ( bit1 @ N3 ) )
% 8.69/5.00                             => ! [M4: num] :
% 8.69/5.00                                  ( ( Xa2
% 8.69/5.00                                    = ( bit0 @ M4 ) )
% 8.69/5.00                                 => ( ( Y
% 8.69/5.00                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 8.69/5.00                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 8.69/5.00                         => ~ ! [N3: num] :
% 8.69/5.00                                ( ( X
% 8.69/5.00                                  = ( bit1 @ N3 ) )
% 8.69/5.00                               => ! [M4: num] :
% 8.69/5.00                                    ( ( Xa2
% 8.69/5.00                                      = ( bit1 @ M4 ) )
% 8.69/5.00                                   => ( ( Y
% 8.69/5.00                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 8.69/5.00                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9371_xor__Suc__0__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/5.00          @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9372_Suc__0__xor__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/5.00        = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/5.00          @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9373_xor__nat__numerals_I1_J,axiom,
% 8.69/5.00      ! [Y: num] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9374_xor__nat__numerals_I2_J,axiom,
% 8.69/5.00      ! [Y: num] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9375_xor__nat__numerals_I3_J,axiom,
% 8.69/5.00      ! [X: num] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9376_xor__nat__numerals_I4_J,axiom,
% 8.69/5.00      ! [X: num] :
% 8.69/5.00        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9377_xor__nat__unfold,axiom,
% 8.69/5.00      ( bit_se6528837805403552850or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9378_xor__nat__rec,axiom,
% 8.69/5.00      ( bit_se6528837805403552850or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] :
% 8.69/5.00            ( plus_plus_nat
% 8.69/5.00            @ ( zero_n2687167440665602831ol_nat
% 8.69/5.00              @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 8.69/5.00               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 8.69/5.00            @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9379_horner__sum__of__bool__2__less,axiom,
% 8.69/5.00      ! [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 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9380_push__bit__nonnegative__int__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 8.69/5.00        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9381_push__bit__negative__int__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 8.69/5.00        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9382_concat__bit__of__zero__1,axiom,
% 8.69/5.00      ! [N: nat,L2: int] :
% 8.69/5.00        ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 8.69/5.00        = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9383_xor__nonnegative__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 8.69/5.00        = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 8.69/5.00          = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9384_xor__negative__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 8.69/5.00        = ( ( ord_less_int @ K @ zero_zero_int )
% 8.69/5.00         != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9385_push__bit__of__Suc__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9386_bit__xor__int__iff,axiom,
% 8.69/5.00      ! [K: int,L2: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 8.69/5.00        = ( ( bit_se1146084159140164899it_int @ K @ N )
% 8.69/5.00         != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9387_flip__bit__int__def,axiom,
% 8.69/5.00      ( bit_se2159334234014336723it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9388_push__bit__nat__eq,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 8.69/5.00        = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9389_XOR__lower,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00         => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9390_set__bit__nat__def,axiom,
% 8.69/5.00      ( bit_se7882103937844011126it_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9391_flip__bit__nat__def,axiom,
% 8.69/5.00      ( bit_se2161824704523386999it_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9392_bit__push__bit__iff__int,axiom,
% 8.69/5.00      ! [M: nat,K: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 8.69/5.00        = ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.00          & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9393_xor__nat__def,axiom,
% 8.69/5.00      ( bit_se6528837805403552850or_nat
% 8.69/5.00      = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9394_bit__push__bit__iff__nat,axiom,
% 8.69/5.00      ! [M: nat,Q2: nat,N: nat] :
% 8.69/5.00        ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 8.69/5.00        = ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.00          & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9395_concat__bit__eq,axiom,
% 8.69/5.00      ( bit_concat_bit
% 8.69/5.00      = ( ^ [N2: nat,K2: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9396_concat__bit__def,axiom,
% 8.69/5.00      ( bit_concat_bit
% 8.69/5.00      = ( ^ [N2: nat,K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9397_set__bit__int__def,axiom,
% 8.69/5.00      ( bit_se7879613467334960850it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9398_push__bit__nat__def,axiom,
% 8.69/5.00      ( bit_se547839408752420682it_nat
% 8.69/5.00      = ( ^ [N2: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9399_push__bit__int__def,axiom,
% 8.69/5.00      ( bit_se545348938243370406it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9400_push__bit__minus__one,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9401_XOR__upper,axiom,
% 8.69/5.00      ! [X: int,N: nat,Y: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00       => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/5.00         => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.69/5.00           => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9402_xor__int__rec,axiom,
% 8.69/5.00      ( bit_se6526347334894502574or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( plus_plus_int
% 8.69/5.00            @ ( zero_n2684676970156552555ol_int
% 8.69/5.00              @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 8.69/5.00               != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 8.69/5.00            @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9403_xor__int__unfold,axiom,
% 8.69/5.00      ( bit_se6526347334894502574or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] :
% 8.69/5.00            ( if_int
% 8.69/5.00            @ ( K2
% 8.69/5.00              = ( uminus_uminus_int @ one_one_int ) )
% 8.69/5.00            @ ( bit_ri7919022796975470100ot_int @ L )
% 8.69/5.00            @ ( if_int
% 8.69/5.00              @ ( L
% 8.69/5.00                = ( uminus_uminus_int @ one_one_int ) )
% 8.69/5.00              @ ( bit_ri7919022796975470100ot_int @ K2 )
% 8.69/5.00              @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9404_Sum__Ico__nat,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( groups3542108847815614940at_nat
% 8.69/5.00          @ ^ [X3: nat] : X3
% 8.69/5.00          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 8.69/5.00        = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9405_finite__atLeastLessThan,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9406_not__negative__int__iff,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 8.69/5.00        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9407_not__nonnegative__int__iff,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 8.69/5.00        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9408_atLeastLessThan__singleton,axiom,
% 8.69/5.00      ! [M: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 8.69/5.00        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9409_or__minus__minus__numerals,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9410_and__minus__minus__numerals,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9411_bit__not__int__iff,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 8.69/5.00        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9412_all__nat__less__eq,axiom,
% 8.69/5.00      ! [N: nat,P: nat > $o] :
% 8.69/5.00        ( ( ! [M3: nat] :
% 8.69/5.00              ( ( ord_less_nat @ M3 @ N )
% 8.69/5.00             => ( P @ M3 ) ) )
% 8.69/5.00        = ( ! [X3: nat] :
% 8.69/5.00              ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.69/5.00             => ( P @ X3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9413_ex__nat__less__eq,axiom,
% 8.69/5.00      ! [N: nat,P: nat > $o] :
% 8.69/5.00        ( ( ? [M3: nat] :
% 8.69/5.00              ( ( ord_less_nat @ M3 @ N )
% 8.69/5.00              & ( P @ M3 ) ) )
% 8.69/5.00        = ( ? [X3: nat] :
% 8.69/5.00              ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.69/5.00              & ( P @ X3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9414_atLeastLessThanSuc__atLeastAtMost,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 8.69/5.00        = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9415_lessThan__atLeast0,axiom,
% 8.69/5.00      ( set_ord_lessThan_nat
% 8.69/5.00      = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9416_atLeastLessThan0,axiom,
% 8.69/5.00      ! [M: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 8.69/5.00        = bot_bot_set_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9417_or__int__def,axiom,
% 8.69/5.00      ( bit_se1409905431419307370or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9418_not__int__def,axiom,
% 8.69/5.00      ( bit_ri7919022796975470100ot_int
% 8.69/5.00      = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9419_and__not__numerals_I1_J,axiom,
% 8.69/5.00      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00      = zero_zero_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9420_or__not__numerals_I1_J,axiom,
% 8.69/5.00      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9421_atLeast0__lessThan__Suc,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.69/5.00        = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9422_unset__bit__int__def,axiom,
% 8.69/5.00      ( bit_se4203085406695923979it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9423_xor__int__def,axiom,
% 8.69/5.00      ( bit_se6526347334894502574or_int
% 8.69/5.00      = ( ^ [K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9424_subset__eq__atLeast0__lessThan__finite,axiom,
% 8.69/5.00      ! [N4: set_nat,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.69/5.00       => ( finite_finite_nat @ N4 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9425_not__int__div__2,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9426_even__not__iff__int,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 8.69/5.00        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9427_and__not__numerals_I4_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9428_and__not__numerals_I2_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = one_one_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9429_or__not__numerals_I2_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9430_or__not__numerals_I4_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9431_bit__minus__int__iff,axiom,
% 8.69/5.00      ! [K: int,N: nat] :
% 8.69/5.00        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 8.69/5.00        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9432_int__numeral__or__not__num__neg,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9433_int__numeral__not__or__num__neg,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9434_numeral__or__not__num__eq,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9435_atLeastLessThanSuc,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.00         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 8.69/5.00            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_nat @ M @ N )
% 8.69/5.00         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 8.69/5.00            = bot_bot_set_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9436_prod__Suc__Suc__fact,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.69/5.00        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9437_prod__Suc__fact,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.69/5.00        = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9438_and__not__numerals_I5_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9439_and__not__numerals_I7_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9440_or__not__numerals_I3_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9441_and__not__numerals_I3_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = zero_zero_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9442_or__not__numerals_I7_J,axiom,
% 8.69/5.00      ! [M: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9443_atLeastLessThan__nat__numeral,axiom,
% 8.69/5.00      ! [M: nat,K: num] :
% 8.69/5.00        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 8.69/5.00         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 8.69/5.00            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 8.69/5.00         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 8.69/5.00            = bot_bot_set_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9444_and__not__numerals_I9_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9445_and__not__numerals_I6_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9446_or__not__numerals_I6_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9447_or__not__numerals_I5_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9448_atLeast1__lessThan__eq__remove0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.69/5.00        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9449_and__not__numerals_I8_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9450_or__not__numerals_I9_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.00        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9451_or__not__numerals_I8_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.00        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9452_not__int__rec,axiom,
% 8.69/5.00      ( bit_ri7919022796975470100ot_int
% 8.69/5.00      = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9453_sum__power2,axiom,
% 8.69/5.00      ! [K: nat] :
% 8.69/5.00        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 8.69/5.00        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9454_Chebyshev__sum__upper__nat,axiom,
% 8.69/5.00      ! [N: nat,A: nat > nat,B: nat > nat] :
% 8.69/5.00        ( ! [I4: nat,J2: nat] :
% 8.69/5.00            ( ( ord_less_eq_nat @ I4 @ J2 )
% 8.69/5.00           => ( ( ord_less_nat @ J2 @ N )
% 8.69/5.00             => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 8.69/5.00       => ( ! [I4: nat,J2: nat] :
% 8.69/5.00              ( ( ord_less_eq_nat @ I4 @ J2 )
% 8.69/5.00             => ( ( ord_less_nat @ J2 @ N )
% 8.69/5.00               => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 8.69/5.00         => ( ord_less_eq_nat
% 8.69/5.00            @ ( times_times_nat @ N
% 8.69/5.00              @ ( groups3542108847815614940at_nat
% 8.69/5.00                @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 8.69/5.00                @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 8.69/5.00            @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9455_finite__atLeastLessThan__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9456_finite__atLeastZeroLessThan__int,axiom,
% 8.69/5.00      ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9457_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 8.69/5.00        = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9458_Cauchy__iff2,axiom,
% 8.69/5.00      ( topolo4055970368930404560y_real
% 8.69/5.00      = ( ^ [X2: nat > real] :
% 8.69/5.00          ! [J3: nat] :
% 8.69/5.00          ? [M8: nat] :
% 8.69/5.00          ! [M3: nat] :
% 8.69/5.00            ( ( ord_less_eq_nat @ M8 @ M3 )
% 8.69/5.00           => ! [N2: nat] :
% 8.69/5.00                ( ( ord_less_eq_nat @ M8 @ N2 )
% 8.69/5.00               => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X2 @ M3 ) @ ( X2 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9459_VEBT_Osize_I3_J,axiom,
% 8.69/5.00      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.69/5.00        ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.69/5.00        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9460_VEBT_Osize__gen_I1_J,axiom,
% 8.69/5.00      ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.69/5.00        ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.69/5.00        = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9461_valid__eq,axiom,
% 8.69/5.00      vEBT_VEBT_valid = vEBT_invar_vebt ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9462_valid__eq1,axiom,
% 8.69/5.00      ! [T: vEBT_VEBT,D: nat] :
% 8.69/5.00        ( ( vEBT_invar_vebt @ T @ D )
% 8.69/5.00       => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9463_valid__eq2,axiom,
% 8.69/5.00      ! [T: vEBT_VEBT,D: nat] :
% 8.69/5.00        ( ( vEBT_VEBT_valid @ T @ D )
% 8.69/5.00       => ( vEBT_invar_vebt @ T @ D ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9464_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 8.69/5.00      ! [Uu: $o,Uv: $o,D: nat] :
% 8.69/5.00        ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 8.69/5.00        = ( D = one_one_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9465_VEBT_Osize__gen_I2_J,axiom,
% 8.69/5.00      ! [X21: $o,X222: $o] :
% 8.69/5.00        ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 8.69/5.00        = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9466_Code__Target__Int_Opositive__def,axiom,
% 8.69/5.00      code_Target_positive = numeral_numeral_int ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9467_csqrt_Osimps_I1_J,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( re @ ( csqrt @ Z ) )
% 8.69/5.00        = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9468_complex__Re__numeral,axiom,
% 8.69/5.00      ! [V: num] :
% 8.69/5.00        ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 8.69/5.00        = ( numeral_numeral_real @ V ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9469_Re__divide__numeral,axiom,
% 8.69/5.00      ! [Z: complex,W: num] :
% 8.69/5.00        ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/5.00        = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9470_cos__Arg__i__mult__zero,axiom,
% 8.69/5.00      ! [Y: complex] :
% 8.69/5.00        ( ( Y != zero_zero_complex )
% 8.69/5.00       => ( ( ( re @ Y )
% 8.69/5.00            = zero_zero_real )
% 8.69/5.00         => ( ( cos_real @ ( arg @ Y ) )
% 8.69/5.00            = zero_zero_real ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9471_imaginary__unit_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( re @ imaginary_unit )
% 8.69/5.00      = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9472_complex__Re__le__cmod,axiom,
% 8.69/5.00      ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9473_zero__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( re @ zero_zero_complex )
% 8.69/5.00      = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9474_one__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( re @ one_one_complex )
% 8.69/5.00      = one_one_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9475_plus__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9476_scaleR__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ! [R: real,X: complex] :
% 8.69/5.00        ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 8.69/5.00        = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9477_minus__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 8.69/5.00        = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9478_abs__Re__le__cmod,axiom,
% 8.69/5.00      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9479_Re__csqrt,axiom,
% 8.69/5.00      ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9480_cmod__plus__Re__le__0__iff,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 8.69/5.00        = ( ( re @ Z )
% 8.69/5.00          = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9481_cos__n__Re__cis__pow__n,axiom,
% 8.69/5.00      ! [N: nat,A: real] :
% 8.69/5.00        ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.69/5.00        = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9482_csqrt_Ocode,axiom,
% 8.69/5.00      ( csqrt
% 8.69/5.00      = ( ^ [Z3: complex] :
% 8.69/5.00            ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/5.00            @ ( times_times_real
% 8.69/5.00              @ ( if_real
% 8.69/5.00                @ ( ( im @ Z3 )
% 8.69/5.00                  = zero_zero_real )
% 8.69/5.00                @ one_one_real
% 8.69/5.00                @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 8.69/5.00              @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9483_csqrt_Osimps_I2_J,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( im @ ( csqrt @ Z ) )
% 8.69/5.00        = ( times_times_real
% 8.69/5.00          @ ( if_real
% 8.69/5.00            @ ( ( im @ Z )
% 8.69/5.00              = zero_zero_real )
% 8.69/5.00            @ one_one_real
% 8.69/5.00            @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 8.69/5.00          @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9484_csqrt__of__real__nonpos,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( ( im @ X )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 8.69/5.00         => ( ( csqrt @ X )
% 8.69/5.00            = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9485_complex__Im__fact,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9486_complex__Im__of__int,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9487_complex__Im__of__nat,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9488_Im__complex__of__real,axiom,
% 8.69/5.00      ! [Z: real] :
% 8.69/5.00        ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9489_Im__power__real,axiom,
% 8.69/5.00      ! [X: complex,N: nat] :
% 8.69/5.00        ( ( ( im @ X )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( im @ ( power_power_complex @ X @ N ) )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9490_complex__Im__numeral,axiom,
% 8.69/5.00      ! [V: num] :
% 8.69/5.00        ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9491_Im__i__times,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 8.69/5.00        = ( re @ Z ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9492_Re__power__real,axiom,
% 8.69/5.00      ! [X: complex,N: nat] :
% 8.69/5.00        ( ( ( im @ X )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( re @ ( power_power_complex @ X @ N ) )
% 8.69/5.00          = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9493_Re__i__times,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 8.69/5.00        = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9494_Im__divide__numeral,axiom,
% 8.69/5.00      ! [Z: complex,W: num] :
% 8.69/5.00        ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/5.00        = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9495_csqrt__of__real__nonneg,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( ( im @ X )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 8.69/5.00         => ( ( csqrt @ X )
% 8.69/5.00            = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9496_csqrt__minus,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 8.69/5.00          | ( ( ( im @ X )
% 8.69/5.00              = zero_zero_real )
% 8.69/5.00            & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 8.69/5.00       => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 8.69/5.00          = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9497_imaginary__unit_Osimps_I2_J,axiom,
% 8.69/5.00      ( ( im @ imaginary_unit )
% 8.69/5.00      = one_one_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9498_zero__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ( ( im @ zero_zero_complex )
% 8.69/5.00      = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9499_one__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ( ( im @ one_one_complex )
% 8.69/5.00      = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9500_plus__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9501_scaleR__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ! [R: real,X: complex] :
% 8.69/5.00        ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 8.69/5.00        = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9502_minus__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 8.69/5.00        = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9503_complex__is__Int__iff,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( member_complex @ Z @ ring_1_Ints_complex )
% 8.69/5.00        = ( ( ( im @ Z )
% 8.69/5.00            = zero_zero_real )
% 8.69/5.00          & ? [I5: int] :
% 8.69/5.00              ( ( re @ Z )
% 8.69/5.00              = ( ring_1_of_int_real @ I5 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9504_abs__Im__le__cmod,axiom,
% 8.69/5.00      ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9505_times__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( im @ ( times_times_complex @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9506_cmod__eq__Re,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ( im @ Z )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( real_V1022390504157884413omplex @ Z )
% 8.69/5.00          = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9507_cmod__eq__Im,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ( re @ Z )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00       => ( ( real_V1022390504157884413omplex @ Z )
% 8.69/5.00          = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9508_Im__eq__0,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ( abs_abs_real @ ( re @ Z ) )
% 8.69/5.00          = ( real_V1022390504157884413omplex @ Z ) )
% 8.69/5.00       => ( ( im @ Z )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9509_cmod__Re__le__iff,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( ( im @ X )
% 8.69/5.00          = ( im @ Y ) )
% 8.69/5.00       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 8.69/5.00          = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9510_cmod__Im__le__iff,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( ( re @ X )
% 8.69/5.00          = ( re @ Y ) )
% 8.69/5.00       => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 8.69/5.00          = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9511_times__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( re @ ( times_times_complex @ X @ Y ) )
% 8.69/5.00        = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9512_plus__complex_Ocode,axiom,
% 8.69/5.00      ( plus_plus_complex
% 8.69/5.00      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( plus_plus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9513_scaleR__complex_Ocode,axiom,
% 8.69/5.00      ( real_V2046097035970521341omplex
% 8.69/5.00      = ( ^ [R5: real,X3: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X3 ) ) @ ( times_times_real @ R5 @ ( im @ X3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9514_minus__complex_Ocode,axiom,
% 8.69/5.00      ( minus_minus_complex
% 8.69/5.00      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( minus_minus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9515_csqrt__principal,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 8.69/5.00        | ( ( ( re @ ( csqrt @ Z ) )
% 8.69/5.00            = zero_zero_real )
% 8.69/5.00          & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9516_cmod__le,axiom,
% 8.69/5.00      ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9517_sin__n__Im__cis__pow__n,axiom,
% 8.69/5.00      ! [N: nat,A: real] :
% 8.69/5.00        ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.69/5.00        = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9518_Re__exp,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( re @ ( exp_complex @ Z ) )
% 8.69/5.00        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9519_Im__exp,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( im @ ( exp_complex @ Z ) )
% 8.69/5.00        = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9520_complex__eq,axiom,
% 8.69/5.00      ! [A: complex] :
% 8.69/5.00        ( A
% 8.69/5.00        = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9521_times__complex_Ocode,axiom,
% 8.69/5.00      ( times_times_complex
% 8.69/5.00      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9522_exp__eq__polar,axiom,
% 8.69/5.00      ( exp_complex
% 8.69/5.00      = ( ^ [Z3: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z3 ) ) ) @ ( cis @ ( im @ Z3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9523_cmod__power2,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/5.00        = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9524_Im__power2,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/5.00        = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9525_Re__power2,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/5.00        = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9526_complex__eq__0,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( Z = zero_zero_complex )
% 8.69/5.00        = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9527_norm__complex__def,axiom,
% 8.69/5.00      ( real_V1022390504157884413omplex
% 8.69/5.00      = ( ^ [Z3: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9528_inverse__complex_Osimps_I1_J,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 8.69/5.00        = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9529_complex__neq__0,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( Z != zero_zero_complex )
% 8.69/5.00        = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9530_Re__divide,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.69/5.00        = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9531_csqrt__unique,axiom,
% 8.69/5.00      ! [W: complex,Z: complex] :
% 8.69/5.00        ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.69/5.00          = Z )
% 8.69/5.00       => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 8.69/5.00            | ( ( ( re @ W )
% 8.69/5.00                = zero_zero_real )
% 8.69/5.00              & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 8.69/5.00         => ( ( csqrt @ Z )
% 8.69/5.00            = W ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9532_csqrt__square,axiom,
% 8.69/5.00      ! [B: complex] :
% 8.69/5.00        ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 8.69/5.00          | ( ( ( re @ B )
% 8.69/5.00              = zero_zero_real )
% 8.69/5.00            & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 8.69/5.00       => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/5.00          = B ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9533_inverse__complex_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: complex] :
% 8.69/5.00        ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 8.69/5.00        = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9534_Im__divide,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.69/5.00        = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9535_complex__abs__le__norm,axiom,
% 8.69/5.00      ! [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 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9536_complex__unit__circle,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( Z != zero_zero_complex )
% 8.69/5.00       => ( ( 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 ) ) ) )
% 8.69/5.00          = one_one_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9537_inverse__complex_Ocode,axiom,
% 8.69/5.00      ( invers8013647133539491842omplex
% 8.69/5.00      = ( ^ [X3: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X3 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X3 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9538_Complex__divide,axiom,
% 8.69/5.00      ( divide1717551699836669952omplex
% 8.69/5.00      = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9539_Im__Reals__divide,axiom,
% 8.69/5.00      ! [R: complex,Z: complex] :
% 8.69/5.00        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 8.69/5.00       => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 8.69/5.00          = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9540_Re__Reals__divide,axiom,
% 8.69/5.00      ! [R: complex,Z: complex] :
% 8.69/5.00        ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 8.69/5.00       => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 8.69/5.00          = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9541_imaginary__eq__real__iff,axiom,
% 8.69/5.00      ! [Y: complex,X: complex] :
% 8.69/5.00        ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.69/5.00       => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.69/5.00         => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 8.69/5.00              = X )
% 8.69/5.00            = ( ( X = zero_zero_complex )
% 8.69/5.00              & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9542_real__eq__imaginary__iff,axiom,
% 8.69/5.00      ! [Y: complex,X: complex] :
% 8.69/5.00        ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.69/5.00       => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.69/5.00         => ( ( X
% 8.69/5.00              = ( times_times_complex @ imaginary_unit @ Y ) )
% 8.69/5.00            = ( ( X = zero_zero_complex )
% 8.69/5.00              & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9543_complex__is__Real__iff,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 8.69/5.00        = ( ( im @ Z )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9544_Complex__in__Reals,axiom,
% 8.69/5.00      ! [X: real] : ( member_complex @ ( complex2 @ X @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9545_complex__diff__cnj,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 8.69/5.00        = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9546_complex__mult__cnj,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 8.69/5.00        = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9547_complex__cnj__mult,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 8.69/5.00        = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9548_complex__cnj__zero,axiom,
% 8.69/5.00      ( ( cnj @ zero_zero_complex )
% 8.69/5.00      = zero_zero_complex ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9549_complex__cnj__zero__iff,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ( cnj @ Z )
% 8.69/5.00          = zero_zero_complex )
% 8.69/5.00        = ( Z = zero_zero_complex ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9550_complex__cnj__one__iff,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( ( cnj @ Z )
% 8.69/5.00          = one_one_complex )
% 8.69/5.00        = ( Z = one_one_complex ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9551_complex__cnj__one,axiom,
% 8.69/5.00      ( ( cnj @ one_one_complex )
% 8.69/5.00      = one_one_complex ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9552_complex__cnj__power,axiom,
% 8.69/5.00      ! [X: complex,N: nat] :
% 8.69/5.00        ( ( cnj @ ( power_power_complex @ X @ N ) )
% 8.69/5.00        = ( power_power_complex @ ( cnj @ X ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9553_complex__cnj__add,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( cnj @ ( plus_plus_complex @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9554_complex__cnj__numeral,axiom,
% 8.69/5.00      ! [W: num] :
% 8.69/5.00        ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 8.69/5.00        = ( numera6690914467698888265omplex @ W ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9555_complex__cnj__diff,axiom,
% 8.69/5.00      ! [X: complex,Y: complex] :
% 8.69/5.00        ( ( cnj @ ( minus_minus_complex @ X @ Y ) )
% 8.69/5.00        = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9556_complex__cnj__neg__numeral,axiom,
% 8.69/5.00      ! [W: num] :
% 8.69/5.00        ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 8.69/5.00        = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9557_complex__In__mult__cnj__zero,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 8.69/5.00        = zero_zero_real ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9558_Re__complex__div__eq__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00        = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9559_Im__complex__div__eq__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.69/5.00          = zero_zero_real )
% 8.69/5.00        = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.69/5.00          = zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9560_complex__mod__sqrt__Re__mult__cnj,axiom,
% 8.69/5.00      ( real_V1022390504157884413omplex
% 8.69/5.00      = ( ^ [Z3: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9561_Re__complex__div__gt__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00        = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9562_Re__complex__div__lt__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.69/5.00        = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9563_Re__complex__div__ge__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00        = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9564_Re__complex__div__le__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.69/5.00        = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9565_Im__complex__div__gt__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00        = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9566_Im__complex__div__lt__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.69/5.00        = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9567_Im__complex__div__ge__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00        = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9568_Im__complex__div__le__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.69/5.00        = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9569_complex__mod__mult__cnj,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 8.69/5.00        = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9570_complex__div__gt__0,axiom,
% 8.69/5.00      ! [A: complex,B: complex] :
% 8.69/5.00        ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00          = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 8.69/5.00        & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.69/5.00          = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9571_complex__norm__square,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.69/5.00        = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9572_complex__add__cnj,axiom,
% 8.69/5.00      ! [Z: complex] :
% 8.69/5.00        ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 8.69/5.00        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9573_complex__div__cnj,axiom,
% 8.69/5.00      ( divide1717551699836669952omplex
% 8.69/5.00      = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9574_cnj__add__mult__eq__Re,axiom,
% 8.69/5.00      ! [Z: complex,W: complex] :
% 8.69/5.00        ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 8.69/5.00        = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9575_divmod__step__integer__def,axiom,
% 8.69/5.00      ( unique4921790084139445826nteger
% 8.69/5.00      = ( ^ [L: num] :
% 8.69/5.00            ( produc6916734918728496179nteger
% 8.69/5.00            @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9576_card__lessThan,axiom,
% 8.69/5.00      ! [U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 8.69/5.00        = U ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9577_card__Collect__less__nat,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( finite_card_nat
% 8.69/5.00          @ ( collect_nat
% 8.69/5.00            @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N ) ) )
% 8.69/5.00        = N ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9578_card__atMost,axiom,
% 8.69/5.00      ! [U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 8.69/5.00        = ( suc @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9579_card__atLeastLessThan,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 8.69/5.00        = ( minus_minus_nat @ U @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9580_card__Collect__le__nat,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( finite_card_nat
% 8.69/5.00          @ ( collect_nat
% 8.69/5.00            @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N ) ) )
% 8.69/5.00        = ( suc @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9581_card__atLeastAtMost,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 8.69/5.00        = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9582_card__atLeastLessThan__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 8.69/5.00        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9583_card__atLeastAtMost__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 8.69/5.00        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9584_minus__integer__code_I1_J,axiom,
% 8.69/5.00      ! [K: code_integer] :
% 8.69/5.00        ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 8.69/5.00        = K ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9585_minus__integer__code_I2_J,axiom,
% 8.69/5.00      ! [L2: code_integer] :
% 8.69/5.00        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 8.69/5.00        = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9586_times__integer__code_I1_J,axiom,
% 8.69/5.00      ! [K: code_integer] :
% 8.69/5.00        ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 8.69/5.00        = zero_z3403309356797280102nteger ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9587_times__integer__code_I2_J,axiom,
% 8.69/5.00      ! [L2: code_integer] :
% 8.69/5.00        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 8.69/5.00        = zero_z3403309356797280102nteger ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9588_plus__integer__code_I2_J,axiom,
% 8.69/5.00      ! [L2: code_integer] :
% 8.69/5.00        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 8.69/5.00        = L2 ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9589_plus__integer__code_I1_J,axiom,
% 8.69/5.00      ! [K: code_integer] :
% 8.69/5.00        ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 8.69/5.00        = K ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9590_less__eq__integer__code_I1_J,axiom,
% 8.69/5.00      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9591_exhaustive__integer_H_Ocases,axiom,
% 8.69/5.00      ! [X: produc8763457246119570046nteger] :
% 8.69/5.00        ~ ! [F2: code_integer > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 8.69/5.00            ( X
% 8.69/5.00           != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9592_full__exhaustive__integer_H_Ocases,axiom,
% 8.69/5.00      ! [X: produc1908205239877642774nteger] :
% 8.69/5.00        ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 8.69/5.00            ( X
% 8.69/5.00           != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9593_divmod__integer_H__def,axiom,
% 8.69/5.00      ( unique3479559517661332726nteger
% 8.69/5.00      = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9594_sgn__integer__code,axiom,
% 8.69/5.00      ( sgn_sgn_Code_integer
% 8.69/5.00      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9595_nat_Odisc__eq__case_I2_J,axiom,
% 8.69/5.00      ! [Nat: nat] :
% 8.69/5.00        ( ( Nat != zero_zero_nat )
% 8.69/5.00        = ( case_nat_o @ $false
% 8.69/5.00          @ ^ [Uu3: nat] : $true
% 8.69/5.00          @ Nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9596_nat_Odisc__eq__case_I1_J,axiom,
% 8.69/5.00      ! [Nat: nat] :
% 8.69/5.00        ( ( Nat = zero_zero_nat )
% 8.69/5.00        = ( case_nat_o @ $true
% 8.69/5.00          @ ^ [Uu3: nat] : $false
% 8.69/5.00          @ Nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9597_zero__natural_Orsp,axiom,
% 8.69/5.00      zero_zero_nat = zero_zero_nat ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9598_card__less,axiom,
% 8.69/5.00      ! [M5: set_nat,I: nat] :
% 8.69/5.00        ( ( member_nat @ zero_zero_nat @ M5 )
% 8.69/5.00       => ( ( finite_card_nat
% 8.69/5.00            @ ( collect_nat
% 8.69/5.00              @ ^ [K2: nat] :
% 8.69/5.00                  ( ( member_nat @ K2 @ M5 )
% 8.69/5.00                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 8.69/5.00         != zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9599_card__less__Suc,axiom,
% 8.69/5.00      ! [M5: set_nat,I: nat] :
% 8.69/5.00        ( ( member_nat @ zero_zero_nat @ M5 )
% 8.69/5.00       => ( ( suc
% 8.69/5.00            @ ( finite_card_nat
% 8.69/5.00              @ ( collect_nat
% 8.69/5.00                @ ^ [K2: nat] :
% 8.69/5.00                    ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 8.69/5.00                    & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 8.69/5.00          = ( finite_card_nat
% 8.69/5.00            @ ( collect_nat
% 8.69/5.00              @ ^ [K2: nat] :
% 8.69/5.00                  ( ( member_nat @ K2 @ M5 )
% 8.69/5.00                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9600_card__less__Suc2,axiom,
% 8.69/5.00      ! [M5: set_nat,I: nat] :
% 8.69/5.00        ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 8.69/5.00       => ( ( finite_card_nat
% 8.69/5.00            @ ( collect_nat
% 8.69/5.00              @ ^ [K2: nat] :
% 8.69/5.00                  ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 8.69/5.00                  & ( ord_less_nat @ K2 @ I ) ) ) )
% 8.69/5.00          = ( finite_card_nat
% 8.69/5.00            @ ( collect_nat
% 8.69/5.00              @ ^ [K2: nat] :
% 8.69/5.00                  ( ( member_nat @ K2 @ M5 )
% 8.69/5.00                  & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9601_card__atLeastZeroLessThan__int,axiom,
% 8.69/5.00      ! [U: int] :
% 8.69/5.00        ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 8.69/5.00        = ( nat2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9602_zero__integer_Orsp,axiom,
% 8.69/5.00      zero_zero_int = zero_zero_int ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9603_one__integer_Orsp,axiom,
% 8.69/5.00      one_one_int = one_one_int ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9604_subset__card__intvl__is__intvl,axiom,
% 8.69/5.00      ! [A2: set_nat,K: nat] :
% 8.69/5.00        ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 8.69/5.00       => ( A2
% 8.69/5.00          = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9605_one__natural_Orsp,axiom,
% 8.69/5.00      one_one_nat = one_one_nat ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9606_less__eq__nat_Osimps_I2_J,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.69/5.00        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9607_max__Suc2,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 8.69/5.00        = ( case_nat_nat @ ( suc @ N )
% 8.69/5.00          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 8.69/5.00          @ M ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9608_max__Suc1,axiom,
% 8.69/5.00      ! [N: nat,M: nat] :
% 8.69/5.00        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 8.69/5.00        = ( case_nat_nat @ ( suc @ N )
% 8.69/5.00          @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 8.69/5.00          @ M ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9609_subset__eq__atLeast0__lessThan__card,axiom,
% 8.69/5.00      ! [N4: set_nat,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.69/5.00       => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9610_card__sum__le__nat__sum,axiom,
% 8.69/5.00      ! [S2: set_nat] :
% 8.69/5.00        ( ord_less_eq_nat
% 8.69/5.00        @ ( groups3542108847815614940at_nat
% 8.69/5.00          @ ^ [X3: nat] : X3
% 8.69/5.00          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 8.69/5.00        @ ( groups3542108847815614940at_nat
% 8.69/5.00          @ ^ [X3: nat] : X3
% 8.69/5.00          @ S2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9611_card__nth__roots,axiom,
% 8.69/5.00      ! [C: complex,N: nat] :
% 8.69/5.00        ( ( C != zero_zero_complex )
% 8.69/5.00       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00         => ( ( finite_card_complex
% 8.69/5.00              @ ( collect_complex
% 8.69/5.00                @ ^ [Z3: complex] :
% 8.69/5.00                    ( ( power_power_complex @ Z3 @ N )
% 8.69/5.00                    = C ) ) )
% 8.69/5.00            = N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9612_card__roots__unity__eq,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( finite_card_complex
% 8.69/5.00            @ ( collect_complex
% 8.69/5.00              @ ^ [Z3: complex] :
% 8.69/5.00                  ( ( power_power_complex @ Z3 @ N )
% 8.69/5.00                  = one_one_complex ) ) )
% 8.69/5.00          = N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9613_diff__Suc,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 8.69/5.00        = ( case_nat_nat @ zero_zero_nat
% 8.69/5.00          @ ^ [K2: nat] : K2
% 8.69/5.00          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9614_integer__of__int__code,axiom,
% 8.69/5.00      ( code_integer_of_int
% 8.69/5.00      = ( ^ [K2: int] :
% 8.69/5.00            ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 8.69/5.00            @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 8.69/5.00              @ ( if_Code_integer
% 8.69/5.00                @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.69/5.00                  = zero_zero_int )
% 8.69/5.00                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.69/5.00                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9615_abs__integer__code,axiom,
% 8.69/5.00      ( abs_abs_Code_integer
% 8.69/5.00      = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9616_uminus__integer__code_I1_J,axiom,
% 8.69/5.00      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 8.69/5.00      = zero_z3403309356797280102nteger ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9617_zero__integer__def,axiom,
% 8.69/5.00      ( zero_z3403309356797280102nteger
% 8.69/5.00      = ( code_integer_of_int @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9618_less__integer__code_I1_J,axiom,
% 8.69/5.00      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9619_modulo__integer_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: int,X: int] :
% 8.69/5.00        ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.69/5.00        = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9620_plus__integer_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: int,X: int] :
% 8.69/5.00        ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.69/5.00        = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9621_times__integer_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: int,X: int] :
% 8.69/5.00        ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.69/5.00        = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9622_one__integer__def,axiom,
% 8.69/5.00      ( one_one_Code_integer
% 8.69/5.00      = ( code_integer_of_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9623_less__eq__integer_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: int,X: int] :
% 8.69/5.00        ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.69/5.00        = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9624_minus__integer_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: int,X: int] :
% 8.69/5.00        ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.69/5.00        = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9625_Code__Numeral_Opositive__def,axiom,
% 8.69/5.00      code_positive = numera6620942414471956472nteger ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9626_integer__of__num_I3_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 8.69/5.00        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9627_integer__of__num__def,axiom,
% 8.69/5.00      code_integer_of_num = numera6620942414471956472nteger ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9628_integer__of__num__triv_I1_J,axiom,
% 8.69/5.00      ( ( code_integer_of_num @ one )
% 8.69/5.00      = one_one_Code_integer ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9629_integer__of__num_I2_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 8.69/5.00        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9630_integer__of__num__triv_I2_J,axiom,
% 8.69/5.00      ( ( code_integer_of_num @ ( bit0 @ one ) )
% 8.69/5.00      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9631_int__of__integer__code,axiom,
% 8.69/5.00      ( code_int_of_integer
% 8.69/5.00      = ( ^ [K2: code_integer] :
% 8.69/5.00            ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 8.69/5.00            @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 8.69/5.00              @ ( produc1553301316500091796er_int
% 8.69/5.00                @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 8.69/5.00                @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9632_bit__cut__integer__def,axiom,
% 8.69/5.00      ( code_bit_cut_integer
% 8.69/5.00      = ( ^ [K2: code_integer] :
% 8.69/5.00            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.69/5.00            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9633_num__of__integer__code,axiom,
% 8.69/5.00      ( code_num_of_integer
% 8.69/5.00      = ( ^ [K2: code_integer] :
% 8.69/5.00            ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 8.69/5.00            @ ( produc7336495610019696514er_num
% 8.69/5.00              @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 8.69/5.00              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9634_zero__integer_Orep__eq,axiom,
% 8.69/5.00      ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 8.69/5.00      = zero_zero_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9635_int__of__integer__numeral,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 8.69/5.00        = ( numeral_numeral_int @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9636_plus__integer_Orep__eq,axiom,
% 8.69/5.00      ! [X: code_integer,Xa2: code_integer] :
% 8.69/5.00        ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 8.69/5.00        = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9637_times__integer_Orep__eq,axiom,
% 8.69/5.00      ! [X: code_integer,Xa2: code_integer] :
% 8.69/5.00        ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 8.69/5.00        = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9638_one__integer_Orep__eq,axiom,
% 8.69/5.00      ( ( code_int_of_integer @ one_one_Code_integer )
% 8.69/5.00      = one_one_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9639_minus__integer_Orep__eq,axiom,
% 8.69/5.00      ! [X: code_integer,Xa2: code_integer] :
% 8.69/5.00        ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 8.69/5.00        = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9640_modulo__integer_Orep__eq,axiom,
% 8.69/5.00      ! [X: code_integer,Xa2: code_integer] :
% 8.69/5.00        ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa2 ) )
% 8.69/5.00        = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9641_integer__less__eq__iff,axiom,
% 8.69/5.00      ( ord_le3102999989581377725nteger
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9642_less__eq__integer_Orep__eq,axiom,
% 8.69/5.00      ( ord_le3102999989581377725nteger
% 8.69/5.00      = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9643_divmod__integer__def,axiom,
% 8.69/5.00      ( code_divmod_integer
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L ) @ ( modulo364778990260209775nteger @ K2 @ L ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9644_bit__cut__integer__code,axiom,
% 8.69/5.00      ( code_bit_cut_integer
% 8.69/5.00      = ( ^ [K2: code_integer] :
% 8.69/5.00            ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 8.69/5.00            @ ( produc9125791028180074456eger_o
% 8.69/5.00              @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 8.69/5.00              @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9645_nat__of__integer__code,axiom,
% 8.69/5.00      ( code_nat_of_integer
% 8.69/5.00      = ( ^ [K2: code_integer] :
% 8.69/5.00            ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 8.69/5.00            @ ( produc1555791787009142072er_nat
% 8.69/5.00              @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 8.69/5.00              @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9646_of__nat__of__integer,axiom,
% 8.69/5.00      ! [K: code_integer] :
% 8.69/5.00        ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 8.69/5.00        = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9647_nat__of__integer__non__positive,axiom,
% 8.69/5.00      ! [K: code_integer] :
% 8.69/5.00        ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 8.69/5.00       => ( ( code_nat_of_integer @ K )
% 8.69/5.00          = zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9648_nat__of__integer__code__post_I1_J,axiom,
% 8.69/5.00      ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 8.69/5.00      = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9649_nat__of__integer__code__post_I3_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 8.69/5.00        = ( numeral_numeral_nat @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9650_divmod__abs__code_I6_J,axiom,
% 8.69/5.00      ! [J: code_integer] :
% 8.69/5.00        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 8.69/5.00        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9651_nat__of__integer__code__post_I2_J,axiom,
% 8.69/5.00      ( ( code_nat_of_integer @ one_one_Code_integer )
% 8.69/5.00      = one_one_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9652_divmod__abs__code_I5_J,axiom,
% 8.69/5.00      ! [J: code_integer] :
% 8.69/5.00        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 8.69/5.00        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9653_pred__def,axiom,
% 8.69/5.00      ( pred
% 8.69/5.00      = ( case_nat_nat @ zero_zero_nat
% 8.69/5.00        @ ^ [X24: nat] : X24 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9654_divmod__abs__def,axiom,
% 8.69/5.00      ( code_divmod_abs
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9655_divmod__integer__code,axiom,
% 8.69/5.00      ( code_divmod_integer
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] :
% 8.69/5.00            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 8.69/5.00            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 8.69/5.00              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L )
% 8.69/5.00                @ ( produc6916734918728496179nteger
% 8.69/5.00                  @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S7 ) ) )
% 8.69/5.00                  @ ( code_divmod_abs @ K2 @ L ) ) )
% 8.69/5.00              @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 8.69/5.00                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 8.69/5.00                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L )
% 8.69/5.00                    @ ( produc6916734918728496179nteger
% 8.69/5.00                      @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S7 ) ) )
% 8.69/5.00                      @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9656_binomial__def,axiom,
% 8.69/5.00      ( binomial
% 8.69/5.00      = ( ^ [N2: nat,K2: nat] :
% 8.69/5.00            ( finite_card_set_nat
% 8.69/5.00            @ ( collect_set_nat
% 8.69/5.00              @ ^ [K7: set_nat] :
% 8.69/5.00                  ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 8.69/5.00                  & ( ( finite_card_nat @ K7 )
% 8.69/5.00                    = K2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9657_bezw__0,axiom,
% 8.69/5.00      ! [X: nat] :
% 8.69/5.00        ( ( bezw @ X @ zero_zero_nat )
% 8.69/5.00        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9658_floor__real__def,axiom,
% 8.69/5.00      ( archim6058952711729229775r_real
% 8.69/5.00      = ( ^ [X3: real] :
% 8.69/5.00            ( the_int
% 8.69/5.00            @ ^ [Z3: int] :
% 8.69/5.00                ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 8.69/5.00                & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9659_floor__rat__def,axiom,
% 8.69/5.00      ( archim3151403230148437115or_rat
% 8.69/5.00      = ( ^ [X3: rat] :
% 8.69/5.00            ( the_int
% 8.69/5.00            @ ^ [Z3: int] :
% 8.69/5.00                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 8.69/5.00                & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9660_drop__bit__numeral__minus__bit1,axiom,
% 8.69/5.00      ! [L2: num,K: num] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/5.00        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9661_Suc__0__mod__numeral,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 8.69/5.00        = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9662_drop__bit__nonnegative__int__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 8.69/5.00        = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9663_drop__bit__negative__int__iff,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 8.69/5.00        = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9664_drop__bit__minus__one,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.69/5.00        = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9665_snd__divmod__nat,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 8.69/5.00        = ( modulo_modulo_nat @ M @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9666_drop__bit__Suc__minus__bit0,axiom,
% 8.69/5.00      ! [N: nat,K: num] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/5.00        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9667_drop__bit__numeral__minus__bit0,axiom,
% 8.69/5.00      ! [L2: num,K: num] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 8.69/5.00        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9668_drop__bit__Suc__minus__bit1,axiom,
% 8.69/5.00      ! [N: nat,K: num] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 8.69/5.00        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9669_less__eq__rat__def,axiom,
% 8.69/5.00      ( ord_less_eq_rat
% 8.69/5.00      = ( ^ [X3: rat,Y3: rat] :
% 8.69/5.00            ( ( ord_less_rat @ X3 @ Y3 )
% 8.69/5.00            | ( X3 = Y3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9670_abs__rat__def,axiom,
% 8.69/5.00      ( abs_abs_rat
% 8.69/5.00      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9671_sgn__rat__def,axiom,
% 8.69/5.00      ( sgn_sgn_rat
% 8.69/5.00      = ( ^ [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 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9672_obtain__pos__sum,axiom,
% 8.69/5.00      ! [R: rat] :
% 8.69/5.00        ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.69/5.00       => ~ ! [S3: rat] :
% 8.69/5.00              ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 8.69/5.00             => ! [T6: rat] :
% 8.69/5.00                  ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 8.69/5.00                 => ( R
% 8.69/5.00                   != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9673_drop__bit__push__bit__int,axiom,
% 8.69/5.00      ! [M: nat,N: nat,K: int] :
% 8.69/5.00        ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 8.69/5.00        = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9674_drop__bit__int__def,axiom,
% 8.69/5.00      ( bit_se8568078237143864401it_int
% 8.69/5.00      = ( ^ [N2: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9675_rat__inverse__code,axiom,
% 8.69/5.00      ! [P5: rat] :
% 8.69/5.00        ( ( quotient_of @ ( inverse_inverse_rat @ P5 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9676_normalize__negative,axiom,
% 8.69/5.00      ! [Q2: int,P5: int] :
% 8.69/5.00        ( ( ord_less_int @ Q2 @ zero_zero_int )
% 8.69/5.00       => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9677_prod__decode__aux_Osimps,axiom,
% 8.69/5.00      ( nat_prod_decode_aux
% 8.69/5.00      = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9678_snd__divmod__integer,axiom,
% 8.69/5.00      ! [K: code_integer,L2: code_integer] :
% 8.69/5.00        ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 8.69/5.00        = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9679_snd__divmod__abs,axiom,
% 8.69/5.00      ! [K: code_integer,L2: code_integer] :
% 8.69/5.00        ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 8.69/5.00        = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9680_quotient__of__number_I3_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 8.69/5.00        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9681_normalize__denom__zero,axiom,
% 8.69/5.00      ! [P5: int] :
% 8.69/5.00        ( ( normalize @ ( product_Pair_int_int @ P5 @ zero_zero_int ) )
% 8.69/5.00        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9682_rat__one__code,axiom,
% 8.69/5.00      ( ( quotient_of @ one_one_rat )
% 8.69/5.00      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9683_drop__bit__of__Suc__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9684_rat__zero__code,axiom,
% 8.69/5.00      ( ( quotient_of @ zero_zero_rat )
% 8.69/5.00      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9685_quotient__of__number_I5_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.69/5.00        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9686_quotient__of__number_I4_J,axiom,
% 8.69/5.00      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.69/5.00      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9687_quotient__of__denom__pos_H,axiom,
% 8.69/5.00      ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9688_divide__rat__def,axiom,
% 8.69/5.00      ( divide_divide_rat
% 8.69/5.00      = ( ^ [Q5: rat,R5: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9689_diff__rat__def,axiom,
% 8.69/5.00      ( minus_minus_rat
% 8.69/5.00      = ( ^ [Q5: rat,R5: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9690_rat__divide__code,axiom,
% 8.69/5.00      ! [P5: rat,Q2: rat] :
% 8.69/5.00        ( ( quotient_of @ ( divide_divide_rat @ P5 @ Q2 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int,C3: int] :
% 8.69/5.00              ( produc4245557441103728435nt_int
% 8.69/5.00              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) ) )
% 8.69/5.00              @ ( quotient_of @ Q2 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9691_rat__times__code,axiom,
% 8.69/5.00      ! [P5: rat,Q2: rat] :
% 8.69/5.00        ( ( quotient_of @ ( times_times_rat @ P5 @ Q2 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int,C3: int] :
% 8.69/5.00              ( produc4245557441103728435nt_int
% 8.69/5.00              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.69/5.00              @ ( quotient_of @ Q2 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9692_drop__bit__nat__eq,axiom,
% 8.69/5.00      ! [N: nat,K: int] :
% 8.69/5.00        ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 8.69/5.00        = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9693_quotient__of__div,axiom,
% 8.69/5.00      ! [R: rat,N: int,D: int] :
% 8.69/5.00        ( ( ( quotient_of @ R )
% 8.69/5.00          = ( product_Pair_int_int @ N @ D ) )
% 8.69/5.00       => ( R
% 8.69/5.00          = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9694_rat__plus__code,axiom,
% 8.69/5.00      ! [P5: rat,Q2: rat] :
% 8.69/5.00        ( ( quotient_of @ ( plus_plus_rat @ P5 @ Q2 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int,C3: int] :
% 8.69/5.00              ( produc4245557441103728435nt_int
% 8.69/5.00              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.69/5.00              @ ( quotient_of @ Q2 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9695_rat__minus__code,axiom,
% 8.69/5.00      ! [P5: rat,Q2: rat] :
% 8.69/5.00        ( ( quotient_of @ ( minus_minus_rat @ P5 @ Q2 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int,C3: int] :
% 8.69/5.00              ( produc4245557441103728435nt_int
% 8.69/5.00              @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.69/5.00              @ ( quotient_of @ Q2 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9696_quotient__of__denom__pos,axiom,
% 8.69/5.00      ! [R: rat,P5: int,Q2: int] :
% 8.69/5.00        ( ( ( quotient_of @ R )
% 8.69/5.00          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9697_rat__uminus__code,axiom,
% 8.69/5.00      ! [P5: rat] :
% 8.69/5.00        ( ( quotient_of @ ( uminus_uminus_rat @ P5 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9698_rat__abs__code,axiom,
% 8.69/5.00      ! [P5: rat] :
% 8.69/5.00        ( ( quotient_of @ ( abs_abs_rat @ P5 ) )
% 8.69/5.00        = ( produc4245557441103728435nt_int
% 8.69/5.00          @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 8.69/5.00          @ ( quotient_of @ P5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9699_normalize__denom__pos,axiom,
% 8.69/5.00      ! [R: product_prod_int_int,P5: int,Q2: int] :
% 8.69/5.00        ( ( ( normalize @ R )
% 8.69/5.00          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00       => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9700_normalize__crossproduct,axiom,
% 8.69/5.00      ! [Q2: int,S: int,P5: int,R: int] :
% 8.69/5.00        ( ( Q2 != zero_zero_int )
% 8.69/5.00       => ( ( S != zero_zero_int )
% 8.69/5.00         => ( ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00              = ( normalize @ ( product_Pair_int_int @ R @ S ) ) )
% 8.69/5.00           => ( ( times_times_int @ P5 @ S )
% 8.69/5.00              = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9701_drop__bit__nat__def,axiom,
% 8.69/5.00      ( bit_se8570568707652914677it_nat
% 8.69/5.00      = ( ^ [N2: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9702_rat__less__code,axiom,
% 8.69/5.00      ( ord_less_rat
% 8.69/5.00      = ( ^ [P2: rat,Q5: rat] :
% 8.69/5.00            ( produc4947309494688390418_int_o
% 8.69/5.00            @ ^ [A3: int,C3: int] :
% 8.69/5.00                ( produc4947309494688390418_int_o
% 8.69/5.00                @ ^ [B2: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 8.69/5.00                @ ( quotient_of @ Q5 ) )
% 8.69/5.00            @ ( quotient_of @ P2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9703_rat__less__eq__code,axiom,
% 8.69/5.00      ( ord_less_eq_rat
% 8.69/5.00      = ( ^ [P2: rat,Q5: rat] :
% 8.69/5.00            ( produc4947309494688390418_int_o
% 8.69/5.00            @ ^ [A3: int,C3: int] :
% 8.69/5.00                ( produc4947309494688390418_int_o
% 8.69/5.00                @ ^ [B2: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 8.69/5.00                @ ( quotient_of @ Q5 ) )
% 8.69/5.00            @ ( quotient_of @ P2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9704_prod__decode__aux_Oelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 8.69/5.00        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9705_minus__one__mod__numeral,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9706_one__mod__minus__numeral,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9707_prod__decode__aux_Opelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 8.69/5.00        ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.69/5.00         => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 8.69/5.00                & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 8.69/5.00             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9708_numeral__mod__minus__numeral,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9709_minus__numeral__mod__numeral,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9710_Divides_Oadjust__mod__def,axiom,
% 8.69/5.00      ( adjust_mod
% 8.69/5.00      = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9711_quotient__of__int,axiom,
% 8.69/5.00      ! [A: int] :
% 8.69/5.00        ( ( quotient_of @ ( of_int @ A ) )
% 8.69/5.00        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9712_Frct__code__post_I5_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 8.69/5.00        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9713_bezw_Osimps,axiom,
% 8.69/5.00      ( bezw
% 8.69/5.00      = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9714_Frct__code__post_I2_J,axiom,
% 8.69/5.00      ! [A: int] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 8.69/5.00        = zero_zero_rat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9715_Frct__code__post_I1_J,axiom,
% 8.69/5.00      ! [A: int] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 8.69/5.00        = zero_zero_rat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9716_Frct__code__post_I7_J,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 8.69/5.00        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9717_Frct__code__post_I8_J,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 8.69/5.00        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9718_Frct__code__post_I3_J,axiom,
% 8.69/5.00      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 8.69/5.00      = one_one_rat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9719_rat__sgn__code,axiom,
% 8.69/5.00      ! [P5: rat] :
% 8.69/5.00        ( ( quotient_of @ ( sgn_sgn_rat @ P5 ) )
% 8.69/5.00        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P5 ) ) ) @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9720_Frct__code__post_I4_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 8.69/5.00        = ( numeral_numeral_rat @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9721_Frct__code__post_I6_J,axiom,
% 8.69/5.00      ! [K: num,L2: num] :
% 8.69/5.00        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 8.69/5.00        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9722_bezw__non__0,axiom,
% 8.69/5.00      ! [Y: nat,X: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 8.69/5.00       => ( ( bezw @ X @ Y )
% 8.69/5.00          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9723_bezw_Oelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 8.69/5.00        ( ( ( bezw @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( Xa2 = zero_zero_nat )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.69/5.00          & ( ( Xa2 != zero_zero_nat )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9724_bezw_Opelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 8.69/5.00        ( ( ( bezw @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.69/5.00         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.69/5.00                & ( ( Xa2 != zero_zero_nat )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 8.69/5.00             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9725_fst__divmod__nat,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 8.69/5.00        = ( divide_divide_nat @ M @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9726_Suc__0__div__numeral,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 8.69/5.00        = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9727_normalize__def,axiom,
% 8.69/5.00      ( normalize
% 8.69/5.00      = ( ^ [P2: product_prod_int_int] :
% 8.69/5.00            ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P2 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) )
% 8.69/5.00            @ ( if_Pro3027730157355071871nt_int
% 8.69/5.00              @ ( ( product_snd_int_int @ P2 )
% 8.69/5.00                = zero_zero_int )
% 8.69/5.00              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 8.69/5.00              @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9728_gcd__1__int,axiom,
% 8.69/5.00      ! [M: int] :
% 8.69/5.00        ( ( gcd_gcd_int @ M @ one_one_int )
% 8.69/5.00        = one_one_int ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9729_gcd__pos__int,axiom,
% 8.69/5.00      ! [M: int,N: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 8.69/5.00        = ( ( M != zero_zero_int )
% 8.69/5.00          | ( N != zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9730_gcd__neg__numeral__1__int,axiom,
% 8.69/5.00      ! [N: num,X: int] :
% 8.69/5.00        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 8.69/5.00        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9731_gcd__neg__numeral__2__int,axiom,
% 8.69/5.00      ! [X: int,N: num] :
% 8.69/5.00        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9732_gcd__0__left__int,axiom,
% 8.69/5.00      ! [X: int] :
% 8.69/5.00        ( ( gcd_gcd_int @ zero_zero_int @ X )
% 8.69/5.00        = ( abs_abs_int @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9733_gcd__0__int,axiom,
% 8.69/5.00      ! [X: int] :
% 8.69/5.00        ( ( gcd_gcd_int @ X @ zero_zero_int )
% 8.69/5.00        = ( abs_abs_int @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9734_gcd__mult__distrib__int,axiom,
% 8.69/5.00      ! [K: int,M: int,N: int] :
% 8.69/5.00        ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 8.69/5.00        = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9735_bezout__int,axiom,
% 8.69/5.00      ! [X: int,Y: int] :
% 8.69/5.00      ? [U3: int,V2: int] :
% 8.69/5.00        ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y ) )
% 8.69/5.00        = ( gcd_gcd_int @ X @ Y ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9736_gcd__red__int,axiom,
% 8.69/5.00      ( gcd_gcd_int
% 8.69/5.00      = ( ^ [X3: int,Y3: int] : ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X3 @ Y3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9737_gcd__ge__0__int,axiom,
% 8.69/5.00      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9738_gcd__le1__int,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ A )
% 8.69/5.00       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9739_gcd__le2__int,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9740_gcd__cases__int,axiom,
% 8.69/5.00      ! [X: int,Y: int,P: int > $o] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00           => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 8.69/5.00       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.69/5.00           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.69/5.00             => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 8.69/5.00         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 8.69/5.00             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.69/5.00               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 8.69/5.00           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 8.69/5.00               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.69/5.00                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 8.69/5.00             => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9741_gcd__unique__int,axiom,
% 8.69/5.00      ! [D: int,A: int,B: int] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 8.69/5.00          & ( dvd_dvd_int @ D @ A )
% 8.69/5.00          & ( dvd_dvd_int @ D @ B )
% 8.69/5.00          & ! [E3: int] :
% 8.69/5.00              ( ( ( dvd_dvd_int @ E3 @ A )
% 8.69/5.00                & ( dvd_dvd_int @ E3 @ B ) )
% 8.69/5.00             => ( dvd_dvd_int @ E3 @ D ) ) )
% 8.69/5.00        = ( D
% 8.69/5.00          = ( gcd_gcd_int @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9742_gcd__non__0__int,axiom,
% 8.69/5.00      ! [Y: int,X: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ Y )
% 8.69/5.00       => ( ( gcd_gcd_int @ X @ Y )
% 8.69/5.00          = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9743_gcd__code__int,axiom,
% 8.69/5.00      ( gcd_gcd_int
% 8.69/5.00      = ( ^ [K2: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9744_nat__descend__induct,axiom,
% 8.69/5.00      ! [N: nat,P: nat > $o,M: nat] :
% 8.69/5.00        ( ! [K3: nat] :
% 8.69/5.00            ( ( ord_less_nat @ N @ K3 )
% 8.69/5.00           => ( P @ K3 ) )
% 8.69/5.00       => ( ! [K3: nat] :
% 8.69/5.00              ( ( ord_less_eq_nat @ K3 @ N )
% 8.69/5.00             => ( ! [I2: nat] :
% 8.69/5.00                    ( ( ord_less_nat @ K3 @ I2 )
% 8.69/5.00                   => ( P @ I2 ) )
% 8.69/5.00               => ( P @ K3 ) ) )
% 8.69/5.00         => ( P @ M ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9745_finite__enumerate,axiom,
% 8.69/5.00      ! [S2: set_nat] :
% 8.69/5.00        ( ( finite_finite_nat @ S2 )
% 8.69/5.00       => ? [R2: nat > nat] :
% 8.69/5.00            ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 8.69/5.00            & ! [N7: nat] :
% 8.69/5.00                ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S2 ) )
% 8.69/5.00               => ( member_nat @ ( R2 @ N7 ) @ S2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9746_divmod__integer__eq__cases,axiom,
% 8.69/5.00      ( code_divmod_integer
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] :
% 8.69/5.00            ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 8.69/5.00            @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 8.69/5.00              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 8.69/5.00                @ ( if_Pro6119634080678213985nteger
% 8.69/5.00                  @ ( ( sgn_sgn_Code_integer @ K2 )
% 8.69/5.00                    = ( sgn_sgn_Code_integer @ L ) )
% 8.69/5.00                  @ ( code_divmod_abs @ K2 @ L )
% 8.69/5.00                  @ ( produc6916734918728496179nteger
% 8.69/5.00                    @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S7 ) ) )
% 8.69/5.00                    @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9747_gcd__nat_Oeq__neutr__iff,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( ( gcd_gcd_nat @ A @ B )
% 8.69/5.00          = zero_zero_nat )
% 8.69/5.00        = ( ( A = zero_zero_nat )
% 8.69/5.00          & ( B = zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9748_gcd__nat_Oleft__neutral,axiom,
% 8.69/5.00      ! [A: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 8.69/5.00        = A ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9749_gcd__nat_Oneutr__eq__iff,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( zero_zero_nat
% 8.69/5.00          = ( gcd_gcd_nat @ A @ B ) )
% 8.69/5.00        = ( ( A = zero_zero_nat )
% 8.69/5.00          & ( B = zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9750_gcd__nat_Oright__neutral,axiom,
% 8.69/5.00      ! [A: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 8.69/5.00        = A ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9751_gcd__0__nat,axiom,
% 8.69/5.00      ! [X: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 8.69/5.00        = X ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9752_gcd__0__left__nat,axiom,
% 8.69/5.00      ! [X: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 8.69/5.00        = X ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9753_gcd__1__nat,axiom,
% 8.69/5.00      ! [M: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 8.69/5.00        = one_one_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9754_gcd__Suc__0,axiom,
% 8.69/5.00      ! [M: nat] :
% 8.69/5.00        ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 8.69/5.00        = ( suc @ zero_zero_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9755_gcd__pos__nat,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 8.69/5.00        = ( ( M != zero_zero_nat )
% 8.69/5.00          | ( N != zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9756_gcd__mult__distrib__nat,axiom,
% 8.69/5.00      ! [K: nat,M: nat,N: nat] :
% 8.69/5.00        ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 8.69/5.00        = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9757_gcd__diff1__nat,axiom,
% 8.69/5.00      ! [N: nat,M: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ N @ M )
% 8.69/5.00       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 8.69/5.00          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9758_gcd__diff2__nat,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.00       => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 8.69/5.00          = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9759_gcd__red__nat,axiom,
% 8.69/5.00      ( gcd_gcd_nat
% 8.69/5.00      = ( ^ [X3: nat,Y3: nat] : ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9760_gcd__nat_Oelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: nat] :
% 8.69/5.00        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( Xa2 = zero_zero_nat )
% 8.69/5.00           => ( Y = X ) )
% 8.69/5.00          & ( ( Xa2 != zero_zero_nat )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9761_gcd__nat_Osimps,axiom,
% 8.69/5.00      ( gcd_gcd_nat
% 8.69/5.00      = ( ^ [X3: nat,Y3: nat] : ( if_nat @ ( Y3 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9762_gcd__non__0__nat,axiom,
% 8.69/5.00      ! [Y: nat,X: nat] :
% 8.69/5.00        ( ( Y != zero_zero_nat )
% 8.69/5.00       => ( ( gcd_gcd_nat @ X @ Y )
% 8.69/5.00          = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9763_gcd__le1__nat,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( A != zero_zero_nat )
% 8.69/5.00       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9764_gcd__le2__nat,axiom,
% 8.69/5.00      ! [B: nat,A: nat] :
% 8.69/5.00        ( ( B != zero_zero_nat )
% 8.69/5.00       => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9765_bezout__nat,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( A != zero_zero_nat )
% 8.69/5.00       => ? [X6: nat,Y5: nat] :
% 8.69/5.00            ( ( times_times_nat @ A @ X6 )
% 8.69/5.00            = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9766_bezout__gcd__nat_H,axiom,
% 8.69/5.00      ! [B: nat,A: nat] :
% 8.69/5.00      ? [X6: nat,Y5: nat] :
% 8.69/5.00        ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y5 ) @ ( times_times_nat @ A @ X6 ) )
% 8.69/5.00          & ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 8.69/5.00            = ( gcd_gcd_nat @ A @ B ) ) )
% 8.69/5.00        | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y5 ) @ ( times_times_nat @ B @ X6 ) )
% 8.69/5.00          & ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 8.69/5.00            = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9767_gcd__code__integer,axiom,
% 8.69/5.00      ( gcd_gcd_Code_integer
% 8.69/5.00      = ( ^ [K2: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9768_bezw__aux,axiom,
% 8.69/5.00      ! [X: nat,Y: nat] :
% 8.69/5.00        ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 8.69/5.00        = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9769_gcd__nat_Opelims,axiom,
% 8.69/5.00      ! [X: nat,Xa2: nat,Y: nat] :
% 8.69/5.00        ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.69/5.00         => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 8.69/5.00                 => ( Y = X ) )
% 8.69/5.00                & ( ( Xa2 != zero_zero_nat )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 8.69/5.00             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9770_Code__Numeral_Onegative__def,axiom,
% 8.69/5.00      ( code_negative
% 8.69/5.00      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9771_Code__Target__Int_Onegative__def,axiom,
% 8.69/5.00      ( code_Target_negative
% 8.69/5.00      = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9772_card__greaterThanLessThan__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 8.69/5.00        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9773_finite__greaterThanLessThan__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9774_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 8.69/5.00        = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9775_xor__minus__numerals_I1_J,axiom,
% 8.69/5.00      ! [N: num,K: int] :
% 8.69/5.00        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9776_xor__minus__numerals_I2_J,axiom,
% 8.69/5.00      ! [K: int,N: num] :
% 8.69/5.00        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9777_finite__greaterThanLessThan,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9778_card__greaterThanLessThan,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 8.69/5.00        = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9779_atLeastSucLessThan__greaterThanLessThan,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 8.69/5.00        = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9780_tanh__real__bounds,axiom,
% 8.69/5.00      ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9781_sub__BitM__One__eq,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 8.69/5.00        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9782_Suc__funpow,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( compow_nat_nat @ N @ suc )
% 8.69/5.00        = ( plus_plus_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9783_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.69/5.00      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 8.69/5.00      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 8.69/5.00      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9784_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.69/5.00      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 8.69/5.00      @ ^ [M3: nat,N2: nat] :
% 8.69/5.00          ( ( dvd_dvd_nat @ M3 @ N2 )
% 8.69/5.00          & ( M3 != N2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9785_Sup__nat__empty,axiom,
% 8.69/5.00      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 8.69/5.00      = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9786_Gcd__remove0__nat,axiom,
% 8.69/5.00      ! [M5: set_nat] :
% 8.69/5.00        ( ( finite_finite_nat @ M5 )
% 8.69/5.00       => ( ( gcd_Gcd_nat @ M5 )
% 8.69/5.00          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9787_times__int_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.69/5.00        ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( abs_Integ
% 8.69/5.00          @ ( produc27273713700761075at_nat
% 8.69/5.00            @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00                ( produc2626176000494625587at_nat
% 8.69/5.00                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 8.69/5.00            @ Xa2
% 8.69/5.00            @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9788_eq__Abs__Integ,axiom,
% 8.69/5.00      ! [Z: int] :
% 8.69/5.00        ~ ! [X6: nat,Y5: nat] :
% 8.69/5.00            ( Z
% 8.69/5.00           != ( abs_Integ @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9789_Gcd__nat__eq__one,axiom,
% 8.69/5.00      ! [N4: set_nat] :
% 8.69/5.00        ( ( member_nat @ one_one_nat @ N4 )
% 8.69/5.00       => ( ( gcd_Gcd_nat @ N4 )
% 8.69/5.00          = one_one_nat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9790_nat_Oabs__eq,axiom,
% 8.69/5.00      ! [X: product_prod_nat_nat] :
% 8.69/5.00        ( ( nat2 @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9791_zero__int__def,axiom,
% 8.69/5.00      ( zero_zero_int
% 8.69/5.00      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9792_int__def,axiom,
% 8.69/5.00      ( semiri1314217659103216013at_int
% 8.69/5.00      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9793_uminus__int_Oabs__eq,axiom,
% 8.69/5.00      ! [X: product_prod_nat_nat] :
% 8.69/5.00        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( abs_Integ
% 8.69/5.00          @ ( produc2626176000494625587at_nat
% 8.69/5.00            @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 8.69/5.00            @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9794_one__int__def,axiom,
% 8.69/5.00      ( one_one_int
% 8.69/5.00      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9795_less__int_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.69/5.00        ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( produc8739625826339149834_nat_o
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc6081775807080527818_nat_o
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 8.69/5.00          @ Xa2
% 8.69/5.00          @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9796_less__eq__int_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.69/5.00        ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( produc8739625826339149834_nat_o
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc6081775807080527818_nat_o
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 8.69/5.00          @ Xa2
% 8.69/5.00          @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9797_plus__int_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.69/5.00        ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( abs_Integ
% 8.69/5.00          @ ( produc27273713700761075at_nat
% 8.69/5.00            @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00                ( produc2626176000494625587at_nat
% 8.69/5.00                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) )
% 8.69/5.00            @ Xa2
% 8.69/5.00            @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9798_minus__int_Oabs__eq,axiom,
% 8.69/5.00      ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.69/5.00        ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.69/5.00        = ( abs_Integ
% 8.69/5.00          @ ( produc27273713700761075at_nat
% 8.69/5.00            @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00                ( produc2626176000494625587at_nat
% 8.69/5.00                @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 8.69/5.00            @ Xa2
% 8.69/5.00            @ X ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9799_Gcd__int__greater__eq__0,axiom,
% 8.69/5.00      ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9800_less__eq__int_Orep__eq,axiom,
% 8.69/5.00      ( ord_less_eq_int
% 8.69/5.00      = ( ^ [X3: int,Xa4: int] :
% 8.69/5.00            ( produc8739625826339149834_nat_o
% 8.69/5.00            @ ^ [Y3: nat,Z3: nat] :
% 8.69/5.00                ( produc6081775807080527818_nat_o
% 8.69/5.00                @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 8.69/5.00            @ ( rep_Integ @ X3 )
% 8.69/5.00            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9801_less__int_Orep__eq,axiom,
% 8.69/5.00      ( ord_less_int
% 8.69/5.00      = ( ^ [X3: int,Xa4: int] :
% 8.69/5.00            ( produc8739625826339149834_nat_o
% 8.69/5.00            @ ^ [Y3: nat,Z3: nat] :
% 8.69/5.00                ( produc6081775807080527818_nat_o
% 8.69/5.00                @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 8.69/5.00            @ ( rep_Integ @ X3 )
% 8.69/5.00            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9802_nat_Orep__eq,axiom,
% 8.69/5.00      ( nat2
% 8.69/5.00      = ( ^ [X3: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9803_prod__encode__def,axiom,
% 8.69/5.00      ( nat_prod_encode
% 8.69/5.00      = ( produc6842872674320459806at_nat
% 8.69/5.00        @ ^ [M3: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N2 ) ) @ M3 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9804_le__prod__encode__1,axiom,
% 8.69/5.00      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9805_le__prod__encode__2,axiom,
% 8.69/5.00      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9806_prod__encode__prod__decode__aux,axiom,
% 8.69/5.00      ! [K: nat,M: nat] :
% 8.69/5.00        ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 8.69/5.00        = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9807_uminus__int__def,axiom,
% 8.69/5.00      ( uminus_uminus_int
% 8.69/5.00      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 8.69/5.00        @ ( produc2626176000494625587at_nat
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9808_times__int__def,axiom,
% 8.69/5.00      ( times_times_int
% 8.69/5.00      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.69/5.00        @ ( produc27273713700761075at_nat
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc2626176000494625587at_nat
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9809_minus__int__def,axiom,
% 8.69/5.00      ( minus_minus_int
% 8.69/5.00      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.69/5.00        @ ( produc27273713700761075at_nat
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc2626176000494625587at_nat
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9810_plus__int__def,axiom,
% 8.69/5.00      ( plus_plus_int
% 8.69/5.00      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.69/5.00        @ ( produc27273713700761075at_nat
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc2626176000494625587at_nat
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9811_num__of__nat_Osimps_I2_J,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00         => ( ( num_of_nat @ ( suc @ N ) )
% 8.69/5.00            = ( inc @ ( num_of_nat @ N ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00         => ( ( num_of_nat @ ( suc @ N ) )
% 8.69/5.00            = one ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9812_num__of__nat__numeral__eq,axiom,
% 8.69/5.00      ! [Q2: num] :
% 8.69/5.00        ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 8.69/5.00        = Q2 ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9813_num__of__nat_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( num_of_nat @ zero_zero_nat )
% 8.69/5.00      = one ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9814_numeral__num__of__nat,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 8.69/5.00          = N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9815_num__of__nat__One,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 8.69/5.00       => ( ( num_of_nat @ N )
% 8.69/5.00          = one ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9816_num__of__nat__double,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 8.69/5.00          = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9817_num__of__nat__plus__distrib,axiom,
% 8.69/5.00      ! [M: nat,N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.69/5.00       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00         => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 8.69/5.00            = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9818_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 8.69/5.00      ! [N: nat,J: nat,I: nat] :
% 8.69/5.00        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 8.69/5.00       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 8.69/5.00          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9819_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 8.69/5.00      ! [N: nat,J: nat,I: nat] :
% 8.69/5.00        ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 8.69/5.00       => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 8.69/5.00          = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9820_pow_Osimps_I3_J,axiom,
% 8.69/5.00      ! [X: num,Y: num] :
% 8.69/5.00        ( ( pow @ X @ ( bit1 @ Y ) )
% 8.69/5.00        = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9821_finite__greaterThanAtMost,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9822_card__greaterThanAtMost,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 8.69/5.00        = ( minus_minus_nat @ U @ L2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9823_atLeastSucAtMost__greaterThanAtMost,axiom,
% 8.69/5.00      ! [L2: nat,U: nat] :
% 8.69/5.00        ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 8.69/5.00        = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9824_sqr_Osimps_I2_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( sqr @ ( bit0 @ N ) )
% 8.69/5.00        = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9825_sqr_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( sqr @ one )
% 8.69/5.00      = one ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9826_sqr__conv__mult,axiom,
% 8.69/5.00      ( sqr
% 8.69/5.00      = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9827_pow_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: num,Y: num] :
% 8.69/5.00        ( ( pow @ X @ ( bit0 @ Y ) )
% 8.69/5.00        = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9828_sqr_Osimps_I3_J,axiom,
% 8.69/5.00      ! [N: num] :
% 8.69/5.00        ( ( sqr @ ( bit1 @ N ) )
% 8.69/5.00        = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9829_rat__floor__lemma,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 8.69/5.00        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9830_finite__greaterThanAtMost__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9831_mult__rat,axiom,
% 8.69/5.00      ! [A: int,B: int,C: int,D: int] :
% 8.69/5.00        ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00        = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9832_divide__rat,axiom,
% 8.69/5.00      ! [A: int,B: int,C: int,D: int] :
% 8.69/5.00        ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00        = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9833_card__greaterThanAtMost__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 8.69/5.00        = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9834_less__rat,axiom,
% 8.69/5.00      ! [B: int,D: int,A: int,C: int] :
% 8.69/5.00        ( ( B != zero_zero_int )
% 8.69/5.00       => ( ( D != zero_zero_int )
% 8.69/5.00         => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00            = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9835_add__rat,axiom,
% 8.69/5.00      ! [B: int,D: int,A: int,C: int] :
% 8.69/5.00        ( ( B != zero_zero_int )
% 8.69/5.00       => ( ( D != zero_zero_int )
% 8.69/5.00         => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00            = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9836_le__rat,axiom,
% 8.69/5.00      ! [B: int,D: int,A: int,C: int] :
% 8.69/5.00        ( ( B != zero_zero_int )
% 8.69/5.00       => ( ( D != zero_zero_int )
% 8.69/5.00         => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00            = ( 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 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9837_diff__rat,axiom,
% 8.69/5.00      ! [B: int,D: int,A: int,C: int] :
% 8.69/5.00        ( ( B != zero_zero_int )
% 8.69/5.00       => ( ( D != zero_zero_int )
% 8.69/5.00         => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 8.69/5.00            = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9838_sgn__rat,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 8.69/5.00        = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9839_Fract__of__int__eq,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( fract @ K @ one_one_int )
% 8.69/5.00        = ( ring_1_of_int_rat @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9840_quotient__of__eq,axiom,
% 8.69/5.00      ! [A: int,B: int,P5: int,Q2: int] :
% 8.69/5.00        ( ( ( quotient_of @ ( fract @ A @ B ) )
% 8.69/5.00          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00       => ( ( fract @ P5 @ Q2 )
% 8.69/5.00          = ( fract @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9841_One__rat__def,axiom,
% 8.69/5.00      ( one_one_rat
% 8.69/5.00      = ( fract @ one_one_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9842_rat__number__collapse_I1_J,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( fract @ zero_zero_int @ K )
% 8.69/5.00        = zero_zero_rat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9843_rat__number__collapse_I6_J,axiom,
% 8.69/5.00      ! [K: int] :
% 8.69/5.00        ( ( fract @ K @ zero_zero_int )
% 8.69/5.00        = zero_zero_rat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9844_mult__rat__cancel,axiom,
% 8.69/5.00      ! [C: int,A: int,B: int] :
% 8.69/5.00        ( ( C != zero_zero_int )
% 8.69/5.00       => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 8.69/5.00          = ( fract @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9845_eq__rat_I1_J,axiom,
% 8.69/5.00      ! [B: int,D: int,A: int,C: int] :
% 8.69/5.00        ( ( B != zero_zero_int )
% 8.69/5.00       => ( ( D != zero_zero_int )
% 8.69/5.00         => ( ( ( fract @ A @ B )
% 8.69/5.00              = ( fract @ C @ D ) )
% 8.69/5.00            = ( ( times_times_int @ A @ D )
% 8.69/5.00              = ( times_times_int @ C @ B ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9846_Fract__of__nat__eq,axiom,
% 8.69/5.00      ! [K: nat] :
% 8.69/5.00        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 8.69/5.00        = ( semiri681578069525770553at_rat @ K ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9847_eq__rat_I2_J,axiom,
% 8.69/5.00      ! [A: int] :
% 8.69/5.00        ( ( fract @ A @ zero_zero_int )
% 8.69/5.00        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9848_eq__rat_I3_J,axiom,
% 8.69/5.00      ! [A: int,C: int] :
% 8.69/5.00        ( ( fract @ zero_zero_int @ A )
% 8.69/5.00        = ( fract @ zero_zero_int @ C ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9849_Rat__induct__pos,axiom,
% 8.69/5.00      ! [P: rat > $o,Q2: rat] :
% 8.69/5.00        ( ! [A5: int,B5: int] :
% 8.69/5.00            ( ( ord_less_int @ zero_zero_int @ B5 )
% 8.69/5.00           => ( P @ ( fract @ A5 @ B5 ) ) )
% 8.69/5.00       => ( P @ Q2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9850_normalize__eq,axiom,
% 8.69/5.00      ! [A: int,B: int,P5: int,Q2: int] :
% 8.69/5.00        ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 8.69/5.00          = ( product_Pair_int_int @ P5 @ Q2 ) )
% 8.69/5.00       => ( ( fract @ P5 @ Q2 )
% 8.69/5.00          = ( fract @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9851_Zero__rat__def,axiom,
% 8.69/5.00      ( zero_zero_rat
% 8.69/5.00      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9852_rat__number__collapse_I3_J,axiom,
% 8.69/5.00      ! [W: num] :
% 8.69/5.00        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 8.69/5.00        = ( numeral_numeral_rat @ W ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9853_rat__number__expand_I3_J,axiom,
% 8.69/5.00      ( numeral_numeral_rat
% 8.69/5.00      = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9854_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 8.69/5.00        = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9855_quotient__of__Fract,axiom,
% 8.69/5.00      ! [A: int,B: int] :
% 8.69/5.00        ( ( quotient_of @ ( fract @ A @ B ) )
% 8.69/5.00        = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9856_zero__less__Fract__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 8.69/5.00          = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9857_Fract__less__zero__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 8.69/5.00          = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9858_one__less__Fract__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 8.69/5.00          = ( ord_less_int @ B @ A ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9859_Fract__less__one__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 8.69/5.00          = ( ord_less_int @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9860_rat__number__collapse_I5_J,axiom,
% 8.69/5.00      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.69/5.00      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9861_Fract__add__one,axiom,
% 8.69/5.00      ! [N: int,M: int] :
% 8.69/5.00        ( ( N != zero_zero_int )
% 8.69/5.00       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 8.69/5.00          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9862_Fract__le__zero__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 8.69/5.00          = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9863_zero__le__Fract__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 8.69/5.00          = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9864_Fract__le__one__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 8.69/5.00          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9865_one__le__Fract__iff,axiom,
% 8.69/5.00      ! [B: int,A: int] :
% 8.69/5.00        ( ( ord_less_int @ zero_zero_int @ B )
% 8.69/5.00       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 8.69/5.00          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9866_rat__number__collapse_I4_J,axiom,
% 8.69/5.00      ! [W: num] :
% 8.69/5.00        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 8.69/5.00        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9867_rat__number__expand_I5_J,axiom,
% 8.69/5.00      ! [K: num] :
% 8.69/5.00        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 8.69/5.00        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9868_image__minus__const__atLeastLessThan__nat,axiom,
% 8.69/5.00      ! [C: nat,Y: nat,X: nat] :
% 8.69/5.00        ( ( ( ord_less_nat @ C @ Y )
% 8.69/5.00         => ( ( image_nat_nat
% 8.69/5.00              @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 8.69/5.00              @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.69/5.00            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_nat @ C @ Y )
% 8.69/5.00         => ( ( ( ord_less_nat @ X @ Y )
% 8.69/5.00             => ( ( image_nat_nat
% 8.69/5.00                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 8.69/5.00                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.69/5.00                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 8.69/5.00            & ( ~ ( ord_less_nat @ X @ Y )
% 8.69/5.00             => ( ( image_nat_nat
% 8.69/5.00                  @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 8.69/5.00                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.69/5.00                = bot_bot_set_nat ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9869_of__nat__eq__id,axiom,
% 8.69/5.00      semiri1316708129612266289at_nat = id_nat ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9870_bij__betw__Suc,axiom,
% 8.69/5.00      ! [M5: set_nat,N4: set_nat] :
% 8.69/5.00        ( ( bij_betw_nat_nat @ suc @ M5 @ N4 )
% 8.69/5.00        = ( ( image_nat_nat @ suc @ M5 )
% 8.69/5.00          = N4 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9871_image__Suc__atLeastAtMost,axiom,
% 8.69/5.00      ! [I: nat,J: nat] :
% 8.69/5.00        ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 8.69/5.00        = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9872_image__Suc__atLeastLessThan,axiom,
% 8.69/5.00      ! [I: nat,J: nat] :
% 8.69/5.00        ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 8.69/5.00        = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9873_less__eq__int__def,axiom,
% 8.69/5.00      ( ord_less_eq_int
% 8.69/5.00      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 8.69/5.00        @ ( produc8739625826339149834_nat_o
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc6081775807080527818_nat_o
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9874_zero__notin__Suc__image,axiom,
% 8.69/5.00      ! [A2: set_nat] :
% 8.69/5.00        ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9875_less__int__def,axiom,
% 8.69/5.00      ( ord_less_int
% 8.69/5.00      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 8.69/5.00        @ ( produc8739625826339149834_nat_o
% 8.69/5.00          @ ^ [X3: nat,Y3: nat] :
% 8.69/5.00              ( produc6081775807080527818_nat_o
% 8.69/5.00              @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9876_nat__def,axiom,
% 8.69/5.00      ( nat2
% 8.69/5.00      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9877_image__Suc__lessThan,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.00        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9878_image__Suc__atMost,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 8.69/5.00        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9879_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.69/5.00        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9880_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.69/5.00        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9881_lessThan__Suc__eq__insert__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 8.69/5.00        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9882_atMost__Suc__eq__insert__0,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 8.69/5.00        = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9883_UN__lessThan__UNIV,axiom,
% 8.69/5.00      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 8.69/5.00      = top_top_set_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9884_UN__atMost__UNIV,axiom,
% 8.69/5.00      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 8.69/5.00      = top_top_set_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9885_Inf__real__def,axiom,
% 8.69/5.00      ( comple4887499456419720421f_real
% 8.69/5.00      = ( ^ [X2: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9886_finite__int__iff__bounded__le,axiom,
% 8.69/5.00      ( finite_finite_int
% 8.69/5.00      = ( ^ [S6: set_int] :
% 8.69/5.00          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9887_finite__int__iff__bounded,axiom,
% 8.69/5.00      ( finite_finite_int
% 8.69/5.00      = ( ^ [S6: set_int] :
% 8.69/5.00          ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9888_image__int__atLeastAtMost,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.69/5.00        = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9889_image__int__atLeastLessThan,axiom,
% 8.69/5.00      ! [A: nat,B: nat] :
% 8.69/5.00        ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 8.69/5.00        = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9890_suminf__eq__SUP__real,axiom,
% 8.69/5.00      ! [X8: nat > real] :
% 8.69/5.00        ( ( summable_real @ X8 )
% 8.69/5.00       => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 8.69/5.00         => ( ( suminf_real @ X8 )
% 8.69/5.00            = ( comple1385675409528146559p_real
% 8.69/5.00              @ ( image_nat_real
% 8.69/5.00                @ ^ [I5: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I5 ) )
% 8.69/5.00                @ top_top_set_nat ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9891_image__add__int__atLeastLessThan,axiom,
% 8.69/5.00      ! [L2: int,U: int] :
% 8.69/5.00        ( ( image_int_int
% 8.69/5.00          @ ^ [X3: int] : ( plus_plus_int @ X3 @ L2 )
% 8.69/5.00          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 8.69/5.00        = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9892_range__mod,axiom,
% 8.69/5.00      ! [N: nat] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( image_nat_nat
% 8.69/5.00            @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 8.69/5.00            @ top_top_set_nat )
% 8.69/5.00          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9893_image__atLeastZeroLessThan__int,axiom,
% 8.69/5.00      ! [U: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.69/5.00       => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 8.69/5.00          = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9894_UNIV__nat__eq,axiom,
% 8.69/5.00      ( top_top_set_nat
% 8.69/5.00      = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9895_card__UNIV__unit,axiom,
% 8.69/5.00      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 8.69/5.00      = one_one_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9896_card__UNIV__bool,axiom,
% 8.69/5.00      ( ( finite_card_o @ top_top_set_o )
% 8.69/5.00      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9897_range__mult,axiom,
% 8.69/5.00      ! [A: real] :
% 8.69/5.00        ( ( ( A = zero_zero_real )
% 8.69/5.00         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.69/5.00            = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 8.69/5.00        & ( ( A != zero_zero_real )
% 8.69/5.00         => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.69/5.00            = top_top_set_real ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9898_root__def,axiom,
% 8.69/5.00      ( root
% 8.69/5.00      = ( ^ [N2: nat,X3: real] :
% 8.69/5.00            ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 8.69/5.00            @ ( the_in5290026491893676941l_real @ top_top_set_real
% 8.69/5.00              @ ^ [Y3: real] : ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N2 ) )
% 8.69/5.00              @ X3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9899_card__UNIV__char,axiom,
% 8.69/5.00      ( ( finite_card_char @ top_top_set_char )
% 8.69/5.00      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9900_UNIV__char__of__nat,axiom,
% 8.69/5.00      ( top_top_set_char
% 8.69/5.00      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9901_char_Osize_I2_J,axiom,
% 8.69/5.00      ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.69/5.00        ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.69/5.00        = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9902_nat__of__char__less__256,axiom,
% 8.69/5.00      ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9903_range__nat__of__char,axiom,
% 8.69/5.00      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 8.69/5.00      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9904_integer__of__char__code,axiom,
% 8.69/5.00      ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 8.69/5.00        ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 8.69/5.00        = ( 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 ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9905_char_Osize__gen,axiom,
% 8.69/5.00      ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.69/5.00        ( ( size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.69/5.00        = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9906_String_Ochar__of__ascii__of,axiom,
% 8.69/5.00      ! [C: char] :
% 8.69/5.00        ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 8.69/5.00        = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9907_sorted__list__of__set__lessThan__Suc,axiom,
% 8.69/5.00      ! [K: nat] :
% 8.69/5.00        ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 8.69/5.00        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9908_sorted__list__of__set__atMost__Suc,axiom,
% 8.69/5.00      ! [K: nat] :
% 8.69/5.00        ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 8.69/5.00        = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9909_sorted__list__of__set__greaterThanAtMost,axiom,
% 8.69/5.00      ! [I: nat,J: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 8.69/5.00       => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 8.69/5.00          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9910_sorted__list__of__set__greaterThanLessThan,axiom,
% 8.69/5.00      ! [I: nat,J: nat] :
% 8.69/5.00        ( ( ord_less_nat @ ( suc @ I ) @ J )
% 8.69/5.00       => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 8.69/5.00          = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9911_list__encode_Oelims,axiom,
% 8.69/5.00      ! [X: list_nat,Y: nat] :
% 8.69/5.00        ( ( ( nat_list_encode @ X )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( X = nil_nat )
% 8.69/5.00           => ( Y != zero_zero_nat ) )
% 8.69/5.00         => ~ ! [X6: nat,Xs3: list_nat] :
% 8.69/5.00                ( ( X
% 8.69/5.00                  = ( cons_nat @ X6 @ Xs3 ) )
% 8.69/5.00               => ( Y
% 8.69/5.00                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9912_upto__aux__rec,axiom,
% 8.69/5.00      ( upto_aux
% 8.69/5.00      = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9913_sup__enat__def,axiom,
% 8.69/5.00      sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9914_sup__nat__def,axiom,
% 8.69/5.00      sup_sup_nat = ord_max_nat ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9915_atLeastLessThan__add__Un,axiom,
% 8.69/5.00      ! [I: nat,J: nat,K: nat] :
% 8.69/5.00        ( ( ord_less_eq_nat @ I @ J )
% 8.69/5.00       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 8.69/5.00          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9916_list__encode_Osimps_I1_J,axiom,
% 8.69/5.00      ( ( nat_list_encode @ nil_nat )
% 8.69/5.00      = zero_zero_nat ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9917_list__encode_Osimps_I2_J,axiom,
% 8.69/5.00      ! [X: nat,Xs: list_nat] :
% 8.69/5.00        ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 8.69/5.00        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9918_list__encode_Opelims,axiom,
% 8.69/5.00      ! [X: list_nat,Y: nat] :
% 8.69/5.00        ( ( ( nat_list_encode @ X )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 8.69/5.00         => ( ( ( X = nil_nat )
% 8.69/5.00             => ( ( Y = zero_zero_nat )
% 8.69/5.00               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 8.69/5.00           => ~ ! [X6: nat,Xs3: list_nat] :
% 8.69/5.00                  ( ( X
% 8.69/5.00                    = ( cons_nat @ X6 @ Xs3 ) )
% 8.69/5.00                 => ( ( Y
% 8.69/5.00                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 8.69/5.00                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X6 @ Xs3 ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9919_upto_Opelims,axiom,
% 8.69/5.00      ! [X: int,Xa2: int,Y: list_int] :
% 8.69/5.00        ( ( ( upto @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 8.69/5.00         => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 8.69/5.00                 => ( Y
% 8.69/5.00                    = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 8.69/5.00                & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 8.69/5.00                 => ( Y = nil_int ) ) )
% 8.69/5.00             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9920_upto__Nil,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( ( upto @ I @ J )
% 8.69/5.00          = nil_int )
% 8.69/5.00        = ( ord_less_int @ J @ I ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9921_upto__Nil2,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( nil_int
% 8.69/5.00          = ( upto @ I @ J ) )
% 8.69/5.00        = ( ord_less_int @ J @ I ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9922_upto__empty,axiom,
% 8.69/5.00      ! [J: int,I: int] :
% 8.69/5.00        ( ( ord_less_int @ J @ I )
% 8.69/5.00       => ( ( upto @ I @ J )
% 8.69/5.00          = nil_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9923_upto__single,axiom,
% 8.69/5.00      ! [I: int] :
% 8.69/5.00        ( ( upto @ I @ I )
% 8.69/5.00        = ( cons_int @ I @ nil_int ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9924_nth__upto,axiom,
% 8.69/5.00      ! [I: int,K: nat,J: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 8.69/5.00       => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 8.69/5.00          = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9925_length__upto,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 8.69/5.00        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9926_upto__rec__numeral_I1_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00            = nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9927_upto__rec__numeral_I2_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00            = nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9928_upto__rec__numeral_I3_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.00            = nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9929_upto__rec__numeral_I4_J,axiom,
% 8.69/5.00      ! [M: num,N: num] :
% 8.69/5.00        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.69/5.00        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.00            = nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9930_upto__aux__def,axiom,
% 8.69/5.00      ( upto_aux
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9931_upto__code,axiom,
% 8.69/5.00      ( upto
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9932_distinct__upto,axiom,
% 8.69/5.00      ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9933_atLeastAtMost__upto,axiom,
% 8.69/5.00      ( set_or1266510415728281911st_int
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9934_upto__split2,axiom,
% 8.69/5.00      ! [I: int,J: int,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00       => ( ( ord_less_eq_int @ J @ K )
% 8.69/5.00         => ( ( upto @ I @ K )
% 8.69/5.00            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9935_upto__split1,axiom,
% 8.69/5.00      ! [I: int,J: int,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00       => ( ( ord_less_eq_int @ J @ K )
% 8.69/5.00         => ( ( upto @ I @ K )
% 8.69/5.00            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9936_atLeastLessThan__upto,axiom,
% 8.69/5.00      ( set_or4662586982721622107an_int
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9937_greaterThanAtMost__upto,axiom,
% 8.69/5.00      ( set_or6656581121297822940st_int
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9938_upto_Oelims,axiom,
% 8.69/5.00      ! [X: int,Xa2: int,Y: list_int] :
% 8.69/5.00        ( ( ( upto @ X @ Xa2 )
% 8.69/5.00          = Y )
% 8.69/5.00       => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 8.69/5.00           => ( Y
% 8.69/5.00              = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 8.69/5.00           => ( Y = nil_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9939_upto_Osimps,axiom,
% 8.69/5.00      ( upto
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9940_upto__rec1,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00       => ( ( upto @ I @ J )
% 8.69/5.00          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9941_upto__rec2,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00       => ( ( upto @ I @ J )
% 8.69/5.00          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9942_greaterThanLessThan__upto,axiom,
% 8.69/5.00      ( set_or5832277885323065728an_int
% 8.69/5.00      = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9943_upto__split3,axiom,
% 8.69/5.00      ! [I: int,J: int,K: int] :
% 8.69/5.00        ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00       => ( ( ord_less_eq_int @ J @ K )
% 8.69/5.00         => ( ( upto @ I @ K )
% 8.69/5.00            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9944_upto_Opsimps,axiom,
% 8.69/5.00      ! [I: int,J: int] :
% 8.69/5.00        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 8.69/5.00       => ( ( ( ord_less_eq_int @ I @ J )
% 8.69/5.00           => ( ( upto @ I @ J )
% 8.69/5.00              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 8.69/5.00          & ( ~ ( ord_less_eq_int @ I @ J )
% 8.69/5.00           => ( ( upto @ I @ J )
% 8.69/5.00              = nil_int ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9945_DERIV__real__root__generic,axiom,
% 8.69/5.00      ! [N: nat,X: real,D4: real] :
% 8.69/5.00        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.00       => ( ( X != zero_zero_real )
% 8.69/5.00         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00             => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00               => ( D4
% 8.69/5.00                  = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 8.69/5.00           => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00               => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/5.00                 => ( D4
% 8.69/5.00                    = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 8.69/5.00             => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.00                 => ( D4
% 8.69/5.00                    = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 8.69/5.00               => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9946_DERIV__local__const,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real,D: real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ D )
% 8.69/5.00         => ( ! [Y5: real] :
% 8.69/5.00                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 8.69/5.00               => ( ( F @ X )
% 8.69/5.00                  = ( F @ Y5 ) ) )
% 8.69/5.00           => ( L2 = zero_zero_real ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9947_DERIV__pos__inc__left,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                   => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9948_DERIV__neg__dec__left,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.00       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9949_DERIV__const__ratio__const,axiom,
% 8.69/5.00      ! [A: real,B: real,F: real > real,K: real] :
% 8.69/5.00        ( ( A != B )
% 8.69/5.00       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.00         => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.69/5.00            = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9950_DERIV__const__ratio__const2,axiom,
% 8.69/5.00      ! [A: real,B: real,F: real > real,K: real] :
% 8.69/5.00        ( ( A != B )
% 8.69/5.00       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.00         => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 8.69/5.00            = K ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9951_DERIV__isconst__all,axiom,
% 8.69/5.00      ! [F: real > real,X: real,Y: real] :
% 8.69/5.00        ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.00       => ( ( F @ X )
% 8.69/5.00          = ( F @ Y ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9952_DERIV__neg__dec__right,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.00       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                   => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9953_DERIV__pos__inc__right,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                   => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9954_DERIV__ln,axiom,
% 8.69/5.00      ! [X: real] :
% 8.69/5.00        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.00       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9955_DERIV__isconst3,axiom,
% 8.69/5.00      ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 8.69/5.00        ( ( ord_less_real @ A @ B )
% 8.69/5.00       => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.00         => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.00           => ( ! [X6: real] :
% 8.69/5.00                  ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.00                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 8.69/5.00             => ( ( F @ X )
% 8.69/5.00                = ( F @ Y ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9956_has__real__derivative__pos__inc__right,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 8.69/5.00                   => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9957_has__real__derivative__neg__dec__right,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 8.69/5.00       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 8.69/5.00                   => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                     => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9958_has__real__derivative__pos__inc__left,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 8.69/5.00       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 8.69/5.00                   => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                     => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 8.69/5.00  
% 8.69/5.00  thf(fact_9959_has__real__derivative__neg__dec__left,axiom,
% 8.69/5.00      ! [F: real > real,L2: real,X: real,S2: set_real] :
% 8.69/5.00        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 8.69/5.00       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 8.69/5.00         => ? [D3: real] :
% 8.69/5.00              ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.69/5.00              & ! [H4: real] :
% 8.69/5.00                  ( ( ord_less_real @ zero_zero_real @ H4 )
% 8.69/5.00                 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 8.69/5.00                   => ( ( ord_less_real @ H4 @ D3 )
% 8.69/5.00                     => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9960_MVT2,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,F5: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01               => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01         => ? [Z5: real] :
% 8.69/5.01              ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01              & ( ord_less_real @ Z5 @ B )
% 8.69/5.01              & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.69/5.01                = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z5 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9961_DERIV__neg__imp__decreasing,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 8.69/5.01         => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9962_DERIV__pos__imp__increasing,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 8.69/5.01         => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9963_deriv__nonneg__imp__mono,axiom,
% 8.69/5.01      ! [A: real,B: real,G: real > real,G2: real > real] :
% 8.69/5.01        ( ! [X6: real] :
% 8.69/5.01            ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.69/5.01           => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.69/5.01             => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X6 ) ) )
% 8.69/5.01         => ( ( ord_less_eq_real @ A @ B )
% 8.69/5.01           => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9964_DERIV__nonpos__imp__nonincreasing,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_eq_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_eq_real @ Y2 @ zero_zero_real ) ) ) )
% 8.69/5.01         => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9965_DERIV__nonneg__imp__nondecreasing,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_eq_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) )
% 8.69/5.01         => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9966_DERIV__const__average,axiom,
% 8.69/5.01      ! [A: real,B: real,V: real > real,K: real] :
% 8.69/5.01        ( ( A != B )
% 8.69/5.01       => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01         => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.69/5.01            = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9967_DERIV__local__min,axiom,
% 8.69/5.01      ! [F: real > real,L2: real,X: real,D: real] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ D )
% 8.69/5.01         => ( ! [Y5: real] :
% 8.69/5.01                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 8.69/5.01               => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y5 ) ) )
% 8.69/5.01           => ( L2 = zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9968_DERIV__local__max,axiom,
% 8.69/5.01      ! [F: real > real,L2: real,X: real,D: real] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ D )
% 8.69/5.01         => ( ! [Y5: real] :
% 8.69/5.01                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 8.69/5.01               => ( ord_less_eq_real @ ( F @ Y5 ) @ ( F @ X ) ) )
% 8.69/5.01           => ( L2 = zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9969_DERIV__ln__divide,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.01       => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9970_DERIV__pow,axiom,
% 8.69/5.01      ! [N: nat,X: real,S: set_real] :
% 8.69/5.01        ( has_fi5821293074295781190e_real
% 8.69/5.01        @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 8.69/5.01        @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 8.69/5.01        @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9971_DERIV__fun__pow,axiom,
% 8.69/5.01      ! [G: real > real,M: real,X: real,N: nat] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( has_fi5821293074295781190e_real
% 8.69/5.01          @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 8.69/5.01          @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9972_has__real__derivative__powr,axiom,
% 8.69/5.01      ! [Z: real,R: real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ Z )
% 8.69/5.01       => ( has_fi5821293074295781190e_real
% 8.69/5.01          @ ^ [Z3: real] : ( powr_real @ Z3 @ R )
% 8.69/5.01          @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9973_DERIV__log,axiom,
% 8.69/5.01      ! [X: real,B: real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.01       => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9974_DERIV__fun__powr,axiom,
% 8.69/5.01      ! [G: real > real,M: real,X: real,R: real] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 8.69/5.01         => ( has_fi5821293074295781190e_real
% 8.69/5.01            @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R )
% 8.69/5.01            @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9975_DERIV__powr,axiom,
% 8.69/5.01      ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 8.69/5.01         => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01           => ( has_fi5821293074295781190e_real
% 8.69/5.01              @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 8.69/5.01              @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9976_DERIV__real__sqrt,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.01       => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9977_DERIV__series_H,axiom,
% 8.69/5.01      ! [F: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 8.69/5.01        ( ! [N3: nat] :
% 8.69/5.01            ( has_fi5821293074295781190e_real
% 8.69/5.01            @ ^ [X3: real] : ( F @ X3 @ N3 )
% 8.69/5.01            @ ( F5 @ X0 @ N3 )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.01             => ( summable_real @ ( F @ X6 ) ) )
% 8.69/5.01         => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.01           => ( ( summable_real @ ( F5 @ X0 ) )
% 8.69/5.01             => ( ( summable_real @ L5 )
% 8.69/5.01               => ( ! [N3: nat,X6: real,Y5: real] :
% 8.69/5.01                      ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.01                     => ( ( member_real @ Y5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.69/5.01                       => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X6 @ N3 ) @ ( F @ Y5 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X6 @ Y5 ) ) ) ) ) )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real
% 8.69/5.01                    @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 8.69/5.01                    @ ( suminf_real @ ( F5 @ X0 ) )
% 8.69/5.01                    @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9978_DERIV__arctan,axiom,
% 8.69/5.01      ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9979_arsinh__real__has__field__derivative,axiom,
% 8.69/5.01      ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9980_DERIV__real__sqrt__generic,axiom,
% 8.69/5.01      ! [X: real,D4: real] :
% 8.69/5.01        ( ( X != zero_zero_real )
% 8.69/5.01       => ( ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.01           => ( D4
% 8.69/5.01              = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01         => ( ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/5.01             => ( D4
% 8.69/5.01                = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01           => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9981_arcosh__real__has__field__derivative,axiom,
% 8.69/5.01      ! [X: real,A2: set_real] :
% 8.69/5.01        ( ( ord_less_real @ one_one_real @ X )
% 8.69/5.01       => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9982_artanh__real__has__field__derivative,axiom,
% 8.69/5.01      ! [X: real,A2: set_real] :
% 8.69/5.01        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/5.01       => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9983_DERIV__power__series_H,axiom,
% 8.69/5.01      ! [R4: real,F: nat > real,X0: real] :
% 8.69/5.01        ( ! [X6: real] :
% 8.69/5.01            ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 8.69/5.01           => ( summable_real
% 8.69/5.01              @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X6 @ N2 ) ) ) )
% 8.69/5.01       => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 8.69/5.01         => ( ( ord_less_real @ zero_zero_real @ R4 )
% 8.69/5.01           => ( has_fi5821293074295781190e_real
% 8.69/5.01              @ ^ [X3: real] :
% 8.69/5.01                  ( suminf_real
% 8.69/5.01                  @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) )
% 8.69/5.01              @ ( suminf_real
% 8.69/5.01                @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9984_DERIV__real__root,axiom,
% 8.69/5.01      ! [N: nat,X: real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ X )
% 8.69/5.01         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9985_DERIV__arccos,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9986_DERIV__arcsin,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9987_Maclaurin__all__le__objl,axiom,
% 8.69/5.01      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 8.69/5.01        ( ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01            = F )
% 8.69/5.01          & ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 8.69/5.01       => ? [T6: real] :
% 8.69/5.01            ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/5.01            & ( ( F @ X )
% 8.69/5.01              = ( plus_plus_real
% 8.69/5.01                @ ( groups6591440286371151544t_real
% 8.69/5.01                  @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 8.69/5.01                  @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9988_Maclaurin__all__le,axiom,
% 8.69/5.01      ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 8.69/5.01        ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01          = F )
% 8.69/5.01       => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01         => ? [T6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/5.01              & ( ( F @ X )
% 8.69/5.01                = ( plus_plus_real
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9989_DERIV__odd__real__root,axiom,
% 8.69/5.01      ! [N: nat,X: real] :
% 8.69/5.01        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.01       => ( ( X != zero_zero_real )
% 8.69/5.01         => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9990_Maclaurin__minus,axiom,
% 8.69/5.01      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ H2 @ zero_zero_real )
% 8.69/5.01       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01         => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01              = F )
% 8.69/5.01           => ( ! [M4: nat,T6: real] :
% 8.69/5.01                  ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                    & ( ord_less_eq_real @ H2 @ T6 )
% 8.69/5.01                    & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01             => ? [T6: real] :
% 8.69/5.01                  ( ( ord_less_real @ H2 @ T6 )
% 8.69/5.01                  & ( ord_less_real @ T6 @ zero_zero_real )
% 8.69/5.01                  & ( ( F @ H2 )
% 8.69/5.01                    = ( plus_plus_real
% 8.69/5.01                      @ ( groups6591440286371151544t_real
% 8.69/5.01                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 8.69/5.01                        @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9991_Maclaurin2,axiom,
% 8.69/5.01      ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ H2 )
% 8.69/5.01       => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01            = F )
% 8.69/5.01         => ( ! [M4: nat,T6: real] :
% 8.69/5.01                ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                  & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/5.01                  & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.69/5.01               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01           => ? [T6: real] :
% 8.69/5.01                ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.69/5.01                & ( ord_less_eq_real @ T6 @ H2 )
% 8.69/5.01                & ( ( F @ H2 )
% 8.69/5.01                  = ( plus_plus_real
% 8.69/5.01                    @ ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                    @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9992_Maclaurin,axiom,
% 8.69/5.01      ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ H2 )
% 8.69/5.01       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01         => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01              = F )
% 8.69/5.01           => ( ! [M4: nat,T6: real] :
% 8.69/5.01                  ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                    & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/5.01                    & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01             => ? [T6: real] :
% 8.69/5.01                  ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.69/5.01                  & ( ord_less_real @ T6 @ H2 )
% 8.69/5.01                  & ( ( F @ H2 )
% 8.69/5.01                    = ( plus_plus_real
% 8.69/5.01                      @ ( groups6591440286371151544t_real
% 8.69/5.01                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 8.69/5.01                        @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9993_Maclaurin__all__lt,axiom,
% 8.69/5.01      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 8.69/5.01        ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01          = F )
% 8.69/5.01       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01         => ( ( X != zero_zero_real )
% 8.69/5.01           => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01             => ? [T6: real] :
% 8.69/5.01                  ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 8.69/5.01                  & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/5.01                  & ( ( F @ X )
% 8.69/5.01                    = ( plus_plus_real
% 8.69/5.01                      @ ( groups6591440286371151544t_real
% 8.69/5.01                        @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 8.69/5.01                        @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                      @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9994_Maclaurin__bi__le,axiom,
% 8.69/5.01      ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 8.69/5.01        ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01          = F )
% 8.69/5.01       => ( ! [M4: nat,T6: real] :
% 8.69/5.01              ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 8.69/5.01             => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01         => ? [T6: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.69/5.01              & ( ( F @ X )
% 8.69/5.01                = ( plus_plus_real
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                  @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9995_Taylor__down,axiom,
% 8.69/5.01      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01            = F )
% 8.69/5.01         => ( ! [M4: nat,T6: real] :
% 8.69/5.01                ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                  & ( ord_less_eq_real @ A @ T6 )
% 8.69/5.01                  & ( ord_less_eq_real @ T6 @ B ) )
% 8.69/5.01               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01           => ( ( ord_less_real @ A @ C )
% 8.69/5.01             => ( ( ord_less_eq_real @ C @ B )
% 8.69/5.01               => ? [T6: real] :
% 8.69/5.01                    ( ( ord_less_real @ A @ T6 )
% 8.69/5.01                    & ( ord_less_real @ T6 @ C )
% 8.69/5.01                    & ( ( F @ A )
% 8.69/5.01                      = ( plus_plus_real
% 8.69/5.01                        @ ( groups6591440286371151544t_real
% 8.69/5.01                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 8.69/5.01                          @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9996_Taylor__up,axiom,
% 8.69/5.01      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01            = F )
% 8.69/5.01         => ( ! [M4: nat,T6: real] :
% 8.69/5.01                ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                  & ( ord_less_eq_real @ A @ T6 )
% 8.69/5.01                  & ( ord_less_eq_real @ T6 @ B ) )
% 8.69/5.01               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01           => ( ( ord_less_eq_real @ A @ C )
% 8.69/5.01             => ( ( ord_less_real @ C @ B )
% 8.69/5.01               => ? [T6: real] :
% 8.69/5.01                    ( ( ord_less_real @ C @ T6 )
% 8.69/5.01                    & ( ord_less_real @ T6 @ B )
% 8.69/5.01                    & ( ( F @ B )
% 8.69/5.01                      = ( plus_plus_real
% 8.69/5.01                        @ ( groups6591440286371151544t_real
% 8.69/5.01                          @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 8.69/5.01                          @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                        @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9997_Taylor,axiom,
% 8.69/5.01      ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( ( Diff @ zero_zero_nat )
% 8.69/5.01            = F )
% 8.69/5.01         => ( ! [M4: nat,T6: real] :
% 8.69/5.01                ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01                  & ( ord_less_eq_real @ A @ T6 )
% 8.69/5.01                  & ( ord_less_eq_real @ T6 @ B ) )
% 8.69/5.01               => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01           => ( ( ord_less_eq_real @ A @ C )
% 8.69/5.01             => ( ( ord_less_eq_real @ C @ B )
% 8.69/5.01               => ( ( ord_less_eq_real @ A @ X )
% 8.69/5.01                 => ( ( ord_less_eq_real @ X @ B )
% 8.69/5.01                   => ( ( X != C )
% 8.69/5.01                     => ? [T6: real] :
% 8.69/5.01                          ( ( ( ord_less_real @ X @ C )
% 8.69/5.01                           => ( ( ord_less_real @ X @ T6 )
% 8.69/5.01                              & ( ord_less_real @ T6 @ C ) ) )
% 8.69/5.01                          & ( ~ ( ord_less_real @ X @ C )
% 8.69/5.01                           => ( ( ord_less_real @ C @ T6 )
% 8.69/5.01                              & ( ord_less_real @ T6 @ X ) ) )
% 8.69/5.01                          & ( ( F @ X )
% 8.69/5.01                            = ( plus_plus_real
% 8.69/5.01                              @ ( groups6591440286371151544t_real
% 8.69/5.01                                @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M3 ) )
% 8.69/5.01                                @ ( set_ord_lessThan_nat @ N ) )
% 8.69/5.01                              @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9998_Maclaurin__lemma2,axiom,
% 8.69/5.01      ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 8.69/5.01        ( ! [M4: nat,T6: real] :
% 8.69/5.01            ( ( ( ord_less_nat @ M4 @ N )
% 8.69/5.01              & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.69/5.01              & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.69/5.01           => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.69/5.01       => ( ( N
% 8.69/5.01            = ( suc @ K ) )
% 8.69/5.01         => ! [M2: nat,T7: real] :
% 8.69/5.01              ( ( ( ord_less_nat @ M2 @ N )
% 8.69/5.01                & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 8.69/5.01                & ( ord_less_eq_real @ T7 @ H2 ) )
% 8.69/5.01             => ( has_fi5821293074295781190e_real
% 8.69/5.01                @ ^ [U2: real] :
% 8.69/5.01                    ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 8.69/5.01                    @ ( plus_plus_real
% 8.69/5.01                      @ ( groups6591440286371151544t_real
% 8.69/5.01                        @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ U2 @ P2 ) )
% 8.69/5.01                        @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 8.69/5.01                      @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 8.69/5.01                @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 8.69/5.01                  @ ( plus_plus_real
% 8.69/5.01                    @ ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ T7 @ P2 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 8.69/5.01                    @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_9999_DERIV__arctan__series,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/5.01       => ( has_fi5821293074295781190e_real
% 8.69/5.01          @ ^ [X9: real] :
% 8.69/5.01              ( suminf_real
% 8.69/5.01              @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 8.69/5.01          @ ( suminf_real
% 8.69/5.01            @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10000_DERIV__even__real__root,axiom,
% 8.69/5.01      ! [N: nat,X: real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.01         => ( ( ord_less_real @ X @ zero_zero_real )
% 8.69/5.01           => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10001_take__bit__numeral__minus__numeral__int,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int
% 8.69/5.01          @ ^ [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 ) ) )
% 8.69/5.01          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10002_take__bit__num__simps_I1_J,axiom,
% 8.69/5.01      ! [M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 8.69/5.01        = none_num ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10003_take__bit__num__simps_I2_J,axiom,
% 8.69/5.01      ! [N: nat] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 8.69/5.01        = ( some_num @ one ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10004_take__bit__num__simps_I5_J,axiom,
% 8.69/5.01      ! [R: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 8.69/5.01        = ( some_num @ one ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10005_take__bit__num__simps_I3_J,axiom,
% 8.69/5.01      ! [N: nat,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 8.69/5.01        = ( case_o6005452278849405969um_num @ none_num
% 8.69/5.01          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 8.69/5.01          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10006_take__bit__num__simps_I4_J,axiom,
% 8.69/5.01      ! [N: nat,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 8.69/5.01        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10007_take__bit__num__simps_I6_J,axiom,
% 8.69/5.01      ! [R: num,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 8.69/5.01        = ( case_o6005452278849405969um_num @ none_num
% 8.69/5.01          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 8.69/5.01          @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10008_take__bit__num__simps_I7_J,axiom,
% 8.69/5.01      ! [R: num,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 8.69/5.01        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10009_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 8.69/5.01      ! [N: nat,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 8.69/5.01        = ( case_nat_option_num @ none_num
% 8.69/5.01          @ ^ [N2: nat] :
% 8.69/5.01              ( case_o6005452278849405969um_num @ none_num
% 8.69/5.01              @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 8.69/5.01              @ ( bit_take_bit_num @ N2 @ M ) )
% 8.69/5.01          @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10010_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 8.69/5.01      ! [N: nat] :
% 8.69/5.01        ( ( bit_take_bit_num @ N @ one )
% 8.69/5.01        = ( case_nat_option_num @ none_num
% 8.69/5.01          @ ^ [N2: nat] : ( some_num @ one )
% 8.69/5.01          @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10011_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 8.69/5.01      ! [N: nat,M: num] :
% 8.69/5.01        ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 8.69/5.01        = ( case_nat_option_num @ none_num
% 8.69/5.01          @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 8.69/5.01          @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10012_take__bit__num__def,axiom,
% 8.69/5.01      ( bit_take_bit_num
% 8.69/5.01      = ( ^ [N2: nat,M3: num] :
% 8.69/5.01            ( if_option_num
% 8.69/5.01            @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) )
% 8.69/5.01              = zero_zero_nat )
% 8.69/5.01            @ none_num
% 8.69/5.01            @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10013_and__minus__numerals_I7_J,axiom,
% 8.69/5.01      ! [N: num,M: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10014_and__minus__numerals_I3_J,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10015_and__minus__numerals_I4_J,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10016_and__minus__numerals_I8_J,axiom,
% 8.69/5.01      ! [N: num,M: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10017_and__not__num_Osimps_I3_J,axiom,
% 8.69/5.01      ! [N: num] :
% 8.69/5.01        ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 8.69/5.01        = none_num ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10018_and__not__num_Osimps_I1_J,axiom,
% 8.69/5.01      ( ( bit_and_not_num @ one @ one )
% 8.69/5.01      = none_num ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10019_and__not__num_Osimps_I4_J,axiom,
% 8.69/5.01      ! [M: num] :
% 8.69/5.01        ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 8.69/5.01        = ( some_num @ ( bit0 @ M ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10020_and__not__num_Osimps_I2_J,axiom,
% 8.69/5.01      ! [N: num] :
% 8.69/5.01        ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 8.69/5.01        = ( some_num @ one ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10021_and__not__num_Osimps_I7_J,axiom,
% 8.69/5.01      ! [M: num] :
% 8.69/5.01        ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 8.69/5.01        = ( some_num @ ( bit0 @ M ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10022_and__not__num__eq__Some__iff,axiom,
% 8.69/5.01      ! [M: num,N: num,Q2: num] :
% 8.69/5.01        ( ( ( bit_and_not_num @ M @ N )
% 8.69/5.01          = ( some_num @ Q2 ) )
% 8.69/5.01        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.01          = ( numeral_numeral_int @ Q2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10023_and__not__num_Osimps_I8_J,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.69/5.01        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.69/5.01          @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 8.69/5.01          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10024_and__not__num__eq__None__iff,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( ( bit_and_not_num @ M @ N )
% 8.69/5.01          = none_num )
% 8.69/5.01        = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.01          = zero_zero_int ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10025_int__numeral__not__and__num,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10026_int__numeral__and__not__num,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.69/5.01        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10027_Bit__Operations_Otake__bit__num__code,axiom,
% 8.69/5.01      ( bit_take_bit_num
% 8.69/5.01      = ( ^ [N2: nat,M3: num] :
% 8.69/5.01            ( produc478579273971653890on_num
% 8.69/5.01            @ ^ [A3: nat,X3: num] :
% 8.69/5.01                ( case_nat_option_num @ none_num
% 8.69/5.01                @ ^ [O: nat] :
% 8.69/5.01                    ( case_num_option_num @ ( some_num @ one )
% 8.69/5.01                    @ ^ [P2: num] :
% 8.69/5.01                        ( case_o6005452278849405969um_num @ none_num
% 8.69/5.01                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 8.69/5.01                        @ ( bit_take_bit_num @ O @ P2 ) )
% 8.69/5.01                    @ ^ [P2: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P2 ) ) )
% 8.69/5.01                    @ X3 )
% 8.69/5.01                @ A3 )
% 8.69/5.01            @ ( product_Pair_nat_num @ N2 @ M3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10028_isCont__Lb__Ub,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_eq_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01                & ( ord_less_eq_real @ X6 @ B ) )
% 8.69/5.01             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 8.69/5.01         => ? [L6: real,M9: real] :
% 8.69/5.01              ( ! [X4: real] :
% 8.69/5.01                  ( ( ( ord_less_eq_real @ A @ X4 )
% 8.69/5.01                    & ( ord_less_eq_real @ X4 @ B ) )
% 8.69/5.01                 => ( ( ord_less_eq_real @ L6 @ ( F @ X4 ) )
% 8.69/5.01                    & ( ord_less_eq_real @ ( F @ X4 ) @ M9 ) ) )
% 8.69/5.01              & ! [Y2: real] :
% 8.69/5.01                  ( ( ( ord_less_eq_real @ L6 @ Y2 )
% 8.69/5.01                    & ( ord_less_eq_real @ Y2 @ M9 ) )
% 8.69/5.01                 => ? [X6: real] :
% 8.69/5.01                      ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01                      & ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01                      & ( ( F @ X6 )
% 8.69/5.01                        = Y2 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10029_isCont__real__sqrt,axiom,
% 8.69/5.01      ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10030_isCont__real__root,axiom,
% 8.69/5.01      ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10031_isCont__inverse__function2,axiom,
% 8.69/5.01      ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ B )
% 8.69/5.01         => ( ! [Z5: real] :
% 8.69/5.01                ( ( ord_less_eq_real @ A @ Z5 )
% 8.69/5.01               => ( ( ord_less_eq_real @ Z5 @ B )
% 8.69/5.01                 => ( ( G @ ( F @ Z5 ) )
% 8.69/5.01                    = Z5 ) ) )
% 8.69/5.01           => ( ! [Z5: real] :
% 8.69/5.01                  ( ( ord_less_eq_real @ A @ Z5 )
% 8.69/5.01                 => ( ( ord_less_eq_real @ Z5 @ B )
% 8.69/5.01                   => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 8.69/5.01             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10032_isCont__ln,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( X != zero_zero_real )
% 8.69/5.01       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10033_isCont__arcosh,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ one_one_real @ X )
% 8.69/5.01       => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10034_DERIV__inverse__function,axiom,
% 8.69/5.01      ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 8.69/5.01        ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 8.69/5.01       => ( ( D4 != zero_zero_real )
% 8.69/5.01         => ( ( ord_less_real @ A @ X )
% 8.69/5.01           => ( ( ord_less_real @ X @ B )
% 8.69/5.01             => ( ! [Y5: real] :
% 8.69/5.01                    ( ( ord_less_real @ A @ Y5 )
% 8.69/5.01                   => ( ( ord_less_real @ Y5 @ B )
% 8.69/5.01                     => ( ( F @ ( G @ Y5 ) )
% 8.69/5.01                        = Y5 ) ) )
% 8.69/5.01               => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10035_isCont__arccos,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10036_isCont__arcsin,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10037_LIM__less__bound,axiom,
% 8.69/5.01      ! [B: real,X: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ B @ X )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 8.69/5.01             => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 8.69/5.01         => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 8.69/5.01           => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10038_isCont__artanh,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10039_isCont__inverse__function,axiom,
% 8.69/5.01      ! [D: real,X: real,G: real > real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ D )
% 8.69/5.01       => ( ! [Z5: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 8.69/5.01             => ( ( G @ ( F @ Z5 ) )
% 8.69/5.01                = Z5 ) )
% 8.69/5.01         => ( ! [Z5: real] :
% 8.69/5.01                ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 8.69/5.01               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) )
% 8.69/5.01           => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10040_GMVT_H,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [Z5: real] :
% 8.69/5.01              ( ( ord_less_eq_real @ A @ Z5 )
% 8.69/5.01             => ( ( ord_less_eq_real @ Z5 @ B )
% 8.69/5.01               => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 8.69/5.01         => ( ! [Z5: real] :
% 8.69/5.01                ( ( ord_less_eq_real @ A @ Z5 )
% 8.69/5.01               => ( ( ord_less_eq_real @ Z5 @ B )
% 8.69/5.01                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ G ) ) )
% 8.69/5.01           => ( ! [Z5: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01                 => ( ( ord_less_real @ Z5 @ B )
% 8.69/5.01                   => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 8.69/5.01             => ( ! [Z5: real] :
% 8.69/5.01                    ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01                   => ( ( ord_less_real @ Z5 @ B )
% 8.69/5.01                     => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 8.69/5.01               => ? [C2: real] :
% 8.69/5.01                    ( ( ord_less_real @ A @ C2 )
% 8.69/5.01                    & ( ord_less_real @ C2 @ B )
% 8.69/5.01                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 8.69/5.01                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F5 @ C2 ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10041_Gcd__eq__Max,axiom,
% 8.69/5.01      ! [M5: set_nat] :
% 8.69/5.01        ( ( finite_finite_nat @ M5 )
% 8.69/5.01       => ( ( M5 != bot_bot_set_nat )
% 8.69/5.01         => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 8.69/5.01           => ( ( gcd_Gcd_nat @ M5 )
% 8.69/5.01              = ( lattic8265883725875713057ax_nat
% 8.69/5.01                @ ( comple7806235888213564991et_nat
% 8.69/5.01                  @ ( image_nat_set_nat
% 8.69/5.01                    @ ^ [M3: nat] :
% 8.69/5.01                        ( collect_nat
% 8.69/5.01                        @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M3 ) )
% 8.69/5.01                    @ M5 ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10042_Max__divisors__self__nat,axiom,
% 8.69/5.01      ! [N: nat] :
% 8.69/5.01        ( ( N != zero_zero_nat )
% 8.69/5.01       => ( ( lattic8265883725875713057ax_nat
% 8.69/5.01            @ ( collect_nat
% 8.69/5.01              @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 8.69/5.01          = N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10043_LIM__fun__less__zero,axiom,
% 8.69/5.01      ! [F: real > real,L2: real,C: real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ L2 @ zero_zero_real )
% 8.69/5.01         => ? [R2: real] :
% 8.69/5.01              ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.69/5.01              & ! [X4: real] :
% 8.69/5.01                  ( ( ( X4 != C )
% 8.69/5.01                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 8.69/5.01                 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10044_LIM__fun__not__zero,axiom,
% 8.69/5.01      ! [F: real > real,L2: real,C: real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.69/5.01       => ( ( L2 != zero_zero_real )
% 8.69/5.01         => ? [R2: real] :
% 8.69/5.01              ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.69/5.01              & ! [X4: real] :
% 8.69/5.01                  ( ( ( X4 != C )
% 8.69/5.01                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 8.69/5.01                 => ( ( F @ X4 )
% 8.69/5.01                   != zero_zero_real ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10045_LIM__fun__gt__zero,axiom,
% 8.69/5.01      ! [F: real > real,L2: real,C: real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.69/5.01       => ( ( ord_less_real @ zero_zero_real @ L2 )
% 8.69/5.01         => ? [R2: real] :
% 8.69/5.01              ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.69/5.01              & ! [X4: real] :
% 8.69/5.01                  ( ( ( X4 != C )
% 8.69/5.01                    & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 8.69/5.01                 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10046_card__le__Suc__Max,axiom,
% 8.69/5.01      ! [S2: set_nat] :
% 8.69/5.01        ( ( finite_finite_nat @ S2 )
% 8.69/5.01       => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10047_Sup__nat__def,axiom,
% 8.69/5.01      ( complete_Sup_Sup_nat
% 8.69/5.01      = ( ^ [X2: set_nat] : ( if_nat @ ( X2 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X2 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10048_divide__nat__def,axiom,
% 8.69/5.01      ( divide_divide_nat
% 8.69/5.01      = ( ^ [M3: nat,N2: nat] :
% 8.69/5.01            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 8.69/5.01            @ ( lattic8265883725875713057ax_nat
% 8.69/5.01              @ ( collect_nat
% 8.69/5.01                @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N2 ) @ M3 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10049_gcd__is__Max__divisors__nat,axiom,
% 8.69/5.01      ! [N: nat,M: nat] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( gcd_gcd_nat @ M @ N )
% 8.69/5.01          = ( lattic8265883725875713057ax_nat
% 8.69/5.01            @ ( collect_nat
% 8.69/5.01              @ ^ [D2: nat] :
% 8.69/5.01                  ( ( dvd_dvd_nat @ D2 @ M )
% 8.69/5.01                  & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10050_LIM__cos__div__sin,axiom,
% 8.69/5.01      ( filterlim_real_real
% 8.69/5.01      @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 8.69/5.01      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01      @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10051_summable__Leibniz_I3_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ( topolo6980174941875973593q_real @ A )
% 8.69/5.01         => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 8.69/5.01           => ! [N7: nat] :
% 8.69/5.01                ( member_real
% 8.69/5.01                @ ( suminf_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 8.69/5.01                @ ( set_or1222579329274155063t_real
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10052_summable__Leibniz_I2_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ( topolo6980174941875973593q_real @ A )
% 8.69/5.01         => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 8.69/5.01           => ! [N7: nat] :
% 8.69/5.01                ( member_real
% 8.69/5.01                @ ( suminf_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 8.69/5.01                @ ( set_or1222579329274155063t_real
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 8.69/5.01                  @ ( groups6591440286371151544t_real
% 8.69/5.01                    @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                    @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10053_Max__divisors__self__int,axiom,
% 8.69/5.01      ! [N: int] :
% 8.69/5.01        ( ( N != zero_zero_int )
% 8.69/5.01       => ( ( lattic8263393255366662781ax_int
% 8.69/5.01            @ ( collect_int
% 8.69/5.01              @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ N ) ) )
% 8.69/5.01          = ( abs_abs_int @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10054_mult__nat__right__at__top,axiom,
% 8.69/5.01      ! [C: nat] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.69/5.01       => ( filterlim_nat_nat
% 8.69/5.01          @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 8.69/5.01          @ at_top_nat
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10055_mult__nat__left__at__top,axiom,
% 8.69/5.01      ! [C: nat] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.69/5.01       => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10056_monoseq__convergent,axiom,
% 8.69/5.01      ! [X8: nat > real,B3: real] :
% 8.69/5.01        ( ( topolo6980174941875973593q_real @ X8 )
% 8.69/5.01       => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 8.69/5.01         => ~ ! [L6: real] :
% 8.69/5.01                ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10057_LIMSEQ__root,axiom,
% 8.69/5.01      ( filterlim_nat_real
% 8.69/5.01      @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 8.69/5.01      @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.69/5.01      @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10058_gcd__is__Max__divisors__int,axiom,
% 8.69/5.01      ! [N: int,M: int] :
% 8.69/5.01        ( ( N != zero_zero_int )
% 8.69/5.01       => ( ( gcd_gcd_int @ M @ N )
% 8.69/5.01          = ( lattic8263393255366662781ax_int
% 8.69/5.01            @ ( collect_int
% 8.69/5.01              @ ^ [D2: int] :
% 8.69/5.01                  ( ( dvd_dvd_int @ D2 @ M )
% 8.69/5.01                  & ( dvd_dvd_int @ D2 @ N ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10059_nested__sequence__unique,axiom,
% 8.69/5.01      ! [F: nat > real,G: nat > real] :
% 8.69/5.01        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 8.69/5.01           => ( ( filterlim_nat_real
% 8.69/5.01                @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 8.69/5.01                @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01                @ at_top_nat )
% 8.69/5.01             => ? [L4: real] :
% 8.69/5.01                  ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 8.69/5.01                  & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 8.69/5.01                  & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 8.69/5.01                  & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10060_LIMSEQ__inverse__zero,axiom,
% 8.69/5.01      ! [X8: nat > real] :
% 8.69/5.01        ( ! [R2: real] :
% 8.69/5.01          ? [N8: nat] :
% 8.69/5.01          ! [N3: nat] :
% 8.69/5.01            ( ( ord_less_eq_nat @ N8 @ N3 )
% 8.69/5.01           => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 8.69/5.01       => ( filterlim_nat_real
% 8.69/5.01          @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10061_lim__inverse__n_H,axiom,
% 8.69/5.01      ( filterlim_nat_real
% 8.69/5.01      @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 8.69/5.01      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01      @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10062_LIMSEQ__root__const,axiom,
% 8.69/5.01      ! [C: real] :
% 8.69/5.01        ( ( ord_less_real @ zero_zero_real @ C )
% 8.69/5.01       => ( filterlim_nat_real
% 8.69/5.01          @ ^ [N2: nat] : ( root @ N2 @ C )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10063_LIMSEQ__inverse__real__of__nat,axiom,
% 8.69/5.01      ( filterlim_nat_real
% 8.69/5.01      @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 8.69/5.01      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01      @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10064_LIMSEQ__inverse__real__of__nat__add,axiom,
% 8.69/5.01      ! [R: real] :
% 8.69/5.01        ( filterlim_nat_real
% 8.69/5.01        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ R )
% 8.69/5.01        @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10065_increasing__LIMSEQ,axiom,
% 8.69/5.01      ! [F: nat > real,L2: real] :
% 8.69/5.01        ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 8.69/5.01         => ( ! [E2: real] :
% 8.69/5.01                ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.69/5.01               => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 8.69/5.01           => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10066_LIMSEQ__realpow__zero,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/5.01       => ( ( ord_less_real @ X @ one_one_real )
% 8.69/5.01         => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10067_LIMSEQ__divide__realpow__zero,axiom,
% 8.69/5.01      ! [X: real,A: real] :
% 8.69/5.01        ( ( ord_less_real @ one_one_real @ X )
% 8.69/5.01       => ( filterlim_nat_real
% 8.69/5.01          @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10068_LIMSEQ__abs__realpow__zero,axiom,
% 8.69/5.01      ! [C: real] :
% 8.69/5.01        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 8.69/5.01       => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10069_LIMSEQ__abs__realpow__zero2,axiom,
% 8.69/5.01      ! [C: real] :
% 8.69/5.01        ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 8.69/5.01       => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10070_LIMSEQ__inverse__realpow__zero,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_real @ one_one_real @ X )
% 8.69/5.01       => ( filterlim_nat_real
% 8.69/5.01          @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10071_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 8.69/5.01      ! [R: real] :
% 8.69/5.01        ( filterlim_nat_real
% 8.69/5.01        @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ R )
% 8.69/5.01        @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10072_tendsto__exp__limit__sequentially,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( filterlim_nat_real
% 8.69/5.01        @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.69/5.01        @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10073_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 8.69/5.01      ! [R: real] :
% 8.69/5.01        ( filterlim_nat_real
% 8.69/5.01        @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ R )
% 8.69/5.01        @ at_top_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10074_summable__Leibniz_I1_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ( topolo6980174941875973593q_real @ A )
% 8.69/5.01         => ( summable_real
% 8.69/5.01            @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10075_summable,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01           => ( summable_real
% 8.69/5.01              @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10076_cos__diff__limit__1,axiom,
% 8.69/5.01      ! [Theta: nat > real,Theta2: real] :
% 8.69/5.01        ( ( filterlim_nat_real
% 8.69/5.01          @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.69/5.01          @ at_top_nat )
% 8.69/5.01       => ~ ! [K3: nat > int] :
% 8.69/5.01              ~ ( filterlim_nat_real
% 8.69/5.01                @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/5.01                @ ( topolo2815343760600316023s_real @ Theta2 )
% 8.69/5.01                @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10077_cos__limit__1,axiom,
% 8.69/5.01      ! [Theta: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real
% 8.69/5.01          @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.69/5.01          @ at_top_nat )
% 8.69/5.01       => ? [K3: nat > int] :
% 8.69/5.01            ( filterlim_nat_real
% 8.69/5.01            @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.69/5.01            @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01            @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10078_summable__Leibniz_I4_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ( topolo6980174941875973593q_real @ A )
% 8.69/5.01         => ( filterlim_nat_real
% 8.69/5.01            @ ^ [N2: nat] :
% 8.69/5.01                ( groups6591440286371151544t_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/5.01            @ ( topolo2815343760600316023s_real
% 8.69/5.01              @ ( suminf_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 8.69/5.01            @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10079_zeroseq__arctan__series,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.69/5.01       => ( filterlim_nat_real
% 8.69/5.01          @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 8.69/5.01          @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10080_summable__Leibniz_H_I2_J,axiom,
% 8.69/5.01      ! [A: nat > real,N: nat] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01           => ( ord_less_eq_real
% 8.69/5.01              @ ( groups6591440286371151544t_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.69/5.01              @ ( suminf_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10081_summable__Leibniz_H_I3_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01           => ( filterlim_nat_real
% 8.69/5.01              @ ^ [N2: nat] :
% 8.69/5.01                  ( groups6591440286371151544t_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                  @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/5.01              @ ( topolo2815343760600316023s_real
% 8.69/5.01                @ ( suminf_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 8.69/5.01              @ at_top_nat ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10082_sums__alternating__upper__lower,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01           => ? [L4: real] :
% 8.69/5.01                ( ! [N7: nat] :
% 8.69/5.01                    ( ord_less_eq_real
% 8.69/5.01                    @ ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 8.69/5.01                    @ L4 )
% 8.69/5.01                & ( filterlim_nat_real
% 8.69/5.01                  @ ^ [N2: nat] :
% 8.69/5.01                      ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ L4 )
% 8.69/5.01                  @ at_top_nat )
% 8.69/5.01                & ! [N7: nat] :
% 8.69/5.01                    ( ord_less_eq_real @ L4
% 8.69/5.01                    @ ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 8.69/5.01                & ( filterlim_nat_real
% 8.69/5.01                  @ ^ [N2: nat] :
% 8.69/5.01                      ( groups6591440286371151544t_real
% 8.69/5.01                      @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                      @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ L4 )
% 8.69/5.01                  @ at_top_nat ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10083_summable__Leibniz_I5_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ( topolo6980174941875973593q_real @ A )
% 8.69/5.01         => ( filterlim_nat_real
% 8.69/5.01            @ ^ [N2: nat] :
% 8.69/5.01                ( groups6591440286371151544t_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 8.69/5.01            @ ( topolo2815343760600316023s_real
% 8.69/5.01              @ ( suminf_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 8.69/5.01            @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10084_summable__Leibniz_H_I4_J,axiom,
% 8.69/5.01      ! [A: nat > real,N: nat] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01           => ( ord_less_eq_real
% 8.69/5.01              @ ( suminf_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 8.69/5.01              @ ( groups6591440286371151544t_real
% 8.69/5.01                @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10085_summable__Leibniz_H_I5_J,axiom,
% 8.69/5.01      ! [A: nat > real] :
% 8.69/5.01        ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.69/5.01       => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.69/5.01         => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.69/5.01           => ( filterlim_nat_real
% 8.69/5.01              @ ^ [N2: nat] :
% 8.69/5.01                  ( groups6591440286371151544t_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 8.69/5.01                  @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 8.69/5.01              @ ( topolo2815343760600316023s_real
% 8.69/5.01                @ ( suminf_real
% 8.69/5.01                  @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 8.69/5.01              @ at_top_nat ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10086_real__bounded__linear,axiom,
% 8.69/5.01      ( real_V5970128139526366754l_real
% 8.69/5.01      = ( ^ [F6: real > real] :
% 8.69/5.01          ? [C3: real] :
% 8.69/5.01            ( F6
% 8.69/5.01            = ( ^ [X3: real] : ( times_times_real @ X3 @ C3 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10087_tendsto__exp__limit__at__right,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( filterlim_real_real
% 8.69/5.01        @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y3 ) ) @ ( divide_divide_real @ one_one_real @ Y3 ) )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.69/5.01        @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10088_dist__real__def,axiom,
% 8.69/5.01      ( real_V975177566351809787t_real
% 8.69/5.01      = ( ^ [X3: real,Y3: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10089_dist__complex__def,axiom,
% 8.69/5.01      ( real_V3694042436643373181omplex
% 8.69/5.01      = ( ^ [X3: complex,Y3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10090_tendsto__arcosh__at__left__1,axiom,
% 8.69/5.01      filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10091_greaterThan__0,axiom,
% 8.69/5.01      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 8.69/5.01      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10092_greaterThan__Suc,axiom,
% 8.69/5.01      ! [K: nat] :
% 8.69/5.01        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 8.69/5.01        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10093_INT__greaterThan__UNIV,axiom,
% 8.69/5.01      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 8.69/5.01      = bot_bot_set_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10094_filterlim__tan__at__right,axiom,
% 8.69/5.01      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 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10095_atLeast__0,axiom,
% 8.69/5.01      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 8.69/5.01      = top_top_set_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10096_atLeast__Suc__greaterThan,axiom,
% 8.69/5.01      ! [K: nat] :
% 8.69/5.01        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 8.69/5.01        = ( set_or1210151606488870762an_nat @ K ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10097_exp__at__bot,axiom,
% 8.69/5.01      filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10098_filterlim__inverse__at__bot__neg,axiom,
% 8.69/5.01      filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10099_UN__atLeast__UNIV,axiom,
% 8.69/5.01      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 8.69/5.01      = top_top_set_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10100_atLeast__Suc,axiom,
% 8.69/5.01      ! [K: nat] :
% 8.69/5.01        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 8.69/5.01        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10101_tanh__real__at__bot,axiom,
% 8.69/5.01      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10102_ln__at__0,axiom,
% 8.69/5.01      filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10103_artanh__real__at__right__1,axiom,
% 8.69/5.01      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 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10104_DERIV__pos__imp__increasing__at__bot,axiom,
% 8.69/5.01      ! [B: real,F: real > real,Flim: real] :
% 8.69/5.01        ( ! [X6: real] :
% 8.69/5.01            ( ( ord_less_eq_real @ X6 @ B )
% 8.69/5.01           => ? [Y2: real] :
% 8.69/5.01                ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                & ( ord_less_real @ zero_zero_real @ Y2 ) ) )
% 8.69/5.01       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 8.69/5.01         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10105_filterlim__pow__at__bot__odd,axiom,
% 8.69/5.01      ! [N: nat,F: real > real,F3: filter_real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 8.69/5.01         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.01           => ( filterlim_real_real
% 8.69/5.01              @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 8.69/5.01              @ at_bot_real
% 8.69/5.01              @ F3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10106_tendsto__arctan__at__bot,axiom,
% 8.69/5.01      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10107_filterlim__pow__at__bot__even,axiom,
% 8.69/5.01      ! [N: nat,F: real > real,F3: filter_real] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 8.69/5.01         => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.69/5.01           => ( filterlim_real_real
% 8.69/5.01              @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 8.69/5.01              @ at_top_real
% 8.69/5.01              @ F3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10108_at__bot__le__at__infinity,axiom,
% 8.69/5.01      ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10109_at__top__le__at__infinity,axiom,
% 8.69/5.01      ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10110_sqrt__at__top,axiom,
% 8.69/5.01      filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10111_tanh__real__at__top,axiom,
% 8.69/5.01      filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10112_artanh__real__at__left__1,axiom,
% 8.69/5.01      filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10113_ln__x__over__x__tendsto__0,axiom,
% 8.69/5.01      ( filterlim_real_real
% 8.69/5.01      @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 8.69/5.01      @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01      @ at_top_real ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10114_filterlim__inverse__at__top__right,axiom,
% 8.69/5.01      filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10115_filterlim__inverse__at__right__top,axiom,
% 8.69/5.01      filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10116_tendsto__power__div__exp__0,axiom,
% 8.69/5.01      ! [K: nat] :
% 8.69/5.01        ( filterlim_real_real
% 8.69/5.01        @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.69/5.01        @ at_top_real ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10117_tendsto__exp__limit__at__top,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( filterlim_real_real
% 8.69/5.01        @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y3 ) ) @ Y3 )
% 8.69/5.01        @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.69/5.01        @ at_top_real ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10118_filterlim__tan__at__left,axiom,
% 8.69/5.01      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 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10119_DERIV__neg__imp__decreasing__at__top,axiom,
% 8.69/5.01      ! [B: real,F: real > real,Flim: real] :
% 8.69/5.01        ( ! [X6: real] :
% 8.69/5.01            ( ( ord_less_eq_real @ B @ X6 )
% 8.69/5.01           => ? [Y2: real] :
% 8.69/5.01                ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                & ( ord_less_real @ Y2 @ zero_zero_real ) ) )
% 8.69/5.01       => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 8.69/5.01         => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10120_tendsto__arctan__at__top,axiom,
% 8.69/5.01      filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10121_lhopital__left__at__top,axiom,
% 8.69/5.01      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 8.69/5.01        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01       => ( ( eventually_real
% 8.69/5.01            @ ^ [X3: real] :
% 8.69/5.01                ( ( G2 @ X3 )
% 8.69/5.01               != zero_zero_real )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01             => ( ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01               => ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10122_eventually__sequentially__seg,axiom,
% 8.69/5.01      ! [P: nat > $o,K: nat] :
% 8.69/5.01        ( ( eventually_nat
% 8.69/5.01          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 8.69/5.01          @ at_top_nat )
% 8.69/5.01        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10123_eventually__sequentiallyI,axiom,
% 8.69/5.01      ! [C: nat,P: nat > $o] :
% 8.69/5.01        ( ! [X6: nat] :
% 8.69/5.01            ( ( ord_less_eq_nat @ C @ X6 )
% 8.69/5.01           => ( P @ X6 ) )
% 8.69/5.01       => ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10124_eventually__sequentially,axiom,
% 8.69/5.01      ! [P: nat > $o] :
% 8.69/5.01        ( ( eventually_nat @ P @ at_top_nat )
% 8.69/5.01        = ( ? [N6: nat] :
% 8.69/5.01            ! [N2: nat] :
% 8.69/5.01              ( ( ord_less_eq_nat @ N6 @ N2 )
% 8.69/5.01             => ( P @ N2 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10125_le__sequentially,axiom,
% 8.69/5.01      ! [F3: filter_nat] :
% 8.69/5.01        ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 8.69/5.01        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F3 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10126_sequentially__offset,axiom,
% 8.69/5.01      ! [P: nat > $o,K: nat] :
% 8.69/5.01        ( ( eventually_nat @ P @ at_top_nat )
% 8.69/5.01       => ( eventually_nat
% 8.69/5.01          @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 8.69/5.01          @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10127_eventually__at__right__to__0,axiom,
% 8.69/5.01      ! [P: real > $o,A: real] :
% 8.69/5.01        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.69/5.01        = ( eventually_real
% 8.69/5.01          @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A ) )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10128_eventually__at__top__to__right,axiom,
% 8.69/5.01      ! [P: real > $o] :
% 8.69/5.01        ( ( eventually_real @ P @ at_top_real )
% 8.69/5.01        = ( eventually_real
% 8.69/5.01          @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10129_eventually__at__right__to__top,axiom,
% 8.69/5.01      ! [P: real > $o] :
% 8.69/5.01        ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01        = ( eventually_real
% 8.69/5.01          @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 8.69/5.01          @ at_top_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10130_lhopital,axiom,
% 8.69/5.01      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] :
% 8.69/5.01                  ( ( G @ X3 )
% 8.69/5.01                 != zero_zero_real )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] :
% 8.69/5.01                    ( ( G2 @ X3 )
% 8.69/5.01                   != zero_zero_real )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01             => ( ( eventually_real
% 8.69/5.01                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01               => ( ( eventually_real
% 8.69/5.01                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                    @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01                 => ( ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01                   => ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10131_lhopital__at__top,axiom,
% 8.69/5.01      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 8.69/5.01        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01       => ( ( eventually_real
% 8.69/5.01            @ ^ [X3: real] :
% 8.69/5.01                ( ( G2 @ X3 )
% 8.69/5.01               != zero_zero_real )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01             => ( ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.69/5.01               => ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10132_lhospital__at__top__at__top,axiom,
% 8.69/5.01      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 8.69/5.01        ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 8.69/5.01       => ( ( eventually_real
% 8.69/5.01            @ ^ [X3: real] :
% 8.69/5.01                ( ( G2 @ X3 )
% 8.69/5.01               != zero_zero_real )
% 8.69/5.01            @ at_top_real )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01              @ at_top_real )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                @ at_top_real )
% 8.69/5.01             => ( ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ X )
% 8.69/5.01                  @ at_top_real )
% 8.69/5.01               => ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ X )
% 8.69/5.01                  @ at_top_real ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10133_lhopital__right,axiom,
% 8.69/5.01      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] :
% 8.69/5.01                  ( ( G @ X3 )
% 8.69/5.01                 != zero_zero_real )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] :
% 8.69/5.01                    ( ( G2 @ X3 )
% 8.69/5.01                   != zero_zero_real )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01             => ( ( eventually_real
% 8.69/5.01                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01               => ( ( eventually_real
% 8.69/5.01                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01                 => ( ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01                   => ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10134_lhopital__right__0,axiom,
% 8.69/5.01      ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 8.69/5.01        ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01       => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] :
% 8.69/5.01                  ( ( G0 @ X3 )
% 8.69/5.01                 != zero_zero_real )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] :
% 8.69/5.01                    ( ( G2 @ X3 )
% 8.69/5.01                   != zero_zero_real )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01             => ( ( eventually_real
% 8.69/5.01                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01               => ( ( eventually_real
% 8.69/5.01                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                    @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01                 => ( ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01                   => ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10135_lhopital__left,axiom,
% 8.69/5.01      ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 8.69/5.01        ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01       => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] :
% 8.69/5.01                  ( ( G @ X3 )
% 8.69/5.01                 != zero_zero_real )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] :
% 8.69/5.01                    ( ( G2 @ X3 )
% 8.69/5.01                   != zero_zero_real )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01             => ( ( eventually_real
% 8.69/5.01                  @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01               => ( ( eventually_real
% 8.69/5.01                    @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                    @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01                 => ( ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.69/5.01                   => ( filterlim_real_real
% 8.69/5.01                      @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                      @ F3
% 8.69/5.01                      @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10136_lhopital__right__at__top,axiom,
% 8.69/5.01      ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 8.69/5.01        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01       => ( ( eventually_real
% 8.69/5.01            @ ^ [X3: real] :
% 8.69/5.01                ( ( G2 @ X3 )
% 8.69/5.01               != zero_zero_real )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01             => ( ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.69/5.01               => ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ Y )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10137_lhopital__right__0__at__top,axiom,
% 8.69/5.01      ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 8.69/5.01        ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01       => ( ( eventually_real
% 8.69/5.01            @ ^ [X3: real] :
% 8.69/5.01                ( ( G2 @ X3 )
% 8.69/5.01               != zero_zero_real )
% 8.69/5.01            @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01         => ( ( eventually_real
% 8.69/5.01              @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01              @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01           => ( ( eventually_real
% 8.69/5.01                @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.69/5.01                @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01             => ( ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ X )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01               => ( filterlim_real_real
% 8.69/5.01                  @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 8.69/5.01                  @ ( topolo2815343760600316023s_real @ X )
% 8.69/5.01                  @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10138_GreatestI__nat,axiom,
% 8.69/5.01      ! [P: nat > $o,K: nat,B: nat] :
% 8.69/5.01        ( ( P @ K )
% 8.69/5.01       => ( ! [Y5: nat] :
% 8.69/5.01              ( ( P @ Y5 )
% 8.69/5.01             => ( ord_less_eq_nat @ Y5 @ B ) )
% 8.69/5.01         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10139_Greatest__le__nat,axiom,
% 8.69/5.01      ! [P: nat > $o,K: nat,B: nat] :
% 8.69/5.01        ( ( P @ K )
% 8.69/5.01       => ( ! [Y5: nat] :
% 8.69/5.01              ( ( P @ Y5 )
% 8.69/5.01             => ( ord_less_eq_nat @ Y5 @ B ) )
% 8.69/5.01         => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10140_GreatestI__ex__nat,axiom,
% 8.69/5.01      ! [P: nat > $o,B: nat] :
% 8.69/5.01        ( ? [X_12: nat] : ( P @ X_12 )
% 8.69/5.01       => ( ! [Y5: nat] :
% 8.69/5.01              ( ( P @ Y5 )
% 8.69/5.01             => ( ord_less_eq_nat @ Y5 @ B ) )
% 8.69/5.01         => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10141_Bseq__eq__bounded,axiom,
% 8.69/5.01      ! [F: nat > real,A: real,B: real] :
% 8.69/5.01        ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.69/5.01       => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10142_Bseq__realpow,axiom,
% 8.69/5.01      ! [X: real] :
% 8.69/5.01        ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.69/5.01       => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.69/5.01         => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10143_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/5.01        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01       => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( X
% 8.69/5.01                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01           => ( Xa2 = one_one_nat ) )
% 8.69/5.01         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01               => ( ( Deg2 = Xa2 )
% 8.69/5.01                  & ! [X6: vEBT_VEBT] :
% 8.69/5.01                      ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                     => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                  & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                  & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                    = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                  & ( case_o184042715313410164at_nat
% 8.69/5.01                    @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                      & ! [X3: vEBT_VEBT] :
% 8.69/5.01                          ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                         => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                    @ ( produc6081775807080527818_nat_o
% 8.69/5.01                      @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                          ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                          & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                          & ! [I5: nat] :
% 8.69/5.01                              ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                             => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                          & ( ( Mi3 = Ma3 )
% 8.69/5.01                           => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                          & ( ( Mi3 != Ma3 )
% 8.69/5.01                           => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                              & ! [X3: nat] :
% 8.69/5.01                                  ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                   => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                      & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                    @ Mima ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10144_decseq__bounded,axiom,
% 8.69/5.01      ! [X8: nat > real,B3: real] :
% 8.69/5.01        ( ( order_9091379641038594480t_real @ X8 )
% 8.69/5.01       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 8.69/5.01         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10145_decseq__convergent,axiom,
% 8.69/5.01      ! [X8: nat > real,B3: real] :
% 8.69/5.01        ( ( order_9091379641038594480t_real @ X8 )
% 8.69/5.01       => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 8.69/5.01         => ~ ! [L6: real] :
% 8.69/5.01                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 8.69/5.01               => ~ ! [I2: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I2 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10146_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 8.69/5.01      ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 8.69/5.01        ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 8.69/5.01        = ( ( Deg = Deg4 )
% 8.69/5.01          & ! [X3: vEBT_VEBT] :
% 8.69/5.01              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.69/5.01             => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01          & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01          & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.69/5.01            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01          & ( case_o184042715313410164at_nat
% 8.69/5.01            @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X2 )
% 8.69/5.01              & ! [X3: vEBT_VEBT] :
% 8.69/5.01                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.69/5.01                 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01            @ ( produc6081775807080527818_nat_o
% 8.69/5.01              @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                  ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                  & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.69/5.01                  & ! [I5: nat] :
% 8.69/5.01                      ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                     => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X2 ) )
% 8.69/5.01                        = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 8.69/5.01                  & ( ( Mi3 = Ma3 )
% 8.69/5.01                   => ! [X3: vEBT_VEBT] :
% 8.69/5.01                        ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.69/5.01                       => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                  & ( ( Mi3 != Ma3 )
% 8.69/5.01                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.69/5.01                      & ! [X3: nat] :
% 8.69/5.01                          ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.69/5.01                         => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 8.69/5.01                           => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                              & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01            @ Mima2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10147_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.69/5.01        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01          = Y )
% 8.69/5.01       => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( X
% 8.69/5.01                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01           => ( Y
% 8.69/5.01              = ( Xa2 != one_one_nat ) ) )
% 8.69/5.01         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01               => ( Y
% 8.69/5.01                  = ( ~ ( ( Deg2 = Xa2 )
% 8.69/5.01                        & ! [X3: vEBT_VEBT] :
% 8.69/5.01                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                           => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                        & ( case_o184042715313410164at_nat
% 8.69/5.01                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                            & ! [X3: vEBT_VEBT] :
% 8.69/5.01                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                          @ ( produc6081775807080527818_nat_o
% 8.69/5.01                            @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                & ! [I5: nat] :
% 8.69/5.01                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                                & ( ( Mi3 = Ma3 )
% 8.69/5.01                                 => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                                & ( ( Mi3 != Ma3 )
% 8.69/5.01                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                                    & ! [X3: nat] :
% 8.69/5.01                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                          @ Mima ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10148_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/5.01        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01       => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( X
% 8.69/5.01                = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01           => ( Xa2 != one_one_nat ) )
% 8.69/5.01         => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01               => ~ ( ( Deg2 = Xa2 )
% 8.69/5.01                    & ! [X4: vEBT_VEBT] :
% 8.69/5.01                        ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                       => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                    & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                    & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                    & ( case_o184042715313410164at_nat
% 8.69/5.01                      @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                        & ! [X3: vEBT_VEBT] :
% 8.69/5.01                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                           => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                      @ ( produc6081775807080527818_nat_o
% 8.69/5.01                        @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                            ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                            & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                            & ! [I5: nat] :
% 8.69/5.01                                ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                               => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                  = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                            & ( ( Mi3 = Ma3 )
% 8.69/5.01                             => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                  ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                                 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                            & ( ( Mi3 != Ma3 )
% 8.69/5.01                             => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                                & ! [X3: nat] :
% 8.69/5.01                                    ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                   => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                     => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                        & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                      @ Mima ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10149_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/5.01        ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/5.01         => ( ! [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 8.69/5.01                 => ( Xa2 = one_one_nat ) ) )
% 8.69/5.01           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                  ( ( X
% 8.69/5.01                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 8.69/5.01                   => ( ( Deg2 = Xa2 )
% 8.69/5.01                      & ! [X6: vEBT_VEBT] :
% 8.69/5.01                          ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                         => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                      & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                      & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                      & ( case_o184042715313410164at_nat
% 8.69/5.01                        @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                          & ! [X3: vEBT_VEBT] :
% 8.69/5.01                              ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                             => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                        @ ( produc6081775807080527818_nat_o
% 8.69/5.01                          @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                              ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                              & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                              & ! [I5: nat] :
% 8.69/5.01                                  ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                                 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                    = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                              & ( ( Mi3 = Ma3 )
% 8.69/5.01                               => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                    ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                                   => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                              & ( ( Mi3 != Ma3 )
% 8.69/5.01                               => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                                  & ! [X3: nat] :
% 8.69/5.01                                      ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                     => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                       => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                          & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                        @ Mima ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10150_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat] :
% 8.69/5.01        ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/5.01         => ( ! [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01               => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 8.69/5.01                 => ( Xa2 != one_one_nat ) ) )
% 8.69/5.01           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                  ( ( X
% 8.69/5.01                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01                 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 8.69/5.01                   => ~ ( ( Deg2 = Xa2 )
% 8.69/5.01                        & ! [X4: vEBT_VEBT] :
% 8.69/5.01                            ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                           => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                        & ( case_o184042715313410164at_nat
% 8.69/5.01                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                            & ! [X3: vEBT_VEBT] :
% 8.69/5.01                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                          @ ( produc6081775807080527818_nat_o
% 8.69/5.01                            @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                & ! [I5: nat] :
% 8.69/5.01                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                                & ( ( Mi3 = Ma3 )
% 8.69/5.01                                 => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                                & ( ( Mi3 != Ma3 )
% 8.69/5.01                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                                    & ! [X3: nat] :
% 8.69/5.01                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                          @ Mima ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10151_Sup__int__def,axiom,
% 8.69/5.01      ( complete_Sup_Sup_int
% 8.69/5.01      = ( ^ [X2: set_int] :
% 8.69/5.01            ( the_int
% 8.69/5.01            @ ^ [X3: int] :
% 8.69/5.01                ( ( member_int @ X3 @ X2 )
% 8.69/5.01                & ! [Y3: int] :
% 8.69/5.01                    ( ( member_int @ Y3 @ X2 )
% 8.69/5.01                   => ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10152_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.69/5.01        ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.69/5.01          = Y )
% 8.69/5.01       => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.69/5.01         => ( ! [Uu2: $o,Uv2: $o] :
% 8.69/5.01                ( ( X
% 8.69/5.01                  = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.69/5.01               => ( ( Y
% 8.69/5.01                    = ( Xa2 = one_one_nat ) )
% 8.69/5.01                 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 8.69/5.01           => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.69/5.01                  ( ( X
% 8.69/5.01                    = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 8.69/5.01                 => ( ( Y
% 8.69/5.01                      = ( ( Deg2 = Xa2 )
% 8.69/5.01                        & ! [X3: vEBT_VEBT] :
% 8.69/5.01                            ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                           => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.69/5.01                        & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.69/5.01                          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                        & ( case_o184042715313410164at_nat
% 8.69/5.01                          @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 8.69/5.01                            & ! [X3: vEBT_VEBT] :
% 8.69/5.01                                ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                               => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                          @ ( produc6081775807080527818_nat_o
% 8.69/5.01                            @ ^ [Mi3: nat,Ma3: nat] :
% 8.69/5.01                                ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.69/5.01                                & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                & ! [I5: nat] :
% 8.69/5.01                                    ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.69/5.01                                   => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 8.69/5.01                                      = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 8.69/5.01                                & ( ( Mi3 = Ma3 )
% 8.69/5.01                                 => ! [X3: vEBT_VEBT] :
% 8.69/5.01                                      ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.69/5.01                                     => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 8.69/5.01                                & ( ( Mi3 != Ma3 )
% 8.69/5.01                                 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 8.69/5.01                                    & ! [X3: nat] :
% 8.69/5.01                                        ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.69/5.01                                       => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 8.69/5.01                                         => ( ( ord_less_nat @ Mi3 @ X3 )
% 8.69/5.01                                            & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 8.69/5.01                          @ Mima ) ) )
% 8.69/5.01                   => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10153_GMVT,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,G: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01                & ( ord_less_eq_real @ X6 @ B ) )
% 8.69/5.01             => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 8.69/5.01         => ( ! [X6: real] :
% 8.69/5.01                ( ( ( ord_less_real @ A @ X6 )
% 8.69/5.01                  & ( ord_less_real @ X6 @ B ) )
% 8.69/5.01               => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 8.69/5.01           => ( ! [X6: real] :
% 8.69/5.01                  ( ( ( ord_less_eq_real @ A @ X6 )
% 8.69/5.01                    & ( ord_less_eq_real @ X6 @ B ) )
% 8.69/5.01                 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ G ) )
% 8.69/5.01             => ( ! [X6: real] :
% 8.69/5.01                    ( ( ( ord_less_real @ A @ X6 )
% 8.69/5.01                      & ( ord_less_real @ X6 @ B ) )
% 8.69/5.01                   => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 8.69/5.01               => ? [G_c: real,F_c: real,C2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 8.69/5.01                    & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_real @ A @ C2 )
% 8.69/5.01                    & ( ord_less_real @ C2 @ B )
% 8.69/5.01                    & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 8.69/5.01                      = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10154_MVT,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01         => ( ! [X6: real] :
% 8.69/5.01                ( ( ord_less_real @ A @ X6 )
% 8.69/5.01               => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01           => ? [L4: real,Z5: real] :
% 8.69/5.01                ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01                & ( ord_less_real @ Z5 @ B )
% 8.69/5.01                & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) )
% 8.69/5.01                & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.69/5.01                  = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10155_continuous__on__arcosh_H,axiom,
% 8.69/5.01      ! [A2: set_real,F: real > real] :
% 8.69/5.01        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( member_real @ X6 @ A2 )
% 8.69/5.01             => ( ord_less_eq_real @ one_one_real @ ( F @ X6 ) ) )
% 8.69/5.01         => ( topolo5044208981011980120l_real @ A2
% 8.69/5.01            @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10156_continuous__image__closed__interval,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_eq_real @ A @ B )
% 8.69/5.01       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01         => ? [C2: real,D3: real] :
% 8.69/5.01              ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.69/5.01                = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 8.69/5.01              & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10157_continuous__on__arcosh,axiom,
% 8.69/5.01      ! [A2: set_real] :
% 8.69/5.01        ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 8.69/5.01       => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10158_continuous__on__arccos_H,axiom,
% 8.69/5.01      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10159_continuous__on__arcsin_H,axiom,
% 8.69/5.01      topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10160_continuous__on__artanh_H,axiom,
% 8.69/5.01      ! [A2: set_real,F: real > real] :
% 8.69/5.01        ( ( topolo5044208981011980120l_real @ A2 @ F )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( member_real @ X6 @ A2 )
% 8.69/5.01             => ( member_real @ ( F @ X6 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 8.69/5.01         => ( topolo5044208981011980120l_real @ A2
% 8.69/5.01            @ ^ [X3: real] : ( artanh_real @ ( F @ X3 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10161_Rolle__deriv,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( ( F @ A )
% 8.69/5.01            = ( F @ B ) )
% 8.69/5.01         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01           => ( ! [X6: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ X6 )
% 8.69/5.01                 => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                   => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01             => ? [Z5: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01                  & ( ord_less_real @ Z5 @ B )
% 8.69/5.01                  & ( ( F5 @ Z5 )
% 8.69/5.01                    = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10162_mvt,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01         => ( ! [X6: real] :
% 8.69/5.01                ( ( ord_less_real @ A @ X6 )
% 8.69/5.01               => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01           => ~ ! [Xi: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ Xi )
% 8.69/5.01                 => ( ( ord_less_real @ Xi @ B )
% 8.69/5.01                   => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.69/5.01                     != ( F5 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10163_DERIV__isconst__end,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01         => ( ! [X6: real] :
% 8.69/5.01                ( ( ord_less_real @ A @ X6 )
% 8.69/5.01               => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01           => ( ( F @ B )
% 8.69/5.01              = ( F @ A ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10164_DERIV__neg__imp__decreasing__open,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 8.69/5.01         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01           => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10165_DERIV__pos__imp__increasing__open,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ! [X6: real] :
% 8.69/5.01              ( ( ord_less_real @ A @ X6 )
% 8.69/5.01             => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01               => ? [Y2: real] :
% 8.69/5.01                    ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 8.69/5.01                    & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 8.69/5.01         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01           => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10166_continuous__on__artanh,axiom,
% 8.69/5.01      ! [A2: set_real] :
% 8.69/5.01        ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 8.69/5.01       => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10167_DERIV__isconst2,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real,X: real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01         => ( ! [X6: real] :
% 8.69/5.01                ( ( ord_less_real @ A @ X6 )
% 8.69/5.01               => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01           => ( ( ord_less_eq_real @ A @ X )
% 8.69/5.01             => ( ( ord_less_eq_real @ X @ B )
% 8.69/5.01               => ( ( F @ X )
% 8.69/5.01                  = ( F @ A ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10168_Rolle,axiom,
% 8.69/5.01      ! [A: real,B: real,F: real > real] :
% 8.69/5.01        ( ( ord_less_real @ A @ B )
% 8.69/5.01       => ( ( ( F @ A )
% 8.69/5.01            = ( F @ B ) )
% 8.69/5.01         => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.69/5.01           => ( ! [X6: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ X6 )
% 8.69/5.01                 => ( ( ord_less_real @ X6 @ B )
% 8.69/5.01                   => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 8.69/5.01             => ? [Z5: real] :
% 8.69/5.01                  ( ( ord_less_real @ A @ Z5 )
% 8.69/5.01                  & ( ord_less_real @ Z5 @ B )
% 8.69/5.01                  & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10169_uniformity__real__def,axiom,
% 8.69/5.01      ( topolo1511823702728130853y_real
% 8.69/5.01      = ( comple2936214249959783750l_real
% 8.69/5.01        @ ( image_2178119161166701260l_real
% 8.69/5.01          @ ^ [E3: real] :
% 8.69/5.01              ( princi6114159922880469582l_real
% 8.69/5.01              @ ( collec3799799289383736868l_real
% 8.69/5.01                @ ( produc5414030515140494994real_o
% 8.69/5.01                  @ ^ [X3: real,Y3: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X3 @ Y3 ) @ E3 ) ) ) )
% 8.69/5.01          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10170_uniformity__complex__def,axiom,
% 8.69/5.01      ( topolo896644834953643431omplex
% 8.69/5.01      = ( comple8358262395181532106omplex
% 8.69/5.01        @ ( image_5971271580939081552omplex
% 8.69/5.01          @ ^ [E3: real] :
% 8.69/5.01              ( princi3496590319149328850omplex
% 8.69/5.01              @ ( collec8663557070575231912omplex
% 8.69/5.01                @ ( produc6771430404735790350plex_o
% 8.69/5.01                  @ ^ [X3: complex,Y3: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X3 @ Y3 ) @ E3 ) ) ) )
% 8.69/5.01          @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10171_eventually__prod__sequentially,axiom,
% 8.69/5.01      ! [P: product_prod_nat_nat > $o] :
% 8.69/5.01        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 8.69/5.01        = ( ? [N6: nat] :
% 8.69/5.01            ! [M3: nat] :
% 8.69/5.01              ( ( ord_less_eq_nat @ N6 @ M3 )
% 8.69/5.01             => ! [N2: nat] :
% 8.69/5.01                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 8.69/5.01                 => ( P @ ( product_Pair_nat_nat @ N2 @ M3 ) ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10172_mono__times__nat,axiom,
% 8.69/5.01      ! [N: nat] :
% 8.69/5.01        ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.69/5.01       => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10173_mono__Suc,axiom,
% 8.69/5.01      order_mono_nat_nat @ suc ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10174_incseq__bounded,axiom,
% 8.69/5.01      ! [X8: nat > real,B3: real] :
% 8.69/5.01        ( ( order_mono_nat_real @ X8 )
% 8.69/5.01       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 8.69/5.01         => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10175_filtermap__at__right__shift,axiom,
% 8.69/5.01      ! [D: real,A: real] :
% 8.69/5.01        ( ( filtermap_real_real
% 8.69/5.01          @ ^ [X3: real] : ( minus_minus_real @ X3 @ D )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.69/5.01        = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10176_incseq__convergent,axiom,
% 8.69/5.01      ! [X8: nat > real,B3: real] :
% 8.69/5.01        ( ( order_mono_nat_real @ X8 )
% 8.69/5.01       => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 8.69/5.01         => ~ ! [L6: real] :
% 8.69/5.01                ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 8.69/5.01               => ~ ! [I2: nat] : ( ord_less_eq_real @ ( X8 @ I2 ) @ L6 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10177_at__right__to__0,axiom,
% 8.69/5.01      ! [A: real] :
% 8.69/5.01        ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 8.69/5.01        = ( filtermap_real_real
% 8.69/5.01          @ ^ [X3: real] : ( plus_plus_real @ X3 @ A )
% 8.69/5.01          @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10178_at__right__to__top,axiom,
% 8.69/5.01      ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 8.69/5.01      = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10179_at__top__to__right,axiom,
% 8.69/5.01      ( at_top_real
% 8.69/5.01      = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10180_filtermap__ln__at__right,axiom,
% 8.69/5.01      ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.69/5.01      = at_bot_real ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10181_mono__ge2__power__minus__self,axiom,
% 8.69/5.01      ! [K: nat] :
% 8.69/5.01        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 8.69/5.01       => ( order_mono_nat_nat
% 8.69/5.01          @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10182_remdups__upt,axiom,
% 8.69/5.01      ! [M: nat,N: nat] :
% 8.69/5.01        ( ( remdups_nat @ ( upt @ M @ N ) )
% 8.69/5.01        = ( upt @ M @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10183_length__upt,axiom,
% 8.69/5.01      ! [I: nat,J: nat] :
% 8.69/5.01        ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 8.69/5.01        = ( minus_minus_nat @ J @ I ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10184_upt__conv__Nil,axiom,
% 8.69/5.01      ! [J: nat,I: nat] :
% 8.69/5.01        ( ( ord_less_eq_nat @ J @ I )
% 8.69/5.01       => ( ( upt @ I @ J )
% 8.69/5.01          = nil_nat ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10185_sorted__list__of__set__range,axiom,
% 8.69/5.01      ! [M: nat,N: nat] :
% 8.69/5.01        ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 8.69/5.01        = ( upt @ M @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10186_upt__eq__Nil__conv,axiom,
% 8.69/5.01      ! [I: nat,J: nat] :
% 8.69/5.01        ( ( ( upt @ I @ J )
% 8.69/5.01          = nil_nat )
% 8.69/5.01        = ( ( J = zero_zero_nat )
% 8.69/5.01          | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10187_nth__upt,axiom,
% 8.69/5.01      ! [I: nat,K: nat,J: nat] :
% 8.69/5.01        ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 8.69/5.01       => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 8.69/5.01          = ( plus_plus_nat @ I @ K ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10188_upt__rec__numeral,axiom,
% 8.69/5.01      ! [M: num,N: num] :
% 8.69/5.01        ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.01         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.01            = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 8.69/5.01        & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.01         => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.69/5.01            = nil_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10189_atLeast__upt,axiom,
% 8.69/5.01      ( set_ord_lessThan_nat
% 8.69/5.01      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10190_atMost__upto,axiom,
% 8.69/5.01      ( set_ord_atMost_nat
% 8.69/5.01      = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10191_atLeastAtMost__upt,axiom,
% 8.69/5.01      ( set_or1269000886237332187st_nat
% 8.69/5.01      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M3 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10192_greaterThanLessThan__upt,axiom,
% 8.69/5.01      ( set_or5834768355832116004an_nat
% 8.69/5.01      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10193_greaterThanAtMost__upt,axiom,
% 8.69/5.01      ( set_or6659071591806873216st_nat
% 8.69/5.01      = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M3 ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10194_atLeastLessThan__upt,axiom,
% 8.69/5.01      ( set_or4665077453230672383an_nat
% 8.69/5.01      = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10195_upt__0,axiom,
% 8.69/5.01      ! [I: nat] :
% 8.69/5.01        ( ( upt @ I @ zero_zero_nat )
% 8.69/5.01        = nil_nat ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10196_upt__conv__Cons__Cons,axiom,
% 8.69/5.01      ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 8.69/5.01        ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 8.69/5.01          = ( upt @ M @ Q2 ) )
% 8.69/5.01        = ( ( cons_nat @ N @ Ns )
% 8.69/5.01          = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10197_upt__conv__Cons,axiom,
% 8.69/5.01      ! [I: nat,J: nat] :
% 8.69/5.01        ( ( ord_less_nat @ I @ J )
% 8.69/5.01       => ( ( upt @ I @ J )
% 8.69/5.01          = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10198_distinct__upt,axiom,
% 8.69/5.01      ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10199_map__add__upt,axiom,
% 8.69/5.01      ! [N: nat,M: nat] :
% 8.69/5.01        ( ( map_nat_nat
% 8.69/5.01          @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N )
% 8.69/5.01          @ ( upt @ zero_zero_nat @ M ) )
% 8.69/5.01        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10200_map__Suc__upt,axiom,
% 8.69/5.01      ! [M: nat,N: nat] :
% 8.69/5.01        ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 8.69/5.01        = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10201_map__decr__upt,axiom,
% 8.69/5.01      ! [M: nat,N: nat] :
% 8.69/5.01        ( ( map_nat_nat
% 8.69/5.01          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 8.69/5.01          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 8.69/5.01        = ( upt @ M @ N ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10202_upt__add__eq__append,axiom,
% 8.69/5.01      ! [I: nat,J: nat,K: nat] :
% 8.69/5.01        ( ( ord_less_eq_nat @ I @ J )
% 8.69/5.01       => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 8.69/5.01          = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10203_upt__eq__Cons__conv,axiom,
% 8.69/5.01      ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 8.69/5.01        ( ( ( upt @ I @ J )
% 8.69/5.01          = ( cons_nat @ X @ Xs ) )
% 8.69/5.01        = ( ( ord_less_nat @ I @ J )
% 8.69/5.01          & ( I = X )
% 8.69/5.01          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 8.69/5.01            = Xs ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10204_upt__rec,axiom,
% 8.69/5.01      ( upt
% 8.69/5.01      = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10205_upt__Suc__append,axiom,
% 8.69/5.01      ! [I: nat,J: nat] :
% 8.69/5.01        ( ( ord_less_eq_nat @ I @ J )
% 8.69/5.01       => ( ( upt @ I @ ( suc @ J ) )
% 8.69/5.01          = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10206_upt__Suc,axiom,
% 8.69/5.01      ! [I: nat,J: nat] :
% 8.69/5.01        ( ( ( ord_less_eq_nat @ I @ J )
% 8.69/5.01         => ( ( upt @ I @ ( suc @ J ) )
% 8.69/5.01            = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 8.69/5.01        & ( ~ ( ord_less_eq_nat @ I @ J )
% 8.69/5.01         => ( ( upt @ I @ ( suc @ J ) )
% 8.69/5.01            = nil_nat ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(fact_10207_sum__list__upt,axiom,
% 8.69/5.01      ! [M: nat,N: nat] :
% 8.69/5.01        ( ( ord_less_eq_nat @ M @ N )
% 8.69/5.01       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 8.69/5.01          = ( groups3542108847815614940at_nat
% 8.69/5.01            @ ^ [X3: nat] : X3
% 8.69/5.01            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 8.69/5.01      ! [X: int,Y: int] :
% 8.69/5.01        ( ( if_int @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 8.69/5.01      ! [X: int,Y: int] :
% 8.69/5.01        ( ( if_int @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 8.69/5.01      ! [X: nat,Y: nat] :
% 8.69/5.01        ( ( if_nat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 8.69/5.01      ! [X: nat,Y: nat] :
% 8.69/5.01        ( ( if_nat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 8.69/5.01      ! [X: num,Y: num] :
% 8.69/5.01        ( ( if_num @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 8.69/5.01      ! [X: num,Y: num] :
% 8.69/5.01        ( ( if_num @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 8.69/5.01      ! [X: rat,Y: rat] :
% 8.69/5.01        ( ( if_rat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 8.69/5.01      ! [X: rat,Y: rat] :
% 8.69/5.01        ( ( if_rat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 8.69/5.01      ! [X: real,Y: real] :
% 8.69/5.01        ( ( if_real @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 8.69/5.01      ! [X: real,Y: real] :
% 8.69/5.01        ( ( if_real @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 8.69/5.01      ! [P: real > $o] :
% 8.69/5.01        ( ( P @ ( fChoice_real @ P ) )
% 8.69/5.01        = ( ? [X2: real] : ( P @ X2 ) ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.69/5.01      ! [X: complex,Y: complex] :
% 8.69/5.01        ( ( if_complex @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.69/5.01      ! [X: complex,Y: complex] :
% 8.69/5.01        ( ( if_complex @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.69/5.01      ! [X: extended_enat,Y: extended_enat] :
% 8.69/5.01        ( ( if_Extended_enat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.69/5.01      ! [X: extended_enat,Y: extended_enat] :
% 8.69/5.01        ( ( if_Extended_enat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.69/5.01      ! [X: code_integer,Y: code_integer] :
% 8.69/5.01        ( ( if_Code_integer @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.69/5.01      ! [X: code_integer,Y: code_integer] :
% 8.69/5.01        ( ( if_Code_integer @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: set_int,Y: set_int] :
% 8.69/5.01        ( ( if_set_int @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: set_int,Y: set_int] :
% 8.69/5.01        ( ( if_set_int @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.69/5.01        ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.69/5.01      ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.69/5.01        ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: list_int,Y: list_int] :
% 8.69/5.01        ( ( if_list_int @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: list_int,Y: list_int] :
% 8.69/5.01        ( ( if_list_int @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: list_nat,Y: list_nat] :
% 8.69/5.01        ( ( if_list_nat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: list_nat,Y: list_nat] :
% 8.69/5.01        ( ( if_list_nat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: int > int,Y: int > int] :
% 8.69/5.01        ( ( if_int_int @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: int > int,Y: int > int] :
% 8.69/5.01        ( ( if_int_int @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: option_nat,Y: option_nat] :
% 8.69/5.01        ( ( if_option_nat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: option_nat,Y: option_nat] :
% 8.69/5.01        ( ( if_option_nat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.69/5.01      ! [X: option_num,Y: option_num] :
% 8.69/5.01        ( ( if_option_num @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.69/5.01      ! [X: option_num,Y: option_num] :
% 8.69/5.01        ( ( if_option_num @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.69/5.01        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.69/5.01      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.69/5.01        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.69/5.01        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.69/5.01      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.69/5.01        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 8.69/5.01      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 8.69/5.01        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 8.69/5.01      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 8.69/5.01        ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.69/5.01      ! [P: $o] :
% 8.69/5.01        ( ( P = $true )
% 8.69/5.01        | ( P = $false ) ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.69/5.01      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.69/5.01        ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 8.69/5.01        = Y ) ).
% 8.69/5.01  
% 8.69/5.01  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.69/5.01      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.69/5.01        ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 8.69/5.01        = X ) ).
% 8.69/5.01  
% 8.69/5.01  thf(conj_0,conjecture,
% 8.69/5.01      ? [Y2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ Y2 ) ).
% 8.69/5.01  ------------------------
% 8.70/5.36  % (3869)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/18Mi)
% 8.70/5.37  % (3863)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_3754 for (2996ds/4Mi)
% 8.70/5.37  % (3862)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/183Mi)
% 8.70/5.37  % (3864)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_3754 for (2996ds/27Mi)
% 8.70/5.37  % (3865)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/2Mi)
% 8.70/5.37  % (3866)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_3754 for (2996ds/2Mi)
% 8.70/5.37  % (3868)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_3754 for (2996ds/275Mi)
% 8.70/5.37  % (3865)Instruction limit reached!
% 8.70/5.37  % (3865)------------------------------
% 8.70/5.37  % (3865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.37  % (3865)Termination reason: Unknown
% 8.70/5.37  % (3865)Termination phase: shuffling
% 8.70/5.37  
% 8.70/5.37  % (3865)Memory used [KB]: 12792
% 8.70/5.37  % (3865)Time elapsed: 0.003 s
% 8.70/5.37  % (3865)Instructions burned: 2 (million)
% 8.70/5.37  % (3865)------------------------------
% 8.70/5.37  % (3865)------------------------------
% 8.70/5.37  % (3866)Instruction limit reached!
% 8.70/5.37  % (3866)------------------------------
% 8.70/5.37  % (3866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.37  % (3866)Termination reason: Unknown
% 8.70/5.37  % (3866)Termination phase: shuffling
% 8.70/5.37  
% 8.70/5.37  % (3866)Memory used [KB]: 12792
% 8.70/5.37  % (3866)Time elapsed: 0.003 s
% 8.70/5.37  % (3866)Instructions burned: 2 (million)
% 8.70/5.37  % (3866)------------------------------
% 8.70/5.37  % (3866)------------------------------
% 8.70/5.38  % (3863)Instruction limit reached!
% 8.70/5.38  % (3863)------------------------------
% 8.70/5.38  % (3863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.38  % (3863)Termination reason: Unknown
% 8.70/5.38  % (3863)Termination phase: shuffling
% 8.70/5.38  
% 8.70/5.38  % (3863)Memory used [KB]: 13048
% 8.70/5.38  % (3863)Time elapsed: 0.007 s
% 8.70/5.38  % (3863)Instructions burned: 4 (million)
% 8.70/5.38  % (3863)------------------------------
% 8.70/5.38  % (3863)------------------------------
% 8.70/5.38  % (3869)Instruction limit reached!
% 8.70/5.38  % (3869)------------------------------
% 8.70/5.38  % (3869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.38  % (3869)Termination reason: Unknown
% 8.70/5.38  % (3869)Termination phase: shuffling
% 8.70/5.38  
% 8.70/5.38  % (3869)Memory used [KB]: 13816
% 8.70/5.38  % (3869)Time elapsed: 0.016 s
% 8.70/5.38  % (3869)Instructions burned: 20 (million)
% 8.70/5.38  % (3869)------------------------------
% 8.70/5.38  % (3869)------------------------------
% 8.70/5.39  % (3873)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_3754 for (2996ds/3Mi)
% 8.70/5.39  % (3873)Instruction limit reached!
% 8.70/5.39  % (3873)------------------------------
% 8.70/5.39  % (3873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.39  % (3873)Termination reason: Unknown
% 8.70/5.39  % (3873)Termination phase: shuffling
% 8.70/5.39  
% 8.70/5.39  % (3873)Memory used [KB]: 12920
% 8.70/5.39  % (3873)Time elapsed: 0.004 s
% 8.70/5.39  % (3873)Instructions burned: 3 (million)
% 8.70/5.39  % (3873)------------------------------
% 8.70/5.39  % (3873)------------------------------
% 8.70/5.39  % (3870)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/3Mi)
% 8.70/5.39  % (3871)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_3754 for (2996ds/37Mi)
% 8.70/5.40  % (3870)Instruction limit reached!
% 8.70/5.40  % (3870)------------------------------
% 8.70/5.40  % (3870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.40  % (3870)Termination reason: Unknown
% 8.70/5.40  % (3870)Termination phase: shuffling
% 8.70/5.40  
% 8.70/5.40  % (3870)Memory used [KB]: 12920
% 8.70/5.40  % (3870)Time elapsed: 0.005 s
% 8.70/5.40  % (3870)Instructions burned: 3 (million)
% 8.70/5.40  % (3870)------------------------------
% 8.70/5.40  % (3870)------------------------------
% 8.70/5.40  % (3872)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_3754 for (2996ds/15Mi)
% 8.70/5.40  % (3864)Instruction limit reached!
% 8.70/5.40  % (3864)------------------------------
% 8.70/5.40  % (3864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.40  % (3864)Termination reason: Unknown
% 8.70/5.40  % (3864)Termination phase: shuffling
% 8.70/5.40  
% 8.70/5.40  % (3864)Memory used [KB]: 13816
% 8.70/5.40  % (3864)Time elapsed: 0.030 s
% 8.70/5.40  % (3864)Instructions burned: 27 (million)
% 8.70/5.40  % (3864)------------------------------
% 8.70/5.40  % (3864)------------------------------
% 8.70/5.40  % (3874)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_3754 for (2996ds/1041Mi)
% 8.70/5.41  % (3875)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/7Mi)
% 8.70/5.42  % (3872)Instruction limit reached!
% 8.70/5.42  % (3872)------------------------------
% 8.70/5.42  % (3872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.42  % (3872)Termination reason: Unknown
% 8.70/5.42  % (3872)Termination phase: shuffling
% 8.70/5.42  
% 8.70/5.42  % (3872)Memory used [KB]: 13688
% 8.70/5.42  % (3872)Time elapsed: 0.022 s
% 8.70/5.42  % (3872)Instructions burned: 15 (million)
% 8.70/5.42  % (3872)------------------------------
% 8.70/5.42  % (3872)------------------------------
% 8.70/5.42  % (3876)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3754 for (2996ds/16Mi)
% 8.70/5.42  % (3875)Instruction limit reached!
% 8.70/5.42  % (3875)------------------------------
% 8.70/5.42  % (3875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.42  % (3875)Termination reason: Unknown
% 8.70/5.42  % (3875)Termination phase: shuffling
% 8.70/5.42  
% 8.70/5.42  % (3875)Memory used [KB]: 13176
% 8.70/5.42  % (3875)Time elapsed: 0.011 s
% 8.70/5.42  % (3875)Instructions burned: 7 (million)
% 8.70/5.42  % (3875)------------------------------
% 8.70/5.42  % (3875)------------------------------
% 8.70/5.42  % (3871)Instruction limit reached!
% 8.70/5.42  % (3871)------------------------------
% 8.70/5.42  % (3871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.42  % (3871)Termination reason: Unknown
% 8.70/5.42  % (3871)Termination phase: shuffling
% 8.70/5.42  
% 8.70/5.42  % (3871)Memory used [KB]: 14072
% 8.70/5.42  % (3871)Time elapsed: 0.034 s
% 8.70/5.42  % (3871)Instructions burned: 37 (million)
% 8.70/5.42  % (3871)------------------------------
% 8.70/5.42  % (3871)------------------------------
% 8.70/5.44  % (3877)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_3754 for (2996ds/3Mi)
% 8.70/5.44  % (3877)Instruction limit reached!
% 8.70/5.44  % (3877)------------------------------
% 8.70/5.44  % (3877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.44  % (3877)Termination reason: Unknown
% 8.70/5.44  % (3877)Termination phase: shuffling
% 8.70/5.44  
% 8.70/5.44  % (3877)Memory used [KB]: 12920
% 8.70/5.44  % (3877)Time elapsed: 0.005 s
% 8.70/5.44  % (3877)Instructions burned: 3 (million)
% 8.70/5.44  % (3877)------------------------------
% 8.70/5.44  % (3877)------------------------------
% 8.70/5.44  % (3876)Instruction limit reached!
% 8.70/5.44  % (3876)------------------------------
% 8.70/5.44  % (3876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.44  % (3876)Termination reason: Unknown
% 8.70/5.44  % (3876)Termination phase: shuffling
% 8.70/5.44  
% 8.70/5.44  % (3876)Memory used [KB]: 13688
% 8.70/5.44  % (3876)Time elapsed: 0.023 s
% 8.70/5.44  % (3876)Instructions burned: 16 (million)
% 8.70/5.44  % (3876)------------------------------
% 8.70/5.44  % (3876)------------------------------
% 8.70/5.44  % (3878)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_3754 for (2995ds/3Mi)
% 8.70/5.44  % (3879)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/7Mi)
% 8.70/5.45  % (3878)Instruction limit reached!
% 8.70/5.45  % (3878)------------------------------
% 8.70/5.45  % (3878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.45  % (3878)Termination reason: Unknown
% 8.70/5.45  % (3878)Termination phase: shuffling
% 8.70/5.45  
% 8.70/5.45  % (3878)Memory used [KB]: 12920
% 8.70/5.45  % (3878)Time elapsed: 0.005 s
% 8.70/5.45  % (3878)Instructions burned: 3 (million)
% 8.70/5.45  % (3878)------------------------------
% 8.70/5.45  % (3878)------------------------------
% 8.70/5.45  % (3879)Instruction limit reached!
% 8.70/5.45  % (3879)------------------------------
% 8.70/5.45  % (3879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.45  % (3879)Termination reason: Unknown
% 8.70/5.45  % (3879)Termination phase: shuffling
% 8.70/5.45  
% 8.70/5.45  % (3879)Memory used [KB]: 13176
% 8.70/5.45  % (3879)Time elapsed: 0.011 s
% 8.70/5.45  % (3879)Instructions burned: 7 (million)
% 8.70/5.45  % (3879)------------------------------
% 8.70/5.45  % (3879)------------------------------
% 8.70/5.46  % (3880)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/3Mi)
% 8.70/5.46  % (3881)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/4Mi)
% 8.70/5.46  % (3880)Instruction limit reached!
% 8.70/5.46  % (3880)------------------------------
% 8.70/5.46  % (3880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.46  % (3880)Termination reason: Unknown
% 8.70/5.46  % (3880)Termination phase: shuffling
% 8.70/5.46  
% 8.70/5.46  % (3880)Memory used [KB]: 12920
% 8.70/5.46  % (3880)Time elapsed: 0.005 s
% 8.70/5.46  % (3880)Instructions burned: 3 (million)
% 8.70/5.46  % (3880)------------------------------
% 8.70/5.46  % (3880)------------------------------
% 8.70/5.47  % (3881)Instruction limit reached!
% 8.70/5.47  % (3881)------------------------------
% 8.70/5.47  % (3881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.47  % (3881)Termination reason: Unknown
% 8.70/5.47  % (3881)Termination phase: shuffling
% 8.70/5.47  
% 8.70/5.47  % (3881)Memory used [KB]: 13048
% 8.70/5.47  % (3881)Time elapsed: 0.006 s
% 8.70/5.47  % (3881)Instructions burned: 4 (million)
% 8.70/5.47  % (3881)------------------------------
% 8.70/5.47  % (3881)------------------------------
% 8.70/5.47  % (3882)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/18Mi)
% 8.70/5.47  % (3883)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/710Mi)
% 8.70/5.48  % (3884)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/6Mi)
% 8.70/5.48  % (3885)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_3754 for (2995ds/902Mi)
% 8.70/5.48  % (3862)Instruction limit reached!
% 8.70/5.48  % (3862)------------------------------
% 8.70/5.48  % (3862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.48  % (3862)Termination reason: Unknown
% 8.70/5.48  % (3862)Termination phase: shuffling
% 8.70/5.48  
% 8.70/5.48  % (3862)Memory used [KB]: 15991
% 8.70/5.48  % (3862)Time elapsed: 0.115 s
% 8.70/5.48  % (3862)Instructions burned: 184 (million)
% 8.70/5.48  % (3862)------------------------------
% 8.70/5.48  % (3862)------------------------------
% 8.70/5.49  % (3884)Instruction limit reached!
% 8.70/5.49  % (3884)------------------------------
% 8.70/5.49  % (3884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.49  % (3884)Termination reason: Unknown
% 8.70/5.49  % (3884)Termination phase: shuffling
% 8.70/5.49  
% 8.70/5.49  % (3884)Memory used [KB]: 13176
% 8.70/5.49  % (3884)Time elapsed: 0.009 s
% 8.70/5.49  % (3884)Instructions burned: 6 (million)
% 8.70/5.49  % (3884)------------------------------
% 8.70/5.49  % (3884)------------------------------
% 8.70/5.49  % (3882)Instruction limit reached!
% 8.70/5.49  % (3882)------------------------------
% 8.70/5.49  % (3882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.49  % (3882)Termination reason: Unknown
% 8.70/5.49  % (3882)Termination phase: shuffling
% 8.70/5.49  
% 8.70/5.49  % (3882)Memory used [KB]: 13688
% 8.70/5.49  % (3882)Time elapsed: 0.024 s
% 8.70/5.49  % (3882)Instructions burned: 18 (million)
% 8.70/5.49  % (3882)------------------------------
% 8.70/5.49  % (3882)------------------------------
% 8.70/5.50  % (3886)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_3754 for (2995ds/21Mi)
% 8.70/5.50  % (3887)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/5Mi)
% 8.70/5.50  % (3887)Instruction limit reached!
% 8.70/5.50  % (3887)------------------------------
% 8.70/5.50  % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.50  % (3887)Termination reason: Unknown
% 8.70/5.50  % (3887)Termination phase: shuffling
% 8.70/5.50  
% 8.70/5.50  % (3887)Memory used [KB]: 13048
% 8.70/5.50  % (3887)Time elapsed: 0.005 s
% 8.70/5.50  % (3887)Instructions burned: 5 (million)
% 8.70/5.50  % (3887)------------------------------
% 8.70/5.50  % (3887)------------------------------
% 8.70/5.51  % (3888)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_3754 for (2995ds/6Mi)
% 8.70/5.51  % (3886)Instruction limit reached!
% 8.70/5.51  % (3886)------------------------------
% 8.70/5.51  % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.51  % (3886)Termination reason: Unknown
% 8.70/5.51  % (3886)Termination phase: shuffling
% 8.70/5.51  
% 8.70/5.51  % (3886)Memory used [KB]: 13816
% 8.70/5.51  % (3886)Time elapsed: 0.017 s
% 8.70/5.51  % (3886)Instructions burned: 21 (million)
% 8.70/5.51  % (3886)------------------------------
% 8.70/5.51  % (3886)------------------------------
% 8.70/5.51  % (3888)Instruction limit reached!
% 8.70/5.51  % (3888)------------------------------
% 8.70/5.51  % (3888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.51  % (3888)Termination reason: Unknown
% 8.70/5.51  % (3888)Termination phase: shuffling
% 8.70/5.51  
% 8.70/5.51  % (3888)Memory used [KB]: 13176
% 8.70/5.51  % (3888)Time elapsed: 0.009 s
% 8.70/5.51  % (3888)Instructions burned: 6 (million)
% 8.70/5.51  % (3888)------------------------------
% 8.70/5.51  % (3888)------------------------------
% 8.70/5.51  % (3889)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3754 for (2995ds/377Mi)
% 8.70/5.52  % (3890)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_3754 for (2994ds/779Mi)
% 8.70/5.53  % (3868)Instruction limit reached!
% 8.70/5.53  % (3868)------------------------------
% 8.70/5.53  % (3868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.53  % (3868)Termination reason: Unknown
% 8.70/5.53  % (3868)Termination phase: shuffling
% 8.70/5.53  
% 8.70/5.53  % (3868)Memory used [KB]: 17398
% 8.70/5.53  % (3868)Time elapsed: 0.158 s
% 8.70/5.53  % (3868)Instructions burned: 275 (million)
% 8.70/5.53  % (3868)------------------------------
% 8.70/5.53  % (3868)------------------------------
% 8.70/5.53  % (3891)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_3754 for (2994ds/19Mi)
% 8.70/5.54  % (3892)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3754 for (2994ds/879Mi)
% 8.70/5.54  % (3891)Instruction limit reached!
% 8.70/5.54  % (3891)------------------------------
% 8.70/5.54  % (3891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.54  % (3891)Termination reason: Unknown
% 8.70/5.54  % (3891)Termination phase: shuffling
% 8.70/5.54  
% 8.70/5.54  % (3891)Memory used [KB]: 13816
% 8.70/5.54  % (3891)Time elapsed: 0.017 s
% 8.70/5.54  % (3891)Instructions burned: 22 (million)
% 8.70/5.54  % (3891)------------------------------
% 8.70/5.54  % (3891)------------------------------
% 8.70/5.56  % (3893)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3754 for (2994ds/17Mi)
% 8.70/5.57  % (3893)Instruction limit reached!
% 8.70/5.57  % (3893)------------------------------
% 8.70/5.57  % (3893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.57  % (3893)Termination reason: Unknown
% 8.70/5.57  % (3893)Termination phase: shuffling
% 8.70/5.57  
% 8.70/5.57  % (3893)Memory used [KB]: 13688
% 8.70/5.57  % (3893)Time elapsed: 0.015 s
% 8.70/5.57  % (3893)Instructions burned: 17 (million)
% 8.70/5.57  % (3893)------------------------------
% 8.70/5.57  % (3893)------------------------------
% 8.70/5.58  % (3894)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3754 for (2994ds/3Mi)
% 8.70/5.58  % (3894)Instruction limit reached!
% 8.70/5.58  % (3894)------------------------------
% 8.70/5.58  % (3894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.58  % (3894)Termination reason: Unknown
% 8.70/5.58  % (3894)Termination phase: shuffling
% 8.70/5.58  
% 8.70/5.58  % (3894)Memory used [KB]: 12920
% 8.70/5.58  % (3894)Time elapsed: 0.004 s
% 8.70/5.58  % (3894)Instructions burned: 4 (million)
% 8.70/5.58  % (3894)------------------------------
% 8.70/5.58  % (3894)------------------------------
% 8.70/5.60  % (3895)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3754 for (2994ds/30Mi)
% 8.70/5.61  % (3895)Instruction limit reached!
% 8.70/5.61  % (3895)------------------------------
% 8.70/5.61  % (3895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.61  % (3895)Termination reason: Unknown
% 8.70/5.61  % (3895)Termination phase: shuffling
% 8.70/5.61  
% 8.70/5.61  % (3895)Memory used [KB]: 13944
% 8.70/5.61  % (3895)Time elapsed: 0.020 s
% 8.70/5.61  % (3895)Instructions burned: 31 (million)
% 8.70/5.61  % (3895)------------------------------
% 8.70/5.61  % (3895)------------------------------
% 8.70/5.63  % (3896)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3754 for (2993ds/127Mi)
% 8.70/5.66  % (3889)Instruction limit reached!
% 8.70/5.66  % (3889)------------------------------
% 8.70/5.66  % (3889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.66  % (3889)Termination reason: Unknown
% 8.70/5.66  % (3889)Termination phase: shuffling
% 8.70/5.66  
% 8.70/5.66  % (3889)Memory used [KB]: 18421
% 8.70/5.66  % (3889)Time elapsed: 0.144 s
% 8.70/5.66  % (3889)Instructions burned: 377 (million)
% 8.70/5.66  % (3889)------------------------------
% 8.70/5.66  % (3889)------------------------------
% 8.70/5.67  % (3897)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3754 for (2993ds/100Mi)
% 8.70/5.68  % (3896)Instruction limit reached!
% 8.70/5.68  % (3896)------------------------------
% 8.70/5.68  % (3896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.68  % (3896)Termination reason: Unknown
% 8.70/5.68  % (3896)Termination phase: shuffling
% 8.70/5.68  
% 8.70/5.68  % (3896)Memory used [KB]: 15223
% 8.70/5.68  % (3896)Time elapsed: 0.055 s
% 8.70/5.68  % (3896)Instructions burned: 129 (million)
% 8.70/5.68  % (3896)------------------------------
% 8.70/5.68  % (3896)------------------------------
% 8.70/5.69  % (3898)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_3754 for (2993ds/3Mi)
% 8.70/5.69  % (3898)Instruction limit reached!
% 8.70/5.69  % (3898)------------------------------
% 8.70/5.69  % (3898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.69  % (3898)Termination reason: Unknown
% 8.70/5.69  % (3898)Termination phase: shuffling
% 8.70/5.69  
% 8.70/5.69  % (3898)Memory used [KB]: 12920
% 8.70/5.69  % (3898)Time elapsed: 0.004 s
% 8.70/5.69  % (3898)Instructions burned: 3 (million)
% 8.70/5.69  % (3898)------------------------------
% 8.70/5.69  % (3898)------------------------------
% 8.70/5.71  % (3897)Instruction limit reached!
% 8.70/5.71  % (3897)------------------------------
% 8.70/5.71  % (3897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.71  % (3897)Termination reason: Unknown
% 8.70/5.71  % (3897)Termination phase: shuffling
% 8.70/5.71  
% 8.70/5.71  % (3897)Memory used [KB]: 14967
% 8.70/5.71  % (3897)Time elapsed: 0.040 s
% 8.70/5.71  % (3897)Instructions burned: 100 (million)
% 8.70/5.71  % (3897)------------------------------
% 8.70/5.71  % (3897)------------------------------
% 8.70/5.71  % (3899)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_3754 for (2993ds/20Mi)
% 8.70/5.72  % (3874)Instruction limit reached!
% 8.70/5.72  % (3874)------------------------------
% 8.70/5.72  % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.72  % (3874)Termination reason: Unknown
% 8.70/5.72  % (3874)Termination phase: shuffling
% 8.70/5.72  
% 8.70/5.72  % (3874)Memory used [KB]: 33901
% 8.70/5.72  % (3874)Time elapsed: 0.316 s
% 8.70/5.72  % (3874)Instructions burned: 1043 (million)
% 8.70/5.72  % (3874)------------------------------
% 8.70/5.72  % (3874)------------------------------
% 8.70/5.72  % (3900)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_3754 for (2993ds/86Mi)
% 8.70/5.73  % (3901)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_3754 for (2992ds/107Mi)
% 8.70/5.74  % (3899)Instruction limit reached!
% 8.70/5.74  % (3899)------------------------------
% 8.70/5.74  % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.74  % (3899)Termination reason: Unknown
% 8.70/5.74  % (3899)Termination phase: shuffling
% 8.70/5.74  
% 8.70/5.74  % (3899)Memory used [KB]: 13816
% 8.70/5.74  % (3899)Time elapsed: 0.026 s
% 8.70/5.74  % (3899)Instructions burned: 20 (million)
% 8.70/5.74  % (3899)------------------------------
% 8.70/5.74  % (3899)------------------------------
% 8.70/5.75  % (3883)Instruction limit reached!
% 8.70/5.75  % (3883)------------------------------
% 8.70/5.75  % (3883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.75  % (3883)Termination reason: Unknown
% 8.70/5.75  % (3883)Termination phase: shuffling
% 8.70/5.75  
% 8.70/5.75  % (3883)Memory used [KB]: 22643
% 8.70/5.75  % (3883)Time elapsed: 0.276 s
% 8.70/5.75  % (3883)Instructions burned: 710 (million)
% 8.70/5.75  % (3883)------------------------------
% 8.70/5.75  % (3883)------------------------------
% 8.70/5.76  % (3902)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_3754 for (2992ds/39Mi)
% 8.70/5.76  % (3900)Instruction limit reached!
% 8.70/5.76  % (3900)------------------------------
% 8.70/5.76  % (3900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.76  % (3900)Termination reason: Unknown
% 8.70/5.76  % (3900)Termination phase: shuffling
% 8.70/5.76  
% 8.70/5.76  % (3900)Memory used [KB]: 14711
% 8.70/5.76  % (3900)Time elapsed: 0.041 s
% 8.70/5.76  % (3900)Instructions burned: 88 (million)
% 8.70/5.76  % (3900)------------------------------
% 8.70/5.76  % (3900)------------------------------
% 8.70/5.76  % (3903)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_3754 for (2992ds/448Mi)
% 8.70/5.77  % (3904)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_3754 for (2992ds/46Mi)
% 8.70/5.77  % (3901)Instruction limit reached!
% 8.70/5.77  % (3901)------------------------------
% 8.70/5.77  % (3901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.77  % (3901)Termination reason: Unknown
% 8.70/5.77  % (3901)Termination phase: shuffling
% 8.70/5.77  
% 8.70/5.77  % (3901)Memory used [KB]: 15095
% 8.70/5.77  % (3901)Time elapsed: 0.045 s
% 8.70/5.77  % (3901)Instructions burned: 108 (million)
% 8.70/5.77  % (3901)------------------------------
% 8.70/5.77  % (3901)------------------------------
% 8.70/5.78  % (3890)Instruction limit reached!
% 8.70/5.78  % (3890)------------------------------
% 8.70/5.78  % (3890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.78  % (3890)Termination reason: Unknown
% 8.70/5.78  % (3890)Termination phase: shuffling
% 8.70/5.78  
% 8.70/5.78  % (3890)Memory used [KB]: 26225
% 8.70/5.78  % (3890)Time elapsed: 0.256 s
% 8.70/5.78  % (3890)Instructions burned: 779 (million)
% 8.70/5.78  % (3890)------------------------------
% 8.70/5.78  % (3890)------------------------------
% 8.70/5.78  % (3905)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_3754 for (2992ds/98Mi)
% 8.70/5.79  % (3902)Instruction limit reached!
% 8.70/5.79  % (3902)------------------------------
% 8.70/5.79  % (3902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.79  % (3902)Termination reason: Unknown
% 8.70/5.79  % (3902)Termination phase: shuffling
% 8.70/5.79  
% 8.70/5.79  % (3902)Memory used [KB]: 14072
% 8.70/5.79  % (3902)Time elapsed: 0.036 s
% 8.70/5.79  % (3902)Instructions burned: 40 (million)
% 8.70/5.79  % (3902)------------------------------
% 8.70/5.79  % (3902)------------------------------
% 8.70/5.79  % (3906)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_3754 for (2992ds/507Mi)
% 8.70/5.80  % (3904)Instruction limit reached!
% 8.70/5.80  % (3904)------------------------------
% 8.70/5.80  % (3904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.80  % (3904)Termination reason: Unknown
% 8.70/5.80  % (3904)Termination phase: shuffling
% 8.70/5.80  
% 8.70/5.80  % (3904)Memory used [KB]: 14200
% 8.70/5.80  % (3904)Time elapsed: 0.027 s
% 8.70/5.80  % (3904)Instructions burned: 48 (million)
% 8.70/5.80  % (3904)------------------------------
% 8.70/5.80  % (3904)------------------------------
% 8.70/5.81  % (3908)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3754 for (2992ds/39Mi)
% 8.70/5.81  % (3907)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_3754 for (2992ds/149Mi)
% 8.70/5.82  % (3905)Instruction limit reached!
% 8.70/5.82  % (3905)------------------------------
% 8.70/5.82  % (3905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.82  % (3905)Termination reason: Unknown
% 8.70/5.82  % (3905)Termination phase: shuffling
% 8.70/5.82  
% 8.70/5.82  % (3905)Memory used [KB]: 14967
% 8.70/5.82  % (3905)Time elapsed: 0.038 s
% 8.70/5.82  % (3905)Instructions burned: 99 (million)
% 8.70/5.82  % (3905)------------------------------
% 8.70/5.82  % (3905)------------------------------
% 8.70/5.83  % (3885)Instruction limit reached!
% 8.70/5.83  % (3885)------------------------------
% 8.70/5.83  % (3885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.83  % (3885)Termination reason: Unknown
% 8.70/5.83  % (3885)Termination phase: Property scanning
% 8.70/5.83  
% 8.70/5.83  % (3885)Memory used [KB]: 26609
% 8.70/5.83  % (3885)Time elapsed: 0.344 s
% 8.70/5.83  % (3885)Instructions burned: 904 (million)
% 8.70/5.83  % (3885)------------------------------
% 8.70/5.83  % (3885)------------------------------
% 8.70/5.83  % (3908)Instruction limit reached!
% 8.70/5.83  % (3908)------------------------------
% 8.70/5.83  % (3908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.83  % (3908)Termination reason: Unknown
% 8.70/5.83  % (3908)Termination phase: shuffling
% 8.70/5.83  
% 8.70/5.83  % (3908)Memory used [KB]: 14072
% 8.70/5.83  % (3908)Time elapsed: 0.023 s
% 8.70/5.83  % (3908)Instructions burned: 39 (million)
% 8.70/5.83  % (3908)------------------------------
% 8.70/5.83  % (3908)------------------------------
% 8.70/5.83  % (3909)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_3754 for (2992ds/6Mi)
% 8.70/5.84  % (3909)Instruction limit reached!
% 8.70/5.84  % (3909)------------------------------
% 8.70/5.84  % (3909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.84  % (3909)Termination reason: Unknown
% 8.70/5.84  % (3909)Termination phase: shuffling
% 8.70/5.84  
% 8.70/5.84  % (3909)Memory used [KB]: 13176
% 8.70/5.84  % (3909)Time elapsed: 0.007 s
% 8.70/5.84  % (3909)Instructions burned: 6 (million)
% 8.70/5.84  % (3909)------------------------------
% 8.70/5.84  % (3909)------------------------------
% 8.70/5.84  % (3910)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_3754 for (2991ds/1087Mi)
% 8.70/5.84  % (3911)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3754 for (2991ds/47Mi)
% 8.70/5.85  % (3912)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_3754 for (2991ds/44Mi)
% 8.70/5.87  % (3912)Instruction limit reached!
% 8.70/5.87  % (3912)------------------------------
% 8.70/5.87  % (3912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.87  % (3912)Termination reason: Unknown
% 8.70/5.87  % (3912)Termination phase: shuffling
% 8.70/5.87  
% 8.70/5.87  % (3912)Memory used [KB]: 14200
% 8.70/5.87  % (3912)Time elapsed: 0.022 s
% 8.70/5.87  % (3912)Instructions burned: 44 (million)
% 8.70/5.87  % (3912)------------------------------
% 8.70/5.87  % (3912)------------------------------
% 8.70/5.87  % (3911)Instruction limit reached!
% 8.70/5.87  % (3911)------------------------------
% 8.70/5.87  % (3911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.87  % (3911)Termination reason: Unknown
% 8.70/5.87  % (3911)Termination phase: shuffling
% 8.70/5.87  
% 8.70/5.87  % (3911)Memory used [KB]: 14200
% 8.70/5.87  % (3911)Time elapsed: 0.027 s
% 8.70/5.87  % (3911)Instructions burned: 49 (million)
% 8.70/5.87  % (3911)------------------------------
% 8.70/5.87  % (3911)------------------------------
% 8.70/5.87  % (3892)Instruction limit reached!
% 8.70/5.87  % (3892)------------------------------
% 8.70/5.87  % (3892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.87  % (3892)Termination reason: Unknown
% 8.70/5.87  % (3892)Termination phase: Property scanning
% 8.70/5.87  
% 8.70/5.87  % (3892)Memory used [KB]: 26481
% 8.70/5.87  % (3892)Time elapsed: 0.333 s
% 8.70/5.87  % (3892)Instructions burned: 881 (million)
% 8.70/5.87  % (3892)------------------------------
% 8.70/5.87  % (3892)------------------------------
% 8.70/5.88  % (3913)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_3754 for (2991ds/432Mi)
% 8.70/5.88  % (3914)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3754 for (2991ds/62Mi)
% 8.70/5.88  % (3907)Instruction limit reached!
% 8.70/5.88  % (3907)------------------------------
% 8.70/5.88  % (3907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.88  % (3907)Termination reason: Unknown
% 8.70/5.88  % (3907)Termination phase: shuffling
% 8.70/5.88  
% 8.70/5.88  % (3907)Memory used [KB]: 15607
% 8.70/5.88  % (3907)Time elapsed: 0.071 s
% 8.70/5.88  % (3907)Instructions burned: 150 (million)
% 8.70/5.88  % (3907)------------------------------
% 8.70/5.88  % (3907)------------------------------
% 8.70/5.88  % (3915)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_3754 for (2991ds/31Mi)
% 8.70/5.89  % (3916)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3754 for (2991ds/96Mi)
% 8.70/5.90  % (3915)Instruction limit reached!
% 8.70/5.90  % (3915)------------------------------
% 8.70/5.90  % (3915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.90  % (3915)Termination reason: Unknown
% 8.70/5.90  % (3915)Termination phase: shuffling
% 8.70/5.90  
% 8.70/5.90  % (3915)Memory used [KB]: 13944
% 8.70/5.90  % (3915)Time elapsed: 0.019 s
% 8.70/5.90  % (3915)Instructions burned: 31 (million)
% 8.70/5.90  % (3915)------------------------------
% 8.70/5.90  % (3915)------------------------------
% 8.70/5.91  % (3914)Instruction limit reached!
% 8.70/5.91  % (3914)------------------------------
% 8.70/5.91  % (3914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.91  % (3914)Termination reason: Unknown
% 8.70/5.91  % (3914)Termination phase: shuffling
% 8.70/5.91  
% 8.70/5.91  % (3914)Memory used [KB]: 14456
% 8.70/5.91  % (3914)Time elapsed: 0.027 s
% 8.70/5.91  % (3914)Instructions burned: 64 (million)
% 8.70/5.91  % (3914)------------------------------
% 8.70/5.91  % (3914)------------------------------
% 8.70/5.91  % (3903)Instruction limit reached!
% 8.70/5.91  % (3903)------------------------------
% 8.70/5.91  % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.91  % (3903)Termination reason: Unknown
% 8.70/5.91  % (3903)Termination phase: shuffling
% 8.70/5.91  
% 8.70/5.91  % (3903)Memory used [KB]: 21875
% 8.70/5.91  % (3903)Time elapsed: 0.148 s
% 8.70/5.91  % (3903)Instructions burned: 448 (million)
% 8.70/5.91  % (3903)------------------------------
% 8.70/5.91  % (3903)------------------------------
% 8.70/5.91  % (3917)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_3754 for (2991ds/453Mi)
% 8.70/5.92  % (3919)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3754 for (2991ds/83Mi)
% 8.70/5.93  % (3918)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_3754 for (2991ds/71Mi)
% 8.70/5.94  % (3916)Instruction limit reached!
% 8.70/5.94  % (3916)------------------------------
% 8.70/5.94  % (3916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.94  % (3916)Termination reason: Unknown
% 8.70/5.94  % (3916)Termination phase: shuffling
% 8.70/5.94  
% 8.70/5.94  % (3916)Memory used [KB]: 14967
% 8.70/5.94  % (3916)Time elapsed: 0.045 s
% 8.70/5.94  % (3916)Instructions burned: 96 (million)
% 8.70/5.94  % (3916)------------------------------
% 8.70/5.94  % (3916)------------------------------
% 8.70/5.95  % (3920)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3754 for (2990ds/11Mi)
% 8.70/5.95  % (3919)Instruction limit reached!
% 8.70/5.95  % (3919)------------------------------
% 8.70/5.95  % (3919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.95  % (3919)Termination reason: Unknown
% 8.70/5.95  % (3919)Termination phase: shuffling
% 8.70/5.95  
% 8.70/5.95  % (3919)Memory used [KB]: 14711
% 8.70/5.95  % (3919)Time elapsed: 0.037 s
% 8.70/5.95  % (3919)Instructions burned: 83 (million)
% 8.70/5.95  % (3919)------------------------------
% 8.70/5.95  % (3919)------------------------------
% 8.70/5.96  % (3920)Instruction limit reached!
% 8.70/5.96  % (3920)------------------------------
% 8.70/5.96  % (3920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.96  % (3920)Termination reason: Unknown
% 8.70/5.96  % (3920)Termination phase: shuffling
% 8.70/5.96  
% 8.70/5.96  % (3920)Memory used [KB]: 13560
% 8.70/5.96  % (3920)Time elapsed: 0.012 s
% 8.70/5.96  % (3920)Instructions burned: 11 (million)
% 8.70/5.96  % (3920)------------------------------
% 8.70/5.96  % (3920)------------------------------
% 8.70/5.97  % (3921)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_3754 for (2990ds/41Mi)
% 8.70/5.97  % (3918)Instruction limit reached!
% 8.70/5.97  % (3918)------------------------------
% 8.70/5.97  % (3918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.97  % (3918)Termination reason: Unknown
% 8.70/5.97  % (3918)Termination phase: shuffling
% 8.70/5.97  
% 8.70/5.97  % (3918)Memory used [KB]: 14456
% 8.70/5.97  % (3918)Time elapsed: 0.047 s
% 8.70/5.97  % (3918)Instructions burned: 71 (million)
% 8.70/5.97  % (3918)------------------------------
% 8.70/5.97  % (3918)------------------------------
% 8.70/5.97  % (3922)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3754 for (2990ds/6Mi)
% 8.70/5.98  % (3906)Instruction limit reached!
% 8.70/5.98  % (3906)------------------------------
% 8.70/5.98  % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.98  % (3906)Termination reason: Unknown
% 8.70/5.98  % (3906)Termination phase: shuffling
% 8.70/5.98  
% 8.70/5.98  % (3906)Memory used [KB]: 20212
% 8.70/5.98  % (3906)Time elapsed: 0.185 s
% 8.70/5.98  % (3906)Instructions burned: 508 (million)
% 8.70/5.98  % (3906)------------------------------
% 8.70/5.98  % (3906)------------------------------
% 8.70/5.98  % (3922)Instruction limit reached!
% 8.70/5.98  % (3922)------------------------------
% 8.70/5.98  % (3922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.98  % (3922)Termination reason: Unknown
% 8.70/5.98  % (3922)Termination phase: shuffling
% 8.70/5.98  
% 8.70/5.98  % (3922)Memory used [KB]: 13176
% 8.70/5.98  % (3922)Time elapsed: 0.007 s
% 8.70/5.98  % (3922)Instructions burned: 6 (million)
% 8.70/5.98  % (3922)------------------------------
% 8.70/5.98  % (3922)------------------------------
% 8.70/5.98  % (3923)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3754 for (2990ds/150Mi)
% 8.70/5.99  % (3921)Instruction limit reached!
% 8.70/5.99  % (3921)------------------------------
% 8.70/5.99  % (3921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/5.99  % (3921)Termination reason: Unknown
% 8.70/5.99  % (3921)Termination phase: shuffling
% 8.70/5.99  
% 8.70/5.99  % (3921)Memory used [KB]: 14072
% 8.70/5.99  % (3921)Time elapsed: 0.022 s
% 8.70/5.99  % (3921)Instructions burned: 44 (million)
% 8.70/5.99  % (3921)------------------------------
% 8.70/5.99  % (3921)------------------------------
% 8.70/5.99  % (3924)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3754 for (2990ds/343Mi)
% 8.70/5.99  % (3925)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_3754 for (2990ds/109Mi)
% 8.70/6.00  % (3926)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_3754 for (2990ds/253Mi)
% 13.56/6.01  % (3913)Instruction limit reached!
% 13.56/6.01  % (3913)------------------------------
% 13.56/6.01  % (3913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.01  % (3913)Termination reason: Unknown
% 13.56/6.01  % (3913)Termination phase: shuffling
% 13.56/6.01  
% 13.56/6.01  % (3913)Memory used [KB]: 21620
% 13.56/6.01  % (3913)Time elapsed: 0.136 s
% 13.56/6.01  % (3913)Instructions burned: 433 (million)
% 13.56/6.01  % (3913)------------------------------
% 13.56/6.01  % (3913)------------------------------
% 13.56/6.03  % (3927)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3754 for (2989ds/140Mi)
% 13.56/6.04  % (3925)Instruction limit reached!
% 13.56/6.04  % (3925)------------------------------
% 13.56/6.04  % (3925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.04  % (3925)Termination reason: Unknown
% 13.56/6.04  % (3925)Termination phase: shuffling
% 13.56/6.04  
% 13.56/6.04  % (3925)Memory used [KB]: 15095
% 13.56/6.04  % (3925)Time elapsed: 0.048 s
% 13.56/6.04  % (3925)Instructions burned: 110 (million)
% 13.56/6.04  % (3925)------------------------------
% 13.56/6.04  % (3925)------------------------------
% 13.56/6.04  % (3923)Instruction limit reached!
% 13.56/6.04  % (3923)------------------------------
% 13.56/6.04  % (3923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.04  % (3923)Termination reason: Unknown
% 13.56/6.04  % (3923)Termination phase: shuffling
% 13.56/6.04  
% 13.56/6.04  % (3923)Memory used [KB]: 15607
% 13.56/6.04  % (3923)Time elapsed: 0.061 s
% 13.56/6.04  % (3923)Instructions burned: 150 (million)
% 13.56/6.04  % (3923)------------------------------
% 13.56/6.04  % (3923)------------------------------
% 13.56/6.05  % (3928)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_3754 for (2989ds/614Mi)
% 13.56/6.05  % (3917)Instruction limit reached!
% 13.56/6.05  % (3917)------------------------------
% 13.56/6.05  % (3917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.05  % (3917)Termination reason: Unknown
% 13.56/6.05  % (3917)Termination phase: shuffling
% 13.56/6.05  
% 13.56/6.05  % (3917)Memory used [KB]: 21875
% 13.56/6.05  % (3917)Time elapsed: 0.140 s
% 13.56/6.05  % (3917)Instructions burned: 453 (million)
% 13.56/6.05  % (3917)------------------------------
% 13.56/6.05  % (3917)------------------------------
% 13.56/6.05  % (3929)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_3754 for (2989ds/202Mi)
% 13.56/6.06  % (3930)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_3754 for (2989ds/339Mi)
% 13.56/6.08  % (3927)Instruction limit reached!
% 13.56/6.08  % (3927)------------------------------
% 13.56/6.08  % (3927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.08  % (3927)Termination reason: Unknown
% 13.56/6.08  % (3927)Termination phase: shuffling
% 13.56/6.08  
% 13.56/6.08  % (3927)Memory used [KB]: 15351
% 13.56/6.08  % (3927)Time elapsed: 0.055 s
% 13.56/6.08  % (3927)Instructions burned: 142 (million)
% 13.56/6.08  % (3927)------------------------------
% 13.56/6.08  % (3927)------------------------------
% 13.56/6.09  % (3926)Instruction limit reached!
% 13.56/6.09  % (3926)------------------------------
% 13.56/6.09  % (3926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.09  % (3926)Termination reason: Unknown
% 13.56/6.09  % (3926)Termination phase: shuffling
% 13.56/6.09  
% 13.56/6.09  % (3926)Memory used [KB]: 16758
% 13.56/6.09  % (3926)Time elapsed: 0.092 s
% 13.56/6.09  % (3926)Instructions burned: 255 (million)
% 13.56/6.09  % (3926)------------------------------
% 13.56/6.09  % (3926)------------------------------
% 13.56/6.09  % (3931)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_3754 for (2989ds/283Mi)
% 13.56/6.10  % (3932)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3754 for (2989ds/134Mi)
% 13.56/6.11  % (3924)Instruction limit reached!
% 13.56/6.11  % (3924)------------------------------
% 13.56/6.11  % (3924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/6.11  % (3924)Termination reason: Unknown
% 13.56/6.11  % (3924)Termination phase: shuffling
% 13.56/6.11  
% 13.56/6.11  % (3924)Memory used [KB]: 18166
% 13.56/6.11  % (3924)Time elapsed: 0.123 s
% 13.56/6.11  % (3924)Instructions burned: 343 (million)
% 13.56/6.11  % (3924)------------------------------
% 13.56/6.11  % (3924)------------------------------
% 14.08/6.12  % (3933)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3754 for (2989ds/298Mi)
% 14.08/6.13  % (3929)Instruction limit reached!
% 14.08/6.13  % (3929)------------------------------
% 14.08/6.13  % (3929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.08/6.13  % (3929)Termination reason: Unknown
% 14.08/6.13  % (3929)Termination phase: shuffling
% 14.08/6.13  
% 14.08/6.13  % (3929)Memory used [KB]: 16119
% 14.08/6.13  % (3929)Time elapsed: 0.076 s
% 14.08/6.13  % (3929)Instructions burned: 203 (million)
% 14.08/6.13  % (3929)------------------------------
% 14.08/6.13  % (3929)------------------------------
% 14.08/6.14  % (3934)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3754 for (2988ds/192Mi)
% 14.08/6.15  % (3932)Instruction limit reached!
% 14.08/6.15  % (3932)------------------------------
% 14.08/6.15  % (3932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.08/6.15  % (3932)Termination reason: Unknown
% 14.08/6.15  % (3932)Termination phase: shuffling
% 14.08/6.15  
% 14.08/6.15  % (3932)Memory used [KB]: 15479
% 14.08/6.15  % (3932)Time elapsed: 0.054 s
% 14.08/6.15  % (3932)Instructions burned: 135 (million)
% 14.08/6.15  % (3932)------------------------------
% 14.08/6.15  % (3932)------------------------------
% 14.08/6.16  % (3935)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_3754 for (2988ds/258Mi)
% 14.08/6.18  % (3931)Instruction limit reached!
% 14.08/6.18  % (3931)------------------------------
% 14.08/6.18  % (3931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.08/6.18  % (3931)Termination reason: Unknown
% 14.08/6.18  % (3931)Termination phase: shuffling
% 14.08/6.18  
% 14.08/6.18  % (3931)Memory used [KB]: 19701
% 14.08/6.18  % (3931)Time elapsed: 0.092 s
% 14.08/6.18  % (3931)Instructions burned: 285 (million)
% 14.08/6.18  % (3931)------------------------------
% 14.08/6.18  % (3931)------------------------------
% 14.08/6.18  % (3930)Instruction limit reached!
% 14.08/6.18  % (3930)------------------------------
% 14.08/6.18  % (3930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.08/6.18  % (3930)Termination reason: Unknown
% 14.08/6.18  % (3930)Termination phase: shuffling
% 14.08/6.18  
% 14.08/6.18  % (3930)Memory used [KB]: 18038
% 14.08/6.18  % (3930)Time elapsed: 0.122 s
% 14.08/6.18  % (3930)Instructions burned: 340 (million)
% 14.08/6.18  % (3930)------------------------------
% 14.08/6.18  % (3930)------------------------------
% 14.08/6.19  % (3936)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_3754 for (2988ds/90Mi)
% 14.08/6.19  % (3937)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_3754 for (2988ds/231Mi)
% 14.55/6.20  % (3910)Instruction limit reached!
% 14.55/6.20  % (3910)------------------------------
% 14.55/6.20  % (3910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.20  % (3910)Termination reason: Unknown
% 14.55/6.20  % (3910)Termination phase: Property scanning
% 14.55/6.20  
% 14.55/6.20  % (3910)Memory used [KB]: 26609
% 14.55/6.20  % (3910)Time elapsed: 0.367 s
% 14.55/6.20  % (3910)Instructions burned: 1089 (million)
% 14.55/6.20  % (3910)------------------------------
% 14.55/6.20  % (3910)------------------------------
% 14.55/6.21  % (3934)Instruction limit reached!
% 14.55/6.21  % (3934)------------------------------
% 14.55/6.21  % (3934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.21  % (3934)Termination reason: Unknown
% 14.55/6.21  % (3934)Termination phase: shuffling
% 14.55/6.21  
% 14.55/6.21  % (3934)Memory used [KB]: 16119
% 14.55/6.21  % (3934)Time elapsed: 0.073 s
% 14.55/6.21  % (3934)Instructions burned: 194 (million)
% 14.55/6.21  % (3934)------------------------------
% 14.55/6.21  % (3934)------------------------------
% 14.55/6.21  % (3933)Instruction limit reached!
% 14.55/6.21  % (3933)------------------------------
% 14.55/6.21  % (3933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.21  % (3933)Termination reason: Unknown
% 14.55/6.21  % (3933)Termination phase: shuffling
% 14.55/6.21  
% 14.55/6.21  % (3933)Memory used [KB]: 19829
% 14.55/6.21  % (3933)Time elapsed: 0.095 s
% 14.55/6.21  % (3933)Instructions burned: 298 (million)
% 14.55/6.21  % (3933)------------------------------
% 14.55/6.21  % (3933)------------------------------
% 14.55/6.22  % (3938)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_3754 for (2988ds/458Mi)
% 14.55/6.22  % (3939)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_3754 for (2988ds/31Mi)
% 14.55/6.23  % (3940)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_3754 for (2987ds/297Mi)
% 14.55/6.23  % (3936)Instruction limit reached!
% 14.55/6.23  % (3936)------------------------------
% 14.55/6.23  % (3936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.23  % (3936)Termination reason: Unknown
% 14.55/6.23  % (3936)Termination phase: shuffling
% 14.55/6.23  
% 14.55/6.23  % (3936)Memory used [KB]: 14839
% 14.55/6.23  % (3936)Time elapsed: 0.039 s
% 14.55/6.23  % (3936)Instructions burned: 90 (million)
% 14.55/6.23  % (3936)------------------------------
% 14.55/6.23  % (3936)------------------------------
% 14.55/6.24  % (3939)Instruction limit reached!
% 14.55/6.24  % (3939)------------------------------
% 14.55/6.24  % (3939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.24  % (3939)Termination reason: Unknown
% 14.55/6.24  % (3939)Termination phase: shuffling
% 14.55/6.24  
% 14.55/6.24  % (3939)Memory used [KB]: 13944
% 14.55/6.24  % (3939)Time elapsed: 0.020 s
% 14.55/6.24  % (3939)Instructions burned: 33 (million)
% 14.55/6.24  % (3939)------------------------------
% 14.55/6.24  % (3939)------------------------------
% 14.55/6.24  % (3941)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_3754 for (2987ds/987Mi)
% 14.55/6.25  % (3942)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_3754 for (2987ds/182Mi)
% 14.55/6.26  % (3935)Instruction limit reached!
% 14.55/6.26  % (3935)------------------------------
% 14.55/6.26  % (3935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.26  % (3935)Termination reason: Unknown
% 14.55/6.26  % (3935)Termination phase: shuffling
% 14.55/6.26  
% 14.55/6.26  % (3935)Memory used [KB]: 17014
% 14.55/6.26  % (3935)Time elapsed: 0.096 s
% 14.55/6.26  % (3935)Instructions burned: 260 (million)
% 14.55/6.26  % (3935)------------------------------
% 14.55/6.26  % (3935)------------------------------
% 14.55/6.27  % (3937)Instruction limit reached!
% 14.55/6.27  % (3937)------------------------------
% 14.55/6.27  % (3937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.27  % (3937)Termination reason: Unknown
% 14.55/6.27  % (3937)Termination phase: shuffling
% 14.55/6.27  
% 14.55/6.27  % (3937)Memory used [KB]: 16886
% 14.55/6.27  % (3937)Time elapsed: 0.075 s
% 14.55/6.27  % (3937)Instructions burned: 232 (million)
% 14.55/6.27  % (3937)------------------------------
% 14.55/6.27  % (3937)------------------------------
% 14.55/6.27  % (3943)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_3754 for (2987ds/182Mi)
% 14.55/6.27  % (3928)Instruction limit reached!
% 14.55/6.27  % (3928)------------------------------
% 14.55/6.27  % (3928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/6.27  % (3928)Termination reason: Unknown
% 14.55/6.27  % (3928)Termination phase: shuffling
% 14.55/6.27  
% 14.55/6.27  % (3928)Memory used [KB]: 21236
% 14.55/6.27  % (3928)Time elapsed: 0.224 s
% 14.55/6.27  % (3928)Instructions burned: 616 (million)
% 14.55/6.27  % (3928)------------------------------
% 14.55/6.27  % (3928)------------------------------
% 14.55/6.28  % (3944)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_3754 for (2987ds/154Mi)
% 14.55/6.28  % (3945)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_3754 for (2987ds/79Mi)
% 15.26/6.32  % (3945)Instruction limit reached!
% 15.26/6.32  % (3945)------------------------------
% 15.26/6.32  % (3945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.32  % (3945)Termination reason: Unknown
% 15.26/6.32  % (3945)Termination phase: shuffling
% 15.26/6.32  
% 15.26/6.32  % (3945)Memory used [KB]: 14583
% 15.26/6.32  % (3945)Time elapsed: 0.035 s
% 15.26/6.32  % (3945)Instructions burned: 80 (million)
% 15.26/6.32  % (3945)------------------------------
% 15.26/6.32  % (3945)------------------------------
% 15.26/6.32  % (3940)Instruction limit reached!
% 15.26/6.32  % (3940)------------------------------
% 15.26/6.32  % (3940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.32  % (3940)Termination reason: Unknown
% 15.26/6.32  % (3940)Termination phase: shuffling
% 15.26/6.32  
% 15.26/6.32  % (3940)Memory used [KB]: 19701
% 15.26/6.32  % (3940)Time elapsed: 0.096 s
% 15.26/6.32  % (3940)Instructions burned: 298 (million)
% 15.26/6.32  % (3940)------------------------------
% 15.26/6.32  % (3940)------------------------------
% 15.26/6.32  % (3942)Instruction limit reached!
% 15.26/6.32  % (3942)------------------------------
% 15.26/6.32  % (3942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.32  % (3942)Termination reason: Unknown
% 15.26/6.32  % (3942)Termination phase: shuffling
% 15.26/6.32  
% 15.26/6.32  % (3942)Memory used [KB]: 15863
% 15.26/6.32  % (3942)Time elapsed: 0.071 s
% 15.26/6.32  % (3942)Instructions burned: 184 (million)
% 15.26/6.32  % (3942)------------------------------
% 15.26/6.32  % (3942)------------------------------
% 15.26/6.33  % (3946)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_3754 for (2986ds/216Mi)
% 15.26/6.33  % (3947)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3754 for (2986ds/114Mi)
% 15.26/6.33  % (3944)Instruction limit reached!
% 15.26/6.33  % (3944)------------------------------
% 15.26/6.33  % (3944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.33  % (3944)Termination reason: Unknown
% 15.26/6.33  % (3944)Termination phase: shuffling
% 15.26/6.33  
% 15.26/6.33  % (3944)Memory used [KB]: 15863
% 15.26/6.33  % (3944)Time elapsed: 0.054 s
% 15.26/6.33  % (3944)Instructions burned: 155 (million)
% 15.26/6.33  % (3944)------------------------------
% 15.26/6.33  % (3944)------------------------------
% 15.26/6.33  % (3948)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_3754 for (2986ds/922Mi)
% 15.26/6.34  % (3943)Instruction limit reached!
% 15.26/6.34  % (3943)------------------------------
% 15.26/6.34  % (3943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.34  % (3943)Termination reason: Unknown
% 15.26/6.34  % (3943)Termination phase: shuffling
% 15.26/6.34  
% 15.26/6.34  % (3943)Memory used [KB]: 16247
% 15.26/6.34  % (3943)Time elapsed: 0.072 s
% 15.26/6.34  % (3943)Instructions burned: 183 (million)
% 15.26/6.34  % (3943)------------------------------
% 15.26/6.34  % (3943)------------------------------
% 15.26/6.34  % (3949)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_3754 for (2986ds/182Mi)
% 15.26/6.35  % (3950)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_3754 for (2986ds/164Mi)
% 15.26/6.38  % (3947)Instruction limit reached!
% 15.26/6.38  % (3947)------------------------------
% 15.26/6.38  % (3947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.38  % (3947)Termination reason: Unknown
% 15.26/6.38  % (3947)Termination phase: shuffling
% 15.26/6.38  
% 15.26/6.38  % (3947)Memory used [KB]: 14967
% 15.26/6.38  % (3947)Time elapsed: 0.046 s
% 15.26/6.38  % (3947)Instructions burned: 114 (million)
% 15.26/6.38  % (3947)------------------------------
% 15.26/6.38  % (3947)------------------------------
% 15.26/6.38  % (3938)Instruction limit reached!
% 15.26/6.38  % (3938)------------------------------
% 15.26/6.38  % (3938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/6.38  % (3938)Termination reason: Unknown
% 15.26/6.38  % (3938)Termination phase: shuffling
% 15.26/6.38  
% 15.26/6.38  % (3938)Memory used [KB]: 19445
% 15.26/6.38  % (3938)Time elapsed: 0.163 s
% 15.26/6.38  % (3938)Instructions burned: 458 (million)
% 15.26/6.38  % (3938)------------------------------
% 15.26/6.38  % (3938)------------------------------
% 15.26/6.39  % (3951)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_3754 for (2986ds/50Mi)
% 15.26/6.39  % (3952)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3754 for (2986ds/368Mi)
% 15.88/6.40  % (3946)Instruction limit reached!
% 15.88/6.40  % (3946)------------------------------
% 15.88/6.40  % (3946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.40  % (3946)Termination reason: Unknown
% 15.88/6.40  % (3946)Termination phase: shuffling
% 15.88/6.40  
% 15.88/6.40  % (3946)Memory used [KB]: 16630
% 15.88/6.40  % (3946)Time elapsed: 0.071 s
% 15.88/6.40  % (3946)Instructions burned: 216 (million)
% 15.88/6.40  % (3946)------------------------------
% 15.88/6.40  % (3946)------------------------------
% 15.88/6.40  % (3949)Instruction limit reached!
% 15.88/6.40  % (3949)------------------------------
% 15.88/6.40  % (3949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.40  % (3949)Termination reason: Unknown
% 15.88/6.40  % (3949)Termination phase: shuffling
% 15.88/6.40  
% 15.88/6.40  % (3949)Memory used [KB]: 16119
% 15.88/6.40  % (3949)Time elapsed: 0.061 s
% 15.88/6.40  % (3949)Instructions burned: 185 (million)
% 15.88/6.40  % (3949)------------------------------
% 15.88/6.40  % (3949)------------------------------
% 15.88/6.41  % (3950)Instruction limit reached!
% 15.88/6.41  % (3950)------------------------------
% 15.88/6.41  % (3950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.41  % (3950)Termination reason: Unknown
% 15.88/6.41  % (3950)Termination phase: shuffling
% 15.88/6.41  
% 15.88/6.41  % (3950)Memory used [KB]: 15863
% 15.88/6.41  % (3950)Time elapsed: 0.055 s
% 15.88/6.41  % (3950)Instructions burned: 164 (million)
% 15.88/6.41  % (3950)------------------------------
% 15.88/6.41  % (3950)------------------------------
% 15.88/6.41  % (3953)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_3754 for (2986ds/1021Mi)
% 15.88/6.41  % (3951)Instruction limit reached!
% 15.88/6.41  % (3951)------------------------------
% 15.88/6.41  % (3951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.41  % (3951)Termination reason: Unknown
% 15.88/6.41  % (3951)Termination phase: shuffling
% 15.88/6.41  
% 15.88/6.41  % (3951)Memory used [KB]: 14200
% 15.88/6.41  % (3951)Time elapsed: 0.024 s
% 15.88/6.41  % (3951)Instructions burned: 51 (million)
% 15.88/6.41  % (3951)------------------------------
% 15.88/6.41  % (3951)------------------------------
% 15.88/6.42  % (3954)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_3754 for (2986ds/267Mi)
% 15.88/6.42  % (3955)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_3754 for (2986ds/204Mi)
% 15.88/6.42  % (3956)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_3754 for (2986ds/26Mi)
% 15.88/6.44  % (3956)Instruction limit reached!
% 15.88/6.44  % (3956)------------------------------
% 15.88/6.44  % (3956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.44  % (3956)Termination reason: Unknown
% 15.88/6.44  % (3956)Termination phase: shuffling
% 15.88/6.44  
% 15.88/6.44  % (3956)Memory used [KB]: 13944
% 15.88/6.44  % (3956)Time elapsed: 0.018 s
% 15.88/6.44  % (3956)Instructions burned: 28 (million)
% 15.88/6.44  % (3956)------------------------------
% 15.88/6.44  % (3956)------------------------------
% 15.88/6.45  % (3957)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_3754 for (2985ds/53Mi)
% 15.88/6.47  % (3957)Instruction limit reached!
% 15.88/6.47  % (3957)------------------------------
% 15.88/6.47  % (3957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.47  % (3957)Termination reason: Unknown
% 15.88/6.47  % (3957)Termination phase: shuffling
% 15.88/6.47  
% 15.88/6.47  % (3957)Memory used [KB]: 14328
% 15.88/6.47  % (3957)Time elapsed: 0.025 s
% 15.88/6.47  % (3957)Instructions burned: 53 (million)
% 15.88/6.47  % (3957)------------------------------
% 15.88/6.47  % (3957)------------------------------
% 15.88/6.48  % (3958)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_3754 for (2985ds/4436Mi)
% 15.88/6.49  % (3955)Instruction limit reached!
% 15.88/6.49  % (3955)------------------------------
% 15.88/6.49  % (3955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.88/6.49  % (3955)Termination reason: Unknown
% 15.88/6.49  % (3955)Termination phase: shuffling
% 15.88/6.49  
% 15.88/6.49  % (3955)Memory used [KB]: 16502
% 15.88/6.49  % (3955)Time elapsed: 0.079 s
% 15.88/6.49  % (3955)Instructions burned: 206 (million)
% 15.88/6.49  % (3955)------------------------------
% 15.88/6.49  % (3955)------------------------------
% 16.19/6.50  % (3954)Instruction limit reached!
% 16.19/6.50  % (3954)------------------------------
% 16.19/6.50  % (3954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/6.50  % (3954)Termination reason: Unknown
% 16.19/6.50  % (3954)Termination phase: shuffling
% 16.19/6.50  
% 16.19/6.50  % (3954)Memory used [KB]: 19445
% 16.19/6.50  % (3954)Time elapsed: 0.088 s
% 16.19/6.50  % (3954)Instructions burned: 269 (million)
% 16.19/6.50  % (3954)------------------------------
% 16.19/6.50  % (3954)------------------------------
% 16.19/6.51  % (3959)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_3754 for (2985ds/1539Mi)
% 16.19/6.51  % (3960)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_3754 for (2985ds/408Mi)
% 16.19/6.52  % (3952)Instruction limit reached!
% 16.19/6.52  % (3952)------------------------------
% 16.19/6.52  % (3952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/6.52  % (3952)Termination reason: Unknown
% 16.19/6.52  % (3952)Termination phase: shuffling
% 16.19/6.52  
% 16.19/6.52  % (3952)Memory used [KB]: 18293
% 16.19/6.52  % (3952)Time elapsed: 0.132 s
% 16.19/6.52  % (3952)Instructions burned: 369 (million)
% 16.19/6.52  % (3952)------------------------------
% 16.19/6.52  % (3952)------------------------------
% 16.19/6.53  % (3961)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_3754 for (2985ds/5205Mi)
% 16.19/6.54  % (3941)Instruction limit reached!
% 16.19/6.54  % (3941)------------------------------
% 16.19/6.54  % (3941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.19/6.54  % (3941)Termination reason: Unknown
% 16.19/6.54  % (3941)Termination phase: shuffling
% 16.19/6.54  
% 16.19/6.54  % (3941)Memory used [KB]: 33133
% 16.19/6.54  % (3941)Time elapsed: 0.303 s
% 16.19/6.54  % (3941)Instructions burned: 987 (million)
% 16.19/6.54  % (3941)------------------------------
% 16.19/6.54  % (3941)------------------------------
% 16.19/6.56  % (3962)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_3754 for (2984ds/1913Mi)
% 16.84/6.65  % (3948)Instruction limit reached!
% 16.84/6.65  % (3948)------------------------------
% 16.84/6.65  % (3948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.84/6.65  % (3948)Termination reason: Unknown
% 16.84/6.65  % (3948)Termination phase: Property scanning
% 16.84/6.65  
% 16.84/6.65  % (3948)Memory used [KB]: 26609
% 16.84/6.65  % (3948)Time elapsed: 0.318 s
% 16.84/6.65  % (3948)Instructions burned: 922 (million)
% 16.84/6.65  % (3948)------------------------------
% 16.84/6.65  % (3948)------------------------------
% 16.84/6.66  % (3960)Instruction limit reached!
% 16.84/6.66  % (3960)------------------------------
% 16.84/6.66  % (3960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.84/6.66  % (3960)Termination reason: Unknown
% 16.84/6.66  % (3960)Termination phase: shuffling
% 16.84/6.66  
% 16.84/6.66  % (3960)Memory used [KB]: 19061
% 16.84/6.66  % (3960)Time elapsed: 0.144 s
% 16.84/6.66  % (3960)Instructions burned: 409 (million)
% 16.84/6.66  % (3960)------------------------------
% 16.84/6.66  % (3960)------------------------------
% 16.84/6.66  % (3963)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_3754 for (2983ds/4350Mi)
% 16.84/6.67  % (3964)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_3754 for (2983ds/68Mi)
% 16.84/6.70  % (3964)Instruction limit reached!
% 16.84/6.70  % (3964)------------------------------
% 16.84/6.70  % (3964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.32/6.70  % (3964)Termination reason: Unknown
% 17.32/6.70  % (3964)Termination phase: shuffling
% 17.32/6.70  
% 17.32/6.70  % (3964)Memory used [KB]: 14456
% 17.32/6.70  % (3964)Time elapsed: 0.031 s
% 17.32/6.70  % (3964)Instructions burned: 69 (million)
% 17.32/6.70  % (3964)------------------------------
% 17.32/6.70  % (3964)------------------------------
% 17.32/6.71  % (3965)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_3754 for (2983ds/358Mi)
% 17.32/6.75  % (3953)Instruction limit reached!
% 17.32/6.75  % (3953)------------------------------
% 17.32/6.75  % (3953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.32/6.75  % (3953)Termination reason: Unknown
% 17.32/6.75  % (3953)Termination phase: Property scanning
% 17.32/6.75  
% 17.32/6.75  % (3953)Memory used [KB]: 26609
% 17.32/6.75  % (3953)Time elapsed: 0.343 s
% 17.32/6.75  % (3953)Instructions burned: 1024 (million)
% 17.32/6.75  % (3953)------------------------------
% 17.32/6.75  % (3953)------------------------------
% 17.32/6.76  % (3966)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_3754 for (2982ds/31Mi)
% 17.32/6.78  % (3966)Instruction limit reached!
% 17.32/6.78  % (3966)------------------------------
% 17.32/6.78  % (3966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.32/6.78  % (3966)Termination reason: Unknown
% 17.32/6.78  % (3966)Termination phase: shuffling
% 17.32/6.78  
% 17.32/6.78  % (3966)Memory used [KB]: 13944
% 17.32/6.78  % (3966)Time elapsed: 0.020 s
% 17.32/6.78  % (3966)Instructions burned: 33 (million)
% 17.32/6.78  % (3966)------------------------------
% 17.32/6.78  % (3966)------------------------------
% 17.32/6.79  % (3967)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3754 for (2982ds/279Mi)
% 17.74/6.83  % (3965)Instruction limit reached!
% 17.74/6.83  % (3965)------------------------------
% 17.74/6.83  % (3965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/6.83  % (3965)Termination reason: Unknown
% 17.74/6.83  % (3965)Termination phase: shuffling
% 17.74/6.83  
% 17.74/6.83  % (3965)Memory used [KB]: 18038
% 17.74/6.83  % (3965)Time elapsed: 0.126 s
% 17.74/6.83  % (3965)Instructions burned: 360 (million)
% 17.74/6.83  % (3965)------------------------------
% 17.74/6.83  % (3965)------------------------------
% 17.74/6.84  % (3968)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3754 for (2981ds/258Mi)
% 17.74/6.88  % (3967)Instruction limit reached!
% 17.74/6.88  % (3967)------------------------------
% 17.74/6.88  % (3967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.74/6.88  % (3967)Termination reason: Unknown
% 17.74/6.88  % (3967)Termination phase: shuffling
% 17.74/6.88  
% 17.74/6.88  % (3967)Memory used [KB]: 19573
% 17.74/6.88  % (3967)Time elapsed: 0.088 s
% 17.74/6.88  % (3967)Instructions burned: 279 (million)
% 17.74/6.88  % (3967)------------------------------
% 17.74/6.88  % (3967)------------------------------
% 17.74/6.89  % (3969)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_3754 for (2981ds/26Mi)
% 17.99/6.91  % (3969)Instruction limit reached!
% 17.99/6.91  % (3969)------------------------------
% 17.99/6.91  % (3969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.99/6.91  % (3969)Termination reason: Unknown
% 17.99/6.91  % (3969)Termination phase: shuffling
% 17.99/6.91  
% 17.99/6.91  % (3969)Memory used [KB]: 13816
% 17.99/6.91  % (3969)Time elapsed: 0.017 s
% 17.99/6.91  % (3969)Instructions burned: 26 (million)
% 17.99/6.91  % (3969)------------------------------
% 17.99/6.91  % (3969)------------------------------
% 17.99/6.92  % (3970)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3754 for (2980ds/995Mi)
% 17.99/6.94  % (3968)Instruction limit reached!
% 17.99/6.94  % (3968)------------------------------
% 17.99/6.94  % (3968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.99/6.94  % (3968)Termination reason: Unknown
% 17.99/6.94  % (3968)Termination phase: shuffling
% 17.99/6.94  
% 17.99/6.94  % (3968)Memory used [KB]: 16886
% 17.99/6.94  % (3968)Time elapsed: 0.093 s
% 17.99/6.94  % (3968)Instructions burned: 259 (million)
% 17.99/6.94  % (3968)------------------------------
% 17.99/6.94  % (3968)------------------------------
% 17.99/6.95  % (3971)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3754 for (2980ds/373Mi)
% 17.99/6.98  % (3959)Instruction limit reached!
% 17.99/6.98  % (3959)------------------------------
% 17.99/6.98  % (3959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.99/6.98  % (3959)Termination reason: Unknown
% 17.99/6.98  % (3959)Termination phase: SInE selection
% 17.99/6.98  
% 17.99/6.98  % (3959)Memory used [KB]: 26481
% 17.99/6.98  % (3959)Time elapsed: 0.478 s
% 17.99/6.98  % (3959)Instructions burned: 1540 (million)
% 17.99/6.98  % (3959)------------------------------
% 17.99/6.98  % (3959)------------------------------
% 17.99/7.00  % (3972)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3754 for (2980ds/253Mi)
% 20.64/7.07  % (3972)Instruction limit reached!
% 20.64/7.07  % (3972)------------------------------
% 20.64/7.07  % (3972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/7.07  % (3972)Termination reason: Unknown
% 20.64/7.07  % (3972)Termination phase: shuffling
% 20.64/7.07  
% 20.64/7.07  % (3972)Memory used [KB]: 17270
% 20.64/7.07  % (3972)Time elapsed: 0.080 s
% 20.64/7.07  % (3972)Instructions burned: 255 (million)
% 20.64/7.07  % (3972)------------------------------
% 20.64/7.07  % (3972)------------------------------
% 20.64/7.08  % (3971)Instruction limit reached!
% 20.64/7.08  % (3971)------------------------------
% 20.64/7.08  % (3971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/7.08  % (3971)Termination reason: Unknown
% 20.64/7.08  % (3971)Termination phase: shuffling
% 20.64/7.08  
% 20.64/7.08  % (3971)Memory used [KB]: 18421
% 20.64/7.08  % (3971)Time elapsed: 0.130 s
% 20.64/7.08  % (3971)Instructions burned: 375 (million)
% 20.64/7.08  % (3971)------------------------------
% 20.64/7.08  % (3971)------------------------------
% 20.64/7.09  % (3973)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3754 for (2979ds/832Mi)
% 20.64/7.09  % (3974)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3754 for (2979ds/668Mi)
% 21.31/7.15  % (3962)Instruction limit reached!
% 21.31/7.15  % (3962)------------------------------
% 21.31/7.15  % (3962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.31/7.15  % (3962)Termination reason: Unknown
% 21.31/7.15  % (3962)Termination phase: SInE selection
% 21.31/7.15  
% 21.31/7.15  % (3962)Memory used [KB]: 27376
% 21.31/7.15  % (3962)Time elapsed: 0.596 s
% 21.31/7.15  % (3962)Instructions burned: 1913 (million)
% 21.31/7.15  % (3962)------------------------------
% 21.31/7.15  % (3962)------------------------------
% 21.31/7.16  % (3975)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3754 for (2978ds/40Mi)
% 21.31/7.18  % (3975)Instruction limit reached!
% 21.31/7.18  % (3975)------------------------------
% 21.31/7.18  % (3975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.31/7.18  % (3975)Termination reason: Unknown
% 21.31/7.18  % (3975)Termination phase: shuffling
% 21.31/7.18  
% 21.31/7.18  % (3975)Memory used [KB]: 14072
% 21.31/7.18  % (3975)Time elapsed: 0.021 s
% 21.31/7.18  % (3975)Instructions burned: 41 (million)
% 21.31/7.18  % (3975)------------------------------
% 21.31/7.18  % (3975)------------------------------
% 21.31/7.20  % (3976)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3754 for (2978ds/294Mi)
% 21.31/7.20  % (3963)Refutation not found, incomplete strategy
% 21.31/7.20  % (3963)------------------------------
% 21.31/7.20  % (3963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.31/7.20  % (3963)Termination reason: Refutation not found, incomplete strategy
% 21.31/7.20  
% 21.31/7.20  
% 21.31/7.20  % (3963)Memory used [KB]: 31470
% 21.31/7.20  % (3963)Time elapsed: 0.557 s
% 21.31/7.20  % (3963)Instructions burned: 1711 (million)
% 21.31/7.20  % (3963)------------------------------
% 21.31/7.20  % (3963)------------------------------
% 21.68/7.21  % (3977)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3754 for (2978ds/187Mi)
% 21.68/7.21  % (3970)Instruction limit reached!
% 21.68/7.21  % (3970)------------------------------
% 21.68/7.21  % (3970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/7.21  % (3970)Termination reason: Unknown
% 21.68/7.21  % (3970)Termination phase: shuffling
% 21.68/7.21  
% 21.68/7.21  % (3970)Memory used [KB]: 33261
% 21.68/7.21  % (3970)Time elapsed: 0.295 s
% 21.68/7.21  % (3970)Instructions burned: 995 (million)
% 21.68/7.21  % (3970)------------------------------
% 21.68/7.21  % (3970)------------------------------
% 21.68/7.22  % (3978)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3754 for (2977ds/371Mi)
% 21.68/7.28  % (3977)Instruction limit reached!
% 21.68/7.28  % (3977)------------------------------
% 21.68/7.28  % (3977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/7.28  % (3977)Termination reason: Unknown
% 21.68/7.28  % (3977)Termination phase: shuffling
% 21.68/7.28  
% 21.68/7.28  % (3977)Memory used [KB]: 16119
% 21.68/7.28  % (3977)Time elapsed: 0.072 s
% 21.68/7.28  % (3977)Instructions burned: 189 (million)
% 21.68/7.28  % (3977)------------------------------
% 21.68/7.28  % (3977)------------------------------
% 21.68/7.29  % (3974)Instruction limit reached!
% 21.68/7.29  % (3974)------------------------------
% 21.68/7.29  % (3974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/7.29  % (3974)Termination reason: Unknown
% 21.68/7.29  % (3974)Termination phase: shuffling
% 21.68/7.29  
% 21.68/7.29  % (3974)Memory used [KB]: 24946
% 21.68/7.29  % (3974)Time elapsed: 0.201 s
% 21.68/7.29  % (3974)Instructions burned: 669 (million)
% 21.68/7.29  % (3974)------------------------------
% 21.68/7.29  % (3974)------------------------------
% 21.68/7.29  % (3976)Instruction limit reached!
% 21.68/7.29  % (3976)------------------------------
% 21.68/7.29  % (3976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/7.29  % (3976)Termination reason: Unknown
% 21.68/7.29  % (3976)Termination phase: shuffling
% 21.68/7.29  
% 21.68/7.29  % (3976)Memory used [KB]: 19701
% 21.68/7.29  % (3976)Time elapsed: 0.095 s
% 21.68/7.29  % (3976)Instructions burned: 294 (million)
% 21.68/7.29  % (3976)------------------------------
% 21.68/7.29  % (3976)------------------------------
% 21.68/7.29  % (3979)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3754 for (2977ds/1827Mi)
% 22.32/7.30  % (3980)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3754 for (2977ds/70Mi)
% 22.32/7.30  % (3981)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3754 for (2977ds/316Mi)
% 22.32/7.33  % (3980)Instruction limit reached!
% 22.32/7.33  % (3980)------------------------------
% 22.32/7.33  % (3980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/7.33  % (3980)Termination reason: Unknown
% 22.32/7.33  % (3980)Termination phase: shuffling
% 22.32/7.33  
% 22.32/7.33  % (3980)Memory used [KB]: 14456
% 22.32/7.33  % (3980)Time elapsed: 0.029 s
% 22.32/7.33  % (3980)Instructions burned: 70 (million)
% 22.32/7.33  % (3980)------------------------------
% 22.32/7.33  % (3980)------------------------------
% 22.32/7.34  % (3982)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3754 for (2976ds/932Mi)
% 22.32/7.35  % (3978)Instruction limit reached!
% 22.32/7.35  % (3978)------------------------------
% 22.32/7.35  % (3978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/7.35  % (3978)Termination reason: Unknown
% 22.32/7.35  % (3978)Termination phase: shuffling
% 22.32/7.35  
% 22.32/7.35  % (3978)Memory used [KB]: 18166
% 22.32/7.35  % (3978)Time elapsed: 0.131 s
% 22.32/7.35  % (3978)Instructions burned: 372 (million)
% 22.32/7.35  % (3978)------------------------------
% 22.32/7.35  % (3978)------------------------------
% 22.32/7.37  % (3983)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3754 for (2976ds/4714Mi)
% 22.32/7.38  % (3973)Instruction limit reached!
% 22.32/7.38  % (3973)------------------------------
% 22.32/7.38  % (3973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.32/7.38  % (3973)Termination reason: Unknown
% 22.32/7.38  % (3973)Termination phase: shuffling
% 22.32/7.38  
% 22.32/7.38  % (3973)Memory used [KB]: 26353
% 22.32/7.38  % (3973)Time elapsed: 0.294 s
% 22.32/7.38  % (3973)Instructions burned: 833 (million)
% 22.32/7.38  % (3973)------------------------------
% 22.32/7.38  % (3973)------------------------------
% 22.32/7.39  % (3984)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3754 for (2976ds/8250Mi)
% 23.01/7.40  % (3981)Instruction limit reached!
% 23.01/7.40  % (3981)------------------------------
% 23.01/7.40  % (3981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.01/7.40  % (3981)Termination reason: Unknown
% 23.01/7.40  % (3981)Termination phase: shuffling
% 23.01/7.40  
% 23.01/7.40  % (3981)Memory used [KB]: 20084
% 23.01/7.40  % (3981)Time elapsed: 0.100 s
% 23.01/7.40  % (3981)Instructions burned: 316 (million)
% 23.01/7.40  % (3981)------------------------------
% 23.01/7.40  % (3981)------------------------------
% 23.01/7.41  % (3985)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3754 for (2976ds/770Mi)
% 23.51/7.62  % (3982)Instruction limit reached!
% 23.51/7.62  % (3982)------------------------------
% 23.51/7.62  % (3982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.51/7.62  % (3982)Termination reason: Unknown
% 23.51/7.62  % (3982)Termination phase: shuffling
% 23.51/7.62  
% 23.51/7.62  % (3982)Memory used [KB]: 32366
% 23.51/7.62  % (3982)Time elapsed: 0.284 s
% 23.51/7.62  % (3982)Instructions burned: 932 (million)
% 23.51/7.62  % (3982)------------------------------
% 23.51/7.62  % (3982)------------------------------
% 23.51/7.63  % (3986)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3754 for (2973ds/794Mi)
% 23.51/7.68  % (3985)Instruction limit reached!
% 23.51/7.68  % (3985)------------------------------
% 23.51/7.68  % (3985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.51/7.68  % (3985)Termination reason: Unknown
% 23.51/7.68  % (3985)Termination phase: shuffling
% 23.51/7.68  
% 23.51/7.68  % (3985)Memory used [KB]: 25074
% 23.51/7.68  % (3985)Time elapsed: 0.270 s
% 23.51/7.68  % (3985)Instructions burned: 771 (million)
% 23.51/7.68  % (3985)------------------------------
% 23.51/7.68  % (3985)------------------------------
% 23.51/7.69  % (3987)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3754 for (2973ds/464Mi)
% 24.50/7.85  % (3987)Instruction limit reached!
% 24.50/7.85  % (3987)------------------------------
% 24.50/7.85  % (3987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/7.85  % (3987)Termination reason: Unknown
% 24.50/7.85  % (3987)Termination phase: shuffling
% 24.50/7.85  
% 24.50/7.85  % (3987)Memory used [KB]: 19701
% 24.50/7.85  % (3987)Time elapsed: 0.163 s
% 24.50/7.85  % (3987)Instructions burned: 464 (million)
% 24.50/7.85  % (3987)------------------------------
% 24.50/7.85  % (3987)------------------------------
% 24.50/7.87  % (3988)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3754 for (2971ds/1376Mi)
% 24.50/7.88  % (3979)Instruction limit reached!
% 24.50/7.88  % (3979)------------------------------
% 24.50/7.88  % (3979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/7.88  % (3979)Termination reason: Unknown
% 24.50/7.88  % (3979)Termination phase: Preprocessing 3
% 24.50/7.88  
% 24.50/7.88  % (3979)Memory used [KB]: 33517
% 24.50/7.88  % (3979)Time elapsed: 0.585 s
% 24.50/7.88  % (3979)Instructions burned: 1829 (million)
% 24.50/7.88  % (3979)------------------------------
% 24.50/7.88  % (3979)------------------------------
% 24.50/7.89  % (3958)Instruction limit reached!
% 24.50/7.89  % (3958)------------------------------
% 24.50/7.89  % (3958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/7.89  % (3958)Termination reason: Unknown
% 24.50/7.89  % (3958)Termination phase: Saturation
% 24.50/7.89  
% 24.50/7.89  % (3958)Memory used [KB]: 35564
% 24.50/7.89  % (3958)Time elapsed: 1.404 s
% 24.50/7.89  % (3958)Instructions burned: 4436 (million)
% 24.50/7.89  % (3958)------------------------------
% 24.50/7.89  % (3958)------------------------------
% 24.50/7.89  % (3989)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3754 for (2971ds/906Mi)
% 25.48/7.90  % (3990)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3754 for (2971ds/434Mi)
% 25.48/7.91  % (3986)Instruction limit reached!
% 25.48/7.91  % (3986)------------------------------
% 25.48/7.91  % (3986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.48/7.91  % (3986)Termination reason: Unknown
% 25.48/7.91  % (3986)Termination phase: shuffling
% 25.48/7.91  
% 25.48/7.91  % (3986)Memory used [KB]: 25713
% 25.48/7.91  % (3986)Time elapsed: 0.276 s
% 25.48/7.91  % (3986)Instructions burned: 796 (million)
% 25.48/7.91  % (3986)------------------------------
% 25.48/7.91  % (3986)------------------------------
% 25.48/7.92  % (3991)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3754 for (2971ds/865Mi)
% 25.48/7.93  % (3961)Instruction limit reached!
% 25.48/7.93  % (3961)------------------------------
% 25.48/7.93  % (3961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.48/7.93  % (3961)Termination reason: Unknown
% 25.48/7.93  % (3961)Termination phase: Function definition elimination
% 25.48/7.93  
% 25.48/7.93  % (3961)Memory used [KB]: 58847
% 25.48/7.93  % (3961)Time elapsed: 1.404 s
% 25.48/7.93  % (3961)Instructions burned: 5206 (million)
% 25.48/7.93  % (3961)------------------------------
% 25.48/7.93  % (3961)------------------------------
% 25.48/7.95  % (3992)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3754 for (2970ds/593Mi)
% 27.67/8.05  % (3990)Instruction limit reached!
% 27.67/8.05  % (3990)------------------------------
% 27.67/8.05  % (3990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.67/8.05  % (3990)Termination reason: Unknown
% 27.67/8.05  % (3990)Termination phase: shuffling
% 27.67/8.05  
% 27.67/8.05  % (3990)Memory used [KB]: 19317
% 27.67/8.05  % (3990)Time elapsed: 0.154 s
% 27.67/8.05  % (3990)Instructions burned: 434 (million)
% 27.67/8.05  % (3990)------------------------------
% 27.67/8.05  % (3990)------------------------------
% 27.67/8.06  % (3993)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3754 for (2969ds/443Mi)
% 27.67/8.12  % (3992)Instruction limit reached!
% 27.67/8.12  % (3992)------------------------------
% 27.67/8.12  % (3992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.67/8.12  % (3992)Termination reason: Unknown
% 27.67/8.12  % (3992)Termination phase: shuffling
% 27.67/8.12  
% 27.67/8.12  % (3992)Memory used [KB]: 23794
% 27.67/8.12  % (3992)Time elapsed: 0.176 s
% 27.67/8.12  % (3992)Instructions burned: 593 (million)
% 27.67/8.12  % (3992)------------------------------
% 27.67/8.12  % (3992)------------------------------
% 28.17/8.14  % (3994)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3754 for (2968ds/594Mi)
% 28.17/8.18  % (3991)Instruction limit reached!
% 28.17/8.18  % (3991)------------------------------
% 28.17/8.18  % (3991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/8.18  % (3991)Termination reason: Unknown
% 28.17/8.18  % (3991)Termination phase: shuffling
% 28.17/8.18  
% 28.17/8.18  % (3991)Memory used [KB]: 27376
% 28.17/8.18  % (3991)Time elapsed: 0.257 s
% 28.17/8.18  % (3991)Instructions burned: 866 (million)
% 28.17/8.18  % (3991)------------------------------
% 28.17/8.18  % (3991)------------------------------
% 28.17/8.19  % (3995)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3754 for (2968ds/327Mi)
% 28.17/8.20  % (3989)Instruction limit reached!
% 28.17/8.20  % (3989)------------------------------
% 28.17/8.20  % (3989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/8.20  % (3989)Termination reason: Unknown
% 28.17/8.20  % (3989)Termination phase: Property scanning
% 28.17/8.20  
% 28.17/8.20  % (3989)Memory used [KB]: 26481
% 28.17/8.20  % (3989)Time elapsed: 0.309 s
% 28.17/8.20  % (3989)Instructions burned: 906 (million)
% 28.17/8.20  % (3989)------------------------------
% 28.17/8.20  % (3989)------------------------------
% 28.41/8.21  % (3996)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3754 for (2968ds/5411Mi)
% 28.41/8.22  % (3993)Instruction limit reached!
% 28.41/8.22  % (3993)------------------------------
% 28.41/8.22  % (3993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.41/8.22  % (3993)Termination reason: Unknown
% 28.41/8.22  % (3993)Termination phase: shuffling
% 28.41/8.22  
% 28.41/8.22  % (3993)Memory used [KB]: 19317
% 28.41/8.22  % (3993)Time elapsed: 0.156 s
% 28.41/8.22  % (3993)Instructions burned: 443 (million)
% 28.41/8.22  % (3993)------------------------------
% 28.41/8.22  % (3993)------------------------------
% 28.41/8.23  % (3997)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3754 for (2967ds/1762Mi)
% 28.41/8.28  % (3988)Instruction limit reached!
% 28.41/8.28  % (3988)------------------------------
% 28.41/8.28  % (3988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.41/8.28  % (3988)Termination reason: Unknown
% 28.41/8.28  % (3988)Termination phase: shuffling
% 28.41/8.28  
% 28.41/8.28  % (3988)Memory used [KB]: 38250
% 28.41/8.28  % (3988)Time elapsed: 0.412 s
% 28.41/8.28  % (3988)Instructions burned: 1376 (million)
% 28.41/8.28  % (3988)------------------------------
% 28.41/8.28  % (3988)------------------------------
% 28.41/8.29  % (3998)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3754 for (2967ds/96Mi)
% 29.19/8.31  % (3995)Instruction limit reached!
% 29.19/8.31  % (3995)------------------------------
% 29.19/8.31  % (3995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/8.31  % (3995)Termination reason: Unknown
% 29.19/8.31  % (3995)Termination phase: shuffling
% 29.19/8.31  
% 29.19/8.31  % (3995)Memory used [KB]: 17910
% 29.19/8.31  % (3995)Time elapsed: 0.119 s
% 29.19/8.31  % (3995)Instructions burned: 328 (million)
% 29.19/8.31  % (3995)------------------------------
% 29.19/8.31  % (3995)------------------------------
% 29.19/8.32  % (3999)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3754 for (2967ds/503Mi)
% 29.19/8.32  % (3998)Instruction limit reached!
% 29.19/8.32  % (3998)------------------------------
% 29.19/8.32  % (3998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/8.32  % (3998)Termination reason: Unknown
% 29.19/8.32  % (3998)Termination phase: shuffling
% 29.19/8.32  
% 29.19/8.32  % (3998)Memory used [KB]: 14839
% 29.19/8.32  % (3998)Time elapsed: 0.036 s
% 29.19/8.32  % (3998)Instructions burned: 96 (million)
% 29.19/8.32  % (3998)------------------------------
% 29.19/8.32  % (3998)------------------------------
% 29.19/8.34  % (4000)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_3754 for (2966ds/90Mi)
% 29.19/8.34  % (3994)Instruction limit reached!
% 29.19/8.34  % (3994)------------------------------
% 29.19/8.34  % (3994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/8.34  % (3994)Termination reason: Unknown
% 29.19/8.34  % (3994)Termination phase: shuffling
% 29.19/8.34  
% 29.19/8.34  % (3994)Memory used [KB]: 21108
% 29.19/8.34  % (3994)Time elapsed: 0.208 s
% 29.19/8.34  % (3994)Instructions burned: 596 (million)
% 29.19/8.34  % (3994)------------------------------
% 29.19/8.34  % (3994)------------------------------
% 29.19/8.35  % (4001)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3754 for (2966ds/593Mi)
% 29.19/8.37  % (4000)Instruction limit reached!
% 29.19/8.37  % (4000)------------------------------
% 29.19/8.37  % (4000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.19/8.37  % (4000)Termination reason: Unknown
% 29.19/8.37  % (4000)Termination phase: shuffling
% 29.19/8.37  
% 29.19/8.37  % (4000)Memory used [KB]: 14839
% 29.19/8.37  % (4000)Time elapsed: 0.039 s
% 29.19/8.37  % (4000)Instructions burned: 91 (million)
% 29.19/8.37  % (4000)------------------------------
% 29.19/8.37  % (4000)------------------------------
% 29.19/8.39  % (4002)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3754 for (2966ds/1512Mi)
% 29.84/8.49  % (3999)Instruction limit reached!
% 29.84/8.49  % (3999)------------------------------
% 29.84/8.49  % (3999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.84/8.49  % (3999)Termination reason: Unknown
% 29.84/8.49  % (3999)Termination phase: shuffling
% 29.84/8.49  
% 29.84/8.49  % (3999)Memory used [KB]: 20084
% 29.84/8.49  % (3999)Time elapsed: 0.175 s
% 29.84/8.49  % (3999)Instructions burned: 503 (million)
% 29.84/8.49  % (3999)------------------------------
% 29.84/8.49  % (3999)------------------------------
% 30.23/8.50  % (4003)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3754 for (2965ds/569Mi)
% 30.23/8.56  % (4001)Instruction limit reached!
% 30.23/8.56  % (4001)------------------------------
% 30.23/8.56  % (4001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.23/8.56  % (4001)Termination reason: Unknown
% 30.23/8.56  % (4001)Termination phase: shuffling
% 30.23/8.56  
% 30.23/8.56  % (4001)Memory used [KB]: 21108
% 30.23/8.56  % (4001)Time elapsed: 0.206 s
% 30.23/8.56  % (4001)Instructions burned: 594 (million)
% 30.23/8.56  % (4001)------------------------------
% 30.23/8.56  % (4001)------------------------------
% 30.23/8.57  % (4004)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3754 for (2964ds/501Mi)
% 30.65/8.67  % (4003)Instruction limit reached!
% 30.65/8.67  % (4003)------------------------------
% 30.65/8.67  % (4003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/8.67  % (4003)Termination reason: Unknown
% 30.65/8.67  % (4003)Termination phase: shuffling
% 30.65/8.67  
% 30.65/8.67  % (4003)Memory used [KB]: 23539
% 30.65/8.67  % (4003)Time elapsed: 0.172 s
% 30.65/8.67  % (4003)Instructions burned: 570 (million)
% 30.65/8.67  % (4003)------------------------------
% 30.65/8.67  % (4003)------------------------------
% 30.65/8.67  % (3983)Instruction limit reached!
% 30.65/8.67  % (3983)------------------------------
% 30.65/8.67  % (3983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/8.67  % (3983)Termination reason: Unknown
% 30.65/8.67  % (3983)Termination phase: Function definition elimination
% 30.65/8.67  
% 30.65/8.67  % (3983)Memory used [KB]: 58975
% 30.65/8.67  % (3983)Time elapsed: 1.310 s
% 30.65/8.67  % (3983)Instructions burned: 4716 (million)
% 30.65/8.67  % (3983)------------------------------
% 30.65/8.67  % (3983)------------------------------
% 30.65/8.69  % (4005)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3754 for (2963ds/562Mi)
% 30.65/8.69  % (4006)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3754 for (2963ds/406Mi)
% 31.03/8.74  % (3997)Instruction limit reached!
% 31.03/8.74  % (3997)------------------------------
% 31.03/8.74  % (3997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.03/8.74  % (3997)Termination reason: Unknown
% 31.03/8.74  % (3997)Termination phase: Property scanning
% 31.03/8.74  
% 31.03/8.74  % (3997)Memory used [KB]: 41577
% 31.03/8.74  % (3997)Time elapsed: 0.515 s
% 31.03/8.74  % (3997)Instructions burned: 1765 (million)
% 31.03/8.74  % (3997)------------------------------
% 31.03/8.74  % (3997)------------------------------
% 31.03/8.74  % (4004)Instruction limit reached!
% 31.03/8.74  % (4004)------------------------------
% 31.03/8.74  % (4004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.03/8.74  % (4004)Termination reason: Unknown
% 31.03/8.74  % (4004)Termination phase: shuffling
% 31.03/8.74  
% 31.03/8.74  % (4004)Memory used [KB]: 19957
% 31.03/8.74  % (4004)Time elapsed: 0.175 s
% 31.03/8.74  % (4004)Instructions burned: 503 (million)
% 31.03/8.74  % (4004)------------------------------
% 31.03/8.74  % (4004)------------------------------
% 31.03/8.76  % (4007)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3754 for (2962ds/582Mi)
% 31.03/8.76  % (4008)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3754 for (2962ds/456Mi)
% 31.83/8.83  % (4006)Instruction limit reached!
% 31.83/8.83  % (4006)------------------------------
% 31.83/8.83  % (4006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/8.83  % (4006)Termination reason: Unknown
% 31.83/8.83  % (4006)Termination phase: shuffling
% 31.83/8.83  
% 31.83/8.83  % (4006)Memory used [KB]: 18805
% 31.83/8.83  % (4006)Time elapsed: 0.143 s
% 31.83/8.83  % (4006)Instructions burned: 407 (million)
% 31.83/8.83  % (4006)------------------------------
% 31.83/8.83  % (4006)------------------------------
% 31.83/8.84  % (4009)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3754 for (2961ds/393Mi)
% 31.83/8.85  % (4005)Instruction limit reached!
% 31.83/8.85  % (4005)------------------------------
% 31.83/8.85  % (4005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/8.85  % (4005)Termination reason: Unknown
% 31.83/8.85  % (4005)Termination phase: shuffling
% 31.83/8.85  
% 31.83/8.85  % (4005)Memory used [KB]: 23411
% 31.83/8.85  % (4005)Time elapsed: 0.171 s
% 31.83/8.85  % (4005)Instructions burned: 563 (million)
% 31.83/8.85  % (4005)------------------------------
% 31.83/8.85  % (4005)------------------------------
% 31.83/8.87  % (4010)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3754 for (2961ds/1335Mi)
% 31.83/8.87  % (4002)Instruction limit reached!
% 31.83/8.87  % (4002)------------------------------
% 31.83/8.87  % (4002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/8.87  % (4002)Termination reason: Unknown
% 31.83/8.87  % (4002)Termination phase: Property scanning
% 31.83/8.87  
% 31.83/8.87  % (4002)Memory used [KB]: 29167
% 31.83/8.87  % (4002)Time elapsed: 0.491 s
% 31.83/8.87  % (4002)Instructions burned: 1515 (million)
% 31.83/8.87  % (4002)------------------------------
% 31.83/8.87  % (4002)------------------------------
% 31.83/8.89  % (4011)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3754 for (2961ds/3373Mi)
% 32.77/8.92  % (4008)Instruction limit reached!
% 32.77/8.92  % (4008)------------------------------
% 32.77/8.92  % (4008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.77/8.92  % (4008)Termination reason: Unknown
% 32.77/8.92  % (4008)Termination phase: shuffling
% 32.77/8.92  
% 32.77/8.92  % (4008)Memory used [KB]: 19317
% 32.77/8.92  % (4008)Time elapsed: 0.161 s
% 32.77/8.92  % (4008)Instructions burned: 456 (million)
% 32.77/8.92  % (4008)------------------------------
% 32.77/8.92  % (4008)------------------------------
% 32.77/8.93  % (4012)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3754 for (2961ds/474Mi)
% 32.77/8.96  % (4007)Instruction limit reached!
% 32.77/8.96  % (4007)------------------------------
% 32.77/8.96  % (4007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.77/8.96  % (4007)Termination reason: Unknown
% 32.77/8.96  % (4007)Termination phase: shuffling
% 32.77/8.96  
% 32.77/8.96  % (4007)Memory used [KB]: 21236
% 32.77/8.96  % (4007)Time elapsed: 0.208 s
% 32.77/8.96  % (4007)Instructions burned: 584 (million)
% 32.77/8.96  % (4007)------------------------------
% 32.77/8.96  % (4007)------------------------------
% 32.77/8.96  % (4009)Instruction limit reached!
% 32.77/8.96  % (4009)------------------------------
% 32.77/8.96  % (4009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.77/8.96  % (4009)Termination reason: Unknown
% 32.77/8.96  % (4009)Termination phase: shuffling
% 32.77/8.96  
% 32.77/8.96  % (4009)Memory used [KB]: 21108
% 32.77/8.96  % (4009)Time elapsed: 0.122 s
% 32.77/8.96  % (4009)Instructions burned: 393 (million)
% 32.77/8.96  % (4009)------------------------------
% 32.77/8.96  % (4009)------------------------------
% 32.77/8.98  % (4014)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3754 for (2960ds/590Mi)
% 32.77/8.98  % (4013)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3754 for (2960ds/157Mi)
% 32.77/9.00  % (3984)First to succeed.
% 32.77/9.02  % (3984)Refutation found. Thanks to Tanya!
% 32.77/9.02  % SZS status Theorem for DTF2THF_3754
% 32.77/9.02  % SZS output start Proof for DTF2THF_3754
% 32.77/9.02  thf(type_def_5, type, real: $tType).
% 32.77/9.02  thf(type_def_6, type, int: $tType).
% 32.77/9.02  thf(type_def_8, type, rat: $tType).
% 32.77/9.02  thf(type_def_9, type, nat: $tType).
% 32.77/9.02  thf(type_def_10, type, product_prod_int_int: $tType).
% 32.77/9.02  thf(type_def_11, type, num: $tType).
% 32.77/9.02  thf(type_def_12, type, option_num: $tType).
% 32.77/9.02  thf(type_def_13, type, product_prod_num_num: $tType).
% 32.77/9.02  thf(type_def_14, type, code_integer: $tType).
% 32.77/9.02  thf(type_def_15, type, produc6271795597528267376eger_o: $tType).
% 32.77/9.02  thf(type_def_16, type, produc8923325533196201883nteger: $tType).
% 32.77/9.02  thf(type_def_17, type, set_fi4554929511873752355omplex: $tType).
% 32.77/9.02  thf(type_def_18, type, filter6041513312241820739omplex: $tType).
% 32.77/9.02  thf(type_def_19, type, set_fi7789364187291644575l_real: $tType).
% 32.77/9.02  thf(type_def_20, type, filter2146258269922977983l_real: $tType).
% 32.77/9.02  thf(type_def_21, type, set_real: $tType).
% 32.77/9.02  thf(type_def_22, type, set_set_nat: $tType).
% 32.77/9.02  thf(type_def_23, type, set_nat: $tType).
% 32.77/9.02  thf(type_def_24, type, set_int: $tType).
% 32.77/9.02  thf(type_def_25, type, complex: $tType).
% 32.77/9.02  thf(type_def_26, type, filter_real: $tType).
% 32.77/9.02  thf(type_def_27, type, product_prod_nat_nat: $tType).
% 32.77/9.02  thf(type_def_28, type, filter_nat: $tType).
% 32.77/9.02  thf(type_def_29, type, filter1242075044329608583at_nat: $tType).
% 32.77/9.02  thf(type_def_30, type, set_Pr5085853215250843933omplex: $tType).
% 32.77/9.02  thf(type_def_31, type, set_Pr6218003697084177305l_real: $tType).
% 32.77/9.02  thf(type_def_32, type, set_o: $tType).
% 32.77/9.02  thf(type_def_33, type, set_complex: $tType).
% 32.77/9.02  thf(type_def_34, type, set_Product_unit: $tType).
% 32.77/9.02  thf(type_def_35, type, set_char: $tType).
% 32.77/9.02  thf(type_def_36, type, set_list_o: $tType).
% 32.77/9.02  thf(type_def_37, type, set_list_complex: $tType).
% 32.77/9.02  thf(type_def_38, type, set_list_int: $tType).
% 32.77/9.02  thf(type_def_39, type, set_list_nat: $tType).
% 32.77/9.02  thf(type_def_40, type, set_list_VEBT_VEBT: $tType).
% 32.77/9.02  thf(type_def_41, type, set_num: $tType).
% 32.77/9.02  thf(type_def_42, type, set_rat: $tType).
% 32.77/9.02  thf(type_def_43, type, set_set_complex: $tType).
% 32.77/9.02  thf(type_def_44, type, set_set_int: $tType).
% 32.77/9.02  thf(type_def_45, type, set_VEBT_VEBT: $tType).
% 32.77/9.02  thf(type_def_46, type, extended_enat: $tType).
% 32.77/9.02  thf(type_def_47, type, set_Pr958786334691620121nt_int: $tType).
% 32.77/9.02  thf(type_def_48, type, list_o: $tType).
% 32.77/9.02  thf(type_def_49, type, list_nat: $tType).
% 32.77/9.02  thf(type_def_50, type, list_int: $tType).
% 32.77/9.02  thf(type_def_51, type, option_nat: $tType).
% 32.77/9.02  thf(type_def_52, type, vEBT_VEBT: $tType).
% 32.77/9.02  thf(type_def_53, type, list_complex: $tType).
% 32.77/9.02  thf(type_def_54, type, list_real: $tType).
% 32.77/9.02  thf(type_def_55, type, list_set_nat: $tType).
% 32.77/9.02  thf(type_def_56, type, list_VEBT_VEBT: $tType).
% 32.77/9.02  thf(type_def_57, type, list_P4002435161011370285od_o_o: $tType).
% 32.77/9.02  thf(type_def_58, type, product_prod_o_o: $tType).
% 32.77/9.02  thf(type_def_59, type, list_P3795440434834930179_o_int: $tType).
% 32.77/9.02  thf(type_def_60, type, product_prod_o_int: $tType).
% 32.77/9.02  thf(type_def_61, type, list_P6285523579766656935_o_nat: $tType).
% 32.77/9.02  thf(type_def_62, type, product_prod_o_nat: $tType).
% 32.77/9.02  thf(type_def_63, type, list_P7495141550334521929T_VEBT: $tType).
% 32.77/9.02  thf(type_def_64, type, produc2504756804600209347T_VEBT: $tType).
% 32.77/9.02  thf(type_def_65, type, list_P7333126701944960589_nat_o: $tType).
% 32.77/9.02  thf(type_def_66, type, product_prod_nat_o: $tType).
% 32.77/9.02  thf(type_def_67, type, list_P5647936690300460905T_VEBT: $tType).
% 32.77/9.02  thf(type_def_68, type, produc8025551001238799321T_VEBT: $tType).
% 32.77/9.02  thf(type_def_69, type, list_P3126845725202233233VEBT_o: $tType).
% 32.77/9.02  thf(type_def_70, type, produc334124729049499915VEBT_o: $tType).
% 32.77/9.02  thf(type_def_71, type, list_P4547456442757143711BT_int: $tType).
% 32.77/9.02  thf(type_def_72, type, produc4894624898956917775BT_int: $tType).
% 32.77/9.02  thf(type_def_73, type, list_P7037539587688870467BT_nat: $tType).
% 32.77/9.02  thf(type_def_74, type, produc9072475918466114483BT_nat: $tType).
% 32.77/9.02  thf(type_def_75, type, list_P7413028617227757229T_VEBT: $tType).
% 32.77/9.02  thf(type_def_76, type, produc8243902056947475879T_VEBT: $tType).
% 32.77/9.02  thf(type_def_77, type, option4927543243414619207at_nat: $tType).
% 32.77/9.02  thf(type_def_78, type, char: $tType).
% 32.77/9.02  thf(type_def_79, type, set_Extended_enat: $tType).
% 32.77/9.02  thf(type_def_80, type, set_Code_integer: $tType).
% 32.77/9.02  thf(type_def_81, type, option6357759511663192854e_term: $tType).
% 32.77/9.02  thf(type_def_82, type, produc8763457246119570046nteger: $tType).
% 32.77/9.02  thf(type_def_83, type, produc7773217078559923341nt_int: $tType).
% 32.77/9.02  thf(type_def_84, type, produc4953844613479565601on_nat: $tType).
% 32.77/9.02  thf(type_def_85, type, produc2233624965454879586on_nat: $tType).
% 32.77/9.02  thf(type_def_86, type, produc8306885398267862888on_nat: $tType).
% 32.77/9.02  thf(type_def_87, type, produc3447558737645232053on_num: $tType).
% 32.77/9.02  thf(type_def_88, type, produc7036089656553540234on_num: $tType).
% 32.77/9.02  thf(type_def_89, type, produc1193250871479095198on_num: $tType).
% 32.77/9.02  thf(type_def_90, type, produc6241069584506657477e_term: $tType).
% 32.77/9.02  thf(type_def_91, type, produc1908205239877642774nteger: $tType).
% 32.77/9.02  thf(type_def_92, type, produc8551481072490612790e_term: $tType).
% 32.77/9.02  thf(type_def_93, type, produc2285326912895808259nt_int: $tType).
% 32.77/9.02  thf(type_def_94, type, produc6121120109295599847at_nat: $tType).
% 32.77/9.02  thf(type_def_95, type, produc5491161045314408544at_nat: $tType).
% 32.77/9.02  thf(type_def_96, type, produc5542196010084753463at_nat: $tType).
% 32.77/9.02  thf(type_def_97, type, product_prod_nat_num: $tType).
% 32.77/9.02  thf(type_def_98, type, produc4411394909380815293omplex: $tType).
% 32.77/9.02  thf(type_def_99, type, produc2422161461964618553l_real: $tType).
% 32.77/9.02  thf(func_def_0, type, produc5542196010084753463at_nat: $tType).
% 32.77/9.02  thf(func_def_1, type, produc1908205239877642774nteger: $tType).
% 32.77/9.02  thf(func_def_2, type, produc5491161045314408544at_nat: $tType).
% 32.77/9.02  thf(func_def_3, type, produc2285326912895808259nt_int: $tType).
% 32.77/9.02  thf(func_def_4, type, produc8763457246119570046nteger: $tType).
% 32.77/9.02  thf(func_def_5, type, produc7773217078559923341nt_int: $tType).
% 32.77/9.02  thf(func_def_6, type, produc1193250871479095198on_num: $tType).
% 32.77/9.02  thf(func_def_7, type, produc8306885398267862888on_nat: $tType).
% 32.77/9.02  thf(func_def_8, type, produc6121120109295599847at_nat: $tType).
% 32.77/9.02  thf(func_def_9, type, produc7036089656553540234on_num: $tType).
% 32.77/9.02  thf(func_def_10, type, produc2233624965454879586on_nat: $tType).
% 32.77/9.02  thf(func_def_11, type, produc6241069584506657477e_term: $tType).
% 32.77/9.02  thf(func_def_12, type, set_fi4554929511873752355omplex: $tType).
% 32.77/9.02  thf(func_def_13, type, list_P7413028617227757229T_VEBT: $tType).
% 32.77/9.02  thf(func_def_14, type, produc8551481072490612790e_term: $tType).
% 32.77/9.02  thf(func_def_15, type, option6357759511663192854e_term: $tType).
% 32.77/9.02  thf(func_def_16, type, produc3447558737645232053on_num: $tType).
% 32.77/9.02  thf(func_def_17, type, produc4953844613479565601on_nat: $tType).
% 32.77/9.02  thf(func_def_18, type, set_fi7789364187291644575l_real: $tType).
% 32.77/9.02  thf(func_def_19, type, filter6041513312241820739omplex: $tType).
% 32.77/9.02  thf(func_def_20, type, list_P7037539587688870467BT_nat: $tType).
% 32.77/9.02  thf(func_def_21, type, list_P4547456442757143711BT_int: $tType).
% 32.77/9.02  thf(func_def_22, type, list_P5647936690300460905T_VEBT: $tType).
% 32.77/9.02  thf(func_def_23, type, produc8243902056947475879T_VEBT: $tType).
% 32.77/9.02  thf(func_def_24, type, set_Pr5085853215250843933omplex: $tType).
% 32.77/9.02  thf(func_def_25, type, produc8923325533196201883nteger: $tType).
% 32.77/9.02  thf(func_def_26, type, list_P3126845725202233233VEBT_o: $tType).
% 32.77/9.02  thf(func_def_27, type, list_P7495141550334521929T_VEBT: $tType).
% 32.77/9.02  thf(func_def_28, type, filter2146258269922977983l_real: $tType).
% 32.77/9.02  thf(func_def_29, type, option4927543243414619207at_nat: $tType).
% 32.77/9.02  thf(func_def_30, type, filter1242075044329608583at_nat: $tType).
% 32.77/9.02  thf(func_def_31, type, set_Pr6218003697084177305l_real: $tType).
% 32.77/9.02  thf(func_def_32, type, produc9072475918466114483BT_nat: $tType).
% 32.77/9.02  thf(func_def_33, type, produc4894624898956917775BT_int: $tType).
% 32.77/9.02  thf(func_def_34, type, produc8025551001238799321T_VEBT: $tType).
% 32.77/9.02  thf(func_def_35, type, set_Pr958786334691620121nt_int: $tType).
% 32.77/9.02  thf(func_def_36, type, produc4411394909380815293omplex: $tType).
% 32.77/9.02  thf(func_def_37, type, list_P7333126701944960589_nat_o: $tType).
% 32.77/9.02  thf(func_def_38, type, list_P6285523579766656935_o_nat: $tType).
% 32.77/9.02  thf(func_def_39, type, list_P3795440434834930179_o_int: $tType).
% 32.77/9.02  thf(func_def_40, type, set_list_VEBT_VEBT: $tType).
% 32.77/9.02  thf(func_def_41, type, produc334124729049499915VEBT_o: $tType).
% 32.77/9.02  thf(func_def_42, type, produc2504756804600209347T_VEBT: $tType).
% 32.77/9.02  thf(func_def_43, type, produc6271795597528267376eger_o: $tType).
% 32.77/9.02  thf(func_def_44, type, produc2422161461964618553l_real: $tType).
% 32.77/9.02  thf(func_def_45, type, product_prod_num_num: $tType).
% 32.77/9.02  thf(func_def_46, type, product_prod_nat_num: $tType).
% 32.77/9.02  thf(func_def_47, type, product_prod_nat_nat: $tType).
% 32.77/9.02  thf(func_def_48, type, product_prod_int_int: $tType).
% 32.77/9.02  thf(func_def_49, type, list_P4002435161011370285od_o_o: $tType).
% 32.77/9.02  thf(func_def_50, type, set_list_complex: $tType).
% 32.77/9.02  thf(func_def_51, type, set_set_complex: $tType).
% 32.77/9.02  thf(func_def_52, type, list_VEBT_VEBT: $tType).
% 32.77/9.02  thf(func_def_53, type, set_list_nat: $tType).
% 32.77/9.02  thf(func_def_54, type, set_list_int: $tType).
% 32.77/9.02  thf(func_def_55, type, product_prod_nat_o: $tType).
% 32.77/9.02  thf(func_def_56, type, product_prod_o_nat: $tType).
% 32.77/9.02  thf(func_def_57, type, product_prod_o_int: $tType).
% 32.77/9.02  thf(func_def_58, type, list_set_nat: $tType).
% 32.77/9.02  thf(func_def_59, type, set_VEBT_VEBT: $tType).
% 32.77/9.02  thf(func_def_60, type, set_set_nat: $tType).
% 32.77/9.02  thf(func_def_61, type, set_set_int: $tType).
% 32.77/9.02  thf(func_def_62, type, set_Code_integer: $tType).
% 32.77/9.02  thf(func_def_63, type, set_Product_unit: $tType).
% 32.77/9.02  thf(func_def_64, type, set_Extended_enat: $tType).
% 32.77/9.02  thf(func_def_65, type, list_complex: $tType).
% 32.77/9.02  thf(func_def_66, type, set_list_o: $tType).
% 32.77/9.02  thf(func_def_67, type, product_prod_o_o: $tType).
% 32.77/9.02  thf(func_def_68, type, set_complex: $tType).
% 32.77/9.02  thf(func_def_69, type, filter_real: $tType).
% 32.77/9.02  thf(func_def_70, type, option_num: $tType).
% 32.77/9.02  thf(func_def_71, type, option_nat: $tType).
% 32.77/9.02  thf(func_def_72, type, filter_nat: $tType).
% 32.77/9.02  thf(func_def_73, type, set_char: $tType).
% 32.77/9.02  thf(func_def_74, type, list_real: $tType).
% 32.77/9.02  thf(func_def_75, type, set_real: $tType).
% 32.77/9.02  thf(func_def_76, type, list_nat: $tType).
% 32.77/9.02  thf(func_def_77, type, list_int: $tType).
% 32.77/9.02  thf(func_def_78, type, vEBT_VEBT: $tType).
% 32.77/9.02  thf(func_def_79, type, set_rat: $tType).
% 32.77/9.02  thf(func_def_80, type, set_num: $tType).
% 32.77/9.02  thf(func_def_81, type, set_nat: $tType).
% 32.77/9.02  thf(func_def_82, type, set_int: $tType).
% 32.77/9.02  thf(func_def_83, type, code_integer: $tType).
% 32.77/9.02  thf(func_def_84, type, extended_enat: $tType).
% 32.77/9.02  thf(func_def_85, type, list_o: $tType).
% 32.77/9.02  thf(func_def_86, type, complex: $tType).
% 32.77/9.02  thf(func_def_87, type, set_o: $tType).
% 32.77/9.02  thf(func_def_88, type, char: $tType).
% 32.77/9.02  thf(func_def_89, type, real: $tType).
% 32.77/9.02  thf(func_def_90, type, rat: $tType).
% 32.77/9.02  thf(func_def_91, type, num: $tType).
% 32.77/9.02  thf(func_def_92, type, nat: $tType).
% 32.77/9.02  thf(func_def_93, type, int: $tType).
% 32.77/9.02  thf(func_def_94, type, archim7802044766580827645g_real: real > int).
% 32.77/9.02  thf(func_def_95, type, archim3151403230148437115or_rat: rat > int).
% 32.77/9.02  thf(func_def_96, type, archim6058952711729229775r_real: real > int).
% 32.77/9.02  thf(func_def_97, type, archim7778729529865785530nd_rat: rat > int).
% 32.77/9.02  thf(func_def_98, type, archim8280529875227126926d_real: real > int).
% 32.77/9.02  thf(func_def_99, type, binomial: nat > nat > nat).
% 32.77/9.02  thf(func_def_100, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_101, type, bit_and_not_num: num > num > option_num).
% 32.77/9.02  thf(func_def_102, type, bit_concat_bit: nat > int > int > int).
% 32.77/9.02  thf(func_def_103, type, bit_or_not_num_neg: num > num > num).
% 32.77/9.02  thf(func_def_104, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 32.77/9.02  thf(func_def_105, type, bit_ri7919022796975470100ot_int: int > int).
% 32.77/9.02  thf(func_def_106, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 32.77/9.02  thf(func_def_107, type, bit_ri631733984087533419it_int: nat > int > int).
% 32.77/9.02  thf(func_def_108, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_109, type, bit_se725231765392027082nd_int: int > int > int).
% 32.77/9.02  thf(func_def_110, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_111, type, bit_se8568078237143864401it_int: nat > int > int).
% 32.77/9.02  thf(func_def_112, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_113, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 32.77/9.02  thf(func_def_114, type, bit_se2159334234014336723it_int: nat > int > int).
% 32.77/9.02  thf(func_def_115, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_116, type, bit_se2119862282449309892nteger: nat > code_integer).
% 32.77/9.02  thf(func_def_117, type, bit_se2000444600071755411sk_int: nat > int).
% 32.77/9.02  thf(func_def_118, type, bit_se2002935070580805687sk_nat: nat > nat).
% 32.77/9.02  thf(func_def_119, type, bit_se1409905431419307370or_int: int > int > int).
% 32.77/9.02  thf(func_def_120, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_121, type, bit_se545348938243370406it_int: nat > int > int).
% 32.77/9.02  thf(func_def_122, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_123, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 32.77/9.02  thf(func_def_124, type, bit_se7879613467334960850it_int: nat > int > int).
% 32.77/9.02  thf(func_def_125, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_126, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 32.77/9.02  thf(func_def_127, type, bit_se2923211474154528505it_int: nat > int > int).
% 32.77/9.02  thf(func_def_128, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_129, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 32.77/9.02  thf(func_def_130, type, bit_se4203085406695923979it_int: nat > int > int).
% 32.77/9.02  thf(func_def_131, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_132, type, bit_se6526347334894502574or_int: int > int > int).
% 32.77/9.02  thf(func_def_133, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_134, type, bit_se1146084159140164899it_int: int > nat > $o).
% 32.77/9.02  thf(func_def_135, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 32.77/9.02  thf(func_def_136, type, bit_take_bit_num: nat > num > option_num).
% 32.77/9.02  thf(func_def_137, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 32.77/9.02  thf(func_def_138, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_139, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_140, type, code_int_of_integer: code_integer > int).
% 32.77/9.02  thf(func_def_141, type, code_integer_of_int: int > code_integer).
% 32.77/9.02  thf(func_def_142, type, code_integer_of_num: num > code_integer).
% 32.77/9.02  thf(func_def_143, type, code_nat_of_integer: code_integer > nat).
% 32.77/9.02  thf(func_def_144, type, code_negative: num > code_integer).
% 32.77/9.02  thf(func_def_145, type, code_num_of_integer: code_integer > num).
% 32.77/9.02  thf(func_def_146, type, code_positive: num > code_integer).
% 32.77/9.02  thf(func_def_147, type, code_Target_negative: num > int).
% 32.77/9.02  thf(func_def_148, type, code_Target_positive: num > int).
% 32.77/9.02  thf(func_def_149, type, comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex).
% 32.77/9.02  thf(func_def_150, type, comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real).
% 32.77/9.02  thf(func_def_151, type, comple4887499456419720421f_real: set_real > real).
% 32.77/9.02  thf(func_def_152, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_153, type, complete_Sup_Sup_int: set_int > int).
% 32.77/9.02  thf(func_def_154, type, complete_Sup_Sup_nat: set_nat > nat).
% 32.77/9.02  thf(func_def_155, type, comple1385675409528146559p_real: set_real > real).
% 32.77/9.02  thf(func_def_156, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_157, type, arg: complex > real).
% 32.77/9.02  thf(func_def_158, type, cis: real > complex).
% 32.77/9.02  thf(func_def_159, type, cnj: complex > complex).
% 32.77/9.02  thf(func_def_160, type, complex2: real > real > complex).
% 32.77/9.02  thf(func_def_161, type, im: complex > real).
% 32.77/9.02  thf(func_def_162, type, re: complex > real).
% 32.77/9.02  thf(func_def_163, type, csqrt: complex > complex).
% 32.77/9.02  thf(func_def_164, type, imaginary_unit: complex).
% 32.77/9.02  thf(func_def_165, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 32.77/9.02  thf(func_def_166, type, has_de1759254742604945161l_real: (real > real) > (real > real) > filter_real > $o).
% 32.77/9.02  thf(func_def_167, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 32.77/9.02  thf(func_def_168, type, adjust_div: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_169, type, adjust_mod: int > int > int).
% 32.77/9.02  thf(func_def_170, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_171, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_172, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 32.77/9.02  thf(func_def_173, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_174, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_175, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_176, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 32.77/9.02  thf(func_def_177, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_178, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_179, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_180, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_181, type, semiri5044797733671781792omplex: nat > complex).
% 32.77/9.02  thf(func_def_182, type, semiri1408675320244567234ct_nat: nat > nat).
% 32.77/9.02  thf(func_def_183, type, semiri2265585572941072030t_real: nat > real).
% 32.77/9.02  thf(func_def_184, type, invers8013647133539491842omplex: complex > complex).
% 32.77/9.02  thf(func_def_185, type, inverse_inverse_rat: rat > rat).
% 32.77/9.02  thf(func_def_186, type, inverse_inverse_real: real > real).
% 32.77/9.02  thf(func_def_187, type, at_bot_real: filter_real).
% 32.77/9.02  thf(func_def_188, type, at_top_nat: filter_nat).
% 32.77/9.02  thf(func_def_189, type, at_top_real: filter_real).
% 32.77/9.02  thf(func_def_190, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 32.77/9.02  thf(func_def_191, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 32.77/9.02  thf(func_def_192, type, eventually_real: (real > $o) > filter_real > $o).
% 32.77/9.02  thf(func_def_193, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 32.77/9.02  thf(func_def_194, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 32.77/9.02  thf(func_def_195, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 32.77/9.02  thf(func_def_196, type, filtermap_real_real: (real > real) > filter_real > filter_real).
% 32.77/9.02  thf(func_def_197, type, princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex).
% 32.77/9.02  thf(func_def_198, type, princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real).
% 32.77/9.02  thf(func_def_199, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 32.77/9.02  thf(func_def_200, type, finite_card_o: set_o > nat).
% 32.77/9.02  thf(func_def_201, type, finite_card_complex: set_complex > nat).
% 32.77/9.02  thf(func_def_202, type, finite_card_int: set_int > nat).
% 32.77/9.02  thf(func_def_203, type, finite_card_nat: set_nat > nat).
% 32.77/9.02  thf(func_def_204, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 32.77/9.02  thf(func_def_205, type, finite_card_set_nat: set_set_nat > nat).
% 32.77/9.02  thf(func_def_206, type, finite_card_char: set_char > nat).
% 32.77/9.02  thf(func_def_207, type, finite_finite_o: set_o > $o).
% 32.77/9.02  thf(func_def_208, type, finite3207457112153483333omplex: set_complex > $o).
% 32.77/9.02  thf(func_def_209, type, finite_finite_int: set_int > $o).
% 32.77/9.02  thf(func_def_210, type, finite_finite_list_o: set_list_o > $o).
% 32.77/9.02  thf(func_def_211, type, finite8712137658972009173omplex: set_list_complex > $o).
% 32.77/9.02  thf(func_def_212, type, finite3922522038869484883st_int: set_list_int > $o).
% 32.77/9.02  thf(func_def_213, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 32.77/9.02  thf(func_def_214, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_215, type, finite_finite_nat: set_nat > $o).
% 32.77/9.02  thf(func_def_216, type, finite_finite_num: set_num > $o).
% 32.77/9.02  thf(func_def_217, type, finite_finite_rat: set_rat > $o).
% 32.77/9.02  thf(func_def_218, type, finite_finite_real: set_real > $o).
% 32.77/9.02  thf(func_def_219, type, finite6551019134538273531omplex: set_set_complex > $o).
% 32.77/9.02  thf(func_def_220, type, finite6197958912794628473et_int: set_set_int > $o).
% 32.77/9.02  thf(func_def_221, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 32.77/9.02  thf(func_def_222, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_223, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_224, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 32.77/9.02  thf(func_def_225, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 32.77/9.02  thf(func_def_226, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_227, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_228, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 32.77/9.02  thf(func_def_229, type, comp_int_int_num: (int > int) > (num > int) > num > int).
% 32.77/9.02  thf(func_def_230, type, id_o: $o > $o).
% 32.77/9.02  thf(func_def_231, type, id_nat: nat > nat).
% 32.77/9.02  thf(func_def_232, type, map_fu434086159418415080_int_o: (int > product_prod_nat_nat) > ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_233, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 32.77/9.02  thf(func_def_234, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 32.77/9.02  thf(func_def_235, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 32.77/9.02  thf(func_def_236, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 32.77/9.02  thf(func_def_237, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 32.77/9.02  thf(func_def_238, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_239, type, gcd_Gcd_int: set_int > int).
% 32.77/9.02  thf(func_def_240, type, gcd_Gcd_nat: set_nat > nat).
% 32.77/9.02  thf(func_def_241, type, bezw: nat > nat > product_prod_int_int).
% 32.77/9.02  thf(func_def_242, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_243, type, gcd_gcd_Code_integer: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_244, type, gcd_gcd_int: int > int > int).
% 32.77/9.02  thf(func_def_245, type, gcd_gcd_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_246, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_247, type, abs_abs_Code_integer: code_integer > code_integer).
% 32.77/9.02  thf(func_def_248, type, abs_abs_complex: complex > complex).
% 32.77/9.02  thf(func_def_249, type, abs_abs_int: int > int).
% 32.77/9.02  thf(func_def_250, type, abs_abs_rat: rat > rat).
% 32.77/9.02  thf(func_def_251, type, abs_abs_real: real > real).
% 32.77/9.02  thf(func_def_252, type, minus_8727706125548526216plex_o: (complex > $o) > (complex > $o) > complex > $o).
% 32.77/9.02  thf(func_def_253, type, minus_minus_int_o: (int > $o) > (int > $o) > int > $o).
% 32.77/9.02  thf(func_def_254, type, minus_minus_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 32.77/9.02  thf(func_def_255, type, minus_711738161318947805_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_256, type, minus_minus_real_o: (real > $o) > (real > $o) > real > $o).
% 32.77/9.02  thf(func_def_257, type, minus_6910147592129066416_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 32.77/9.02  thf(func_def_258, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_259, type, minus_minus_complex: complex > complex > complex).
% 32.77/9.02  thf(func_def_260, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_261, type, minus_minus_int: int > int > int).
% 32.77/9.02  thf(func_def_262, type, minus_minus_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_263, type, minus_minus_rat: rat > rat > rat).
% 32.77/9.02  thf(func_def_264, type, minus_minus_real: real > real > real).
% 32.77/9.02  thf(func_def_265, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 32.77/9.02  thf(func_def_266, type, minus_minus_set_int: set_int > set_int > set_int).
% 32.77/9.02  thf(func_def_267, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 32.77/9.02  thf(func_def_268, type, minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 32.77/9.02  thf(func_def_269, type, minus_minus_set_real: set_real > set_real > set_real).
% 32.77/9.02  thf(func_def_270, type, minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_271, type, one_one_Code_integer: code_integer).
% 32.77/9.02  thf(func_def_272, type, one_one_complex: complex).
% 32.77/9.02  thf(func_def_273, type, one_on7984719198319812577d_enat: extended_enat).
% 32.77/9.02  thf(func_def_274, type, one_one_int: int).
% 32.77/9.02  thf(func_def_275, type, one_one_nat: nat).
% 32.77/9.02  thf(func_def_276, type, one_one_rat: rat).
% 32.77/9.02  thf(func_def_277, type, one_one_real: real).
% 32.77/9.02  thf(func_def_278, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_279, type, plus_plus_complex: complex > complex > complex).
% 32.77/9.02  thf(func_def_280, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_281, type, plus_plus_int: int > int > int).
% 32.77/9.02  thf(func_def_282, type, plus_plus_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_283, type, plus_plus_num: num > num > num).
% 32.77/9.02  thf(func_def_284, type, plus_plus_rat: rat > rat > rat).
% 32.77/9.02  thf(func_def_285, type, plus_plus_real: real > real > real).
% 32.77/9.02  thf(func_def_286, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 32.77/9.02  thf(func_def_287, type, sgn_sgn_complex: complex > complex).
% 32.77/9.02  thf(func_def_288, type, sgn_sgn_int: int > int).
% 32.77/9.02  thf(func_def_289, type, sgn_sgn_rat: rat > rat).
% 32.77/9.02  thf(func_def_290, type, sgn_sgn_real: real > real).
% 32.77/9.02  thf(func_def_291, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_292, type, times_times_complex: complex > complex > complex).
% 32.77/9.02  thf(func_def_293, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_294, type, times_times_int: int > int > int).
% 32.77/9.02  thf(func_def_295, type, times_times_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_296, type, times_times_num: num > num > num).
% 32.77/9.02  thf(func_def_297, type, times_times_rat: rat > rat > rat).
% 32.77/9.02  thf(func_def_298, type, times_times_real: real > real > real).
% 32.77/9.02  thf(func_def_299, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 32.77/9.02  thf(func_def_300, type, uminus1482373934393186551omplex: complex > complex).
% 32.77/9.02  thf(func_def_301, type, uminus_uminus_int: int > int).
% 32.77/9.02  thf(func_def_302, type, uminus_uminus_rat: rat > rat).
% 32.77/9.02  thf(func_def_303, type, uminus_uminus_real: real > real).
% 32.77/9.02  thf(func_def_304, type, uminus8566677241136511917omplex: set_complex > set_complex).
% 32.77/9.02  thf(func_def_305, type, uminus1532241313380277803et_int: set_int > set_int).
% 32.77/9.02  thf(func_def_306, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 32.77/9.02  thf(func_def_307, type, uminus612125837232591019t_real: set_real > set_real).
% 32.77/9.02  thf(func_def_308, type, uminus613421341184616069et_nat: set_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_309, type, zero_z3403309356797280102nteger: code_integer).
% 32.77/9.02  thf(func_def_310, type, zero_zero_complex: complex).
% 32.77/9.02  thf(func_def_311, type, zero_z5237406670263579293d_enat: extended_enat).
% 32.77/9.02  thf(func_def_312, type, zero_zero_int: int).
% 32.77/9.02  thf(func_def_313, type, zero_zero_nat: nat).
% 32.77/9.02  thf(func_def_314, type, zero_zero_rat: rat).
% 32.77/9.02  thf(func_def_315, type, zero_zero_real: real).
% 32.77/9.02  thf(func_def_316, type, groups6621422865394947399nteger: (complex > code_integer) > set_complex > code_integer).
% 32.77/9.02  thf(func_def_317, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 32.77/9.02  thf(func_def_318, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 32.77/9.02  thf(func_def_319, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 32.77/9.02  thf(func_def_320, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 32.77/9.02  thf(func_def_321, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 32.77/9.02  thf(func_def_322, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 32.77/9.02  thf(func_def_323, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 32.77/9.02  thf(func_def_324, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 32.77/9.02  thf(func_def_325, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 32.77/9.02  thf(func_def_326, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 32.77/9.02  thf(func_def_327, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 32.77/9.02  thf(func_def_328, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 32.77/9.02  thf(func_def_329, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 32.77/9.02  thf(func_def_330, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 32.77/9.02  thf(func_def_331, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_332, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 32.77/9.02  thf(func_def_333, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 32.77/9.02  thf(func_def_334, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 32.77/9.02  thf(func_def_335, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 32.77/9.02  thf(func_def_336, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 32.77/9.02  thf(func_def_337, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 32.77/9.02  thf(func_def_338, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 32.77/9.02  thf(func_def_339, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_340, type, groups8255218700646806128omplex: (set_nat > complex) > set_set_nat > complex).
% 32.77/9.02  thf(func_def_341, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 32.77/9.02  thf(func_def_342, type, groups5107569545109728110t_real: (set_nat > real) > set_set_nat > real).
% 32.77/9.02  thf(func_def_343, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 32.77/9.02  thf(func_def_344, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 32.77/9.02  thf(func_def_345, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_346, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 32.77/9.02  thf(func_def_347, type, groups4561878855575611511st_nat: list_nat > nat).
% 32.77/9.02  thf(func_def_348, type, the_int: (int > $o) > int).
% 32.77/9.02  thf(func_def_349, type, the_real: (real > $o) > real).
% 32.77/9.02  thf(func_def_350, type, if_int_int: $o > (int > int) > (int > int) > int > int).
% 32.77/9.02  thf(func_def_351, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_352, type, if_complex: $o > complex > complex > complex).
% 32.77/9.02  thf(func_def_353, type, if_Extended_enat: $o > extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_354, type, if_int: $o > int > int > int).
% 32.77/9.02  thf(func_def_355, type, if_list_int: $o > list_int > list_int > list_int).
% 32.77/9.02  thf(func_def_356, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 32.77/9.02  thf(func_def_357, type, if_nat: $o > nat > nat > nat).
% 32.77/9.02  thf(func_def_358, type, if_num: $o > num > num > num).
% 32.77/9.02  thf(func_def_359, type, if_option_nat: $o > option_nat > option_nat > option_nat).
% 32.77/9.02  thf(func_def_360, type, if_option_num: $o > option_num > option_num > option_num).
% 32.77/9.02  thf(func_def_361, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 32.77/9.02  thf(func_def_362, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_363, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_364, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_365, type, if_rat: $o > rat > rat > rat).
% 32.77/9.02  thf(func_def_366, type, if_real: $o > real > real > real).
% 32.77/9.02  thf(func_def_367, type, if_set_int: $o > set_int > set_int > set_int).
% 32.77/9.02  thf(func_def_368, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_369, type, abs_Integ: product_prod_nat_nat > int).
% 32.77/9.02  thf(func_def_370, type, rep_Integ: int > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_371, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 32.77/9.02  thf(func_def_372, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 32.77/9.02  thf(func_def_373, type, nat2: int > nat).
% 32.77/9.02  thf(func_def_374, type, ring_1_Ints_complex: set_complex).
% 32.77/9.02  thf(func_def_375, type, ring_1_Ints_real: set_real).
% 32.77/9.02  thf(func_def_376, type, ring_18347121197199848620nteger: int > code_integer).
% 32.77/9.02  thf(func_def_377, type, ring_17405671764205052669omplex: int > complex).
% 32.77/9.02  thf(func_def_378, type, ring_1_of_int_int: int > int).
% 32.77/9.02  thf(func_def_379, type, ring_1_of_int_rat: int > rat).
% 32.77/9.02  thf(func_def_380, type, ring_1_of_int_real: int > real).
% 32.77/9.02  thf(func_def_381, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 32.77/9.02  thf(func_def_382, type, sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_383, type, sup_sup_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_384, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 32.77/9.02  thf(func_def_385, type, lattic8263393255366662781ax_int: set_int > int).
% 32.77/9.02  thf(func_def_386, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 32.77/9.02  thf(func_def_387, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 32.77/9.02  thf(func_def_388, type, at_infinity_real: filter_real).
% 32.77/9.02  thf(func_def_389, type, append_int: list_int > list_int > list_int).
% 32.77/9.02  thf(func_def_390, type, append_nat: list_nat > list_nat > list_nat).
% 32.77/9.02  thf(func_def_391, type, distinct_int: list_int > $o).
% 32.77/9.02  thf(func_def_392, type, distinct_nat: list_nat > $o).
% 32.77/9.02  thf(func_def_393, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 32.77/9.02  thf(func_def_394, type, cons_int: int > list_int > list_int).
% 32.77/9.02  thf(func_def_395, type, cons_nat: nat > list_nat > list_nat).
% 32.77/9.02  thf(func_def_396, type, nil_int: list_int).
% 32.77/9.02  thf(func_def_397, type, nil_nat: list_nat).
% 32.77/9.02  thf(func_def_398, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 32.77/9.02  thf(func_def_399, type, set_o2: list_o > set_o).
% 32.77/9.02  thf(func_def_400, type, set_complex2: list_complex > set_complex).
% 32.77/9.02  thf(func_def_401, type, set_int2: list_int > set_int).
% 32.77/9.02  thf(func_def_402, type, set_nat2: list_nat > set_nat).
% 32.77/9.02  thf(func_def_403, type, set_real2: list_real > set_real).
% 32.77/9.02  thf(func_def_404, type, set_set_nat2: list_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_405, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 32.77/9.02  thf(func_def_406, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_407, type, list_update_o: list_o > nat > $o > list_o).
% 32.77/9.02  thf(func_def_408, type, list_update_complex: list_complex > nat > complex > list_complex).
% 32.77/9.02  thf(func_def_409, type, list_update_int: list_int > nat > int > list_int).
% 32.77/9.02  thf(func_def_410, type, list_update_nat: list_nat > nat > nat > list_nat).
% 32.77/9.02  thf(func_def_411, type, list_update_real: list_real > nat > real > list_real).
% 32.77/9.02  thf(func_def_412, type, list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat).
% 32.77/9.02  thf(func_def_413, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_414, type, nth_o: list_o > nat > $o).
% 32.77/9.02  thf(func_def_415, type, nth_complex: list_complex > nat > complex).
% 32.77/9.02  thf(func_def_416, type, nth_int: list_int > nat > int).
% 32.77/9.02  thf(func_def_417, type, nth_nat: list_nat > nat > nat).
% 32.77/9.02  thf(func_def_418, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 32.77/9.02  thf(func_def_419, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 32.77/9.02  thf(func_def_420, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 32.77/9.02  thf(func_def_421, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 32.77/9.02  thf(func_def_422, type, nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o).
% 32.77/9.02  thf(func_def_423, type, nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT).
% 32.77/9.02  thf(func_def_424, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 32.77/9.02  thf(func_def_425, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 32.77/9.02  thf(func_def_426, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 32.77/9.02  thf(func_def_427, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 32.77/9.02  thf(func_def_428, type, nth_real: list_real > nat > real).
% 32.77/9.02  thf(func_def_429, type, nth_set_nat: list_set_nat > nat > set_nat).
% 32.77/9.02  thf(func_def_430, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_431, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 32.77/9.02  thf(func_def_432, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 32.77/9.02  thf(func_def_433, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 32.77/9.02  thf(func_def_434, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 32.77/9.02  thf(func_def_435, type, product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 32.77/9.02  thf(func_def_436, type, produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 32.77/9.02  thf(func_def_437, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 32.77/9.02  thf(func_def_438, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 32.77/9.02  thf(func_def_439, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 32.77/9.02  thf(func_def_440, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 32.77/9.02  thf(func_def_441, type, remdups_nat: list_nat > list_nat).
% 32.77/9.02  thf(func_def_442, type, replicate_o: nat > $o > list_o).
% 32.77/9.02  thf(func_def_443, type, replicate_complex: nat > complex > list_complex).
% 32.77/9.02  thf(func_def_444, type, replicate_int: nat > int > list_int).
% 32.77/9.02  thf(func_def_445, type, replicate_nat: nat > nat > list_nat).
% 32.77/9.02  thf(func_def_446, type, replicate_real: nat > real > list_real).
% 32.77/9.02  thf(func_def_447, type, replicate_set_nat: nat > set_nat > list_set_nat).
% 32.77/9.02  thf(func_def_448, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_449, type, upt: nat > nat > list_nat).
% 32.77/9.02  thf(func_def_450, type, upto: int > int > list_int).
% 32.77/9.02  thf(func_def_451, type, upto_aux: int > int > list_int > list_int).
% 32.77/9.02  thf(func_def_452, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_453, type, suc: nat > nat).
% 32.77/9.02  thf(func_def_454, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 32.77/9.02  thf(func_def_455, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 32.77/9.02  thf(func_def_456, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 32.77/9.02  thf(func_def_457, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 32.77/9.02  thf(func_def_458, type, pred: nat > nat).
% 32.77/9.02  thf(func_def_459, type, semiri4939895301339042750nteger: nat > code_integer).
% 32.77/9.02  thf(func_def_460, type, semiri8010041392384452111omplex: nat > complex).
% 32.77/9.02  thf(func_def_461, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 32.77/9.02  thf(func_def_462, type, semiri1314217659103216013at_int: nat > int).
% 32.77/9.02  thf(func_def_463, type, semiri1316708129612266289at_nat: nat > nat).
% 32.77/9.02  thf(func_def_464, type, semiri681578069525770553at_rat: nat > rat).
% 32.77/9.02  thf(func_def_465, type, semiri5074537144036343181t_real: nat > real).
% 32.77/9.02  thf(func_def_466, type, size_size_list_o: list_o > nat).
% 32.77/9.02  thf(func_def_467, type, size_s3451745648224563538omplex: list_complex > nat).
% 32.77/9.02  thf(func_def_468, type, size_size_list_int: list_int > nat).
% 32.77/9.02  thf(func_def_469, type, size_size_list_nat: list_nat > nat).
% 32.77/9.02  thf(func_def_470, type, size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat).
% 32.77/9.02  thf(func_def_471, type, size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat).
% 32.77/9.02  thf(func_def_472, type, size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat).
% 32.77/9.02  thf(func_def_473, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 32.77/9.02  thf(func_def_474, type, size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat).
% 32.77/9.02  thf(func_def_475, type, size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat).
% 32.77/9.02  thf(func_def_476, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 32.77/9.02  thf(func_def_477, type, size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat).
% 32.77/9.02  thf(func_def_478, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 32.77/9.02  thf(func_def_479, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 32.77/9.02  thf(func_def_480, type, size_size_list_real: list_real > nat).
% 32.77/9.02  thf(func_def_481, type, size_s3254054031482475050et_nat: list_set_nat > nat).
% 32.77/9.02  thf(func_def_482, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_483, type, size_size_num: num > nat).
% 32.77/9.02  thf(func_def_484, type, size_size_option_nat: option_nat > nat).
% 32.77/9.02  thf(func_def_485, type, size_size_option_num: option_num > nat).
% 32.77/9.02  thf(func_def_486, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 32.77/9.02  thf(func_def_487, type, size_size_char: char > nat).
% 32.77/9.02  thf(func_def_488, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_489, type, nat_list_encode: list_nat > nat).
% 32.77/9.02  thf(func_def_490, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 32.77/9.02  thf(func_def_491, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_492, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_493, type, nat_prod_encode: product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_494, type, nat_set_decode: nat > set_nat).
% 32.77/9.02  thf(func_def_495, type, nat_set_encode: set_nat > nat).
% 32.77/9.02  thf(func_def_496, type, nat_triangle: nat > nat).
% 32.77/9.02  thf(func_def_497, type, root: nat > real > real).
% 32.77/9.02  thf(func_def_498, type, sqrt: real > real).
% 32.77/9.02  thf(func_def_499, type, bitM: num > num).
% 32.77/9.02  thf(func_def_500, type, inc: num > num).
% 32.77/9.02  thf(func_def_501, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 32.77/9.02  thf(func_def_502, type, neg_nu7009210354673126013omplex: complex > complex).
% 32.77/9.02  thf(func_def_503, type, neg_numeral_dbl_int: int > int).
% 32.77/9.02  thf(func_def_504, type, neg_numeral_dbl_rat: rat > rat).
% 32.77/9.02  thf(func_def_505, type, neg_numeral_dbl_real: real > real).
% 32.77/9.02  thf(func_def_506, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 32.77/9.02  thf(func_def_507, type, neg_nu6511756317524482435omplex: complex > complex).
% 32.77/9.02  thf(func_def_508, type, neg_nu3811975205180677377ec_int: int > int).
% 32.77/9.02  thf(func_def_509, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 32.77/9.02  thf(func_def_510, type, neg_nu6075765906172075777c_real: real > real).
% 32.77/9.02  thf(func_def_511, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 32.77/9.02  thf(func_def_512, type, neg_nu8557863876264182079omplex: complex > complex).
% 32.77/9.02  thf(func_def_513, type, neg_nu5851722552734809277nc_int: int > int).
% 32.77/9.02  thf(func_def_514, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 32.77/9.02  thf(func_def_515, type, neg_nu8295874005876285629c_real: real > real).
% 32.77/9.02  thf(func_def_516, type, neg_numeral_sub_int: num > num > int).
% 32.77/9.02  thf(func_def_517, type, bit0: num > num).
% 32.77/9.02  thf(func_def_518, type, bit1: num > num).
% 32.77/9.02  thf(func_def_519, type, one: num).
% 32.77/9.02  thf(func_def_520, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 32.77/9.02  thf(func_def_521, type, size_num: num > nat).
% 32.77/9.02  thf(func_def_522, type, num_of_nat: nat > num).
% 32.77/9.02  thf(func_def_523, type, numera6620942414471956472nteger: num > code_integer).
% 32.77/9.02  thf(func_def_524, type, numera6690914467698888265omplex: num > complex).
% 32.77/9.02  thf(func_def_525, type, numera1916890842035813515d_enat: num > extended_enat).
% 32.77/9.02  thf(func_def_526, type, numeral_numeral_int: num > int).
% 32.77/9.02  thf(func_def_527, type, numeral_numeral_nat: num > nat).
% 32.77/9.02  thf(func_def_528, type, numeral_numeral_rat: num > rat).
% 32.77/9.02  thf(func_def_529, type, numeral_numeral_real: num > real).
% 32.77/9.02  thf(func_def_530, type, pow: num > num > num).
% 32.77/9.02  thf(func_def_531, type, pred_numeral: num > nat).
% 32.77/9.02  thf(func_def_532, type, sqr: num > num).
% 32.77/9.02  thf(func_def_533, type, none_nat: option_nat).
% 32.77/9.02  thf(func_def_534, type, none_num: option_num).
% 32.77/9.02  thf(func_def_535, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_536, type, some_nat: nat > option_nat).
% 32.77/9.02  thf(func_def_537, type, some_num: num > option_num).
% 32.77/9.02  thf(func_def_538, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_539, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_540, type, case_option_int_num: int > (num > int) > option_num > int).
% 32.77/9.02  thf(func_def_541, type, case_option_num_num: num > (num > num) > option_num > num).
% 32.77/9.02  thf(func_def_542, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 32.77/9.02  thf(func_def_543, type, size_option_nat: (nat > nat) > option_nat > nat).
% 32.77/9.02  thf(func_def_544, type, size_option_num: (num > nat) > option_num > nat).
% 32.77/9.02  thf(func_def_545, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 32.77/9.02  thf(func_def_546, type, the_nat: option_nat > nat).
% 32.77/9.02  thf(func_def_547, type, the_num: option_num > num).
% 32.77/9.02  thf(func_def_548, type, the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_549, type, bot_bo4199563552545308370d_enat: extended_enat).
% 32.77/9.02  thf(func_def_550, type, bot_bot_nat: nat).
% 32.77/9.02  thf(func_def_551, type, bot_bot_set_complex: set_complex).
% 32.77/9.02  thf(func_def_552, type, bot_bo7653980558646680370d_enat: set_Extended_enat).
% 32.77/9.02  thf(func_def_553, type, bot_bot_set_int: set_int).
% 32.77/9.02  thf(func_def_554, type, bot_bot_set_nat: set_nat).
% 32.77/9.02  thf(func_def_555, type, bot_bot_set_num: set_num).
% 32.77/9.02  thf(func_def_556, type, bot_bot_set_rat: set_rat).
% 32.77/9.02  thf(func_def_557, type, bot_bot_set_real: set_real).
% 32.77/9.02  thf(func_def_558, type, bot_bot_set_set_int: set_set_int).
% 32.77/9.02  thf(func_def_559, type, bot_bot_set_set_nat: set_set_nat).
% 32.77/9.02  thf(func_def_560, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 32.77/9.02  thf(func_def_561, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 32.77/9.02  thf(func_def_562, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 32.77/9.02  thf(func_def_563, type, ord_less_int: int > int > $o).
% 32.77/9.02  thf(func_def_564, type, ord_less_nat: nat > nat > $o).
% 32.77/9.02  thf(func_def_565, type, ord_less_num: num > num > $o).
% 32.77/9.02  thf(func_def_566, type, ord_less_rat: rat > rat > $o).
% 32.77/9.02  thf(func_def_567, type, ord_less_real: real > real > $o).
% 32.77/9.02  thf(func_def_568, type, ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o).
% 32.77/9.02  thf(func_def_569, type, ord_less_set_complex: set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_570, type, ord_less_set_int: set_int > set_int > $o).
% 32.77/9.02  thf(func_def_571, type, ord_less_set_nat: set_nat > set_nat > $o).
% 32.77/9.02  thf(func_def_572, type, ord_less_set_num: set_num > set_num > $o).
% 32.77/9.02  thf(func_def_573, type, ord_less_set_rat: set_rat > set_rat > $o).
% 32.77/9.02  thf(func_def_574, type, ord_less_set_real: set_real > set_real > $o).
% 32.77/9.02  thf(func_def_575, type, ord_less_set_set_int: set_set_int > set_set_int > $o).
% 32.77/9.02  thf(func_def_576, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 32.77/9.02  thf(func_def_577, type, ord_le4573692005234683329plex_o: (complex > $o) > (complex > $o) > $o).
% 32.77/9.02  thf(func_def_578, type, ord_le6741204236512500942_int_o: (int > int > $o) > (int > int > $o) > $o).
% 32.77/9.02  thf(func_def_579, type, ord_less_eq_int_o: (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_580, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_581, type, ord_less_eq_real_o: (real > $o) > (real > $o) > $o).
% 32.77/9.02  thf(func_def_582, type, ord_le3964352015994296041_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 32.77/9.02  thf(func_def_583, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 32.77/9.02  thf(func_def_584, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 32.77/9.02  thf(func_def_585, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 32.77/9.02  thf(func_def_586, type, ord_le4104064031414453916r_real: filter_real > filter_real > $o).
% 32.77/9.02  thf(func_def_587, type, ord_less_eq_int: int > int > $o).
% 32.77/9.02  thf(func_def_588, type, ord_less_eq_nat: nat > nat > $o).
% 32.77/9.02  thf(func_def_589, type, ord_less_eq_num: num > num > $o).
% 32.77/9.02  thf(func_def_590, type, ord_less_eq_rat: rat > rat > $o).
% 32.77/9.02  thf(func_def_591, type, ord_less_eq_real: real > real > $o).
% 32.77/9.02  thf(func_def_592, type, ord_less_eq_set_o: set_o > set_o > $o).
% 32.77/9.02  thf(func_def_593, type, ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o).
% 32.77/9.02  thf(func_def_594, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_595, type, ord_less_eq_set_int: set_int > set_int > $o).
% 32.77/9.02  thf(func_def_596, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 32.77/9.02  thf(func_def_597, type, ord_less_eq_set_num: set_num > set_num > $o).
% 32.77/9.02  thf(func_def_598, type, ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 32.77/9.02  thf(func_def_599, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 32.77/9.02  thf(func_def_600, type, ord_less_eq_set_real: set_real > set_real > $o).
% 32.77/9.02  thf(func_def_601, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 32.77/9.02  thf(func_def_602, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 32.77/9.02  thf(func_def_603, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_604, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_605, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 32.77/9.02  thf(func_def_606, type, ord_max_int: int > int > int).
% 32.77/9.02  thf(func_def_607, type, ord_max_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_608, type, ord_max_num: num > num > num).
% 32.77/9.02  thf(func_def_609, type, ord_max_rat: rat > rat > rat).
% 32.77/9.02  thf(func_def_610, type, ord_max_real: real > real > real).
% 32.77/9.02  thf(func_def_611, type, ord_max_set_int: set_int > set_int > set_int).
% 32.77/9.02  thf(func_def_612, type, order_Greatest_nat: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_613, type, order_9091379641038594480t_real: (nat > real) > $o).
% 32.77/9.02  thf(func_def_614, type, order_mono_nat_nat: (nat > nat) > $o).
% 32.77/9.02  thf(func_def_615, type, order_mono_nat_real: (nat > real) > $o).
% 32.77/9.02  thf(func_def_616, type, top_top_set_o: set_o).
% 32.77/9.02  thf(func_def_617, type, top_top_set_nat: set_nat).
% 32.77/9.02  thf(func_def_618, type, top_to1996260823553986621t_unit: set_Product_unit).
% 32.77/9.02  thf(func_def_619, type, top_top_set_real: set_real).
% 32.77/9.02  thf(func_def_620, type, top_top_set_char: set_char).
% 32.77/9.02  thf(func_def_621, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 32.77/9.02  thf(func_def_622, type, power_power_complex: complex > nat > complex).
% 32.77/9.02  thf(func_def_623, type, power_power_int: int > nat > int).
% 32.77/9.02  thf(func_def_624, type, power_power_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_625, type, power_power_rat: rat > nat > rat).
% 32.77/9.02  thf(func_def_626, type, power_power_real: real > nat > real).
% 32.77/9.02  thf(func_def_627, type, produc6137756002093451184nteger: (code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > produc8763457246119570046nteger).
% 32.77/9.02  thf(func_def_628, type, produc4305682042979456191nt_int: (int > option6357759511663192854e_term) > product_prod_int_int > produc7773217078559923341nt_int).
% 32.77/9.02  thf(func_def_629, type, produc4035269172776083154on_nat: (nat > nat > $o) > produc4953844613479565601on_nat > produc2233624965454879586on_nat).
% 32.77/9.02  thf(func_def_630, type, produc8929957630744042906on_nat: (nat > nat > nat) > produc4953844613479565601on_nat > produc8306885398267862888on_nat).
% 32.77/9.02  thf(func_def_631, type, produc3576312749637752826on_num: (num > num > $o) > produc3447558737645232053on_num > produc7036089656553540234on_num).
% 32.77/9.02  thf(func_def_632, type, produc5778274026573060048on_num: (num > num > num) > produc3447558737645232053on_num > produc1193250871479095198on_num).
% 32.77/9.02  thf(func_def_633, type, produc8603105652947943368nteger: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc1908205239877642774nteger).
% 32.77/9.02  thf(func_def_634, type, produc5700946648718959541nt_int: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc2285326912895808259nt_int).
% 32.77/9.02  thf(func_def_635, type, produc3994169339658061776at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc6121120109295599847at_nat > produc5491161045314408544at_nat).
% 32.77/9.02  thf(func_def_636, type, produc2899441246263362727at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > produc6121120109295599847at_nat > produc5542196010084753463at_nat).
% 32.77/9.02  thf(func_def_637, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 32.77/9.02  thf(func_def_638, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 32.77/9.02  thf(func_def_639, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 32.77/9.02  thf(func_def_640, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 32.77/9.02  thf(func_def_641, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 32.77/9.02  thf(func_def_642, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_643, type, product_Pair_int_int: int > int > product_prod_int_int).
% 32.77/9.02  thf(func_def_644, type, product_Pair_nat_o: nat > $o > product_prod_nat_o).
% 32.77/9.02  thf(func_def_645, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_646, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 32.77/9.02  thf(func_def_647, type, produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT).
% 32.77/9.02  thf(func_def_648, type, product_Pair_num_num: num > num > product_prod_num_num).
% 32.77/9.02  thf(func_def_649, type, produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat).
% 32.77/9.02  thf(func_def_650, type, produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num).
% 32.77/9.02  thf(func_def_651, type, produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat).
% 32.77/9.02  thf(func_def_652, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 32.77/9.02  thf(func_def_653, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 32.77/9.02  thf(func_def_654, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 32.77/9.02  thf(func_def_655, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 32.77/9.02  thf(func_def_656, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_657, type, produc127349428274296955eger_o: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8763457246119570046nteger > $o).
% 32.77/9.02  thf(func_def_658, type, produc2592262431452330817omplex: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_complex) > produc8763457246119570046nteger > set_complex).
% 32.77/9.02  thf(func_def_659, type, produc8604463032469472703et_int: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > produc8763457246119570046nteger > set_int).
% 32.77/9.02  thf(func_def_660, type, produc3558942015123893603et_nat: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc8763457246119570046nteger > set_nat).
% 32.77/9.02  thf(func_def_661, type, produc815715089573277247t_real: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_real) > produc8763457246119570046nteger > set_real).
% 32.77/9.02  thf(func_def_662, type, produc2558449545302689196_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > $o).
% 32.77/9.02  thf(func_def_663, type, produc7959293469001253456omplex: ((int > option6357759511663192854e_term) > product_prod_int_int > set_complex) > produc7773217078559923341nt_int > set_complex).
% 32.77/9.02  thf(func_def_664, type, produc6253627499356882019eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc1908205239877642774nteger > $o).
% 32.77/9.02  thf(func_def_665, type, produc1573362020775583542_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > $o).
% 32.77/9.02  thf(func_def_666, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 32.77/9.02  thf(func_def_667, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 32.77/9.02  thf(func_def_668, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 32.77/9.02  thf(func_def_669, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 32.77/9.02  thf(func_def_670, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_671, type, produc6771430404735790350plex_o: (complex > complex > $o) > produc4411394909380815293omplex > $o).
% 32.77/9.02  thf(func_def_672, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_673, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_674, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_675, type, produc8580519160106071146omplex: (int > int > set_complex) > product_prod_int_int > set_complex).
% 32.77/9.02  thf(func_def_676, type, produc73460835934605544et_int: (int > int > set_int) > product_prod_int_int > set_int).
% 32.77/9.02  thf(func_def_677, type, produc4251311855443802252et_nat: (int > int > set_nat) > product_prod_int_int > set_nat).
% 32.77/9.02  thf(func_def_678, type, produc6452406959799940328t_real: (int > int > set_real) > product_prod_int_int > set_real).
% 32.77/9.02  thf(func_def_679, type, produc5233655623923918146et_nat: (int > int > set_set_nat) > product_prod_int_int > set_set_nat).
% 32.77/9.02  thf(func_def_680, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_681, 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).
% 32.77/9.02  thf(func_def_682, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_683, type, produc1917071388513777916omplex: (nat > nat > complex) > product_prod_nat_nat > complex).
% 32.77/9.02  thf(func_def_684, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 32.77/9.02  thf(func_def_685, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_686, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_687, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 32.77/9.02  thf(func_def_688, type, produc1703576794950452218t_real: (nat > nat > real) > product_prod_nat_nat > real).
% 32.77/9.02  thf(func_def_689, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 32.77/9.02  thf(func_def_690, type, produc5414030515140494994real_o: (real > real > $o) > produc2422161461964618553l_real > $o).
% 32.77/9.02  thf(func_def_691, type, product_fst_int_int: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_692, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_693, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 32.77/9.02  thf(func_def_694, type, product_snd_int_int: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_695, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_696, type, fract: int > int > rat).
% 32.77/9.02  thf(func_def_697, type, frct: product_prod_int_int > rat).
% 32.77/9.02  thf(func_def_698, type, normalize: product_prod_int_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_699, type, of_int: int > rat).
% 32.77/9.02  thf(func_def_700, type, quotient_of: rat > product_prod_int_int).
% 32.77/9.02  thf(func_def_701, type, real_V2521375963428798218omplex: set_complex).
% 32.77/9.02  thf(func_def_702, type, real_V5970128139526366754l_real: (real > real) > $o).
% 32.77/9.02  thf(func_def_703, type, real_V3694042436643373181omplex: complex > complex > real).
% 32.77/9.02  thf(func_def_704, type, real_V975177566351809787t_real: real > real > real).
% 32.77/9.02  thf(func_def_705, type, real_V1022390504157884413omplex: complex > real).
% 32.77/9.02  thf(func_def_706, type, real_V7735802525324610683m_real: real > real).
% 32.77/9.02  thf(func_def_707, type, real_V4546457046886955230omplex: real > complex).
% 32.77/9.02  thf(func_def_708, type, real_V2046097035970521341omplex: real > complex > complex).
% 32.77/9.02  thf(func_def_709, type, real_V1485227260804924795R_real: real > real > real).
% 32.77/9.02  thf(func_def_710, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_711, type, divide1717551699836669952omplex: complex > complex > complex).
% 32.77/9.02  thf(func_def_712, type, divide_divide_int: int > int > int).
% 32.77/9.02  thf(func_def_713, type, divide_divide_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_714, type, divide_divide_rat: rat > rat > rat).
% 32.77/9.02  thf(func_def_715, type, divide_divide_real: real > real > real).
% 32.77/9.02  thf(func_def_716, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 32.77/9.02  thf(func_def_717, type, dvd_dvd_complex: complex > complex > $o).
% 32.77/9.02  thf(func_def_718, type, dvd_dvd_int: int > int > $o).
% 32.77/9.02  thf(func_def_719, type, dvd_dvd_nat: nat > nat > $o).
% 32.77/9.02  thf(func_def_720, type, dvd_dvd_rat: rat > rat > $o).
% 32.77/9.02  thf(func_def_721, type, dvd_dvd_real: real > real > $o).
% 32.77/9.02  thf(func_def_722, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_723, type, modulo_modulo_int: int > int > int).
% 32.77/9.02  thf(func_def_724, type, modulo_modulo_nat: nat > nat > nat).
% 32.77/9.02  thf(func_def_725, type, zero_n356916108424825756nteger: $o > code_integer).
% 32.77/9.02  thf(func_def_726, type, zero_n1201886186963655149omplex: $o > complex).
% 32.77/9.02  thf(func_def_727, type, zero_n2684676970156552555ol_int: $o > int).
% 32.77/9.02  thf(func_def_728, type, zero_n2687167440665602831ol_nat: $o > nat).
% 32.77/9.02  thf(func_def_729, type, zero_n2052037380579107095ol_rat: $o > rat).
% 32.77/9.02  thf(func_def_730, type, zero_n3304061248610475627l_real: $o > real).
% 32.77/9.02  thf(func_def_731, type, suminf_complex: (nat > complex) > complex).
% 32.77/9.02  thf(func_def_732, type, suminf_real: (nat > real) > real).
% 32.77/9.02  thf(func_def_733, type, summable_real: (nat > real) > $o).
% 32.77/9.02  thf(func_def_734, type, sums_real: (nat > real) > real > $o).
% 32.77/9.02  thf(func_def_735, type, collect_Code_integer: (code_integer > $o) > set_Code_integer).
% 32.77/9.02  thf(func_def_736, type, collect_complex: (complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_737, type, collect_int: (int > $o) > set_int).
% 32.77/9.02  thf(func_def_738, type, collect_list_o: (list_o > $o) > set_list_o).
% 32.77/9.02  thf(func_def_739, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 32.77/9.02  thf(func_def_740, type, collect_list_int: (list_int > $o) > set_list_int).
% 32.77/9.02  thf(func_def_741, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 32.77/9.02  thf(func_def_742, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_743, type, collect_nat: (nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_744, type, collect_num: (num > $o) > set_num).
% 32.77/9.02  thf(func_def_745, type, collec8663557070575231912omplex: (produc4411394909380815293omplex > $o) > set_Pr5085853215250843933omplex).
% 32.77/9.02  thf(func_def_746, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 32.77/9.02  thf(func_def_747, type, collec3799799289383736868l_real: (produc2422161461964618553l_real > $o) > set_Pr6218003697084177305l_real).
% 32.77/9.02  thf(func_def_748, type, collect_rat: (rat > $o) > set_rat).
% 32.77/9.02  thf(func_def_749, type, collect_real: (real > $o) > set_real).
% 32.77/9.02  thf(func_def_750, type, collect_set_complex: (set_complex > $o) > set_set_complex).
% 32.77/9.02  thf(func_def_751, type, collect_set_int: (set_int > $o) > set_set_int).
% 32.77/9.02  thf(func_def_752, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 32.77/9.02  thf(func_def_753, type, pow_nat: set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_754, type, image_int_int: (int > int) > set_int > set_int).
% 32.77/9.02  thf(func_def_755, type, image_nat_int: (nat > int) > set_nat > set_int).
% 32.77/9.02  thf(func_def_756, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 32.77/9.02  thf(func_def_757, type, image_nat_real: (nat > real) > set_nat > set_real).
% 32.77/9.02  thf(func_def_758, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_759, type, image_nat_char: (nat > char) > set_nat > set_char).
% 32.77/9.02  thf(func_def_760, type, image_5971271580939081552omplex: (real > filter6041513312241820739omplex) > set_real > set_fi4554929511873752355omplex).
% 32.77/9.02  thf(func_def_761, type, image_2178119161166701260l_real: (real > filter2146258269922977983l_real) > set_real > set_fi7789364187291644575l_real).
% 32.77/9.02  thf(func_def_762, type, image_real_real: (real > real) > set_real > set_real).
% 32.77/9.02  thf(func_def_763, type, image_char_nat: (char > nat) > set_char > set_nat).
% 32.77/9.02  thf(func_def_764, type, insert_complex: complex > set_complex > set_complex).
% 32.77/9.02  thf(func_def_765, type, insert_int: int > set_int > set_int).
% 32.77/9.02  thf(func_def_766, type, insert_nat: nat > set_nat > set_nat).
% 32.77/9.02  thf(func_def_767, type, insert_num: num > set_num > set_num).
% 32.77/9.02  thf(func_def_768, type, insert_rat: rat > set_rat > set_rat).
% 32.77/9.02  thf(func_def_769, type, insert_real: real > set_real > set_real).
% 32.77/9.02  thf(func_def_770, type, insert_set_nat: set_nat > set_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_771, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 32.77/9.02  thf(func_def_772, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_773, type, set_or1266510415728281911st_int: int > int > set_int).
% 32.77/9.02  thf(func_def_774, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 32.77/9.02  thf(func_def_775, type, set_or7049704709247886629st_num: num > num > set_num).
% 32.77/9.02  thf(func_def_776, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 32.77/9.02  thf(func_def_777, type, set_or1222579329274155063t_real: real > real > set_real).
% 32.77/9.02  thf(func_def_778, type, set_or370866239135849197et_int: set_int > set_int > set_set_int).
% 32.77/9.02  thf(func_def_779, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_780, type, set_or4662586982721622107an_int: int > int > set_int).
% 32.77/9.02  thf(func_def_781, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 32.77/9.02  thf(func_def_782, type, set_ord_atLeast_nat: nat > set_nat).
% 32.77/9.02  thf(func_def_783, type, set_ord_atLeast_real: real > set_real).
% 32.77/9.02  thf(func_def_784, type, set_ord_atMost_int: int > set_int).
% 32.77/9.02  thf(func_def_785, type, set_ord_atMost_nat: nat > set_nat).
% 32.77/9.02  thf(func_def_786, type, set_or6656581121297822940st_int: int > int > set_int).
% 32.77/9.02  thf(func_def_787, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 32.77/9.02  thf(func_def_788, type, set_or5832277885323065728an_int: int > int > set_int).
% 32.77/9.02  thf(func_def_789, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 32.77/9.02  thf(func_def_790, type, set_or1633881224788618240n_real: real > real > set_real).
% 32.77/9.02  thf(func_def_791, type, set_or1210151606488870762an_nat: nat > set_nat).
% 32.77/9.02  thf(func_def_792, type, set_or5849166863359141190n_real: real > set_real).
% 32.77/9.02  thf(func_def_793, type, set_or8419480210114673929d_enat: extended_enat > set_Extended_enat).
% 32.77/9.02  thf(func_def_794, type, set_ord_lessThan_int: int > set_int).
% 32.77/9.02  thf(func_def_795, type, set_ord_lessThan_nat: nat > set_nat).
% 32.77/9.02  thf(func_def_796, type, set_ord_lessThan_num: num > set_num).
% 32.77/9.02  thf(func_def_797, type, set_ord_lessThan_rat: rat > set_rat).
% 32.77/9.02  thf(func_def_798, type, set_or5984915006950818249n_real: real > set_real).
% 32.77/9.02  thf(func_def_799, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_800, type, ascii_of: char > char).
% 32.77/9.02  thf(func_def_801, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 32.77/9.02  thf(func_def_802, type, size_char: char > nat).
% 32.77/9.02  thf(func_def_803, type, comm_s629917340098488124ar_nat: char > nat).
% 32.77/9.02  thf(func_def_804, type, integer_of_char: char > code_integer).
% 32.77/9.02  thf(func_def_805, type, unique3096191561947761185of_nat: nat > char).
% 32.77/9.02  thf(func_def_806, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 32.77/9.02  thf(func_def_807, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 32.77/9.02  thf(func_def_808, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 32.77/9.02  thf(func_def_809, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 32.77/9.02  thf(func_def_810, type, topolo2815343760600316023s_real: real > filter_real).
% 32.77/9.02  thf(func_def_811, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 32.77/9.02  thf(func_def_812, type, topolo896644834953643431omplex: filter6041513312241820739omplex).
% 32.77/9.02  thf(func_def_813, type, topolo1511823702728130853y_real: filter2146258269922977983l_real).
% 32.77/9.02  thf(func_def_814, type, arccos: real > real).
% 32.77/9.02  thf(func_def_815, type, arcosh_real: real > real).
% 32.77/9.02  thf(func_def_816, type, arcsin: real > real).
% 32.77/9.02  thf(func_def_817, type, arctan: real > real).
% 32.77/9.02  thf(func_def_818, type, arsinh_real: real > real).
% 32.77/9.02  thf(func_def_819, type, artanh_real: real > real).
% 32.77/9.02  thf(func_def_820, type, cos_real: real > real).
% 32.77/9.02  thf(func_def_821, type, cos_coeff: nat > real).
% 32.77/9.02  thf(func_def_822, type, cosh_real: real > real).
% 32.77/9.02  thf(func_def_823, type, cot_real: real > real).
% 32.77/9.02  thf(func_def_824, type, exp_complex: complex > complex).
% 32.77/9.02  thf(func_def_825, type, exp_real: real > real).
% 32.77/9.02  thf(func_def_826, type, ln_ln_real: real > real).
% 32.77/9.02  thf(func_def_827, type, log: real > real > real).
% 32.77/9.02  thf(func_def_828, type, pi: real).
% 32.77/9.02  thf(func_def_829, type, powr_real: real > real > real).
% 32.77/9.02  thf(func_def_830, type, sin_real: real > real).
% 32.77/9.02  thf(func_def_831, type, sin_coeff: nat > real).
% 32.77/9.02  thf(func_def_832, type, sinh_real: real > real).
% 32.77/9.02  thf(func_def_833, type, tan_real: real > real).
% 32.77/9.02  thf(func_def_834, type, tanh_complex: complex > complex).
% 32.77/9.02  thf(func_def_835, type, tanh_real: real > real).
% 32.77/9.02  thf(func_def_836, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 32.77/9.02  thf(func_def_837, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_838, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_839, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_840, type, vEBT_VEBT_high: nat > nat > nat).
% 32.77/9.02  thf(func_def_841, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_842, type, vEBT_VEBT_low: nat > nat > nat).
% 32.77/9.02  thf(func_def_843, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_844, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_845, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_846, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_847, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_848, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_849, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_850, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 32.77/9.02  thf(func_def_851, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_852, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 32.77/9.02  thf(func_def_853, type, vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_854, type, vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_855, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_856, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_857, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_858, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_859, type, vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_860, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 32.77/9.02  thf(func_def_861, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_862, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_863, type, vEBT_VEBT_add: option_nat > option_nat > option_nat).
% 32.77/9.02  thf(func_def_864, type, vEBT_VEBT_greater: option_nat > option_nat > $o).
% 32.77/9.02  thf(func_def_865, type, vEBT_VEBT_less: option_nat > option_nat > $o).
% 32.77/9.02  thf(func_def_866, type, vEBT_VEBT_lesseq: option_nat > option_nat > $o).
% 32.77/9.02  thf(func_def_867, type, vEBT_VEBT_max_in_set: set_nat > nat > $o).
% 32.77/9.02  thf(func_def_868, type, vEBT_VEBT_min_in_set: set_nat > nat > $o).
% 32.77/9.02  thf(func_def_869, type, vEBT_VEBT_mul: option_nat > option_nat > option_nat).
% 32.77/9.02  thf(func_def_870, type, vEBT_V4262088993061758097ft_nat: (nat > nat > nat) > option_nat > option_nat > option_nat).
% 32.77/9.02  thf(func_def_871, type, vEBT_V819420779217536731ft_num: (num > num > num) > option_num > option_num > option_num).
% 32.77/9.02  thf(func_def_872, type, vEBT_V1502963449132264192at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_873, type, vEBT_VEBT_power: option_nat > option_nat > option_nat).
% 32.77/9.02  thf(func_def_874, type, vEBT_vebt_maxt: vEBT_VEBT > option_nat).
% 32.77/9.02  thf(func_def_875, type, vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_876, type, vEBT_vebt_mint: vEBT_VEBT > option_nat).
% 32.77/9.02  thf(func_def_877, type, vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_878, type, vEBT_is_pred_in_set: set_nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_879, type, vEBT_vebt_pred: vEBT_VEBT > nat > option_nat).
% 32.77/9.02  thf(func_def_880, type, vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_881, type, vEBT_is_succ_in_set: set_nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_882, type, vEBT_vebt_succ: vEBT_VEBT > nat > option_nat).
% 32.77/9.02  thf(func_def_883, type, vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_884, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 32.77/9.02  thf(func_def_885, type, accp_nat: (nat > nat > $o) > nat > $o).
% 32.77/9.02  thf(func_def_886, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 32.77/9.02  thf(func_def_887, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 32.77/9.02  thf(func_def_888, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 32.77/9.02  thf(func_def_889, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_890, type, accp_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_891, type, fChoice_real: (real > $o) > real).
% 32.77/9.02  thf(func_def_892, type, member_o: $o > set_o > $o).
% 32.77/9.02  thf(func_def_893, type, member_complex: complex > set_complex > $o).
% 32.77/9.02  thf(func_def_894, type, member_int: int > set_int > $o).
% 32.77/9.02  thf(func_def_895, type, member_list_o: list_o > set_list_o > $o).
% 32.77/9.02  thf(func_def_896, type, member_list_int: list_int > set_list_int > $o).
% 32.77/9.02  thf(func_def_897, type, member_list_nat: list_nat > set_list_nat > $o).
% 32.77/9.02  thf(func_def_898, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_899, type, member_nat: nat > set_nat > $o).
% 32.77/9.02  thf(func_def_900, type, member_num: num > set_num > $o).
% 32.77/9.02  thf(func_def_901, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 32.77/9.02  thf(func_def_902, type, member_rat: rat > set_rat > $o).
% 32.77/9.02  thf(func_def_903, type, member_real: real > set_real > $o).
% 32.77/9.02  thf(func_def_904, type, member_set_int: set_int > set_set_int > $o).
% 32.77/9.02  thf(func_def_905, type, member_set_nat: set_nat > set_set_nat > $o).
% 32.77/9.02  thf(func_def_906, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_907, type, deg: nat).
% 32.77/9.02  thf(func_def_908, type, m: nat).
% 32.77/9.02  thf(func_def_909, type, ma: nat).
% 32.77/9.02  thf(func_def_910, type, maxs: nat).
% 32.77/9.02  thf(func_def_911, type, mi: nat).
% 32.77/9.02  thf(func_def_912, type, na: nat).
% 32.77/9.02  thf(func_def_913, type, summary: vEBT_VEBT).
% 32.77/9.02  thf(func_def_914, type, treeList: list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_915, type, xa: nat).
% 32.77/9.02  thf(func_def_934, type, sP0: num > rat > rat > $o).
% 32.77/9.02  thf(func_def_935, type, sP1: option_nat > option_nat > (nat > nat > nat) > option_nat > $o).
% 32.77/9.02  thf(func_def_936, type, sP2: real > real > num > $o).
% 32.77/9.02  thf(func_def_937, type, sP3: (num > $o) > (num > $o) > (num > $o) > (num > $o) > $o).
% 32.77/9.02  thf(func_def_938, type, sP4: (real > real) > set_real > $o).
% 32.77/9.02  thf(func_def_939, type, sP5: (complex > real) > (real > complex) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_940, type, sP6: (complex > real) > set_real > set_real > set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_941, type, sP7: set_real > (real > real) > (complex > real) > (real > complex) > $o).
% 32.77/9.02  thf(func_def_942, type, sP8: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 32.77/9.02  thf(func_def_943, type, sP9: set_set_nat > set_nat > set_set_nat > $o).
% 32.77/9.02  thf(func_def_944, type, sP10: set_real > set_real > (real > int) > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_945, type, sP11: set_real > (real > real) > $o).
% 32.77/9.02  thf(func_def_946, type, sP12: (int > real) > (real > int) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_947, type, sP13: (int > real) > set_real > set_real > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_948, type, sP14: list_nat > nat > $o).
% 32.77/9.02  thf(func_def_949, type, sP15: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_950, type, sP16: (nat > real > real) > nat > real > $o).
% 32.77/9.02  thf(func_def_951, type, sP17: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_952, type, sP18: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_953, type, sP19: $o > list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_954, type, sP20: $o > $o > nat > $o).
% 32.77/9.02  thf(func_def_955, type, sP21: $o > $o > nat > $o > $o).
% 32.77/9.02  thf(func_def_956, type, sP22: $o > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_957, type, sP23: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_958, type, sP24: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_959, type, sP25: $o > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_960, type, sP26: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > $o).
% 32.77/9.02  thf(func_def_961, type, sP27: $o > $o > nat > $o).
% 32.77/9.02  thf(func_def_962, type, sP28: $o > $o > nat > $o > $o).
% 32.77/9.02  thf(func_def_963, type, sP29: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_964, type, sP30: list_VEBT_VEBT > nat > nat > nat > nat > $o > $o).
% 32.77/9.02  thf(func_def_965, type, sP31: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_966, type, sP32: vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_967, type, sP33: nat > nat > (nat > int) > int > $o).
% 32.77/9.02  thf(func_def_968, type, sP34: (int > $o) > (int > $o) > set_int > int > $o).
% 32.77/9.02  thf(func_def_969, type, sP35: set_int > int > (int > $o) > $o).
% 32.77/9.02  thf(func_def_970, type, sP36: (int > $o) > (int > $o) > int > set_int > $o).
% 32.77/9.02  thf(func_def_971, type, sP37: (int > $o) > int > set_int > $o).
% 32.77/9.02  thf(func_def_972, type, sP38: real > real > real > $o).
% 32.77/9.02  thf(func_def_973, type, sP39: (real > real) > real > real > $o).
% 32.77/9.02  thf(func_def_974, type, sP40: (option_num > option_num > $o) > option_num > option_num > $o).
% 32.77/9.02  thf(func_def_975, type, sP41: (int > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_976, type, sP42: (int > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_977, type, sP43: (int > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_978, type, sP44: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_979, type, sP45: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_980, type, sP46: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_981, type, sP47: nat > list_VEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_982, type, sP48: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_983, type, sP49: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_984, type, sP50: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_985, type, sP51: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_986, type, sP52: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_987, type, sP53: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_988, type, sP54: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_989, type, sP55: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_990, type, sP56: real > real > (real > real) > $o).
% 32.77/9.02  thf(func_def_991, type, sP57: (real > real) > (real > real) > (real > real) > real > (real > real) > real > $o).
% 32.77/9.02  thf(func_def_992, type, sP58: real > (real > real) > (real > real) > real > $o).
% 32.77/9.02  thf(func_def_993, type, sP59: real > real > (real > real) > $o).
% 32.77/9.02  thf(func_def_994, type, sP60: num > rat > rat > $o).
% 32.77/9.02  thf(func_def_995, type, sP61: int > int > int > $o).
% 32.77/9.02  thf(func_def_996, type, sP62: int > int > int > $o).
% 32.77/9.02  thf(func_def_997, type, sP63: int > int > int > $o).
% 32.77/9.02  thf(func_def_998, type, sP64: complex > set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_999, type, sP65: int > int > int > $o).
% 32.77/9.02  thf(func_def_1000, type, sP66: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1001, type, sP67: option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1002, type, sP68: (set_nat > $o) > set_nat > $o).
% 32.77/9.02  thf(func_def_1003, type, sP69: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1004, type, sP70: nat > nat > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_1005, type, sP71: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1006, type, sP72: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1007, type, sP73: nat > option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1008, type, sP74: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1009, type, sP75: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1010, type, sP76: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1011, type, sP77: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1012, type, sP78: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1013, type, sP79: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1014, type, sP80: set_int > (int > $o) > (int > $o) > int > $o).
% 32.77/9.02  thf(func_def_1015, type, sP81: (int > $o) > set_int > int > $o).
% 32.77/9.02  thf(func_def_1016, type, sP82: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 32.77/9.02  thf(func_def_1017, type, sP83: (num > $o) > (num > $o) > (num > $o) > (num > $o) > $o).
% 32.77/9.02  thf(func_def_1018, type, sP84: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1019, type, sP85: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1020, type, sP86: $o > $o > nat > $o).
% 32.77/9.02  thf(func_def_1021, type, sP87: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1022, type, sP88: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1023, type, sP89: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1024, type, sP90: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1025, type, sP91: rat > num > rat > $o).
% 32.77/9.02  thf(func_def_1026, type, sP92: real > real > real > $o).
% 32.77/9.02  thf(func_def_1027, type, sP93: set_int > int > (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1028, type, sP94: set_int > int > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1029, type, sP95: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1030, type, sP96: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1031, type, sP97: $o > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1032, type, sP98: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1033, type, sP99: $o > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1034, type, sP100: (int > $o) > int > set_int > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1035, type, sP101: real > nat > real > (nat > real > real) > $o).
% 32.77/9.02  thf(func_def_1036, type, sP102: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1037, type, sP103: real > nat > real > $o).
% 32.77/9.02  thf(func_def_1038, type, sP104: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1039, type, sP105: num > real > real > $o).
% 32.77/9.02  thf(func_def_1040, type, sP106: nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_1041, type, sP107: nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_1042, type, sP108: nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_1043, type, sP109: (real > real) > (real > real) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1044, type, sP110: (real > real) > (real > real) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1045, type, sP111: (real > real) > set_real > set_real > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1046, type, sP112: set_real > (real > real) > (real > real) > (real > real) > $o).
% 32.77/9.02  thf(func_def_1047, type, sP113: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_1048, type, sP114: (int > $o) > $o).
% 32.77/9.02  thf(func_def_1049, type, sP115: num > num > num > $o).
% 32.77/9.02  thf(func_def_1050, type, sP116: num > num > num > $o).
% 32.77/9.02  thf(func_def_1051, type, sP117: num > num > num > $o).
% 32.77/9.02  thf(func_def_1052, type, sP118: num > num > num > $o).
% 32.77/9.02  thf(func_def_1053, type, sP119: num > num > num > $o).
% 32.77/9.02  thf(func_def_1054, type, sP120: num > num > num > $o).
% 32.77/9.02  thf(func_def_1055, type, sP121: num > num > num > $o).
% 32.77/9.02  thf(func_def_1056, type, sP122: num > num > num > $o).
% 32.77/9.02  thf(func_def_1057, type, sP123: (int > real) > (real > int) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1058, type, sP124: set_real > set_real > (real > int) > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_1059, type, sP125: (int > real) > set_real > set_real > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_1060, type, sP126: set_int > set_int > (real > int) > (int > real) > $o).
% 32.77/9.02  thf(func_def_1061, type, sP127: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1062, type, sP128: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1063, type, sP129: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1064, type, sP130: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1065, type, sP131: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1066, type, sP132: (complex > real) > set_complex > $o).
% 32.77/9.02  thf(func_def_1067, type, sP133: set_int > (int > real) > (complex > real) > (int > complex) > $o).
% 32.77/9.02  thf(func_def_1068, type, sP134: set_complex > set_complex > (int > complex) > (complex > int) > $o).
% 32.77/9.02  thf(func_def_1069, type, sP135: set_int > set_int > (int > complex) > set_complex > set_complex > $o).
% 32.77/9.02  thf(func_def_1070, type, sP136: option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1071, type, sP137: (set_int > $o) > set_int > $o).
% 32.77/9.02  thf(func_def_1072, type, sP138: real > real > real > $o).
% 32.77/9.02  thf(func_def_1073, type, sP139: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > $o).
% 32.77/9.02  thf(func_def_1074, type, sP140: (int > real) > set_int > $o).
% 32.77/9.02  thf(func_def_1075, type, sP141: set_int > (int > real) > (int > real) > (int > int) > $o).
% 32.77/9.02  thf(func_def_1076, type, sP142: set_int > set_int > (int > int) > (int > int) > $o).
% 32.77/9.02  thf(func_def_1077, type, sP143: set_int > set_int > (int > int) > (int > int) > $o).
% 32.77/9.02  thf(func_def_1078, type, sP144: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1079, type, sP145: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1080, type, sP146: option_num > option_num > option_num > $o).
% 32.77/9.02  thf(func_def_1081, type, sP147: set_int > (int > real) > (real > real) > (int > real) > $o).
% 32.77/9.02  thf(func_def_1082, type, sP148: (int > real) > set_int > $o).
% 32.77/9.02  thf(func_def_1083, type, sP149: set_int > set_int > (int > real) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1084, type, sP150: (real > real) > set_real > $o).
% 32.77/9.02  thf(func_def_1085, type, sP151: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_1086, type, sP152: (real > complex) > set_real > $o).
% 32.77/9.02  thf(func_def_1087, type, sP153: set_int > (real > complex) > (int > real) > (int > complex) > $o).
% 32.77/9.02  thf(func_def_1088, type, sP154: set_real > set_real > (real > int) > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_1089, type, sP155: (int > complex) > set_int > $o).
% 32.77/9.02  thf(func_def_1090, type, sP156: real > real > (real > real > real) > $o).
% 32.77/9.02  thf(func_def_1091, type, sP157: real > num > real > $o).
% 32.77/9.02  thf(func_def_1092, type, sP158: num > real > real > $o).
% 32.77/9.02  thf(func_def_1093, type, sP159: real > real > real > $o).
% 32.77/9.02  thf(func_def_1094, type, sP160: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1095, type, sP161: (real > real) > real > (real > real) > real > $o).
% 32.77/9.02  thf(func_def_1096, type, sP162: real > real > (real > real) > $o).
% 32.77/9.02  thf(func_def_1097, type, sP163: (real > real) > real > real > $o).
% 32.77/9.02  thf(func_def_1098, type, sP164: real > (real > real) > real > $o).
% 32.77/9.02  thf(func_def_1099, type, sP165: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1100, type, sP166: vEBT_VEBT > nat > $o > $o).
% 32.77/9.02  thf(func_def_1101, type, sP167: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1102, type, sP168: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1103, type, sP169: (real > real) > real > real > $o).
% 32.77/9.02  thf(func_def_1104, type, sP170: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1105, type, sP171: (int > complex) > set_int > $o).
% 32.77/9.02  thf(func_def_1106, type, sP172: set_int > set_int > (int > int) > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_1107, type, sP173: (int > int) > (int > int) > set_int > set_int > $o).
% 32.77/9.02  thf(func_def_1108, type, sP174: (int > complex) > set_int > $o).
% 32.77/9.02  thf(func_def_1109, type, sP175: $o > $o > nat > $o).
% 32.77/9.02  thf(func_def_1110, type, sP176: $o > $o > $o > nat > $o).
% 32.77/9.02  thf(func_def_1111, type, sP177: vEBT_VEBT > nat > $o > $o).
% 32.77/9.02  thf(func_def_1112, type, sP178: nat > $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1113, type, sP179: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1114, type, sP180: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1115, type, sP181: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1116, type, sP182: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1117, type, sP183: (option_nat > option_nat > $o) > option_nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1118, type, sP184: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_1119, type, sP185: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1120, type, sP186: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1121, type, sP187: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1122, type, sP188: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1123, type, sP189: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1124, type, sP190: option_nat > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1125, type, sP191: real > real > real > $o).
% 32.77/9.02  thf(func_def_1126, type, sP192: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1127, type, sP193: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1128, type, sP194: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1129, type, sP195: (set_set_nat > $o) > set_set_nat > $o).
% 32.77/9.02  thf(func_def_1130, type, sP196: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_1131, type, sP197: (real > real) > (real > real) > real > real > $o).
% 32.77/9.02  thf(func_def_1132, type, sP198: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > $o).
% 32.77/9.02  thf(func_def_1133, type, sP199: set_int > int > set_int > $o).
% 32.77/9.02  thf(func_def_1134, type, sP200: product_prod_int_int > int > int > $o).
% 32.77/9.02  thf(func_def_1135, type, sP201: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1136, type, sP202: $o > nat > list_VEBT_VEBT > option4927543243414619207at_nat > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1137, type, sP203: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1138, type, sP204: rat > num > rat > $o).
% 32.77/9.02  thf(func_def_1139, type, sP205: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_1140, type, sP206: set_real > real > set_real > $o).
% 32.77/9.02  thf(func_def_1141, type, sP207: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1142, type, sP208: num > num > num > $o).
% 32.77/9.02  thf(func_def_1143, type, sP209: num > num > num > $o).
% 32.77/9.02  thf(func_def_1144, type, sP210: num > num > num > $o).
% 32.77/9.02  thf(func_def_1145, type, sP211: (nat > real > real) > nat > real > real > $o).
% 32.77/9.02  thf(func_def_1146, type, sP212: num > rat > rat > $o).
% 32.77/9.02  thf(func_def_1147, type, sP213: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1148, type, sP214: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1149, type, sP215: (num > $o) > (num > $o) > (num > $o) > (num > $o) > $o).
% 32.77/9.02  thf(func_def_1150, type, sP216: rat > num > rat > $o).
% 32.77/9.02  thf(func_def_1151, type, sP217: (nat > real > real) > real > nat > $o).
% 32.77/9.02  thf(func_def_1152, type, sP218: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_1153, type, sP219: nat > vEBT_VEBT > list_VEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1154, type, sP220: set_complex > (set_complex > $o) > $o).
% 32.77/9.02  thf(func_def_1155, type, sP221: (int > $o) > int > $o).
% 32.77/9.02  thf(func_def_1156, type, sP222: real > num > real > $o).
% 32.77/9.02  thf(func_def_1157, type, sP223: (int > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_1158, type, sP224: int > int > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1159, type, sP225: (real > real) > (nat > real > real) > nat > real > real > $o).
% 32.77/9.02  thf(func_def_1160, type, sP226: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1161, type, sP227: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1162, type, sP228: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1163, type, sP229: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1164, type, sP230: (option4927543243414619207at_nat > option_num > $o) > option_num > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_1165, type, sP231: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1166, type, sP232: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1167, type, sP233: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1168, type, sP234: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1169, type, sP235: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1170, type, sP236: (option_num > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option_num > $o).
% 32.77/9.02  thf(func_def_1171, type, sP237: (option_num > option_nat > $o) > option_nat > option_num > $o).
% 32.77/9.02  thf(func_def_1172, type, sP238: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 32.77/9.02  thf(func_def_1173, type, sP239: num > num > num > $o).
% 32.77/9.02  thf(func_def_1174, type, sP240: num > num > num > $o).
% 32.77/9.02  thf(func_def_1175, type, sP241: num > num > num > $o).
% 32.77/9.02  thf(func_def_1176, type, sP242: num > num > num > $o).
% 32.77/9.02  thf(func_def_1177, type, sP243: num > num > num > $o).
% 32.77/9.02  thf(func_def_1178, type, sP244: num > num > num > $o).
% 32.77/9.02  thf(func_def_1179, type, sP245: num > num > num > $o).
% 32.77/9.02  thf(func_def_1180, type, sP246: num > num > num > $o).
% 32.77/9.02  thf(func_def_1181, type, sP247: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 32.77/9.02  thf(func_def_1182, type, sP248: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1183, type, sP249: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1184, type, sP250: nat > option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1185, type, sP251: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1186, type, sP252: real > real > real > $o).
% 32.77/9.02  thf(func_def_1187, type, sP253: (num > $o) > (num > $o) > (num > $o) > (num > $o) > $o).
% 32.77/9.02  thf(func_def_1188, type, sP254: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > $o).
% 32.77/9.02  thf(func_def_1189, type, sP255: rat > num > rat > $o).
% 32.77/9.02  thf(func_def_1190, type, sP256: set_real > set_real > (real > real) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1191, type, sP257: set_real > (real > complex) > $o).
% 32.77/9.02  thf(func_def_1192, type, sP258: (real > complex) > (real > real) > (real > complex) > set_real > $o).
% 32.77/9.02  thf(func_def_1193, type, sP259: (real > real) > (real > real) > set_real > set_real > $o).
% 32.77/9.02  thf(func_def_1194, type, sP260: rat > num > rat > $o).
% 32.77/9.02  thf(func_def_1195, type, sP261: real > (real > real) > real > $o).
% 32.77/9.02  thf(func_def_1196, type, sP262: real > num > real > $o).
% 32.77/9.02  thf(func_def_1197, type, sP263: real > (real > real) > (real > real > real) > real > $o).
% 32.77/9.02  thf(func_def_1198, type, sP264: (set_real > $o) > set_real > $o).
% 32.77/9.02  thf(func_def_1199, type, sP265: $o > nat > $o > $o).
% 32.77/9.02  thf(func_def_1200, type, sP266: $o > $o > nat > $o > $o).
% 32.77/9.02  thf(func_def_1201, type, sP267: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1202, type, sP268: real > real > real > $o).
% 32.77/9.02  thf(func_def_1203, type, sP269: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_1204, type, sP270: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1205, type, sP271: (int > $o) > int > set_int > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1206, type, sP272: real > real > (real > real > $o) > $o).
% 32.77/9.02  thf(func_def_1207, type, sP273: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 32.77/9.02  thf(func_def_1208, type, sP274: (real > real) > real > real > $o).
% 32.77/9.02  thf(func_def_1209, type, sP275: $o > nat > $o > $o).
% 32.77/9.02  thf(func_def_1210, type, sP276: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1211, type, sP277: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1212, type, sP278: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1213, type, sP279: (nat > real > real) > real > nat > $o).
% 32.77/9.02  thf(func_def_1214, type, sP280: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1215, type, sP281: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1216, type, sP282: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1217, type, sP283: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1218, type, sP284: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1219, type, sP285: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1220, type, sP286: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 32.77/9.02  thf(func_def_1221, type, sP287: vEBT_VEBT > nat > $o > $o).
% 32.77/9.02  thf(func_def_1222, type, sP288: rat > rat > rat > $o).
% 32.77/9.02  thf(func_def_1223, type, sP289: int > (int > $o) > int > $o).
% 32.77/9.02  thf(func_def_1224, type, sP290: (int > $o) > int > int > $o).
% 32.77/9.02  thf(func_def_1225, type, sP291: num > real > real > $o).
% 32.77/9.02  thf(func_def_1226, type, sP292: (option4927543243414619207at_nat > option_nat > $o) > option_nat > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_1227, type, sP293: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > $o).
% 32.77/9.02  thf(func_def_1228, type, sP294: set_nat > nat > set_nat > $o).
% 32.77/9.02  thf(func_def_1229, type, sP295: real > num > real > $o).
% 32.77/9.02  thf(func_def_1230, type, sP296: nat > (nat > $o) > nat > $o).
% 32.77/9.02  thf(func_def_1231, type, sP297: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1232, type, sP298: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_1233, type, sP299: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_1234, type, sP300: option_nat > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1235, type, sP301: option_nat > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1236, type, sP302: real > real > real > $o).
% 32.77/9.02  thf(func_def_1237, type, sP303: nat > (nat > nat) > $o).
% 32.77/9.02  thf(func_def_1238, type, sP304: (option_nat > option_num > $o) > option_nat > option_num > $o).
% 32.77/9.02  thf(func_def_1239, type, sP305: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 32.77/9.02  thf(func_def_1240, type, sK306: (num > $o) > num).
% 32.77/9.02  thf(func_def_1241, type, sK307: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_1242, type, sK308: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_1243, type, sK309: (real > nat) > set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_1244, type, sK310: set_complex > (complex > rat) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1245, type, sK311: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1246, type, sK312: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1247, type, sK313: (set_nat > nat) > set_set_nat > (set_nat > nat) > set_nat).
% 32.77/9.02  thf(func_def_1248, type, sK314: real > (real > real) > real).
% 32.77/9.02  thf(func_def_1249, type, sK315: (real > complex) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1250, type, sK316: (real > complex) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1251, type, sK317: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1252, type, sK318: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1253, type, sK319: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1254, type, sK320: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1255, type, sK321: set_int > (int > real) > (int > real) > (real > real > $o) > int).
% 32.77/9.02  thf(func_def_1256, type, sK322: set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_1257, type, sK323: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1258, type, sK324: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1259, type, sK325: (num > int) > num).
% 32.77/9.02  thf(func_def_1260, type, sK326: (num > int) > num).
% 32.77/9.02  thf(func_def_1261, type, sK327: produc2285326912895808259nt_int > int).
% 32.77/9.02  thf(func_def_1262, type, sK328: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1263, type, sK329: produc2285326912895808259nt_int > int).
% 32.77/9.02  thf(func_def_1264, type, sK330: (real > rat) > (set_real > $o) > real).
% 32.77/9.02  thf(func_def_1265, type, sK331: (real > rat) > (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_1266, type, sK332: real > real).
% 32.77/9.02  thf(func_def_1267, type, sK333: (produc1908205239877642774nteger > $o) > code_integer).
% 32.77/9.02  thf(func_def_1268, type, sK334: (produc1908205239877642774nteger > $o) > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1269, type, sK335: (produc1908205239877642774nteger > $o) > code_integer).
% 32.77/9.02  thf(func_def_1270, type, sK336: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1271, type, sK337: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1272, type, sK338: rat > rat).
% 32.77/9.02  thf(func_def_1273, type, sK339: option_nat > option_nat > (nat > nat > nat) > option_nat > nat).
% 32.77/9.02  thf(func_def_1274, type, sK340: option_nat > option_nat > (nat > nat > nat) > option_nat > nat).
% 32.77/9.02  thf(func_def_1275, type, sK341: option_nat > nat).
% 32.77/9.02  thf(func_def_1276, type, sK342: produc8763457246119570046nteger > complex > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_complex) > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1277, type, sK343: produc8763457246119570046nteger > complex > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_complex) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_1278, type, sK344: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1279, type, sK345: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1280, type, sK346: (product_prod_int_int > product_prod_int_int) > (int > int > product_prod_int_int) > int).
% 32.77/9.02  thf(func_def_1281, type, sK347: (product_prod_int_int > product_prod_int_int) > (int > int > product_prod_int_int) > int).
% 32.77/9.02  thf(func_def_1282, type, sK348: nat > nat > nat).
% 32.77/9.02  thf(func_def_1283, type, sK349: int > int).
% 32.77/9.02  thf(func_def_1284, type, sK350: nat > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1285, type, sK351: product_prod_int_int > (int > $o) > (int > int > int) > int).
% 32.77/9.02  thf(func_def_1286, type, sK352: product_prod_int_int > (int > $o) > (int > int > int) > int).
% 32.77/9.02  thf(func_def_1287, type, sK353: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_1288, type, sK354: (num > $o) > (num > $o) > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1289, type, sK355: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1290, type, sK356: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1291, type, sK357: (nat > rat) > set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1292, type, sK358: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1293, type, sK359: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1294, type, sK360: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1295, type, sK361: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1296, type, sK362: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1297, type, sK363: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1298, type, sK364: set_nat > (nat > real) > (nat > real) > nat).
% 32.77/9.02  thf(func_def_1299, type, sK365: set_num > num > num).
% 32.77/9.02  thf(func_def_1300, type, sK366: real > nat > real).
% 32.77/9.02  thf(func_def_1301, type, sK367: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_1302, type, sK368: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1303, type, sK369: produc1908205239877642774nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_1304, type, sK370: set_nat > (nat > rat) > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1305, type, sK371: set_real > set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_1306, type, sK372: set_real > (real > nat) > (real > nat) > real).
% 32.77/9.02  thf(func_def_1307, type, sK373: set_real > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1308, type, sK374: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1309, type, sK375: set_real > (real > real) > (complex > real) > (real > complex) > real).
% 32.77/9.02  thf(func_def_1310, type, sK376: (complex > real) > set_real > set_real > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_1311, type, sK377: (complex > real) > (real > complex) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1312, type, sK378: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_1313, type, sK379: set_real > set_complex > set_real > set_complex > (real > complex) > real).
% 32.77/9.02  thf(func_def_1314, type, sK380: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_1315, type, sK381: (complex > real) > set_complex > set_complex > (real > complex) > complex).
% 32.77/9.02  thf(func_def_1316, type, sK382: ((product_prod_nat_nat > $o) > $o) > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_1317, type, sK383: ((product_prod_nat_nat > $o) > $o) > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_1318, type, sK384: nat > real > real).
% 32.77/9.02  thf(func_def_1319, type, sK385: set_complex > set_complex > (complex > int) > complex).
% 32.77/9.02  thf(func_def_1320, type, sK386: set_int > (int > real) > (int > complex) > int).
% 32.77/9.02  thf(func_def_1321, type, sK387: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1322, type, sK388: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1323, type, sK389: list_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1324, type, sK390: (real > rat) > (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_1325, type, sK391: nat > nat).
% 32.77/9.02  thf(func_def_1326, type, sK392: num > num).
% 32.77/9.02  thf(func_def_1327, type, sK393: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1328, type, sK394: real > real > nat).
% 32.77/9.02  thf(func_def_1329, type, sK395: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_1330, type, sK396: (complex > real) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_1331, type, sK397: set_complex > set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_1332, type, sK398: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1333, type, sK399: real > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1334, type, sK400: real > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1335, type, sK401: (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_1336, type, sK402: (set_real > $o) > real).
% 32.77/9.02  thf(func_def_1337, type, sK403: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1338, type, sK404: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1339, type, sK405: (int > nat) > (int > nat) > int).
% 32.77/9.02  thf(func_def_1340, type, sK406: real > real).
% 32.77/9.02  thf(func_def_1341, type, sK407: (set_set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1342, type, sK408: (set_set_nat > $o) > set_set_nat).
% 32.77/9.02  thf(func_def_1343, type, sK409: (nat > $o > $o) > nat > list_o).
% 32.77/9.02  thf(func_def_1344, type, sK410: (nat > $o > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1345, type, sK411: nat > (nat > $o > $o) > $o).
% 32.77/9.02  thf(func_def_1346, type, sK412: list_o > (nat > $o > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1347, type, sK413: (real > real) > real > real).
% 32.77/9.02  thf(func_def_1348, type, sK414: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1349, type, sK415: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1350, type, sK416: num > num).
% 32.77/9.02  thf(func_def_1351, type, sK417: int > int).
% 32.77/9.02  thf(func_def_1352, type, sK418: (int > real) > set_real > set_real > set_int > set_int > int).
% 32.77/9.02  thf(func_def_1353, type, sK419: (int > real) > (real > int) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1354, type, sK420: set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_1355, type, sK421: set_real > set_real > (real > int) > set_int > set_int > real).
% 32.77/9.02  thf(func_def_1356, type, sK422: set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_1357, type, sK423: set_real > (real > real) > (real > int) > (int > real) > real).
% 32.77/9.02  thf(func_def_1358, type, sK424: set_int > (int > real) > set_int > (real > int) > int).
% 32.77/9.02  thf(func_def_1359, type, sK425: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_1360, type, sK426: list_nat > nat > nat).
% 32.77/9.02  thf(func_def_1361, type, sK427: list_nat > nat > list_nat).
% 32.77/9.02  thf(func_def_1362, type, sK428: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1363, type, sK429: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1364, type, sK430: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1365, type, sK431: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_1366, type, sK432: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1367, type, sK433: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1368, type, sK434: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1369, type, sK435: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1370, type, sK436: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1371, type, sK437: set_real > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1372, type, sK438: set_real > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1373, type, sK439: (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1374, type, sK440: nat > (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1375, type, sK441: rat > rat).
% 32.77/9.02  thf(func_def_1376, type, sK442: real > int).
% 32.77/9.02  thf(func_def_1377, type, sK443: (nat > real) > real > nat > nat).
% 32.77/9.02  thf(func_def_1378, type, sK444: set_nat > nat > nat).
% 32.77/9.02  thf(func_def_1379, type, sK445: set_complex > (complex > rat) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1380, type, sK446: real > (int > int > set_real) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1381, type, sK447: real > (int > int > set_real) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1382, type, sK448: set_int > int).
% 32.77/9.02  thf(func_def_1383, type, sK449: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_1384, type, sK450: real > real).
% 32.77/9.02  thf(func_def_1385, type, sK451: set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_1386, type, sK452: (set_nat > real) > (set_nat > complex) > set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_1387, type, sK453: set_real > set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_1388, type, sK454: set_real > set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_1389, type, sK455: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_1390, type, sK456: list_nat > nat > nat).
% 32.77/9.02  thf(func_def_1391, type, sK457: $o > list_o > nat).
% 32.77/9.02  thf(func_def_1392, type, sK458: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1393, type, sK459: produc1908205239877642774nteger > code_integer).
% 32.77/9.02  thf(func_def_1394, type, sK460: produc1908205239877642774nteger > code_integer).
% 32.77/9.02  thf(func_def_1395, type, sK461: (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1396, type, sK462: set_int > (int > code_integer) > int).
% 32.77/9.02  thf(func_def_1397, type, sK463: (int > code_integer) > code_integer > set_int > code_integer > int).
% 32.77/9.02  thf(func_def_1398, type, sK464: produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1399, type, sK465: produc7773217078559923341nt_int > int).
% 32.77/9.02  thf(func_def_1400, type, sK466: produc7773217078559923341nt_int > int).
% 32.77/9.02  thf(func_def_1401, type, sK467: nat > real > real).
% 32.77/9.02  thf(func_def_1402, type, sK468: set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1403, type, sK469: (complex > nat) > set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_1404, type, sK470: (nat > real > real) > nat > real > real).
% 32.77/9.02  thf(func_def_1405, type, sK471: (nat > real > real) > nat > real > nat).
% 32.77/9.02  thf(func_def_1406, type, sK472: real > (real > real) > (nat > real > real) > nat > real).
% 32.77/9.02  thf(func_def_1407, type, sK473: int > nat > (int > $o) > int).
% 32.77/9.02  thf(func_def_1408, type, sK474: (set_rat > $o) > set_rat).
% 32.77/9.02  thf(func_def_1409, type, sK475: (set_rat > $o) > rat).
% 32.77/9.02  thf(func_def_1410, type, sK476: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_1411, type, sK477: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_1412, type, sK478: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_1413, type, sK479: int > nat).
% 32.77/9.02  thf(func_def_1414, type, sK480: nat > nat).
% 32.77/9.02  thf(func_def_1415, type, sK481: int > nat).
% 32.77/9.02  thf(func_def_1416, type, sK482: rat > int).
% 32.77/9.02  thf(func_def_1417, type, sK483: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1418, type, sK484: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1419, type, sK485: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1420, type, sK486: set_nat > (nat > int) > set_nat > nat).
% 32.77/9.02  thf(func_def_1421, type, sK487: nat > real > real).
% 32.77/9.02  thf(func_def_1422, type, sK488: (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_1423, type, sK489: real > nat).
% 32.77/9.02  thf(func_def_1424, type, sK490: (complex > real) > (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_1425, type, sK491: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_1426, type, sK492: (int > $o) > list_int > int).
% 32.77/9.02  thf(func_def_1427, type, sK493: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_1428, type, sK494: (int > rat) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_1429, type, sK495: $o > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1430, type, sK496: $o > vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1431, type, sK497: $o > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1432, type, sK498: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1433, type, sK499: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1434, type, sK500: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1435, type, sK501: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1436, type, sK502: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1437, type, sK503: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1438, type, sK504: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1439, type, sK505: vEBT_VEBT > $o > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1440, type, sK506: $o > vEBT_VEBT > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1441, type, sK507: $o > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1442, type, sK508: $o > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1443, type, sK509: nat > vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_1444, type, sK510: nat > vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_1445, type, sK511: nat > real > (real > real) > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_1446, type, sK512: (nat > real > real) > nat).
% 32.77/9.02  thf(func_def_1447, type, sK513: (nat > real > real) > real).
% 32.77/9.02  thf(func_def_1448, type, sK514: nat > nat).
% 32.77/9.02  thf(func_def_1449, type, sK515: complex > list_complex > nat).
% 32.77/9.02  thf(func_def_1450, type, sK516: (int > int > set_set_nat) > product_prod_int_int > set_nat > int).
% 32.77/9.02  thf(func_def_1451, type, sK517: (int > int > set_set_nat) > product_prod_int_int > set_nat > int).
% 32.77/9.02  thf(func_def_1452, type, sK518: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1453, type, sK519: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1454, type, sK520: set_int > (int > real) > int > int).
% 32.77/9.02  thf(func_def_1455, type, sK521: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_1456, type, sK522: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_1457, type, sK523: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_1458, type, sK524: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1459, type, sK525: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1460, type, sK526: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1461, type, sK527: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1462, type, sK528: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1463, type, sK529: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1464, type, sK530: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1465, type, sK531: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1466, type, sK532: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1467, type, sK533: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_1468, type, sK534: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1469, type, sK535: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1470, type, sK536: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_1471, type, sK537: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1472, type, sK538: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1473, type, sK539: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1474, type, sK540: (int > rat) > (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_1475, type, sK541: (int > rat) > (set_int > $o) > int).
% 32.77/9.02  thf(func_def_1476, type, sK542: list_o > $o > $o).
% 32.77/9.02  thf(func_def_1477, type, sK543: nat > vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1478, type, sK544: rat > rat).
% 32.77/9.02  thf(func_def_1479, type, sK545: nat > nat > (nat > int) > int > nat).
% 32.77/9.02  thf(func_def_1480, type, sK546: (nat > int) > nat > nat > nat).
% 32.77/9.02  thf(func_def_1481, type, sK547: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_1482, type, sK548: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_1483, type, sK549: (num > rat) > num).
% 32.77/9.02  thf(func_def_1484, type, sK550: (num > rat) > num).
% 32.77/9.02  thf(func_def_1485, type, sK551: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_1486, type, sK552: int > int).
% 32.77/9.02  thf(func_def_1487, type, sK553: complex > produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_complex) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_1488, type, sK554: complex > produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_complex) > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1489, type, sK555: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1490, type, sK556: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1491, type, sK557: (complex > complex) > set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_1492, type, sK558: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1493, type, sK559: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1494, type, sK560: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1495, type, sK561: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1496, type, sK562: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1497, type, sK563: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1498, type, sK564: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1499, type, sK565: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1500, type, sK566: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1501, type, sK567: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1502, type, sK568: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1503, type, sK569: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1504, type, sK570: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1505, type, sK571: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1506, type, sK572: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1507, type, sK573: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1508, type, sK574: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1509, type, sK575: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1510, type, sK576: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1511, type, sK577: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1512, type, sK578: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1513, type, sK579: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_1514, type, sK580: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1515, type, sK581: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1516, type, sK582: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1517, type, sK583: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1518, type, sK584: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_1519, type, sK585: set_int > int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1520, type, sK586: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1521, type, sK587: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1522, type, sK588: set_int > (int > $o) > int > int).
% 32.77/9.02  thf(func_def_1523, type, sK589: (nat > rat) > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1524, type, sK590: (nat > rat) > (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_1525, type, sK591: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1526, type, sK592: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1527, type, sK593: (real > complex) > (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_1528, type, sK594: (real > complex) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1529, type, sK595: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1530, type, sK596: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1531, type, sK597: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1532, type, sK598: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1533, type, sK599: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1534, type, sK600: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1535, type, sK601: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1536, type, sK602: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1537, type, sK603: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1538, type, sK604: nat > nat > nat).
% 32.77/9.02  thf(func_def_1539, type, sK605: (rat > real) > rat).
% 32.77/9.02  thf(func_def_1540, type, sK606: (rat > real) > rat).
% 32.77/9.02  thf(func_def_1541, type, sK607: int > nat).
% 32.77/9.02  thf(func_def_1542, type, sK608: (num > rat) > num).
% 32.77/9.02  thf(func_def_1543, type, sK609: (num > rat) > num).
% 32.77/9.02  thf(func_def_1544, type, sK610: (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1545, type, sK611: (int > $o) > int > set_int > int).
% 32.77/9.02  thf(func_def_1546, type, sK612: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1547, type, sK613: int > int > set_int > int).
% 32.77/9.02  thf(func_def_1548, type, sK614: int > set_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1549, type, sK615: rat > int).
% 32.77/9.02  thf(func_def_1550, type, sK616: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1551, type, sK617: real > (nat > real) > real).
% 32.77/9.02  thf(func_def_1552, type, sK618: real > (nat > real) > nat).
% 32.77/9.02  thf(func_def_1553, type, sK619: set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_1554, type, sK620: rat > rat).
% 32.77/9.02  thf(func_def_1555, type, sK621: (num > real) > num).
% 32.77/9.02  thf(func_def_1556, type, sK622: (num > real) > num).
% 32.77/9.02  thf(func_def_1557, type, sK623: (int > int > $o) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1558, type, sK624: (int > int > $o) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1559, type, sK625: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_1560, type, sK626: (int > real) > (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_1561, type, sK627: set_complex > (complex > real) > (complex > real) > complex).
% 32.77/9.02  thf(func_def_1562, type, sK628: real > real).
% 32.77/9.02  thf(func_def_1563, type, sK629: (int > $o) > list_int > nat).
% 32.77/9.02  thf(func_def_1564, type, sK630: (int > $o) > list_int > int).
% 32.77/9.02  thf(func_def_1565, type, sK631: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1566, type, sK632: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1567, type, sK633: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1568, type, sK634: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1569, type, sK635: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1570, type, sK636: list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1571, type, sK637: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_1572, type, sK638: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_1573, type, sK639: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_1574, type, sK640: set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_1575, type, sK641: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_1576, type, sK642: set_nat > (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_1577, type, sK643: set_nat > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1578, type, sK644: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1579, type, sK645: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1580, type, sK646: (set_real > $o) > set_real > set_real).
% 32.77/9.02  thf(func_def_1581, type, sK647: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_1582, type, sK648: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_1583, type, sK649: (option_num > option_num > $o) > option_num > option_num > num).
% 32.77/9.02  thf(func_def_1584, type, sK650: (option_num > option_num > $o) > option_num > option_num > num).
% 32.77/9.02  thf(func_def_1585, type, sK651: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1586, type, sK652: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1587, type, sK653: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_1588, type, sK654: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_1589, type, sK655: real > (real > $o) > real).
% 32.77/9.02  thf(func_def_1590, type, sK656: real > (real > $o) > real).
% 32.77/9.02  thf(func_def_1591, type, sK657: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1592, type, sK658: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1593, type, sK659: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1594, type, sK660: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1595, type, sK661: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1596, type, sK662: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1597, type, sK663: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1598, type, sK664: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1599, type, sK665: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1600, type, sK666: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1601, type, sK667: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1602, type, sK668: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1603, type, sK669: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1604, type, sK670: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1605, type, sK671: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1606, type, sK672: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1607, type, sK673: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1608, type, sK674: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1609, type, sK675: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1610, type, sK676: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1611, type, sK677: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1612, type, sK678: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1613, type, sK679: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1614, type, sK680: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1615, type, sK681: nat > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1616, type, sK682: nat > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1617, type, sK683: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1618, type, sK684: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1619, type, sK685: (int > int > set_set_nat) > set_nat > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1620, type, sK686: (int > int > set_set_nat) > set_nat > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1621, type, sK687: (set_nat > $o) > (nat > nat) > set_nat).
% 32.77/9.02  thf(func_def_1622, type, sK688: (set_nat > $o) > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_1623, type, sK689: (int > rat) > (int > rat) > set_int > (rat > rat > $o) > int).
% 32.77/9.02  thf(func_def_1624, type, sK690: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1625, type, sK691: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1626, type, sK692: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1627, type, sK693: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1628, type, sK694: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1629, type, sK695: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1630, type, sK696: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1631, type, sK697: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1632, type, sK698: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1633, type, sK699: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1634, type, sK700: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1635, type, sK701: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_1636, type, sK702: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1637, type, sK703: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1638, type, sK704: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1639, type, sK705: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1640, type, sK706: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1641, type, sK707: (rat > rat > $o) > set_complex > (complex > rat) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1642, type, sK708: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1643, type, sK709: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1644, type, sK710: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1645, type, sK711: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1646, type, sK712: real > int).
% 32.77/9.02  thf(func_def_1647, type, sK713: produc7036089656553540234on_num > num).
% 32.77/9.02  thf(func_def_1648, type, sK714: produc7036089656553540234on_num > num > num > $o).
% 32.77/9.02  thf(func_def_1649, type, sK715: produc7036089656553540234on_num > num > num > $o).
% 32.77/9.02  thf(func_def_1650, type, sK716: produc7036089656553540234on_num > num).
% 32.77/9.02  thf(func_def_1651, type, sK717: produc7036089656553540234on_num > num).
% 32.77/9.02  thf(func_def_1652, type, sK718: produc7036089656553540234on_num > num > num > $o).
% 32.77/9.02  thf(func_def_1653, type, sK719: produc7036089656553540234on_num > option_num).
% 32.77/9.02  thf(func_def_1654, type, sK720: set_set_nat > (set_set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1655, type, sK721: set_set_nat > (set_set_nat > $o) > set_set_nat).
% 32.77/9.02  thf(func_def_1656, type, sK722: set_nat > set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1657, type, sK723: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1658, type, sK724: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1659, type, sK725: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1660, type, sK726: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1661, type, sK727: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1662, type, sK728: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1663, type, sK729: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1664, type, sK730: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1665, type, sK731: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1666, type, sK732: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1667, type, sK733: set_nat > (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_1668, type, sK734: set_nat > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1669, type, sK735: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1670, type, sK736: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1671, type, sK737: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1672, type, sK738: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1673, type, sK739: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1674, type, sK740: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1675, type, sK741: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1676, type, sK742: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1677, type, sK743: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1678, type, sK744: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1679, type, sK745: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1680, type, sK746: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1681, type, sK747: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1682, type, sK748: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1683, type, sK749: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1684, type, sK750: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1685, type, sK751: int > int > int).
% 32.77/9.02  thf(func_def_1686, type, sK752: int > int > int).
% 32.77/9.02  thf(func_def_1687, type, sK753: set_set_int > set_int).
% 32.77/9.02  thf(func_def_1688, type, sK754: nat > nat > nat).
% 32.77/9.02  thf(func_def_1689, type, sK755: set_rat > rat).
% 32.77/9.02  thf(func_def_1690, type, sK756: (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_1691, type, sK757: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_1692, type, sK758: real > (real > real) > (real > real) > real > real).
% 32.77/9.02  thf(func_def_1693, type, sK759: (real > real) > (real > real) > (real > real) > real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_1694, type, sK760: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_1695, type, sK761: real > real > (real > real) > (real > real) > real).
% 32.77/9.02  thf(func_def_1696, type, sK762: set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1697, type, sK763: set_nat > rat > rat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1698, type, sK764: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_1699, type, sK765: (set_num > $o) > num).
% 32.77/9.02  thf(func_def_1700, type, sK766: (set_num > $o) > set_num).
% 32.77/9.02  thf(func_def_1701, type, sK767: rat > int).
% 32.77/9.02  thf(func_def_1702, type, sK768: produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > int > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_1703, type, sK769: produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > int > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1704, type, sK770: (num > rat) > num).
% 32.77/9.02  thf(func_def_1705, type, sK771: (num > rat) > num).
% 32.77/9.02  thf(func_def_1706, type, sK772: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1707, type, sK773: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1708, type, sK774: rat > int).
% 32.77/9.02  thf(func_def_1709, type, sK775: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1710, type, sK776: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1711, type, sK777: (num > rat) > num).
% 32.77/9.02  thf(func_def_1712, type, sK778: (num > rat) > num).
% 32.77/9.02  thf(func_def_1713, type, sK779: (real > $o) > real).
% 32.77/9.02  thf(func_def_1714, type, sK780: (real > $o) > real).
% 32.77/9.02  thf(func_def_1715, type, sK781: (real > $o) > nat).
% 32.77/9.02  thf(func_def_1716, type, sK782: ($o > $o) > list_o > nat).
% 32.77/9.02  thf(func_def_1717, type, sK783: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1718, type, sK784: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_1719, type, sK785: list_VEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1720, type, sK786: set_nat > nat).
% 32.77/9.02  thf(func_def_1721, type, sK787: product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_1722, type, sK788: product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_1723, type, sK789: (int > nat) > (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_1724, type, sK790: (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_1725, type, sK791: set_rat > rat).
% 32.77/9.02  thf(func_def_1726, type, sK792: (complex > int) > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_1727, type, sK793: (rat > rat > $o) > (nat > rat) > set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1728, type, sK794: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1729, type, sK795: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1730, type, sK796: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1731, type, sK797: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_1732, type, sK798: option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1733, type, sK799: option_nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1734, type, sK800: option_nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1735, type, sK801: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1736, type, sK802: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_1737, type, sK803: option_nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1738, type, sK804: option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1739, type, sK805: option_nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1740, type, sK806: option_nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1741, type, sK807: option_nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1742, type, sK808: set_nat > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_1743, type, sK809: int > nat).
% 32.77/9.02  thf(func_def_1744, type, sK810: int > nat).
% 32.77/9.02  thf(func_def_1745, type, sK811: (complex > real) > (complex > real) > (real > real > $o) > set_complex > complex).
% 32.77/9.02  thf(func_def_1746, type, sK812: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1747, type, sK813: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1748, type, sK814: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1749, type, sK815: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_1750, type, sK816: (set_complex > $o) > (complex > rat) > set_complex).
% 32.77/9.02  thf(func_def_1751, type, sK817: (set_complex > $o) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1752, type, sK818: int > nat).
% 32.77/9.02  thf(func_def_1753, type, sK819: (list_int > $o) > list_int).
% 32.77/9.02  thf(func_def_1754, type, sK820: (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_1755, type, sK821: nat > nat > nat).
% 32.77/9.02  thf(func_def_1756, type, sK822: nat > nat > nat).
% 32.77/9.02  thf(func_def_1757, type, sK823: nat > nat > nat).
% 32.77/9.02  thf(func_def_1758, type, sK824: (int > rat) > set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_1759, type, sK825: (nat > real) > real > nat).
% 32.77/9.02  thf(func_def_1760, type, sK826: produc7773217078559923341nt_int > int).
% 32.77/9.02  thf(func_def_1761, type, sK827: produc7773217078559923341nt_int > int).
% 32.77/9.02  thf(func_def_1762, type, sK828: produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1763, type, sK829: (set_num > $o) > num).
% 32.77/9.02  thf(func_def_1764, type, sK830: (set_num > $o) > set_num).
% 32.77/9.02  thf(func_def_1765, type, sK831: (rat > real) > rat).
% 32.77/9.02  thf(func_def_1766, type, sK832: (rat > real) > rat).
% 32.77/9.02  thf(func_def_1767, type, sK833: (set_nat > $o) > set_nat > set_nat).
% 32.77/9.02  thf(func_def_1768, type, sK834: (rat > num) > rat).
% 32.77/9.02  thf(func_def_1769, type, sK835: (rat > num) > rat).
% 32.77/9.02  thf(func_def_1770, type, sK836: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1771, type, sK837: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1772, type, sK838: real > (real > real) > real).
% 32.77/9.02  thf(func_def_1773, type, sK839: (complex > nat) > (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_1774, type, sK840: (complex > nat) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_1775, type, sK841: (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_1776, type, sK842: (int > rat) > (int > rat) > set_int > set_int > (int > int) > int).
% 32.77/9.02  thf(func_def_1777, type, sK843: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1778, type, sK844: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1779, type, sK845: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1780, type, sK846: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_1781, type, sK847: int > int > int > int).
% 32.77/9.02  thf(func_def_1782, type, sK848: code_integer > code_integer > (real > code_integer) > set_real > real).
% 32.77/9.02  thf(func_def_1783, type, sK849: (real > code_integer) > set_real > real).
% 32.77/9.02  thf(func_def_1784, type, sK850: (num > num) > num).
% 32.77/9.02  thf(func_def_1785, type, sK851: (num > num) > num).
% 32.77/9.02  thf(func_def_1786, type, sK852: list_o > $o > $o).
% 32.77/9.02  thf(func_def_1787, type, sK853: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1788, type, sK854: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_1789, type, sK855: nat > nat).
% 32.77/9.02  thf(func_def_1790, type, sK856: (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1791, type, sK857: (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_1792, type, sK858: (int > rat) > int).
% 32.77/9.02  thf(func_def_1793, type, sK859: (int > rat) > int).
% 32.77/9.02  thf(func_def_1794, type, sK860: list_VEBT_VEBT > set_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1795, type, sK861: set_rat > rat).
% 32.77/9.02  thf(func_def_1796, type, sK862: int > int).
% 32.77/9.02  thf(func_def_1797, type, sK863: option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1798, type, sK864: filter_nat > nat).
% 32.77/9.02  thf(func_def_1799, type, sK865: set_real > set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_1800, type, sK866: set_real > (real > int) > set_real > real).
% 32.77/9.02  thf(func_def_1801, type, sK867: int > list_int > int).
% 32.77/9.02  thf(func_def_1802, type, sK868: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1803, type, sK869: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1804, type, sK870: nat > nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1805, type, sK871: nat > nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1806, type, sK872: set_nat > (nat > rat) > (nat > nat) > (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1807, type, sK873: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1808, type, sK874: (complex > num) > (set_complex > $o) > complex).
% 32.77/9.02  thf(func_def_1809, type, sK875: (complex > num) > (set_complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_1810, type, sK876: int > int).
% 32.77/9.02  thf(func_def_1811, type, sK877: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1812, type, sK878: (rat > int) > rat).
% 32.77/9.02  thf(func_def_1813, type, sK879: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1814, type, sK880: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1815, type, sK881: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1816, type, sK882: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1817, type, sK883: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1818, type, sK884: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1819, type, sK885: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1820, type, sK886: code_integer > code_integer).
% 32.77/9.02  thf(func_def_1821, type, sK887: set_int > set_int > int).
% 32.77/9.02  thf(func_def_1822, type, sK888: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1823, type, sK889: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_1824, type, sK890: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1825, type, sK891: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_1826, type, sK892: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1827, type, sK893: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1828, type, sK894: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1829, type, sK895: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1830, type, sK896: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1831, type, sK897: list_int > set_int > int).
% 32.77/9.02  thf(func_def_1832, type, sK898: rat > rat > nat).
% 32.77/9.02  thf(func_def_1833, type, sK899: (nat > complex) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_1834, type, sK900: set_int > (int > complex) > (int > complex) > (complex > complex > $o) > int).
% 32.77/9.02  thf(func_def_1835, type, sK901: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_1836, type, sK902: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_1837, type, sK903: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_1838, type, sK904: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_1839, type, sK905: nat > nat).
% 32.77/9.02  thf(func_def_1840, type, sK906: nat > nat > nat).
% 32.77/9.02  thf(func_def_1841, type, sK907: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1842, type, sK908: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1843, type, sK909: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1844, type, sK910: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_1845, type, sK911: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1846, type, sK912: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1847, type, sK913: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1848, type, sK914: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1849, type, sK915: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1850, type, sK916: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1851, type, sK917: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1852, type, sK918: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1853, type, sK919: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1854, type, sK920: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1855, type, sK921: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1856, type, sK922: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1857, type, sK923: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1858, type, sK924: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1859, type, sK925: nat > list_int).
% 32.77/9.02  thf(func_def_1860, type, sK926: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1861, type, sK927: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_1862, type, sK928: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_1863, type, sK929: set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_1864, type, sK930: set_complex > (complex > complex) > complex).
% 32.77/9.02  thf(func_def_1865, type, sK931: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1866, type, sK932: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1867, type, sK933: set_nat > (nat > int) > nat).
% 32.77/9.02  thf(func_def_1868, type, sK934: (nat > set_int) > nat).
% 32.77/9.02  thf(func_def_1869, type, sK935: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1870, type, sK936: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1871, type, sK937: set_complex > complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_1872, type, sK938: real > nat).
% 32.77/9.02  thf(func_def_1873, type, sK939: real > nat).
% 32.77/9.02  thf(func_def_1874, type, sK940: nat > nat).
% 32.77/9.02  thf(func_def_1875, type, sK941: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1876, type, sK942: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1877, type, sK943: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_1878, type, sK944: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_1879, type, sK945: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1880, type, sK946: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_1881, type, sK947: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1882, type, sK948: nat > option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1883, type, sK949: nat > option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1884, type, sK950: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1885, type, sK951: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1886, type, sK952: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1887, type, sK953: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1888, type, sK954: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1889, type, sK955: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1890, type, sK956: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1891, type, sK957: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_1892, type, sK958: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1893, type, sK959: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1894, type, sK960: rat > rat > rat).
% 32.77/9.02  thf(func_def_1895, type, sK961: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_1896, type, sK962: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_1897, type, sK963: (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1898, type, sK964: (set_int > $o) > set_int > int).
% 32.77/9.02  thf(func_def_1899, type, sK965: (set_int > $o) > set_int > set_int).
% 32.77/9.02  thf(func_def_1900, type, sK966: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1901, type, sK967: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1902, type, sK968: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1903, type, sK969: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_1904, type, sK970: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1905, type, sK971: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1906, type, sK972: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_1907, type, sK973: list_o > ($o > $o) > nat).
% 32.77/9.02  thf(func_def_1908, type, sK974: list_o > ($o > $o) > $o).
% 32.77/9.02  thf(func_def_1909, type, sK975: (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_1910, type, sK976: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1911, type, sK977: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1912, type, sK978: real > real > nat).
% 32.77/9.02  thf(func_def_1913, type, sK979: nat > list_nat).
% 32.77/9.02  thf(func_def_1914, type, sK980: nat > nat).
% 32.77/9.02  thf(func_def_1915, type, sK981: set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_1916, type, sK982: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1917, type, sK983: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1918, type, sK984: nat > (nat > int > $o) > list_int).
% 32.77/9.02  thf(func_def_1919, type, sK985: nat > (nat > int > $o) > nat).
% 32.77/9.02  thf(func_def_1920, type, sK986: nat > (nat > int > $o) > int).
% 32.77/9.02  thf(func_def_1921, type, sK987: list_int > nat > (nat > int > $o) > nat).
% 32.77/9.02  thf(func_def_1922, type, sK988: (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1923, type, sK989: rat > rat > rat > rat).
% 32.77/9.02  thf(func_def_1924, type, sK990: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1925, type, sK991: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_1926, type, sK992: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1927, type, sK993: real > (real > real) > real).
% 32.77/9.02  thf(func_def_1928, type, sK994: (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_1929, type, sK995: (int > int > $o) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1930, type, sK996: (int > int > $o) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_1931, type, sK997: real > (nat > real) > real).
% 32.77/9.02  thf(func_def_1932, type, sK998: (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_1933, type, sK999: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_1934, type, sK1000: rat > rat).
% 32.77/9.02  thf(func_def_1935, type, sK1001: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_1936, type, sK1002: option_nat > nat).
% 32.77/9.02  thf(func_def_1937, type, sK1003: nat > nat > nat).
% 32.77/9.02  thf(func_def_1938, type, sK1004: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1939, type, sK1005: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1940, type, sK1006: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1941, type, sK1007: vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_1942, type, sK1008: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1943, type, sK1009: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1944, type, sK1010: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_1945, type, sK1011: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1946, type, sK1012: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1947, type, sK1013: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1948, type, sK1014: (nat > real) > nat).
% 32.77/9.02  thf(func_def_1949, type, sK1015: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1950, type, sK1016: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_1951, type, sK1017: complex > real).
% 32.77/9.02  thf(func_def_1952, type, sK1018: complex > real).
% 32.77/9.02  thf(func_def_1953, type, sK1019: list_set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_1954, type, sK1020: (nat > num) > nat).
% 32.77/9.02  thf(func_def_1955, type, sK1021: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1956, type, sK1022: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1957, type, sK1023: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1958, type, sK1024: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1959, type, sK1025: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1960, type, sK1026: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1961, type, sK1027: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1962, type, sK1028: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1963, type, sK1029: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1964, type, sK1030: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1965, type, sK1031: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_1966, type, sK1032: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1967, type, sK1033: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1968, type, sK1034: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_1969, type, sK1035: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1970, type, sK1036: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_1971, type, sK1037: set_nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_1972, type, sK1038: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1973, type, sK1039: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1974, type, sK1040: set_real > (real > int) > set_real > real).
% 32.77/9.02  thf(func_def_1975, type, sK1041: (real > int) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_1976, type, sK1042: (real > int) > real).
% 32.77/9.02  thf(func_def_1977, type, sK1043: (real > int) > real).
% 32.77/9.02  thf(func_def_1978, type, sK1044: rat > rat).
% 32.77/9.02  thf(func_def_1979, type, sK1045: set_real > (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_1980, type, sK1046: set_real > set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_1981, type, sK1047: nat > nat > nat).
% 32.77/9.02  thf(func_def_1982, type, sK1048: (int > $o) > set_int > int > int).
% 32.77/9.02  thf(func_def_1983, type, sK1049: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1984, type, sK1050: int > set_int > int > int).
% 32.77/9.02  thf(func_def_1985, type, sK1051: int > (int > $o) > set_int > int).
% 32.77/9.02  thf(func_def_1986, type, sK1052: int > int > int > int).
% 32.77/9.02  thf(func_def_1987, type, sK1053: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1988, type, sK1054: real > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1989, type, sK1055: real > (real > $o) > (real > $o) > real).
% 32.77/9.02  thf(func_def_1990, type, sK1056: (num > $o) > (num > $o) > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1991, type, sK1057: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1992, type, sK1058: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_1993, type, sK1059: set_real > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_1994, type, sK1060: set_rat > rat > rat).
% 32.77/9.02  thf(func_def_1995, type, sK1061: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_1996, type, sK1062: produc2285326912895808259nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_1997, type, sK1063: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_1998, type, sK1064: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_1999, type, sK1065: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2000, type, sK1066: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2001, type, sK1067: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2002, type, sK1068: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2003, type, sK1069: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2004, type, sK1070: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2005, type, sK1071: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2006, type, sK1072: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2007, type, sK1073: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2008, type, sK1074: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2009, type, sK1075: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2010, type, sK1076: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2011, type, sK1077: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2012, type, sK1078: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2013, type, sK1079: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2014, type, sK1080: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2015, type, sK1081: real > (real > real) > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2016, type, sK1082: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2017, type, sK1083: complex > set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2018, type, sK1084: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2019, type, sK1085: (nat > real) > nat).
% 32.77/9.02  thf(func_def_2020, type, sK1086: (nat > real) > nat).
% 32.77/9.02  thf(func_def_2021, type, sK1087: (real > int) > real).
% 32.77/9.02  thf(func_def_2022, type, sK1088: (real > int) > real).
% 32.77/9.02  thf(func_def_2023, type, sK1089: set_complex > (complex > nat) > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2024, type, sK1090: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2025, type, sK1091: (num > num) > num).
% 32.77/9.02  thf(func_def_2026, type, sK1092: (num > num) > num).
% 32.77/9.02  thf(func_def_2027, type, sK1093: nat > nat).
% 32.77/9.02  thf(func_def_2028, type, sK1094: int > list_int > nat).
% 32.77/9.02  thf(func_def_2029, type, sK1095: set_int > (int > int) > int).
% 32.77/9.02  thf(func_def_2030, type, sK1096: produc2285326912895808259nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_2031, type, sK1097: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2032, type, sK1098: $o > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2033, type, sK1099: $o > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2034, type, sK1100: $o > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2035, type, sK1101: $o > vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2036, type, sK1102: $o > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2037, type, sK1103: $o > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2038, type, sK1104: $o > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2039, type, sK1105: $o > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2040, type, sK1106: vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_2041, type, sK1107: int > nat).
% 32.77/9.02  thf(func_def_2042, type, sK1108: int > nat).
% 32.77/9.02  thf(func_def_2043, type, sK1109: real > nat).
% 32.77/9.02  thf(func_def_2044, type, sK1110: set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_2045, type, sK1111: int > nat).
% 32.77/9.02  thf(func_def_2046, type, sK1112: set_int > int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2047, type, sK1113: int > set_int > int > int).
% 32.77/9.02  thf(func_def_2048, type, sK1114: int > set_int > int > int).
% 32.77/9.02  thf(func_def_2049, type, sK1115: (int > $o) > set_int > int > int).
% 32.77/9.02  thf(func_def_2050, type, sK1116: (num > num) > num).
% 32.77/9.02  thf(func_def_2051, type, sK1117: (num > num) > num).
% 32.77/9.02  thf(func_def_2052, type, sK1118: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2053, type, sK1119: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2054, type, sK1120: (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2055, type, sK1121: (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2056, type, sK1122: $o > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2057, type, sK1123: $o > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2058, type, sK1124: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2059, type, sK1125: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2060, type, sK1126: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2061, type, sK1127: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2062, type, sK1128: $o > vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2063, type, sK1129: $o > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2064, type, sK1130: $o > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2065, type, sK1131: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2066, type, sK1132: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2067, type, sK1133: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2068, type, sK1134: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2069, type, sK1135: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2070, type, sK1136: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2071, type, sK1137: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2072, type, sK1138: rat > rat).
% 32.77/9.02  thf(func_def_2073, type, sK1139: rat > nat).
% 32.77/9.02  thf(func_def_2074, type, sK1140: rat > rat).
% 32.77/9.02  thf(func_def_2075, type, sK1141: produc7773217078559923341nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_2076, type, sK1142: produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2077, type, sK1143: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_2078, type, sK1144: product_prod_int_int > (int > int > set_int) > int > int).
% 32.77/9.02  thf(func_def_2079, type, sK1145: product_prod_int_int > (int > int > set_int) > int > int).
% 32.77/9.02  thf(func_def_2080, type, sK1146: set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_2081, type, sK1147: set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_2082, type, sK1148: real > real).
% 32.77/9.02  thf(func_def_2083, type, sK1149: (int > $o) > int).
% 32.77/9.02  thf(func_def_2084, type, sK1150: int > set_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2085, type, sK1151: int > set_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2086, type, sK1152: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2087, type, sK1153: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2088, type, sK1154: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2089, type, sK1155: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2090, type, sK1156: (int > $o) > set_int > int > int).
% 32.77/9.02  thf(func_def_2091, type, sK1157: set_complex > set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_2092, type, sK1158: set_complex > (complex > rat) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_2093, type, sK1159: int > int > (int > int > $o) > int).
% 32.77/9.02  thf(func_def_2094, type, sK1160: int > int > (int > int > $o) > int).
% 32.77/9.02  thf(func_def_2095, type, sK1161: real > real).
% 32.77/9.02  thf(func_def_2096, type, sK1162: real > (real > $o) > real).
% 32.77/9.02  thf(func_def_2097, type, sK1163: real > (real > $o) > real).
% 32.77/9.02  thf(func_def_2098, type, sK1164: set_int > set_int > (int > complex) > int).
% 32.77/9.02  thf(func_def_2099, type, sK1165: (real > real) > real).
% 32.77/9.02  thf(func_def_2100, type, sK1166: (real > real) > real).
% 32.77/9.02  thf(func_def_2101, type, sK1167: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2102, type, sK1168: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2103, type, sK1169: int > int > int > int).
% 32.77/9.02  thf(func_def_2104, type, sK1170: int > int > int > int).
% 32.77/9.02  thf(func_def_2105, type, sK1171: produc8763457246119570046nteger > code_integer).
% 32.77/9.02  thf(func_def_2106, type, sK1172: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2107, type, sK1173: produc8763457246119570046nteger > code_integer).
% 32.77/9.02  thf(func_def_2108, type, sK1174: real > (real > real) > real).
% 32.77/9.02  thf(func_def_2109, type, sK1175: int > set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_2110, type, sK1176: (real > real) > real).
% 32.77/9.02  thf(func_def_2111, type, sK1177: (real > real) > real).
% 32.77/9.02  thf(func_def_2112, type, sK1178: set_real > set_real > real).
% 32.77/9.02  thf(func_def_2113, type, sK1179: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2114, type, sK1180: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2115, type, sK1181: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2116, type, sK1182: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2117, type, sK1183: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2118, type, sK1184: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2119, type, sK1185: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2120, type, sK1186: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2121, type, sK1187: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2122, type, sK1188: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2123, type, sK1189: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2124, type, sK1190: product_prod_num_num > num).
% 32.77/9.02  thf(func_def_2125, type, sK1191: (set_real > $o) > real).
% 32.77/9.02  thf(func_def_2126, type, sK1192: (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_2127, type, sK1193: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_2128, type, sK1194: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2129, type, sK1195: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2130, type, sK1196: list_nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2131, type, sK1197: list_nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2132, type, sK1198: real > real).
% 32.77/9.02  thf(func_def_2133, type, sK1199: rat > rat).
% 32.77/9.02  thf(func_def_2134, type, sK1200: (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_2135, type, sK1201: (set_int > $o) > int).
% 32.77/9.02  thf(func_def_2136, type, sK1202: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2137, type, sK1203: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2138, type, sK1204: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2139, type, sK1205: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2140, type, sK1206: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2141, type, sK1207: (nat > int) > int > nat > nat).
% 32.77/9.02  thf(func_def_2142, type, sK1208: (nat > int) > nat > nat).
% 32.77/9.02  thf(func_def_2143, type, sK1209: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_2144, type, sK1210: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_2145, type, sK1211: real > nat > real > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_2146, type, sK1212: real > nat > real > (nat > real > real) > nat).
% 32.77/9.02  thf(func_def_2147, type, sK1213: real > real > (real > real) > (nat > real > real) > nat > real).
% 32.77/9.02  thf(func_def_2148, type, sK1214: real > real).
% 32.77/9.02  thf(func_def_2149, type, sK1215: set_complex > (set_complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_2150, type, sK1216: set_complex > (set_complex > $o) > complex).
% 32.77/9.02  thf(func_def_2151, type, sK1217: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2152, type, sK1218: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2153, type, sK1219: nat > nat).
% 32.77/9.02  thf(func_def_2154, type, sK1220: int > int).
% 32.77/9.02  thf(func_def_2155, type, sK1221: rat > rat > rat).
% 32.77/9.02  thf(func_def_2156, type, sK1222: produc7773217078559923341nt_int > complex > ((int > option6357759511663192854e_term) > product_prod_int_int > set_complex) > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2157, type, sK1223: produc7773217078559923341nt_int > complex > ((int > option6357759511663192854e_term) > product_prod_int_int > set_complex) > product_prod_int_int).
% 32.77/9.02  thf(func_def_2158, type, sK1224: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2159, type, sK1225: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2160, type, sK1226: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2161, type, sK1227: real > real).
% 32.77/9.02  thf(func_def_2162, type, sK1228: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2163, type, sK1229: (nat > rat) > set_complex > (complex > rat) > (complex > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_2164, type, sK1230: set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_2165, type, sK1231: (nat > num) > nat).
% 32.77/9.02  thf(func_def_2166, type, sK1232: (real > real) > real > set_real > real).
% 32.77/9.02  thf(func_def_2167, type, sK1233: (nat > set_int) > nat).
% 32.77/9.02  thf(func_def_2168, type, sK1234: complex > int).
% 32.77/9.02  thf(func_def_2169, type, sK1235: (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2170, type, sK1236: (real > real) > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2171, type, sK1237: (int > rat) > int).
% 32.77/9.02  thf(func_def_2172, type, sK1238: (int > rat) > int).
% 32.77/9.02  thf(func_def_2173, type, sK1239: int > int).
% 32.77/9.02  thf(func_def_2174, type, sK1240: nat > (nat > vEBT_VEBT > $o) > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2175, type, sK1241: list_VEBT_VEBT > nat > (nat > vEBT_VEBT > $o) > nat).
% 32.77/9.02  thf(func_def_2176, type, sK1242: nat > (nat > vEBT_VEBT > $o) > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2177, type, sK1243: nat > (nat > vEBT_VEBT > $o) > nat).
% 32.77/9.02  thf(func_def_2178, type, sK1244: set_real > (real > real) > (real > real) > (real > real) > real).
% 32.77/9.02  thf(func_def_2179, type, sK1245: (real > real) > set_real > set_real > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2180, type, sK1246: (real > real) > (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2181, type, sK1247: (real > real) > (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2182, type, sK1248: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2183, type, sK1249: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2184, type, sK1250: set_real > set_real > set_real > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2185, type, sK1251: (real > real > $o) > real).
% 32.77/9.02  thf(func_def_2186, type, sK1252: option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2187, type, sK1253: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2188, type, sK1254: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2189, type, sK1255: nat > (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2190, type, sK1256: list_nat > nat > (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2191, type, sK1257: nat > (nat > nat > $o) > list_nat).
% 32.77/9.02  thf(func_def_2192, type, sK1258: nat > (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2193, type, sK1259: (int > $o) > int).
% 32.77/9.02  thf(func_def_2194, type, sK1260: (int > $o) > int).
% 32.77/9.02  thf(func_def_2195, type, sK1261: nat > nat > nat).
% 32.77/9.02  thf(func_def_2196, type, sK1262: nat > nat > nat).
% 32.77/9.02  thf(func_def_2197, type, sK1263: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_2198, type, sK1264: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_2199, type, sK1265: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_2200, type, sK1266: (rat > rat > $o) > rat).
% 32.77/9.02  thf(func_def_2201, type, sK1267: num > num > num).
% 32.77/9.02  thf(func_def_2202, type, sK1268: num > num > num > num).
% 32.77/9.02  thf(func_def_2203, type, sK1269: num > num > num > num).
% 32.77/9.02  thf(func_def_2204, type, sK1270: num > num > num > num).
% 32.77/9.02  thf(func_def_2205, type, sK1271: num > num > num > num).
% 32.77/9.02  thf(func_def_2206, type, sK1272: num > num > num > num).
% 32.77/9.02  thf(func_def_2207, type, sK1273: num > num > num > num).
% 32.77/9.02  thf(func_def_2208, type, sK1274: num > num > num > num).
% 32.77/9.02  thf(func_def_2209, type, sK1275: num > num > num).
% 32.77/9.02  thf(func_def_2210, type, sK1276: num > num > num > num).
% 32.77/9.02  thf(func_def_2211, type, sK1277: num > num > num > num).
% 32.77/9.02  thf(func_def_2212, type, sK1278: num > num > num > num).
% 32.77/9.02  thf(func_def_2213, type, sK1279: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2214, type, sK1280: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2215, type, sK1281: real > real).
% 32.77/9.02  thf(func_def_2216, type, sK1282: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2217, type, sK1283: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2218, type, sK1284: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2219, type, sK1285: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2220, type, sK1286: product_prod_nat_nat > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2221, type, sK1287: set_int > set_int > (real > int) > (int > real) > int).
% 32.77/9.02  thf(func_def_2222, type, sK1288: (int > real) > set_real > set_real > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2223, type, sK1289: set_real > set_real > (real > int) > set_int > set_int > real).
% 32.77/9.02  thf(func_def_2224, type, sK1290: (int > real) > (real > int) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2225, type, sK1291: (int > complex) > set_int > int).
% 32.77/9.02  thf(func_def_2226, type, sK1292: (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_2227, type, sK1293: (int > complex) > (real > int) > set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_2228, type, sK1294: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2229, type, sK1295: produc5542196010084753463at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2230, type, sK1296: produc5542196010084753463at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2231, type, sK1297: produc5542196010084753463at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2232, type, sK1298: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2233, type, sK1299: produc5542196010084753463at_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2234, type, sK1300: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2235, type, sK1301: set_real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2236, type, sK1302: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2237, type, sK1303: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2238, type, sK1304: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_2239, type, sK1305: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_2240, type, sK1306: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2241, type, sK1307: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2242, type, sK1308: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2243, type, sK1309: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2244, type, sK1310: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2245, type, sK1311: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2246, type, sK1312: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2247, type, sK1313: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2248, type, sK1314: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2249, type, sK1315: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2250, type, sK1316: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2251, type, sK1317: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2252, type, sK1318: vEBT_VEBT > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2253, type, sK1319: vEBT_VEBT > nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2254, type, sK1320: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2255, type, sK1321: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2256, type, sK1322: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2257, type, sK1323: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2258, type, sK1324: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2259, type, sK1325: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2260, type, sK1326: set_real > list_real > real).
% 32.77/9.02  thf(func_def_2261, type, sK1327: set_real > set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_2262, type, sK1328: (real > rat) > set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_2263, type, sK1329: (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_2264, type, sK1330: set_nat > nat).
% 32.77/9.02  thf(func_def_2265, type, sK1331: nat > set_nat > nat).
% 32.77/9.02  thf(func_def_2266, type, sK1332: set_int > set_int > (int > complex) > set_complex > set_complex > int).
% 32.77/9.02  thf(func_def_2267, type, sK1333: set_complex > set_complex > (int > complex) > (complex > int) > complex).
% 32.77/9.02  thf(func_def_2268, type, sK1334: set_int > (int > real) > (complex > real) > (int > complex) > int).
% 32.77/9.02  thf(func_def_2269, type, sK1335: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2270, type, sK1336: set_int > (complex > int) > set_int > (int > complex) > int).
% 32.77/9.02  thf(func_def_2271, type, sK1337: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_2272, type, sK1338: set_int > set_complex > (complex > int) > set_int > set_complex > complex).
% 32.77/9.02  thf(func_def_2273, type, sK1339: nat > nat > nat).
% 32.77/9.02  thf(func_def_2274, type, sK1340: (real > real) > real).
% 32.77/9.02  thf(func_def_2275, type, sK1341: (real > real) > real).
% 32.77/9.02  thf(func_def_2276, type, sK1342: real > real > real > real).
% 32.77/9.02  thf(func_def_2277, type, sK1343: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_2278, type, sK1344: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2279, type, sK1345: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2280, type, sK1346: real > real).
% 32.77/9.02  thf(func_def_2281, type, sK1347: complex > complex).
% 32.77/9.02  thf(func_def_2282, type, sK1348: complex > real).
% 32.77/9.02  thf(func_def_2283, type, sK1349: real > real).
% 32.77/9.02  thf(func_def_2284, type, sK1350: (nat > rat) > (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_2285, type, sK1351: nat > list_o).
% 32.77/9.02  thf(func_def_2286, type, sK1352: (nat > $o) > list_nat > nat).
% 32.77/9.02  thf(func_def_2287, type, sK1353: num > set_num > num).
% 32.77/9.02  thf(func_def_2288, type, sK1354: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2289, type, sK1355: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2290, type, sK1356: set_int > (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_2291, type, sK1357: set_int > (set_int > $o) > int).
% 32.77/9.02  thf(func_def_2292, type, sK1358: option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2293, type, sK1359: option_nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2294, type, sK1360: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2295, type, sK1361: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2296, type, sK1362: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2297, type, sK1363: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2298, type, sK1364: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2299, type, sK1365: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2300, type, sK1366: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2301, type, sK1367: vEBT_VEBT > option_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2302, type, sK1368: produc1908205239877642774nteger > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2303, type, sK1369: produc1908205239877642774nteger > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2304, type, sK1370: nat > nat).
% 32.77/9.02  thf(func_def_2305, type, sK1371: (set_int > $o) > set_int > set_int).
% 32.77/9.02  thf(func_def_2306, type, sK1372: complex > (int > int > set_complex) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2307, type, sK1373: complex > (int > int > set_complex) > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2308, type, sK1374: num > num).
% 32.77/9.02  thf(func_def_2309, type, sK1375: (nat > real) > real > nat).
% 32.77/9.02  thf(func_def_2310, type, sK1376: (nat > real) > real).
% 32.77/9.02  thf(func_def_2311, type, sK1377: set_num > num).
% 32.77/9.02  thf(func_def_2312, type, sK1378: nat > produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2313, type, sK1379: nat > produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2314, type, sK1380: set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_2315, type, sK1381: (complex > complex > $o) > (nat > complex) > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_2316, type, sK1382: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_2317, type, sK1383: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_2318, type, sK1384: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_2319, type, sK1385: (complex > complex > $o) > complex).
% 32.77/9.02  thf(func_def_2320, type, sK1386: num > num).
% 32.77/9.02  thf(func_def_2321, type, sK1387: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2322, type, sK1388: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2323, type, sK1389: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2324, type, sK1390: rat > int).
% 32.77/9.02  thf(func_def_2325, type, sK1391: int > int).
% 32.77/9.02  thf(func_def_2326, type, sK1392: set_int > int > int).
% 32.77/9.02  thf(func_def_2327, type, sK1393: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2328, type, sK1394: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2329, type, sK1395: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2330, type, sK1396: rat > rat > rat).
% 32.77/9.02  thf(func_def_2331, type, sK1397: (int > real) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2332, type, sK1398: option_num > num).
% 32.77/9.02  thf(func_def_2333, type, sK1399: set_complex > (complex > int) > (complex > int) > complex).
% 32.77/9.02  thf(func_def_2334, type, sK1400: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_2335, type, sK1401: (nat > real > real) > nat > real > nat).
% 32.77/9.02  thf(func_def_2336, type, sK1402: (nat > real > real) > nat > real > real).
% 32.77/9.02  thf(func_def_2337, type, sK1403: (real > real) > (nat > real > real) > nat > real > real).
% 32.77/9.02  thf(func_def_2338, type, sK1404: set_int > set_int > (int > int) > (int > int) > int).
% 32.77/9.02  thf(func_def_2339, type, sK1405: set_int > set_int > (int > int) > (int > int) > int).
% 32.77/9.02  thf(func_def_2340, type, sK1406: set_int > (int > real) > (int > real) > (int > int) > int).
% 32.77/9.02  thf(func_def_2341, type, sK1407: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_2342, type, sK1408: (int > int) > set_int > set_int > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2343, type, sK1409: set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_2344, type, sK1410: (int > int) > set_int > set_int > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2345, type, sK1411: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2346, type, sK1412: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2347, type, sK1413: (complex > int) > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_2348, type, sK1414: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2349, type, sK1415: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2350, type, sK1416: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2351, type, sK1417: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2352, type, sK1418: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2353, type, sK1419: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2354, type, sK1420: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2355, type, sK1421: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2356, type, sK1422: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2357, type, sK1423: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2358, type, sK1424: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2359, type, sK1425: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2360, type, sK1426: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2361, type, sK1427: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2362, type, sK1428: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2363, type, sK1429: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2364, type, sK1430: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2365, type, sK1431: set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_2366, type, sK1432: int > int).
% 32.77/9.02  thf(func_def_2367, type, sK1433: int > nat).
% 32.77/9.02  thf(func_def_2368, type, sK1434: (int > real) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2369, type, sK1435: produc1908205239877642774nteger > code_integer).
% 32.77/9.02  thf(func_def_2370, type, sK1436: produc1908205239877642774nteger > code_integer).
% 32.77/9.02  thf(func_def_2371, type, sK1437: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2372, type, sK1438: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2373, type, sK1439: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2374, type, sK1440: real > real > real).
% 32.77/9.02  thf(func_def_2375, type, sK1441: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2376, type, sK1442: (real > num) > real).
% 32.77/9.02  thf(func_def_2377, type, sK1443: (real > num) > real).
% 32.77/9.02  thf(func_def_2378, type, sK1444: nat > real > real).
% 32.77/9.02  thf(func_def_2379, type, sK1445: (nat > complex) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_2380, type, sK1446: (nat > complex) > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_2381, type, sK1447: produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2382, type, sK1448: produc7773217078559923341nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_2383, type, sK1449: (complex > rat) > (complex > int) > (int > rat) > set_int > set_complex > int).
% 32.77/9.02  thf(func_def_2384, type, sK1450: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2385, type, sK1451: (complex > real) > set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_2386, type, sK1452: (complex > real) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_2387, type, sK1453: nat > nat > nat).
% 32.77/9.02  thf(func_def_2388, type, sK1454: nat > nat > nat).
% 32.77/9.02  thf(func_def_2389, type, sK1455: nat > nat > nat).
% 32.77/9.02  thf(func_def_2390, type, sK1456: (num > int) > num).
% 32.77/9.02  thf(func_def_2391, type, sK1457: (num > int) > num).
% 32.77/9.02  thf(func_def_2392, type, sK1458: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2393, type, sK1459: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2394, type, sK1460: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2395, type, sK1461: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2396, type, sK1462: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2397, type, sK1463: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2398, type, sK1464: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2399, type, sK1465: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2400, type, sK1466: (set_complex > $o) > set_complex > complex).
% 32.77/9.02  thf(func_def_2401, type, sK1467: (set_complex > $o) > set_complex > set_complex).
% 32.77/9.02  thf(func_def_2402, type, sK1468: option_num > num).
% 32.77/9.02  thf(func_def_2403, type, sK1469: option_num > option_num > option_num > (num > num > num) > num).
% 32.77/9.02  thf(func_def_2404, type, sK1470: option_num > option_num > option_num > (num > num > num) > num).
% 32.77/9.02  thf(func_def_2405, type, sK1471: set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2406, type, sK1472: int > int > int).
% 32.77/9.02  thf(func_def_2407, type, sK1473: set_complex > (complex > nat) > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2408, type, sK1474: int > int).
% 32.77/9.02  thf(func_def_2409, type, sK1475: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2410, type, sK1476: set_int > set_int > (int > real) > set_real > set_real > int).
% 32.77/9.02  thf(func_def_2411, type, sK1477: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_2412, type, sK1478: set_int > (int > real) > (real > real) > (int > real) > int).
% 32.77/9.02  thf(func_def_2413, type, sK1479: (real > int) > set_int > (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_2414, type, sK1480: set_real > (real > int) > set_real > set_int > set_int > real).
% 32.77/9.02  thf(func_def_2415, type, sK1481: set_real > (real > int) > set_real > (int > real) > real).
% 32.77/9.02  thf(func_def_2416, type, sK1482: (real > nat) > (real > nat) > real).
% 32.77/9.02  thf(func_def_2417, type, sK1483: (real > nat) > real).
% 32.77/9.02  thf(func_def_2418, type, sK1484: (real > nat) > real).
% 32.77/9.02  thf(func_def_2419, type, sK1485: rat > rat > rat).
% 32.77/9.02  thf(func_def_2420, type, sK1486: (rat > num) > rat).
% 32.77/9.02  thf(func_def_2421, type, sK1487: (rat > num) > rat).
% 32.77/9.02  thf(func_def_2422, type, sK1488: (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_2423, type, sK1489: (int > int > $o) > int > int > int).
% 32.77/9.02  thf(func_def_2424, type, sK1490: (int > int > $o) > int > int > int).
% 32.77/9.02  thf(func_def_2425, type, sK1491: nat > nat > nat).
% 32.77/9.02  thf(func_def_2426, type, sK1492: complex > set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2427, type, sK1493: set_complex > (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2428, type, sK1494: real > int).
% 32.77/9.02  thf(func_def_2429, type, sK1495: nat > nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2430, type, sK1496: real > real).
% 32.77/9.02  thf(func_def_2431, type, sK1497: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_2432, type, sK1498: rat > (real > rat) > set_real > rat > real).
% 32.77/9.02  thf(func_def_2433, type, sK1499: option_nat > nat).
% 32.77/9.02  thf(func_def_2434, type, sK1500: set_real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2435, type, sK1501: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2436, type, sK1502: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2437, type, sK1503: (code_integer > $o) > code_integer > code_integer).
% 32.77/9.02  thf(func_def_2438, type, sK1504: (code_integer > $o) > code_integer > code_integer).
% 32.77/9.02  thf(func_def_2439, type, sK1505: (num > rat) > num).
% 32.77/9.02  thf(func_def_2440, type, sK1506: (num > rat) > num).
% 32.77/9.02  thf(func_def_2441, type, sK1507: (num > rat) > num).
% 32.77/9.02  thf(func_def_2442, type, sK1508: (num > rat) > num).
% 32.77/9.02  thf(func_def_2443, type, sK1509: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2444, type, sK1510: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2445, type, sK1511: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2446, type, sK1512: nat > (nat > real) > nat).
% 32.77/9.02  thf(func_def_2447, type, sK1513: product_prod_int_int > (int > int > set_real) > real > int).
% 32.77/9.02  thf(func_def_2448, type, sK1514: product_prod_int_int > (int > int > set_real) > real > int).
% 32.77/9.02  thf(func_def_2449, type, sK1515: nat > nat).
% 32.77/9.02  thf(func_def_2450, type, sK1516: rat > rat > rat).
% 32.77/9.02  thf(func_def_2451, type, sK1517: num > num).
% 32.77/9.02  thf(func_def_2452, type, sK1518: set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_2453, type, sK1519: (int > complex) > set_int > int).
% 32.77/9.02  thf(func_def_2454, type, sK1520: set_real > set_real > (real > int) > set_int > set_int > real).
% 32.77/9.02  thf(func_def_2455, type, sK1521: set_int > (real > complex) > (int > real) > (int > complex) > int).
% 32.77/9.02  thf(func_def_2456, type, sK1522: (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_2457, type, sK1523: set_int > set_int > set_real > (int > real) > set_real > int).
% 32.77/9.02  thf(func_def_2458, type, sK1524: (real > int) > set_int > set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_2459, type, sK1525: (real > int) > set_real > (int > real) > set_real > real).
% 32.77/9.02  thf(func_def_2460, type, sK1526: real > real > (real > real > real) > real).
% 32.77/9.02  thf(func_def_2461, type, sK1527: (real > real) > real > real > (real > real > real) > real).
% 32.77/9.02  thf(func_def_2462, type, sK1528: set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_2463, type, sK1529: int > int).
% 32.77/9.02  thf(func_def_2464, type, sK1530: (product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2465, type, sK1531: nat > (product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2466, type, sK1532: nat > (product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2467, type, sK1533: (complex > int) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_2468, type, sK1534: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_2469, type, sK1535: real > (real > real) > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2470, type, sK1536: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2471, type, sK1537: rat > rat).
% 32.77/9.02  thf(func_def_2472, type, sK1538: (nat > nat) > set_nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2473, type, sK1539: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2474, type, sK1540: set_set_nat > set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_2475, type, sK1541: (nat > num) > (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_2476, type, sK1542: (nat > num) > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_2477, type, sK1543: (nat > int) > set_nat > (nat > int) > nat).
% 32.77/9.02  thf(func_def_2478, type, sK1544: set_nat > (nat > int) > (nat > int) > nat).
% 32.77/9.02  thf(func_def_2479, type, sK1545: set_num > num).
% 32.77/9.02  thf(func_def_2480, type, sK1546: set_real > set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_2481, type, sK1547: real > int).
% 32.77/9.02  thf(func_def_2482, type, sK1548: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2483, type, sK1549: produc8763457246119570046nteger > code_integer).
% 32.77/9.02  thf(func_def_2484, type, sK1550: produc8763457246119570046nteger > code_integer).
% 32.77/9.02  thf(func_def_2485, type, sK1551: nat > nat).
% 32.77/9.02  thf(func_def_2486, type, sK1552: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2487, type, sK1553: set_list_o > nat).
% 32.77/9.02  thf(func_def_2488, type, sK1554: real > real).
% 32.77/9.02  thf(func_def_2489, type, sK1555: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_2490, type, sK1556: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_2491, type, sK1557: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_2492, type, sK1558: (real > $o) > real > real).
% 32.77/9.02  thf(func_def_2493, type, sK1559: (real > nat) > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_2494, type, sK1560: set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_2495, type, sK1561: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2496, type, sK1562: (set_nat > $o) > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_2497, type, sK1563: (num > nat) > num).
% 32.77/9.02  thf(func_def_2498, type, sK1564: (num > nat) > num).
% 32.77/9.02  thf(func_def_2499, type, sK1565: (real > $o) > real).
% 32.77/9.02  thf(func_def_2500, type, sK1566: int > int > set_int > int).
% 32.77/9.02  thf(func_def_2501, type, sK1567: int > int > set_int > int).
% 32.77/9.02  thf(func_def_2502, type, sK1568: (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_2503, type, sK1569: (nat > int) > (nat > int) > set_nat > nat).
% 32.77/9.02  thf(func_def_2504, type, sK1570: set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_2505, type, sK1571: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2506, type, sK1572: set_num > num).
% 32.77/9.02  thf(func_def_2507, type, sK1573: real > int).
% 32.77/9.02  thf(func_def_2508, type, sK1574: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2509, type, sK1575: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_2510, type, sK1576: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2511, type, sK1577: (real > real) > real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2512, type, sK1578: (real > real) > real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2513, type, sK1579: (real > real) > real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_2514, type, sK1580: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2515, type, sK1581: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_2516, type, sK1582: nat > (nat > real) > (nat > real) > nat).
% 32.77/9.02  thf(func_def_2517, type, sK1583: (real > $o) > list_real > real).
% 32.77/9.02  thf(func_def_2518, type, sK1584: (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_2519, type, sK1585: (set_int > $o) > int).
% 32.77/9.02  thf(func_def_2520, type, sK1586: rat > rat).
% 32.77/9.02  thf(func_def_2521, type, sK1587: rat > rat).
% 32.77/9.02  thf(func_def_2522, type, sK1588: set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_2523, type, sK1589: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2524, type, sK1590: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_2525, type, sK1591: rat > rat > rat).
% 32.77/9.02  thf(func_def_2526, type, sK1592: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_2527, type, sK1593: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_2528, type, sK1594: rat > rat).
% 32.77/9.02  thf(func_def_2529, type, sK1595: nat > set_nat > nat).
% 32.77/9.02  thf(func_def_2530, type, sK1596: $o > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2531, type, sK1597: $o > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2532, type, sK1598: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2533, type, sK1599: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2534, type, sK1600: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2535, type, sK1601: vEBT_VEBT > $o > nat > nat).
% 32.77/9.02  thf(func_def_2536, type, sK1602: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2537, type, sK1603: vEBT_VEBT > nat > $o > nat).
% 32.77/9.02  thf(func_def_2538, type, sK1604: vEBT_VEBT > nat > $o > nat).
% 32.77/9.02  thf(func_def_2539, type, sK1605: vEBT_VEBT > nat > $o > nat).
% 32.77/9.02  thf(func_def_2540, type, sK1606: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2541, type, sK1607: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2542, type, sK1608: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2543, type, sK1609: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2544, type, sK1610: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2545, type, sK1611: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2546, type, sK1612: int > int > set_int > int).
% 32.77/9.02  thf(func_def_2547, type, sK1613: int > int > set_int > int).
% 32.77/9.02  thf(func_def_2548, type, sK1614: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2549, type, sK1615: product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2550, type, sK1616: real > real > real).
% 32.77/9.02  thf(func_def_2551, type, sK1617: num > num).
% 32.77/9.02  thf(func_def_2552, type, sK1618: rat > rat > rat).
% 32.77/9.02  thf(func_def_2553, type, sK1619: real > nat > real).
% 32.77/9.02  thf(func_def_2554, type, sK1620: (set_complex > $o) > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2555, type, sK1621: (set_complex > $o) > (complex > nat) > set_complex).
% 32.77/9.02  thf(func_def_2556, type, sK1622: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_2557, type, sK1623: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_2558, type, sK1624: (nat > int) > nat > nat).
% 32.77/9.02  thf(func_def_2559, type, sK1625: (nat > int) > int > nat > nat).
% 32.77/9.02  thf(func_def_2560, type, sK1626: (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_2561, type, sK1627: (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_2562, type, sK1628: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2563, type, sK1629: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_2564, type, sK1630: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2565, type, sK1631: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2566, type, sK1632: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2567, type, sK1633: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2568, type, sK1634: ((int > option6357759511663192854e_term) > product_prod_int_int > set_complex) > complex > produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2569, type, sK1635: ((int > option6357759511663192854e_term) > product_prod_int_int > set_complex) > complex > produc7773217078559923341nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_2570, type, sK1636: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2571, type, sK1637: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_2572, type, sK1638: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2573, type, sK1639: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2574, type, sK1640: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2575, type, sK1641: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2576, type, sK1642: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2577, type, sK1643: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2578, type, sK1644: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2579, type, sK1645: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2580, type, sK1646: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2581, type, sK1647: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2582, type, sK1648: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2583, type, sK1649: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2584, type, sK1650: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2585, type, sK1651: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2586, type, sK1652: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2587, type, sK1653: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2588, type, sK1654: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2589, type, sK1655: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2590, type, sK1656: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2591, type, sK1657: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2592, type, sK1658: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2593, type, sK1659: real > int).
% 32.77/9.02  thf(func_def_2594, type, sK1660: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_2595, type, sK1661: (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_2596, type, sK1662: real > (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_2597, type, sK1663: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2598, type, sK1664: (num > real) > num).
% 32.77/9.02  thf(func_def_2599, type, sK1665: (num > real) > num).
% 32.77/9.02  thf(func_def_2600, type, sK1666: (int > num) > (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_2601, type, sK1667: (int > num) > (set_int > $o) > int).
% 32.77/9.02  thf(func_def_2602, type, sK1668: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2603, type, sK1669: list_real > (real > $o) > nat).
% 32.77/9.02  thf(func_def_2604, type, sK1670: set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2605, type, sK1671: real > (real > real) > real).
% 32.77/9.02  thf(func_def_2606, type, sK1672: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2607, type, sK1673: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2608, type, sK1674: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2609, type, sK1675: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2610, type, sK1676: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2611, type, sK1677: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2612, type, sK1678: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2613, type, sK1679: (set_nat > $o) > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_2614, type, sK1680: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2615, type, sK1681: (list_nat > $o) > list_nat).
% 32.77/9.02  thf(func_def_2616, type, sK1682: (int > complex) > set_int > int).
% 32.77/9.02  thf(func_def_2617, type, sK1683: (int > int) > (int > int) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2618, type, sK1684: set_int > set_int > (int > int) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_2619, type, sK1685: (int > complex) > set_int > int).
% 32.77/9.02  thf(func_def_2620, type, sK1686: set_int > set_int > set_int > (int > int) > set_int > int).
% 32.77/9.02  thf(func_def_2621, type, sK1687: (int > int) > set_int > set_int > (int > int) > int).
% 32.77/9.02  thf(func_def_2622, type, sK1688: (int > complex) > (int > complex) > (int > int) > set_int > int).
% 32.77/9.02  thf(func_def_2623, type, sK1689: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2624, type, sK1690: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_2625, type, sK1691: (nat > real > real) > nat > real > real).
% 32.77/9.02  thf(func_def_2626, type, sK1692: (nat > real > real) > nat > real > nat).
% 32.77/9.02  thf(func_def_2627, type, sK1693: (nat > int) > nat).
% 32.77/9.02  thf(func_def_2628, type, sK1694: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2629, type, sK1695: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2630, type, sK1696: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2631, type, sK1697: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2632, type, sK1698: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2633, type, sK1699: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2634, type, sK1700: nat > $o > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2635, type, sK1701: nat > $o > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2636, type, sK1702: nat > $o > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2637, type, sK1703: vEBT_VEBT > nat > $o > nat).
% 32.77/9.02  thf(func_def_2638, type, sK1704: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2639, type, sK1705: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2640, type, sK1706: vEBT_VEBT > nat > $o > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2641, type, sK1707: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2642, type, sK1708: $o > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2643, type, sK1709: list_VEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2644, type, sK1710: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2645, type, sK1711: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2646, type, sK1712: vEBT_VEBT > option_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2647, type, sK1713: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2648, type, sK1714: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2649, type, sK1715: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2650, type, sK1716: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2651, type, sK1717: option_nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2652, type, sK1718: option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2653, type, sK1719: option_nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2654, type, sK1720: code_integer > code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_2655, type, sK1721: real > real > real).
% 32.77/9.02  thf(func_def_2656, type, sK1722: int > int).
% 32.77/9.02  thf(func_def_2657, type, sK1723: real > real > real).
% 32.77/9.02  thf(func_def_2658, type, sK1724: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2659, type, sK1725: (rat > int) > rat).
% 32.77/9.02  thf(func_def_2660, type, sK1726: nat > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2661, type, sK1727: (real > nat) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_2662, type, sK1728: (real > nat) > set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_2663, type, sK1729: real > real).
% 32.77/9.02  thf(func_def_2664, type, sK1730: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2665, type, sK1731: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2666, type, sK1732: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2667, type, sK1733: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2668, type, sK1734: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2669, type, sK1735: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2670, type, sK1736: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_2671, type, sK1737: (nat > real) > real).
% 32.77/9.02  thf(func_def_2672, type, sK1738: real > (nat > real) > nat).
% 32.77/9.02  thf(func_def_2673, type, sK1739: set_rat > rat > rat).
% 32.77/9.02  thf(func_def_2674, type, sK1740: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2675, type, sK1741: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2676, type, sK1742: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2677, type, sK1743: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2678, type, sK1744: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_2679, type, sK1745: (rat > num) > rat).
% 32.77/9.02  thf(func_def_2680, type, sK1746: (rat > num) > rat).
% 32.77/9.02  thf(func_def_2681, type, sK1747: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2682, type, sK1748: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2683, type, sK1749: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2684, type, sK1750: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2685, type, sK1751: (real > rat) > real).
% 32.77/9.02  thf(func_def_2686, type, sK1752: (real > rat) > real).
% 32.77/9.02  thf(func_def_2687, type, sK1753: int > set_int > int).
% 32.77/9.02  thf(func_def_2688, type, sK1754: set_int > int).
% 32.77/9.02  thf(func_def_2689, type, sK1755: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2690, type, sK1756: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2691, type, sK1757: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2692, type, sK1758: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2693, type, sK1759: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2694, type, sK1760: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2695, type, sK1761: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2696, type, sK1762: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2697, type, sK1763: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2698, type, sK1764: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2699, type, sK1765: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2700, type, sK1766: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2701, type, sK1767: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2702, type, sK1768: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2703, type, sK1769: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2704, type, sK1770: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2705, type, sK1771: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2706, type, sK1772: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2707, type, sK1773: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2708, type, sK1774: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2709, type, sK1775: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2710, type, sK1776: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2711, type, sK1777: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2712, type, sK1778: list_int > (int > $o) > nat).
% 32.77/9.02  thf(func_def_2713, type, sK1779: set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2714, type, sK1780: set_real > (real > nat) > real).
% 32.77/9.02  thf(func_def_2715, type, sK1781: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2716, type, sK1782: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2717, type, sK1783: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2718, type, sK1784: (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_2719, type, sK1785: num > num).
% 32.77/9.02  thf(func_def_2720, type, sK1786: (option_nat > option_nat > $o) > option_nat > option_nat > nat).
% 32.77/9.02  thf(func_def_2721, type, sK1787: (option_nat > option_nat > $o) > option_nat > option_nat > nat).
% 32.77/9.02  thf(func_def_2722, type, sK1788: (complex > rat) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_2723, type, sK1789: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2724, type, sK1790: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2725, type, sK1791: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2726, type, sK1792: option_nat > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2727, type, sK1793: option_nat > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2728, type, sK1794: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2729, type, sK1795: vEBT_VEBT > nat > option_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2730, type, sK1796: vEBT_VEBT > nat > option_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2731, type, sK1797: vEBT_VEBT > nat > option_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2732, type, sK1798: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2733, type, sK1799: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2734, type, sK1800: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_2735, type, sK1801: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_2736, type, sK1802: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_2737, type, sK1803: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2738, type, sK1804: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2739, type, sK1805: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_2740, type, sK1806: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_2741, type, sK1807: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_2742, type, sK1808: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_2743, type, sK1809: vEBT_VEBT > nat > option_nat > nat).
% 32.77/9.02  thf(func_def_2744, type, sK1810: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2745, type, sK1811: nat > option_nat > vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2746, type, sK1812: nat > option_nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2747, type, sK1813: real > real > (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_2748, type, sK1814: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_2749, type, sK1815: set_real > set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_2750, type, sK1816: set_real > (real > int) > (real > int) > real).
% 32.77/9.02  thf(func_def_2751, type, sK1817: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2752, type, sK1818: set_int > set_complex > (int > real) > (complex > real) > (complex > int) > int).
% 32.77/9.02  thf(func_def_2753, type, sK1819: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_2754, type, sK1820: (nat > real) > nat > int).
% 32.77/9.02  thf(func_def_2755, type, sK1821: nat > nat > nat).
% 32.77/9.02  thf(func_def_2756, type, sK1822: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_2757, type, sK1823: set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_2758, type, sK1824: int > int > int > int).
% 32.77/9.02  thf(func_def_2759, type, sK1825: int > int > int > int).
% 32.77/9.02  thf(func_def_2760, type, sK1826: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2761, type, sK1827: vEBT_VEBT > option_nat > $o).
% 32.77/9.02  thf(func_def_2762, type, sK1828: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2763, type, sK1829: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2764, type, sK1830: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2765, type, sK1831: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2766, type, sK1832: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2767, type, sK1833: vEBT_VEBT > option_nat > nat).
% 32.77/9.02  thf(func_def_2768, type, sK1834: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2769, type, sK1835: vEBT_VEBT > option_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2770, type, sK1836: (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2771, type, sK1837: code_integer > code_integer).
% 32.77/9.02  thf(func_def_2772, type, sK1838: (produc7773217078559923341nt_int > $o) > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2773, type, sK1839: (produc7773217078559923341nt_int > $o) > int).
% 32.77/9.02  thf(func_def_2774, type, sK1840: (produc7773217078559923341nt_int > $o) > int).
% 32.77/9.02  thf(func_def_2775, type, sK1841: set_nat > list_nat).
% 32.77/9.02  thf(func_def_2776, type, sK1842: int > set_int > int > int).
% 32.77/9.02  thf(func_def_2777, type, sK1843: int > set_int > int > int).
% 32.77/9.02  thf(func_def_2778, type, sK1844: (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2779, type, sK1845: num > num).
% 32.77/9.02  thf(func_def_2780, type, sK1846: (int > real) > int).
% 32.77/9.02  thf(func_def_2781, type, sK1847: (int > real) > int).
% 32.77/9.02  thf(func_def_2782, type, sK1848: (int > $o) > int).
% 32.77/9.02  thf(func_def_2783, type, sK1849: (int > $o) > int).
% 32.77/9.02  thf(func_def_2784, type, sK1850: (int > $o) > $o).
% 32.77/9.02  thf(func_def_2785, type, sK1851: real > (real > real) > nat > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_2786, type, sK1852: (nat > real > real) > real).
% 32.77/9.02  thf(func_def_2787, type, sK1853: (nat > real > real) > nat).
% 32.77/9.02  thf(func_def_2788, type, sK1854: (real > rat) > real).
% 32.77/9.02  thf(func_def_2789, type, sK1855: (real > rat) > real).
% 32.77/9.02  thf(func_def_2790, type, sK1856: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2791, type, sK1857: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2792, type, sK1858: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2793, type, sK1859: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2794, type, sK1860: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2795, type, sK1861: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2796, type, sK1862: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2797, type, sK1863: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2798, type, sK1864: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2799, type, sK1865: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2800, type, sK1866: nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2801, type, sK1867: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2802, type, sK1868: (set_set_nat > $o) > set_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_2803, type, sK1869: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_2804, type, sK1870: real > int).
% 32.77/9.02  thf(func_def_2805, type, sK1871: ($o > $o) > product_prod_int_int > (int > int > $o) > int).
% 32.77/9.02  thf(func_def_2806, type, sK1872: ($o > $o) > product_prod_int_int > (int > int > $o) > int).
% 32.77/9.02  thf(func_def_2807, type, sK1873: set_real > (real > int) > (real > int) > real).
% 32.77/9.02  thf(func_def_2808, type, sK1874: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2809, type, sK1875: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2810, type, sK1876: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2811, type, sK1877: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_2812, type, sK1878: (real > real) > real > real).
% 32.77/9.02  thf(func_def_2813, type, sK1879: real > real).
% 32.77/9.02  thf(func_def_2814, type, sK1880: nat > nat).
% 32.77/9.02  thf(func_def_2815, type, sK1881: nat > nat).
% 32.77/9.02  thf(func_def_2816, type, sK1882: (real > real) > (real > real) > real > real > real).
% 32.77/9.02  thf(func_def_2817, type, sK1883: (real > real) > real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2818, type, sK1884: set_list_nat > nat).
% 32.77/9.02  thf(func_def_2819, type, sK1885: (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_2820, type, sK1886: nat > nat).
% 32.77/9.02  thf(func_def_2821, type, sK1887: (int > real) > set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_2822, type, sK1888: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2823, type, sK1889: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > int > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2824, type, sK1890: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > int > produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2825, type, sK1891: (num > int) > num).
% 32.77/9.02  thf(func_def_2826, type, sK1892: (num > int) > num).
% 32.77/9.02  thf(func_def_2827, type, sK1893: (num > rat) > num).
% 32.77/9.02  thf(func_def_2828, type, sK1894: (num > rat) > num).
% 32.77/9.02  thf(func_def_2829, type, sK1895: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2830, type, sK1896: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2831, type, sK1897: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_2832, type, sK1898: (int > nat) > set_int > (int > nat) > int).
% 32.77/9.02  thf(func_def_2833, type, sK1899: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2834, type, sK1900: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2835, type, sK1901: real > (real > $o) > nat > real).
% 32.77/9.02  thf(func_def_2836, type, sK1902: set_real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2837, type, sK1903: (real > rat) > real).
% 32.77/9.02  thf(func_def_2838, type, sK1904: (real > rat) > real).
% 32.77/9.02  thf(func_def_2839, type, sK1905: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_2840, type, sK1906: set_nat > nat).
% 32.77/9.02  thf(func_def_2841, type, sK1907: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2842, type, sK1908: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_2843, type, sK1909: produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2844, type, sK1910: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2845, type, sK1911: nat > (vEBT_VEBT > $o) > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2846, type, sK1912: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2847, type, sK1913: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2848, type, sK1914: (real > real) > real).
% 32.77/9.02  thf(func_def_2849, type, sK1915: (product_prod_int_int > $o) > int).
% 32.77/9.02  thf(func_def_2850, type, sK1916: (product_prod_int_int > $o) > int).
% 32.77/9.02  thf(func_def_2851, type, sK1917: (set_complex > $o) > set_complex > set_complex).
% 32.77/9.02  thf(func_def_2852, type, sK1918: (complex > real) > set_complex > complex > complex).
% 32.77/9.02  thf(func_def_2853, type, sK1919: (nat > real) > set_nat > nat).
% 32.77/9.02  thf(func_def_2854, type, sK1920: set_nat > list_set_nat > set_nat).
% 32.77/9.02  thf(func_def_2855, type, sK1921: int > int > int).
% 32.77/9.02  thf(func_def_2856, type, sK1922: int > int > int).
% 32.77/9.02  thf(func_def_2857, type, sK1923: set_nat > nat > nat).
% 32.77/9.02  thf(func_def_2858, type, sK1924: produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2859, type, sK1925: produc8763457246119570046nteger > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2860, type, sK1926: (nat > nat) > nat > nat > nat).
% 32.77/9.02  thf(func_def_2861, type, sK1927: set_set_nat > set_nat > set_nat).
% 32.77/9.02  thf(func_def_2862, type, sK1928: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2863, type, sK1929: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2864, type, sK1930: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2865, type, sK1931: (nat > real) > nat).
% 32.77/9.02  thf(func_def_2866, type, sK1932: int > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2867, type, sK1933: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_2868, type, sK1934: list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2869, type, sK1935: list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2870, type, sK1936: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2871, type, sK1937: nat > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2872, type, sK1938: option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2873, type, sK1939: option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2874, type, sK1940: set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_2875, type, sK1941: rat > rat).
% 32.77/9.02  thf(func_def_2876, type, sK1942: product_prod_int_int > int > int > int).
% 32.77/9.02  thf(func_def_2877, type, sK1943: product_prod_int_int > int > int > int).
% 32.77/9.02  thf(func_def_2878, type, sK1944: int > int > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2879, type, sK1945: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2880, type, sK1946: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2881, type, sK1947: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2882, type, sK1948: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2883, type, sK1949: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2884, type, sK1950: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2885, type, sK1951: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2886, type, sK1952: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2887, type, sK1953: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2888, type, sK1954: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2889, type, sK1955: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2890, type, sK1956: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2891, type, sK1957: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2892, type, sK1958: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2893, type, sK1959: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2894, type, sK1960: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2895, type, sK1961: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2896, type, sK1962: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2897, type, sK1963: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2898, type, sK1964: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2899, type, sK1965: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2900, type, sK1966: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2901, type, sK1967: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_2902, type, sK1968: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2903, type, sK1969: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_2904, type, sK1970: set_real > (real > rat) > (real > rat) > real).
% 32.77/9.02  thf(func_def_2905, type, sK1971: set_real > set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_2906, type, sK1972: set_real > (real > int) > (real > int) > real).
% 32.77/9.02  thf(func_def_2907, type, sK1973: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2908, type, sK1974: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2909, type, sK1975: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2910, type, sK1976: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_2911, type, sK1977: real > nat > real).
% 32.77/9.02  thf(func_def_2912, type, sK1978: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_2913, type, sK1979: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2914, type, sK1980: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2915, type, sK1981: (nat > real) > nat).
% 32.77/9.02  thf(func_def_2916, type, sK1982: set_complex > (complex > int) > (complex > int) > complex).
% 32.77/9.02  thf(func_def_2917, type, sK1983: (real > real) > set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_2918, type, sK1984: rat > rat).
% 32.77/9.02  thf(func_def_2919, type, sK1985: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2920, type, sK1986: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_2921, type, sK1987: set_set_int > set_int).
% 32.77/9.02  thf(func_def_2922, type, sK1988: rat > nat).
% 32.77/9.02  thf(func_def_2923, type, sK1989: nat > nat > nat).
% 32.77/9.02  thf(func_def_2924, type, sK1990: (int > int) > (int > int) > set_int > int).
% 32.77/9.02  thf(func_def_2925, type, sK1991: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_2926, type, sK1992: vEBT_VEBT > $o > nat > $o).
% 32.77/9.02  thf(func_def_2927, type, sK1993: list_VEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2928, type, sK1994: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2929, type, sK1995: $o > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2930, type, sK1996: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2931, type, sK1997: $o > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2932, type, sK1998: (int > int > set_int) > int > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2933, type, sK1999: (int > int > set_int) > int > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_2934, type, sK2000: (int > real) > int).
% 32.77/9.02  thf(func_def_2935, type, sK2001: (int > real) > int).
% 32.77/9.02  thf(func_def_2936, type, sK2002: (num > rat) > num).
% 32.77/9.02  thf(func_def_2937, type, sK2003: (num > rat) > num).
% 32.77/9.02  thf(func_def_2938, type, sK2004: (set_complex > $o) > complex).
% 32.77/9.02  thf(func_def_2939, type, sK2005: (set_complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_2940, type, sK2006: real > (real > real) > real).
% 32.77/9.02  thf(func_def_2941, type, sK2007: produc1908205239877642774nteger > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2942, type, sK2008: produc1908205239877642774nteger > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2943, type, sK2009: (nat > int) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_2944, type, sK2010: int > int > int).
% 32.77/9.02  thf(func_def_2945, type, sK2011: (num > real) > num).
% 32.77/9.02  thf(func_def_2946, type, sK2012: (num > real) > num).
% 32.77/9.02  thf(func_def_2947, type, sK2013: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2948, type, sK2014: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2949, type, sK2015: (real > real) > real > set_real > real).
% 32.77/9.02  thf(func_def_2950, type, sK2016: (rat > $o) > int).
% 32.77/9.02  thf(func_def_2951, type, sK2017: (rat > $o) > int).
% 32.77/9.02  thf(func_def_2952, type, sK2018: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2953, type, sK2019: nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_2954, type, sK2020: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_2955, type, sK2021: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_2956, type, sK2022: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_2957, type, sK2023: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2958, type, sK2024: (num > num) > num).
% 32.77/9.02  thf(func_def_2959, type, sK2025: (num > num) > num).
% 32.77/9.02  thf(func_def_2960, type, sK2026: (nat > real > real) > nat > real > real > real).
% 32.77/9.02  thf(func_def_2961, type, sK2027: (nat > real > real) > nat > real > real > nat).
% 32.77/9.02  thf(func_def_2962, type, sK2028: real > nat > real > (real > real) > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_2963, type, sK2029: (int > rat) > set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_2964, type, sK2030: (produc1908205239877642774nteger > $o) > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_2965, type, sK2031: (produc1908205239877642774nteger > $o) > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_2966, type, sK2032: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2967, type, sK2033: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2968, type, sK2034: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2969, type, sK2035: (vEBT_VEBT > $o) > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_2970, type, sK2036: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2971, type, sK2037: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2972, type, sK2038: nat > nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2973, type, sK2039: (real > $o) > nat).
% 32.77/9.02  thf(func_def_2974, type, sK2040: (real > $o) > real).
% 32.77/9.02  thf(func_def_2975, type, sK2041: (real > $o) > real).
% 32.77/9.02  thf(func_def_2976, type, sK2042: (num > rat) > num).
% 32.77/9.02  thf(func_def_2977, type, sK2043: (num > rat) > num).
% 32.77/9.02  thf(func_def_2978, type, sK2044: nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2979, type, sK2045: nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2980, type, sK2046: (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_2981, type, sK2047: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2982, type, sK2048: (rat > real) > rat).
% 32.77/9.02  thf(func_def_2983, type, sK2049: (nat > real) > real > nat > int).
% 32.77/9.02  thf(func_def_2984, type, sK2050: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_2985, type, sK2051: set_real > real).
% 32.77/9.02  thf(func_def_2986, type, sK2052: real > set_real > real).
% 32.77/9.02  thf(func_def_2987, type, sK2053: real > set_real > real).
% 32.77/9.02  thf(func_def_2988, type, sK2054: (real > real) > real).
% 32.77/9.02  thf(func_def_2989, type, sK2055: (real > real) > real).
% 32.77/9.02  thf(func_def_2990, type, sK2056: list_nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_2991, type, sK2057: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2992, type, sK2058: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_2993, type, sK2059: set_nat > nat).
% 32.77/9.02  thf(func_def_2994, type, sK2060: nat > set_nat > nat).
% 32.77/9.02  thf(func_def_2995, type, sK2061: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_2996, type, sK2062: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_2997, type, sK2063: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_2998, type, sK2064: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_2999, type, sK2065: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3000, type, sK2066: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3001, type, sK2067: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3002, type, sK2068: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3003, type, sK2069: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3004, type, sK2070: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3005, type, sK2071: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3006, type, sK2072: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3007, type, sK2073: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3008, type, sK2074: (nat > $o) > $o).
% 32.77/9.02  thf(func_def_3009, type, sK2075: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3010, type, sK2076: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3011, type, sK2077: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3012, type, sK2078: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3013, type, sK2079: real > real > nat).
% 32.77/9.02  thf(func_def_3014, type, sK2080: set_real > real > (real > rat) > real).
% 32.77/9.02  thf(func_def_3015, type, sK2081: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_3016, type, sK2082: (complex > nat) > set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_3017, type, sK2083: (real > complex) > set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_3018, type, sK2084: set_real > set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_3019, type, sK2085: set_int > set_set_int > set_int).
% 32.77/9.02  thf(func_def_3020, type, sK2086: set_real > real).
% 32.77/9.02  thf(func_def_3021, type, sK2087: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3022, type, sK2088: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3023, type, sK2089: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3024, type, sK2090: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3025, type, sK2091: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3026, type, sK2092: nat > nat > nat).
% 32.77/9.02  thf(func_def_3027, type, sK2093: nat > nat > nat).
% 32.77/9.02  thf(func_def_3028, type, sK2094: nat > nat > nat).
% 32.77/9.02  thf(func_def_3029, type, sK2095: set_int > (int > rat) > (int > rat) > int).
% 32.77/9.02  thf(func_def_3030, type, sK2096: (num > $o) > (num > $o) > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3031, type, sK2097: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3032, type, sK2098: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3033, type, sK2099: set_real > real).
% 32.77/9.02  thf(func_def_3034, type, sK2100: (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_3035, type, sK2101: (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_3036, type, sK2102: produc1193250871479095198on_num > num > num > num).
% 32.77/9.02  thf(func_def_3037, type, sK2103: produc1193250871479095198on_num > num).
% 32.77/9.02  thf(func_def_3038, type, sK2104: produc1193250871479095198on_num > num).
% 32.77/9.02  thf(func_def_3039, type, sK2105: produc1193250871479095198on_num > num > num > num).
% 32.77/9.02  thf(func_def_3040, type, sK2106: produc1193250871479095198on_num > num).
% 32.77/9.02  thf(func_def_3041, type, sK2107: produc1193250871479095198on_num > num > num > num).
% 32.77/9.02  thf(func_def_3042, type, sK2108: produc1193250871479095198on_num > option_num).
% 32.77/9.02  thf(func_def_3043, type, sK2109: real > (nat > real) > nat).
% 32.77/9.02  thf(func_def_3044, type, sK2110: (num > real) > num).
% 32.77/9.02  thf(func_def_3045, type, sK2111: (num > real) > num).
% 32.77/9.02  thf(func_def_3046, type, sK2112: (nat > real > real) > real > nat > real).
% 32.77/9.02  thf(func_def_3047, type, sK2113: (nat > real > real) > real > nat > nat).
% 32.77/9.02  thf(func_def_3048, type, sK2114: (real > real) > nat > real > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_3049, type, sK2115: set_nat > (nat > complex) > set_nat > nat).
% 32.77/9.02  thf(func_def_3050, type, sK2116: set_nat > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_3051, type, sK2117: complex > real).
% 32.77/9.02  thf(func_def_3052, type, sK2118: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3053, type, sK2119: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3054, type, sK2120: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3055, type, sK2121: nat > vEBT_VEBT > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3056, type, sK2122: nat > vEBT_VEBT > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3057, type, sK2123: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3058, type, sK2124: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3059, type, sK2125: list_VEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3060, type, sK2126: list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3061, type, sK2127: list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3062, type, sK2128: nat > nat > nat).
% 32.77/9.02  thf(func_def_3063, type, sK2129: set_real > set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_3064, type, sK2130: (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_3065, type, sK2131: (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3066, type, sK2132: set_set_nat > set_nat > set_nat).
% 32.77/9.02  thf(func_def_3067, type, sK2133: real > real > real).
% 32.77/9.02  thf(func_def_3068, type, sK2134: set_complex > (complex > nat) > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_3069, type, sK2135: ((product_prod_nat_nat > product_prod_nat_nat) > $o) > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 32.77/9.02  thf(func_def_3070, type, sK2136: ((product_prod_nat_nat > product_prod_nat_nat) > $o) > product_prod_nat_nat > (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 32.77/9.02  thf(func_def_3071, type, sK2137: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3072, type, sK2138: rat > (complex > rat) > set_complex > rat > complex).
% 32.77/9.02  thf(func_def_3073, type, sK2139: real > int).
% 32.77/9.02  thf(func_def_3074, type, sK2140: list_nat > nat > nat).
% 32.77/9.02  thf(func_def_3075, type, sK2141: list_nat > nat > list_nat).
% 32.77/9.02  thf(func_def_3076, type, sK2142: list_int > int > int).
% 32.77/9.02  thf(func_def_3077, type, sK2143: real > nat).
% 32.77/9.02  thf(func_def_3078, type, sK2144: (complex > rat) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_3079, type, sK2145: rat > nat).
% 32.77/9.02  thf(func_def_3080, type, sK2146: set_nat > nat).
% 32.77/9.02  thf(func_def_3081, type, sK2147: ($o > $o) > list_o > $o).
% 32.77/9.02  thf(func_def_3082, type, sK2148: (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_3083, type, sK2149: (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_3084, type, sK2150: (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3085, type, sK2151: real > nat > real).
% 32.77/9.02  thf(func_def_3086, type, sK2152: (num > int) > num).
% 32.77/9.02  thf(func_def_3087, type, sK2153: (num > int) > num).
% 32.77/9.02  thf(func_def_3088, type, sK2154: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 32.77/9.02  thf(func_def_3089, type, sK2155: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > nat).
% 32.77/9.02  thf(func_def_3090, type, sK2156: real > real > real).
% 32.77/9.02  thf(func_def_3091, type, sK2157: real > real > real).
% 32.77/9.02  thf(func_def_3092, type, sK2158: set_complex > (set_complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_3093, type, sK2159: real > real > real).
% 32.77/9.02  thf(func_def_3094, type, sK2160: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3095, type, sK2161: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3096, type, sK2162: int > int > set_int > int).
% 32.77/9.02  thf(func_def_3097, type, sK2163: int > int > set_int > int).
% 32.77/9.02  thf(func_def_3098, type, sK2164: int > int).
% 32.77/9.02  thf(func_def_3099, type, sK2165: (num > nat) > num).
% 32.77/9.02  thf(func_def_3100, type, sK2166: (num > nat) > num).
% 32.77/9.02  thf(func_def_3101, type, sK2167: nat).
% 32.77/9.02  thf(func_def_3102, type, sK2168: set_int > int).
% 32.77/9.02  thf(func_def_3103, type, sK2169: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3104, type, sK2170: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3105, type, sK2171: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_3106, type, sK2172: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3107, type, sK2173: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3108, type, sK2174: (complex > real) > set_complex > complex).
% 32.77/9.02  thf(func_def_3109, type, sK2175: int > nat > (nat > int) > nat).
% 32.77/9.02  thf(func_def_3110, type, sK2176: int > int > int).
% 32.77/9.02  thf(func_def_3111, type, sK2177: set_nat > set_nat > (nat > int) > nat).
% 32.77/9.02  thf(func_def_3112, type, sK2178: real > nat).
% 32.77/9.02  thf(func_def_3113, type, sK2179: (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_3114, type, sK2180: int > int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3115, type, sK2181: int > int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3116, type, sK2182: (int > $o) > int > int > int).
% 32.77/9.02  thf(func_def_3117, type, sK2183: (int > $o) > int > int > int).
% 32.77/9.02  thf(func_def_3118, type, sK2184: nat > real > real).
% 32.77/9.02  thf(func_def_3119, type, sK2185: set_int > (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_3120, type, sK2186: (int > int > set_nat) > nat > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_3121, type, sK2187: (int > int > set_nat) > nat > product_prod_int_int > int).
% 32.77/9.02  thf(func_def_3122, type, sK2188: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3123, type, sK2189: (real > real) > (nat > real > real) > nat > real > real > real).
% 32.77/9.02  thf(func_def_3124, type, sK2190: real > real > nat > (nat > real > real) > nat).
% 32.77/9.02  thf(func_def_3125, type, sK2191: real > real > nat > (nat > real > real) > real).
% 32.77/9.02  thf(func_def_3126, type, sK2192: set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_3127, type, sK2193: (real > real) > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3128, type, sK2194: set_real > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3129, type, sK2195: (int > int > int) > (product_prod_int_int > int) > int).
% 32.77/9.02  thf(func_def_3130, type, sK2196: (int > int > int) > (product_prod_int_int > int) > int).
% 32.77/9.02  thf(func_def_3131, type, sK2197: set_real > (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_3132, type, sK2198: set_real > (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_3133, type, sK2199: (real > rat) > set_real > real).
% 32.77/9.02  thf(func_def_3134, type, sK2200: nat > nat).
% 32.77/9.02  thf(func_def_3135, type, sK2201: int > nat).
% 32.77/9.02  thf(func_def_3136, type, sK2202: int > nat).
% 32.77/9.02  thf(func_def_3137, type, sK2203: real > (nat > real) > real > (real > nat > real) > nat).
% 32.77/9.02  thf(func_def_3138, type, sK2204: real > (nat > real) > real > (real > nat > real) > real).
% 32.77/9.02  thf(func_def_3139, type, sK2205: real > (nat > real) > real > (real > nat > real) > real).
% 32.77/9.02  thf(func_def_3140, type, sK2206: real > real > (real > nat > real) > real).
% 32.77/9.02  thf(func_def_3141, type, sK2207: real > (real > nat > real) > (real > nat > real) > nat).
% 32.77/9.02  thf(func_def_3142, type, sK2208: (real > nat) > real).
% 32.77/9.02  thf(func_def_3143, type, sK2209: (real > nat) > real).
% 32.77/9.02  thf(func_def_3144, type, sK2210: set_real > real).
% 32.77/9.02  thf(func_def_3145, type, sK2211: int > nat).
% 32.77/9.02  thf(func_def_3146, type, sK2212: (nat > num) > nat).
% 32.77/9.02  thf(func_def_3147, type, sK2213: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3148, type, sK2214: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3149, type, sK2215: rat > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_3150, type, sK2216: rat > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_3151, type, sK2217: real > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_real) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3152, type, sK2218: real > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_real) > produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_3153, type, sK2219: nat > (nat > rat) > rat > nat).
% 32.77/9.02  thf(func_def_3154, type, sK2220: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3155, type, sK2221: list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3156, type, sK2222: list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3157, type, sK2223: nat > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3158, type, sK2224: (complex > rat) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_3159, type, sK2225: set_complex > set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_3160, type, sK2226: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_3161, type, sK2227: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3162, type, sK2228: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3163, type, sK2229: (int > $o) > int).
% 32.77/9.02  thf(func_def_3164, type, sK2230: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_3165, type, sK2231: set_rat > rat).
% 32.77/9.02  thf(func_def_3166, type, sK2232: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3167, type, sK2233: list_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_3168, type, sK2234: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3169, type, sK2235: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3170, type, sK2236: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3171, type, sK2237: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3172, type, sK2238: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3173, type, sK2239: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3174, type, sK2240: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3175, type, sK2241: nat > nat).
% 32.77/9.02  thf(func_def_3176, type, sK2242: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3177, type, sK2243: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3178, type, sK2244: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3179, type, sK2245: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3180, type, sK2246: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3181, type, sK2247: vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3182, type, sK2248: vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3183, type, sK2249: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3184, type, sK2250: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3185, type, sK2251: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3186, type, sK2252: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3187, type, sK2253: vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3188, type, sK2254: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3189, type, sK2255: vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3190, type, sK2256: vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3191, type, sK2257: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3192, type, sK2258: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3193, type, sK2259: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3194, type, sK2260: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3195, type, sK2261: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3196, type, sK2262: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3197, type, sK2263: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3198, type, sK2264: (real > nat) > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_3199, type, sK2265: (nat > real) > real).
% 32.77/9.02  thf(func_def_3200, type, sK2266: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3201, type, sK2267: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3202, type, sK2268: set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_3203, type, sK2269: real > real).
% 32.77/9.02  thf(func_def_3204, type, sK2270: (nat > rat) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_3205, type, sK2271: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3206, type, sK2272: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3207, type, sK2273: (int > real) > int).
% 32.77/9.02  thf(func_def_3208, type, sK2274: (int > real) > int).
% 32.77/9.02  thf(func_def_3209, type, sK2275: nat > nat > nat).
% 32.77/9.02  thf(func_def_3210, type, sK2276: set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_3211, type, sK2277: (num > num) > num).
% 32.77/9.02  thf(func_def_3212, type, sK2278: (num > num) > num).
% 32.77/9.02  thf(func_def_3213, type, sK2279: (option4927543243414619207at_nat > option_num > $o) > option_num > option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3214, type, sK2280: (option4927543243414619207at_nat > option_num > $o) > option_num > option4927543243414619207at_nat > num).
% 32.77/9.02  thf(func_def_3215, type, sK2281: int > nat).
% 32.77/9.02  thf(func_def_3216, type, sK2282: int > (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3217, type, sK2283: (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3218, type, sK2284: (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3219, type, sK2285: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_3220, type, sK2286: vEBT_VEBT > nat > $o).
% 32.77/9.02  thf(func_def_3221, type, sK2287: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3222, type, sK2288: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3223, type, sK2289: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3224, type, sK2290: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3225, type, sK2291: vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_3226, type, sK2292: vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3227, type, sK2293: vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3228, type, sK2294: set_set_nat > (set_set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_3229, type, sK2295: set_set_nat > (set_set_nat > $o) > set_set_nat).
% 32.77/9.02  thf(func_def_3230, type, sK2296: (nat > nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_3231, type, sK2297: (nat > nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > nat).
% 32.77/9.02  thf(func_def_3232, type, sK2298: real > list_real > real).
% 32.77/9.02  thf(func_def_3233, type, sK2299: set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_3234, type, sK2300: set_nat > (nat > code_integer) > nat).
% 32.77/9.02  thf(func_def_3235, type, sK2301: set_nat > code_integer > code_integer > (nat > code_integer) > nat).
% 32.77/9.02  thf(func_def_3236, type, sK2302: nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3237, type, sK2303: num > num).
% 32.77/9.02  thf(func_def_3238, type, sK2304: (int > nat) > (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3239, type, sK2305: set_int > int).
% 32.77/9.02  thf(func_def_3240, type, sK2306: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3241, type, sK2307: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3242, type, sK2308: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3243, type, sK2309: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3244, type, sK2310: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3245, type, sK2311: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3246, type, sK2312: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3247, type, sK2313: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3248, type, sK2314: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3249, type, sK2315: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3250, type, sK2316: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3251, type, sK2317: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3252, type, sK2318: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3253, type, sK2319: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3254, type, sK2320: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3255, type, sK2321: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3256, type, sK2322: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3257, type, sK2323: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3258, type, sK2324: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_3259, type, sK2325: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_3260, type, sK2326: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3261, type, sK2327: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_3262, type, sK2328: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_3263, type, sK2329: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_3264, type, sK2330: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_3265, type, sK2331: (int > int > $o) > int).
% 32.77/9.02  thf(func_def_3266, type, sK2332: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3267, type, sK2333: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_3268, type, sK2334: (set_real > $o) > set_real > set_real).
% 32.77/9.02  thf(func_def_3269, type, sK2335: (set_real > $o) > set_real > real).
% 32.77/9.02  thf(func_def_3270, type, sK2336: option_num > num).
% 32.77/9.02  thf(func_def_3271, type, sK2337: (real > real) > real).
% 32.77/9.02  thf(func_def_3272, type, sK2338: (real > real) > real).
% 32.77/9.02  thf(func_def_3273, type, sK2339: nat > set_nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3274, type, sK2340: set_nat > (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3275, type, sK2341: (complex > nat) > set_complex > (complex > nat) > complex).
% 32.77/9.02  thf(func_def_3276, type, sK2342: set_nat > nat > nat).
% 32.77/9.02  thf(func_def_3277, type, sK2343: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_3278, type, sK2344: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3279, type, sK2345: produc8306885398267862888on_nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3280, type, sK2346: produc8306885398267862888on_nat > nat).
% 32.77/9.02  thf(func_def_3281, type, sK2347: produc8306885398267862888on_nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3282, type, sK2348: produc8306885398267862888on_nat > option_nat).
% 32.77/9.02  thf(func_def_3283, type, sK2349: produc8306885398267862888on_nat > nat).
% 32.77/9.02  thf(func_def_3284, type, sK2350: produc8306885398267862888on_nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3285, type, sK2351: produc8306885398267862888on_nat > nat).
% 32.77/9.02  thf(func_def_3286, type, sK2352: produc2233624965454879586on_nat > option_nat).
% 32.77/9.02  thf(func_def_3287, type, sK2353: produc2233624965454879586on_nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_3288, type, sK2354: produc2233624965454879586on_nat > nat).
% 32.77/9.02  thf(func_def_3289, type, sK2355: produc2233624965454879586on_nat > nat).
% 32.77/9.02  thf(func_def_3290, type, sK2356: produc2233624965454879586on_nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_3291, type, sK2357: produc2233624965454879586on_nat > nat > nat > $o).
% 32.77/9.02  thf(func_def_3292, type, sK2358: produc2233624965454879586on_nat > nat).
% 32.77/9.02  thf(func_def_3293, type, sK2359: (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3294, type, sK2360: (set_real > $o) > real).
% 32.77/9.02  thf(func_def_3295, type, sK2361: (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_3296, type, sK2362: int > int).
% 32.77/9.02  thf(func_def_3297, type, sK2363: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3298, type, sK2364: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3299, type, sK2365: (nat > nat) > (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_3300, type, sK2366: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3301, type, sK2367: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3302, type, sK2368: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3303, type, sK2369: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3304, type, sK2370: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3305, type, sK2371: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_3306, type, sK2372: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3307, type, sK2373: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3308, type, sK2374: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3309, type, sK2375: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3310, type, sK2376: vEBT_VEBT > vEBT_VEBT > nat > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3311, type, sK2377: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3312, type, sK2378: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3313, type, sK2379: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3314, type, sK2380: nat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3315, type, sK2381: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3316, type, sK2382: list_complex > (complex > $o) > nat).
% 32.77/9.02  thf(func_def_3317, type, sK2383: (option_num > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option_num > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3318, type, sK2384: (option_num > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option_num > num).
% 32.77/9.02  thf(func_def_3319, type, sK2385: set_complex > (complex > rat) > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_3320, type, sK2386: nat > real > real).
% 32.77/9.02  thf(func_def_3321, type, sK2387: (complex > $o) > list_complex > complex).
% 32.77/9.02  thf(func_def_3322, type, sK2388: nat > (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_3323, type, sK2389: nat > nat).
% 32.77/9.02  thf(func_def_3324, type, sK2390: list_nat > list_nat > nat).
% 32.77/9.02  thf(func_def_3325, type, sK2391: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3326, type, sK2392: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3327, type, sK2393: (option_num > option_nat > $o) > option_nat > option_num > num).
% 32.77/9.02  thf(func_def_3328, type, sK2394: (option_num > option_nat > $o) > option_nat > option_num > nat).
% 32.77/9.02  thf(func_def_3329, type, sK2395: nat > nat).
% 32.77/9.02  thf(func_def_3330, type, sK2396: (list_VEBT_VEBT > $o) > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3331, type, sK2397: (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3332, type, sK2398: real > real > real > real).
% 32.77/9.02  thf(func_def_3333, type, sK2399: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3334, type, sK2400: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3335, type, sK2401: num > num).
% 32.77/9.02  thf(func_def_3336, type, sK2402: num > num).
% 32.77/9.02  thf(func_def_3337, type, sK2403: nat > nat).
% 32.77/9.02  thf(func_def_3338, type, sK2404: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3339, type, sK2405: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3340, type, sK2406: set_set_nat > set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_3341, type, sK2407: real > real > real).
% 32.77/9.02  thf(func_def_3342, type, sK2408: set_nat > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_3343, type, sK2409: set_nat > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_3344, type, sK2410: set_num > num).
% 32.77/9.02  thf(func_def_3345, type, sK2411: real > real > nat).
% 32.77/9.02  thf(func_def_3346, type, sK2412: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_3347, type, sK2413: (rat > nat) > rat).
% 32.77/9.02  thf(func_def_3348, type, sK2414: real > real).
% 32.77/9.02  thf(func_def_3349, type, sK2415: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_3350, type, sK2416: set_int > set_int > (int > complex) > int).
% 32.77/9.02  thf(func_def_3351, type, sK2417: real > real > real).
% 32.77/9.02  thf(func_def_3352, type, sK2418: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3353, type, sK2419: rat > rat > rat).
% 32.77/9.02  thf(func_def_3354, type, sK2420: real > (real > real) > real).
% 32.77/9.02  thf(func_def_3355, type, sK2421: (nat > num) > nat).
% 32.77/9.02  thf(func_def_3356, type, sK2422: (nat > num) > nat).
% 32.77/9.02  thf(func_def_3357, type, sK2423: (set_rat > $o) > set_rat).
% 32.77/9.02  thf(func_def_3358, type, sK2424: (set_rat > $o) > rat).
% 32.77/9.02  thf(func_def_3359, type, sK2425: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_3360, type, sK2426: real > real > real > real).
% 32.77/9.02  thf(func_def_3361, type, sK2427: (num > nat) > num).
% 32.77/9.02  thf(func_def_3362, type, sK2428: (num > nat) > num).
% 32.77/9.02  thf(func_def_3363, type, sK2429: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3364, type, sK2430: nat > nat).
% 32.77/9.02  thf(func_def_3365, type, sK2431: num > num > num > num).
% 32.77/9.02  thf(func_def_3366, type, sK2432: num > num > num > num).
% 32.77/9.02  thf(func_def_3367, type, sK2433: num > num > num).
% 32.77/9.02  thf(func_def_3368, type, sK2434: num > num).
% 32.77/9.02  thf(func_def_3369, type, sK2435: num > num > num > num).
% 32.77/9.02  thf(func_def_3370, type, sK2436: num > num > num > num).
% 32.77/9.02  thf(func_def_3371, type, sK2437: num > num).
% 32.77/9.02  thf(func_def_3372, type, sK2438: num > num > num > num).
% 32.77/9.02  thf(func_def_3373, type, sK2439: num > num > num > num).
% 32.77/9.02  thf(func_def_3374, type, sK2440: num > num > num).
% 32.77/9.02  thf(func_def_3375, type, sK2441: num > num > num > num).
% 32.77/9.02  thf(func_def_3376, type, sK2442: num > num > num > num).
% 32.77/9.02  thf(func_def_3377, type, sK2443: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3378, type, sK2444: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3379, type, sK2445: nat > (nat > $o) > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3380, type, sK2446: real > real > real).
% 32.77/9.02  thf(func_def_3381, type, sK2447: nat > list_nat > nat).
% 32.77/9.02  thf(func_def_3382, type, sK2448: (real > num) > real).
% 32.77/9.02  thf(func_def_3383, type, sK2449: (real > num) > real).
% 32.77/9.02  thf(func_def_3384, type, sK2450: real > real > real).
% 32.77/9.02  thf(func_def_3385, type, sK2451: int > nat).
% 32.77/9.02  thf(func_def_3386, type, sK2452: nat > nat).
% 32.77/9.02  thf(func_def_3387, type, sK2453: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_3388, type, sK2454: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3389, type, sK2455: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3390, type, sK2456: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3391, type, sK2457: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3392, type, sK2458: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3393, type, sK2459: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3394, type, sK2460: (num > nat) > num).
% 32.77/9.02  thf(func_def_3395, type, sK2461: (num > nat) > num).
% 32.77/9.02  thf(func_def_3396, type, sK2462: (produc7773217078559923341nt_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_3397, type, sK2463: (produc7773217078559923341nt_int > $o) > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3398, type, sK2464: nat > nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3399, type, sK2465: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3400, type, sK2466: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_3401, type, sK2467: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3402, type, sK2468: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_3403, type, sK2469: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.02  thf(func_def_3404, type, sK2470: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3405, type, sK2471: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3406, type, sK2472: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_3407, type, sK2473: vEBT_VEBT > option_nat > nat > $o).
% 32.77/9.02  thf(func_def_3408, type, sK2474: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_3409, type, sK2475: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.02  thf(func_def_3410, type, sK2476: nat > nat).
% 32.77/9.02  thf(func_def_3411, type, sK2477: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3412, type, sK2478: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3413, type, sK2479: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3414, type, sK2480: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3415, type, sK2481: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3416, type, sK2482: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3417, type, sK2483: vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3418, type, sK2484: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3419, type, sK2485: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3420, type, sK2486: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3421, type, sK2487: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3422, type, sK2488: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3423, type, sK2489: (int > nat) > (int > nat) > set_int > int).
% 32.77/9.02  thf(func_def_3424, type, sK2490: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc8763457246119570046nteger > nat > code_integer > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3425, type, sK2491: ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc8763457246119570046nteger > nat > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_3426, type, sK2492: nat > nat > nat).
% 32.77/9.02  thf(func_def_3427, type, sK2493: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_3428, type, sK2494: list_o > list_o > nat).
% 32.77/9.02  thf(func_def_3429, type, sK2495: real > real).
% 32.77/9.02  thf(func_def_3430, type, sK2496: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3431, type, sK2497: (complex > nat) > set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_3432, type, sK2498: nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3433, type, sK2499: (real > num) > real).
% 32.77/9.02  thf(func_def_3434, type, sK2500: (real > num) > real).
% 32.77/9.02  thf(func_def_3435, type, sK2501: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3436, type, sK2502: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3437, type, sK2503: (num > $o) > (num > $o) > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3438, type, sK2504: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3439, type, sK2505: num > (num > $o) > (num > $o) > num).
% 32.77/9.02  thf(func_def_3440, type, sK2506: (complex > rat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3441, type, sK2507: real > real).
% 32.77/9.02  thf(func_def_3442, type, sK2508: (nat > real) > (nat > real) > real).
% 32.77/9.02  thf(func_def_3443, type, sK2509: (nat > real) > (nat > real) > nat).
% 32.77/9.02  thf(func_def_3444, type, sK2510: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3445, type, sK2511: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3446, type, sK2512: produc2285326912895808259nt_int > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3447, type, sK2513: produc2285326912895808259nt_int > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_3448, type, sK2514: real > real > real).
% 32.77/9.02  thf(func_def_3449, type, sK2515: (complex > complex) > set_complex > (complex > real) > set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_3450, type, sK2516: set_complex > (complex > real) > complex).
% 32.77/9.02  thf(func_def_3451, type, sK2517: nat > nat > nat).
% 32.77/9.02  thf(func_def_3452, type, sK2518: list_set_nat > set_set_nat > set_nat).
% 32.77/9.02  thf(func_def_3453, type, sK2519: real > real > real).
% 32.77/9.02  thf(func_def_3454, type, sK2520: (nat > int) > nat).
% 32.77/9.02  thf(func_def_3455, type, sK2521: (rat > $o) > (rat > $o) > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_3456, type, sK2522: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_3457, type, sK2523: rat > (rat > $o) > (rat > $o) > rat).
% 32.77/9.02  thf(func_def_3458, type, sK2524: real > real).
% 32.77/9.02  thf(func_def_3459, type, sK2525: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3460, type, sK2526: set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3461, type, sK2527: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3462, type, sK2528: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_3463, type, sK2529: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3464, type, sK2530: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3465, type, sK2531: (rat > num) > rat).
% 32.77/9.02  thf(func_def_3466, type, sK2532: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3467, type, sK2533: option_nat > nat).
% 32.77/9.02  thf(func_def_3468, type, sK2534: (set_set_nat > $o) > set_set_nat > set_set_nat).
% 32.77/9.02  thf(func_def_3469, type, sK2535: (complex > $o) > (complex > $o) > complex).
% 32.77/9.02  thf(func_def_3470, type, sK2536: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3471, type, sK2537: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3472, type, sK2538: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3473, type, sK2539: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3474, type, sK2540: (complex > nat) > set_complex > (complex > nat) > (nat > nat > $o) > complex).
% 32.77/9.02  thf(func_def_3475, type, sK2541: set_real > (set_real > $o) > set_real).
% 32.77/9.02  thf(func_def_3476, type, sK2542: set_real > (set_real > $o) > real).
% 32.77/9.02  thf(func_def_3477, type, sK2543: (nat > real > real) > real).
% 32.77/9.02  thf(func_def_3478, type, sK2544: (nat > real > real) > nat).
% 32.77/9.02  thf(func_def_3479, type, sK2545: nat > (nat > real > real) > real > (real > real) > real).
% 32.77/9.02  thf(func_def_3480, type, sK2546: (int > int > set_nat) > product_prod_int_int > nat > int).
% 32.77/9.02  thf(func_def_3481, type, sK2547: (int > int > set_nat) > product_prod_int_int > nat > int).
% 32.77/9.02  thf(func_def_3482, type, sK2548: list_complex > complex > complex).
% 32.77/9.02  thf(func_def_3483, type, sK2549: nat > nat > nat).
% 32.77/9.02  thf(func_def_3484, type, sK2550: real > nat).
% 32.77/9.02  thf(func_def_3485, type, sK2551: real > real > real).
% 32.77/9.02  thf(func_def_3486, type, sK2552: int > int > int).
% 32.77/9.02  thf(func_def_3487, type, sK2553: int > int).
% 32.77/9.02  thf(func_def_3488, type, sK2554: (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_3489, type, sK2555: num > num).
% 32.77/9.02  thf(func_def_3490, type, sK2556: real > nat > real).
% 32.77/9.02  thf(func_def_3491, type, sK2557: nat > nat > nat).
% 32.77/9.02  thf(func_def_3492, type, sK2558: real > real).
% 32.77/9.02  thf(func_def_3493, type, sK2559: nat > (nat > $o) > nat > nat).
% 32.77/9.02  thf(func_def_3494, type, sK2560: (int > $o) > int).
% 32.77/9.02  thf(func_def_3495, type, sK2561: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_3496, type, sK2562: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3497, type, sK2563: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3498, type, sK2564: vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3499, type, sK2565: set_real > (real > rat) > (real > rat) > real).
% 32.77/9.02  thf(func_def_3500, type, sK2566: vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3501, type, sK2567: nat > real > real).
% 32.77/9.02  thf(func_def_3502, type, sK2568: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3503, type, sK2569: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3504, type, sK2570: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3505, type, sK2571: (rat > $o) > rat > rat).
% 32.77/9.02  thf(func_def_3506, type, sK2572: list_real > real > nat).
% 32.77/9.02  thf(func_def_3507, type, sK2573: (real > real) > (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_3508, type, sK2574: (real > complex) > (real > real) > (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_3509, type, sK2575: set_real > (real > complex) > real).
% 32.77/9.02  thf(func_def_3510, type, sK2576: set_real > set_real > (real > real) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_3511, type, sK2577: (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_3512, type, sK2578: set_real > set_real > set_real > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3513, type, sK2579: (real > real) > set_real > (real > real) > set_real > real).
% 32.77/9.02  thf(func_def_3514, type, sK2580: (real > nat) > real).
% 32.77/9.02  thf(func_def_3515, type, sK2581: (real > nat) > real).
% 32.77/9.02  thf(func_def_3516, type, sK2582: (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3517, type, sK2583: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_3518, type, sK2584: produc9072475918466114483BT_nat > $o).
% 32.77/9.02  thf(func_def_3519, type, sK2585: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3520, type, sK2586: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3521, type, sK2587: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3522, type, sK2588: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3523, type, sK2589: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3524, type, sK2590: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3525, type, sK2591: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3526, type, sK2592: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3527, type, sK2593: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3528, type, sK2594: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3529, type, sK2595: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3530, type, sK2596: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3531, type, sK2597: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3532, type, sK2598: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3533, type, sK2599: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3534, type, sK2600: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3535, type, sK2601: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 32.77/9.02  thf(func_def_3536, type, sK2602: produc9072475918466114483BT_nat > nat).
% 32.77/9.02  thf(func_def_3537, type, sK2603: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3538, type, sK2604: rat > rat).
% 32.77/9.02  thf(func_def_3539, type, sK2605: int > int > int).
% 32.77/9.02  thf(func_def_3540, type, sK2606: (real > int) > set_real > (real > int) > real).
% 32.77/9.02  thf(func_def_3541, type, sK2607: (nat > real) > set_nat > (nat > complex) > nat).
% 32.77/9.02  thf(func_def_3542, type, sK2608: (num > nat) > num).
% 32.77/9.02  thf(func_def_3543, type, sK2609: (num > nat) > num).
% 32.77/9.02  thf(func_def_3544, type, sK2610: (code_integer > $o) > $o).
% 32.77/9.02  thf(func_def_3545, type, sK2611: (code_integer > $o) > code_integer).
% 32.77/9.02  thf(func_def_3546, type, sK2612: (code_integer > $o) > code_integer).
% 32.77/9.02  thf(func_def_3547, type, sK2613: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3548, type, sK2614: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3549, type, sK2615: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3550, type, sK2616: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3551, type, sK2617: (num > num > $o) > num).
% 32.77/9.02  thf(func_def_3552, type, sK2618: nat > set_nat > nat).
% 32.77/9.02  thf(func_def_3553, type, sK2619: nat > nat > nat).
% 32.77/9.02  thf(func_def_3554, type, sK2620: produc7773217078559923341nt_int > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > product_prod_int_int).
% 32.77/9.02  thf(func_def_3555, type, sK2621: produc7773217078559923341nt_int > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3556, type, sK2622: (complex > $o) > (complex > $o) > complex).
% 32.77/9.02  thf(func_def_3557, type, sK2623: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > product_prod_int_int).
% 32.77/9.02  thf(func_def_3558, type, sK2624: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > int > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3559, type, sK2625: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3560, type, sK2626: (rat > real) > rat).
% 32.77/9.02  thf(func_def_3561, type, sK2627: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3562, type, sK2628: set_int > set_int > int).
% 32.77/9.02  thf(func_def_3563, type, sK2629: (complex > $o) > (complex > $o) > complex).
% 32.77/9.02  thf(func_def_3564, type, sK2630: (set_nat > $o) > (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_3565, type, sK2631: set_int > int).
% 32.77/9.02  thf(func_def_3566, type, sK2632: nat > set_nat > (nat > rat) > nat).
% 32.77/9.02  thf(func_def_3567, type, sK2633: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_3568, type, sK2634: real > (real > real) > real > real).
% 32.77/9.02  thf(func_def_3569, type, sK2635: int > int).
% 32.77/9.02  thf(func_def_3570, type, sK2636: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3571, type, sK2637: nat > nat > nat).
% 32.77/9.02  thf(func_def_3572, type, sK2638: (nat > complex) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_3573, type, sK2639: (rat > int) > rat).
% 32.77/9.02  thf(func_def_3574, type, sK2640: (rat > int) > rat).
% 32.77/9.02  thf(func_def_3575, type, sK2641: nat > (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3576, type, sK2642: (num > nat) > num).
% 32.77/9.02  thf(func_def_3577, type, sK2643: (num > nat) > num).
% 32.77/9.02  thf(func_def_3578, type, sK2644: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3579, type, sK2645: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3580, type, sK2646: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3581, type, sK2647: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3582, type, sK2648: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3583, type, sK2649: (nat > nat > $o) > nat).
% 32.77/9.02  thf(func_def_3584, type, sK2650: product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_3585, type, sK2651: product_prod_nat_nat > nat).
% 32.77/9.02  thf(func_def_3586, type, sK2652: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3587, type, sK2653: (nat > nat) > nat).
% 32.77/9.02  thf(func_def_3588, type, sK2654: real > int).
% 32.77/9.02  thf(func_def_3589, type, sK2655: set_int > (int > rat) > int).
% 32.77/9.02  thf(func_def_3590, type, sK2656: set_int > (nat > rat) > (int > nat) > (int > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_3591, type, sK2657: real > (real > real) > real).
% 32.77/9.02  thf(func_def_3592, type, sK2658: real > (real > real) > (real > real > real) > real > real).
% 32.77/9.02  thf(func_def_3593, type, sK2659: real > (real > real) > (real > real > real) > real > real).
% 32.77/9.02  thf(func_def_3594, type, sK2660: list_VEBT_VEBT > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3595, type, sK2661: set_list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3596, type, sK2662: list_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_3597, type, sK2663: (real > rat) > real).
% 32.77/9.02  thf(func_def_3598, type, sK2664: (real > rat) > real).
% 32.77/9.02  thf(func_def_3599, type, sK2665: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.02  thf(func_def_3600, type, sK2666: set_complex > set_complex > (complex > int) > complex).
% 32.77/9.02  thf(func_def_3601, type, sK2667: real > real > real > real).
% 32.77/9.02  thf(func_def_3602, type, sK2668: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_3603, type, sK2669: (set_int > $o) > int).
% 32.77/9.02  thf(func_def_3604, type, sK2670: (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_3605, type, sK2671: produc1908205239877642774nteger > produc6241069584506657477e_term > option6357759511663192854e_term).
% 32.77/9.02  thf(func_def_3606, type, sK2672: produc1908205239877642774nteger > produc8923325533196201883nteger).
% 32.77/9.02  thf(func_def_3607, type, sK2673: (vEBT_VEBT > $o) > list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3608, type, sK2674: (set_nat > $o) > list_set_nat > set_nat).
% 32.77/9.02  thf(func_def_3609, type, sK2675: (num > real) > num).
% 32.77/9.02  thf(func_def_3610, type, sK2676: (num > real) > num).
% 32.77/9.02  thf(func_def_3611, type, sK2677: (nat > real) > real).
% 32.77/9.02  thf(func_def_3612, type, sK2678: nat > (nat > real) > nat).
% 32.77/9.02  thf(func_def_3613, type, sK2679: set_int > (int > rat) > (int > rat) > int).
% 32.77/9.02  thf(func_def_3614, type, sK2680: real > real).
% 32.77/9.02  thf(func_def_3615, type, sK2681: real > nat).
% 32.77/9.02  thf(func_def_3616, type, sK2682: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3617, type, sK2683: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3618, type, sK2684: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3619, type, sK2685: (nat > real) > nat).
% 32.77/9.02  thf(func_def_3620, type, sK2686: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_3621, type, sK2687: real > real > set_int > (int > real) > int).
% 32.77/9.02  thf(func_def_3622, type, sK2688: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.02  thf(func_def_3623, type, sK2689: real > real > (real > real) > real).
% 32.77/9.02  thf(func_def_3624, type, sK2690: (complex > rat) > set_complex > (complex > rat) > complex).
% 32.77/9.02  thf(func_def_3625, type, sK2691: (real > rat) > real).
% 32.77/9.02  thf(func_def_3626, type, sK2692: (real > rat) > real).
% 32.77/9.02  thf(func_def_3627, type, sK2693: (product_prod_int_int > $o) > product_prod_int_int > (int > int > product_prod_int_int) > int).
% 32.77/9.02  thf(func_def_3628, type, sK2694: (product_prod_int_int > $o) > product_prod_int_int > (int > int > product_prod_int_int) > int).
% 32.77/9.02  thf(func_def_3629, type, sK2695: (set_real > $o) > set_real > set_real).
% 32.77/9.02  thf(func_def_3630, type, sK2696: rat > rat > rat > rat).
% 32.77/9.02  thf(func_def_3631, type, sK2697: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3632, type, sK2698: (int > real) > set_int > int).
% 32.77/9.02  thf(func_def_3633, type, sK2699: (int > int) > (int > real) > (int > real) > set_int > set_int > int).
% 32.77/9.02  thf(func_def_3634, type, sK2700: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_3635, type, sK2701: (rat > rat) > rat).
% 32.77/9.02  thf(func_def_3636, type, sK2702: num > num).
% 32.77/9.02  thf(func_def_3637, type, sK2703: (nat > complex) > set_nat > set_nat > nat).
% 32.77/9.02  thf(func_def_3638, type, sK2704: (nat > complex) > (nat > complex) > set_nat > nat).
% 32.77/9.02  thf(func_def_3639, type, sK2705: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3640, type, sK2706: int > set_int > int > int).
% 32.77/9.02  thf(func_def_3641, type, sK2707: set_nat > nat > nat).
% 32.77/9.02  thf(func_def_3642, type, sK2708: (nat > rat) > (nat > int) > set_nat > (int > rat) > set_int > int).
% 32.77/9.02  thf(func_def_3643, type, sK2709: (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_3644, type, sK2710: set_real > set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_3645, type, sK2711: set_real > (real > rat) > (real > rat) > real).
% 32.77/9.02  thf(func_def_3646, type, sK2712: set_complex > set_complex > complex).
% 32.77/9.02  thf(func_def_3647, type, sK2713: set_real > set_real > (real > rat) > real).
% 32.77/9.02  thf(func_def_3648, type, sK2714: (vEBT_VEBT > $o) > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3649, type, sK2715: set_int > (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_3650, type, sK2716: (real > complex) > set_real > set_real > real).
% 32.77/9.02  thf(func_def_3651, type, sK2717: set_real > (real > complex) > set_real > real).
% 32.77/9.02  thf(func_def_3652, type, sK2718: $o > nat > vEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3653, type, sK2719: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3654, type, sK2720: $o > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3655, type, sK2721: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3656, type, sK2722: vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.02  thf(func_def_3657, type, sK2723: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3658, type, sK2724: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.02  thf(func_def_3659, type, sK2725: nat > vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_3660, type, sK2726: nat > vEBT_VEBT > $o > $o).
% 32.77/9.02  thf(func_def_3661, type, sK2727: (real > nat) > (real > nat) > set_real > real).
% 32.77/9.02  thf(func_def_3662, type, sK2728: (set_complex > $o) > set_complex).
% 32.77/9.02  thf(func_def_3663, type, sK2729: real > (nat > real) > nat).
% 32.77/9.02  thf(func_def_3664, type, sK2730: (nat > real) > real).
% 32.77/9.02  thf(func_def_3665, type, sK2731: (set_nat > $o) > set_nat).
% 32.77/9.02  thf(func_def_3666, type, sK2732: (set_nat > $o) > nat).
% 32.77/9.02  thf(func_def_3667, type, sK2733: set_list_int > nat).
% 32.77/9.02  thf(func_def_3668, type, sK2734: (list_o > $o) > list_o).
% 32.77/9.02  thf(func_def_3669, type, sK2735: (real > real) > set_real > (real > real) > real).
% 32.77/9.02  thf(func_def_3670, type, sK2736: (extended_enat > $o) > extended_enat).
% 32.77/9.02  thf(func_def_3671, type, sK2737: code_integer > code_integer > code_integer).
% 32.77/9.02  thf(func_def_3672, type, sK2738: vEBT_VEBT > list_VEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_3673, type, sK2739: vEBT_VEBT > list_VEBT_VEBT > nat > nat).
% 32.77/9.02  thf(func_def_3674, type, sK2740: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3675, type, sK2741: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 32.77/9.02  thf(func_def_3676, type, sK2742: list_VEBT_VEBT > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3677, type, sK2743: list_VEBT_VEBT > nat).
% 32.77/9.02  thf(func_def_3678, type, sK2744: list_VEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.02  thf(func_def_3679, type, sK2745: set_complex > list_complex).
% 32.77/9.02  thf(func_def_3680, type, sK2746: int > int).
% 32.77/9.02  thf(func_def_3681, type, sK2747: real > (real > real) > real > (real > real) > real).
% 32.77/9.02  thf(func_def_3682, type, sK2748: (nat > nat) > set_nat > nat).
% 32.77/9.02  thf(func_def_3683, type, sK2749: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3684, type, sK2750: vEBT_VEBT > $o).
% 32.77/9.02  thf(func_def_3685, type, sK2751: set_int > (int > complex) > int).
% 32.77/9.02  thf(func_def_3686, type, sK2752: (int > num) > int).
% 32.77/9.02  thf(func_def_3687, type, sK2753: (int > num) > int).
% 32.77/9.02  thf(func_def_3688, type, sK2754: (nat > $o) > nat).
% 32.77/9.02  thf(func_def_3689, type, sK2755: real > nat).
% 32.77/9.02  thf(func_def_3690, type, sK2756: real > nat).
% 32.77/9.02  thf(func_def_3691, type, sK2757: set_nat > (nat > rat) > set_nat > nat).
% 32.77/9.02  thf(func_def_3692, type, sK2758: set_int > (set_int > $o) > set_int).
% 32.77/9.02  thf(func_def_3693, type, sK2759: (int > $o) > int).
% 32.77/9.02  thf(func_def_3694, type, sK2760: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3695, type, sK2761: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3696, type, sK2762: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3697, type, sK2763: int > set_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3698, type, sK2764: int > set_int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3699, type, sK2765: (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3700, type, sK2766: (int > $o) > int).
% 32.77/9.02  thf(func_def_3701, type, sK2767: set_int > (int > $o) > int > int).
% 32.77/9.02  thf(func_def_3702, type, sK2768: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3703, type, sK2769: int > (int > $o) > int).
% 32.77/9.02  thf(func_def_3704, type, sK2770: int > (int > $o) > (int > $o) > int).
% 32.77/9.02  thf(func_def_3705, type, sK2771: real > real > (real > real > $o) > real).
% 32.77/9.02  thf(func_def_3706, type, sK2772: real > real > real > (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3707, type, sK2773: real > real > real > (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3708, type, sK2774: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3709, type, sK2775: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3710, type, sK2776: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3711, type, sK2777: (nat > rat) > set_nat > (nat > rat) > nat).
% 32.77/9.03  thf(func_def_3712, type, sK2778: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 32.77/9.03  thf(func_def_3713, type, sK2779: int > (int > $o) > (int > $o) > int).
% 32.77/9.03  thf(func_def_3714, type, sK2780: int > (int > $o) > (int > $o) > int).
% 32.77/9.03  thf(func_def_3715, type, sK2781: (real > real) > real > real > real).
% 32.77/9.03  thf(func_def_3716, type, sK2782: real > real > (real > real) > (real > real) > real).
% 32.77/9.03  thf(func_def_3717, type, sK2783: (num > int) > num).
% 32.77/9.03  thf(func_def_3718, type, sK2784: (num > int) > num).
% 32.77/9.03  thf(func_def_3719, type, sK2785: (product_prod_int_int > $o) > (int > int > $o) > int).
% 32.77/9.03  thf(func_def_3720, type, sK2786: (product_prod_int_int > $o) > (int > int > $o) > int).
% 32.77/9.03  thf(func_def_3721, type, sK2787: set_real > (real > real) > real).
% 32.77/9.03  thf(func_def_3722, type, sK2788: set_real > (real > real) > real > real > real).
% 32.77/9.03  thf(func_def_3723, type, sK2789: (set_real > $o) > (real > num) > real).
% 32.77/9.03  thf(func_def_3724, type, sK2790: (set_real > $o) > (real > num) > set_real).
% 32.77/9.03  thf(func_def_3725, type, sK2791: (int > $o) > int > int).
% 32.77/9.03  thf(func_def_3726, type, sK2792: complex > (complex > nat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3727, type, sK2793: (complex > nat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3728, type, sK2794: (code_integer > code_integer > $o) > code_integer).
% 32.77/9.03  thf(func_def_3729, type, sK2795: (real > nat) > real > set_real > real).
% 32.77/9.03  thf(func_def_3730, type, sK2796: produc9072475918466114483BT_nat > nat).
% 32.77/9.03  thf(func_def_3731, type, sK2797: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3732, type, sK2798: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3733, type, sK2799: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3734, type, sK2800: produc9072475918466114483BT_nat > $o).
% 32.77/9.03  thf(func_def_3735, type, sK2801: produc9072475918466114483BT_nat > $o).
% 32.77/9.03  thf(func_def_3736, type, sK2802: produc9072475918466114483BT_nat > nat).
% 32.77/9.03  thf(func_def_3737, type, sK2803: produc9072475918466114483BT_nat > nat).
% 32.77/9.03  thf(func_def_3738, type, sK2804: produc9072475918466114483BT_nat > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3739, type, sK2805: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3740, type, sK2806: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3741, type, sK2807: produc9072475918466114483BT_nat > nat).
% 32.77/9.03  thf(func_def_3742, type, sK2808: set_complex > (complex > rat) > complex).
% 32.77/9.03  thf(func_def_3743, type, sK2809: complex > (complex > $o) > complex).
% 32.77/9.03  thf(func_def_3744, type, sK2810: complex > (complex > $o) > complex).
% 32.77/9.03  thf(func_def_3745, type, sK2811: int > nat).
% 32.77/9.03  thf(func_def_3746, type, sK2812: int > nat).
% 32.77/9.03  thf(func_def_3747, type, sK2813: nat > nat > nat).
% 32.77/9.03  thf(func_def_3748, type, sK2814: nat > (nat > $o) > nat > nat).
% 32.77/9.03  thf(func_def_3749, type, sK2815: option_num > num).
% 32.77/9.03  thf(func_def_3750, type, sK2816: (produc2285326912895808259nt_int > $o) > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3751, type, sK2817: (produc2285326912895808259nt_int > $o) > product_prod_int_int).
% 32.77/9.03  thf(func_def_3752, type, sK2818: produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.03  thf(func_def_3753, type, sK2819: produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3754, type, sK2820: (real > real) > real).
% 32.77/9.03  thf(func_def_3755, type, sK2821: (real > real) > real).
% 32.77/9.03  thf(func_def_3756, type, sK2822: set_complex > (complex > real) > (complex > real) > complex).
% 32.77/9.03  thf(func_def_3757, type, sK2823: set_complex > set_complex > (complex > real) > complex).
% 32.77/9.03  thf(func_def_3758, type, sK2824: real > real > nat).
% 32.77/9.03  thf(func_def_3759, type, sK2825: int > set_int > int > int).
% 32.77/9.03  thf(func_def_3760, type, sK2826: int > set_int > int > int).
% 32.77/9.03  thf(func_def_3761, type, sK2827: (nat > $o) > list_nat > nat).
% 32.77/9.03  thf(func_def_3762, type, sK2828: nat > nat > nat).
% 32.77/9.03  thf(func_def_3763, type, sK2829: set_complex > (complex > nat) > complex).
% 32.77/9.03  thf(func_def_3764, type, sK2830: nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3765, type, sK2831: nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3766, type, sK2832: nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3767, type, sK2833: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3768, type, sK2834: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3769, type, sK2835: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3770, type, sK2836: set_nat > set_nat > nat).
% 32.77/9.03  thf(func_def_3771, type, sK2837: rat > rat > rat).
% 32.77/9.03  thf(func_def_3772, type, sK2838: (real > real) > real > real).
% 32.77/9.03  thf(func_def_3773, type, sK2839: nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3774, type, sK2840: (nat > real > real) > real > nat > real).
% 32.77/9.03  thf(func_def_3775, type, sK2841: (nat > real > real) > real > nat > nat).
% 32.77/9.03  thf(func_def_3776, type, sK2842: (real > real) > nat > (nat > real > real) > real > real).
% 32.77/9.03  thf(func_def_3777, type, sK2843: real > real).
% 32.77/9.03  thf(func_def_3778, type, sK2844: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3779, type, sK2845: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3780, type, sK2846: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3781, type, sK2847: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3782, type, sK2848: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3783, type, sK2849: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3784, type, sK2850: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3785, type, sK2851: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3786, type, sK2852: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3787, type, sK2853: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 32.77/9.03  thf(func_def_3788, type, sK2854: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 32.77/9.03  thf(func_def_3789, type, sK2855: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3790, type, sK2856: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3791, type, sK2857: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3792, type, sK2858: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3793, type, sK2859: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3794, type, sK2860: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.03  thf(func_def_3795, type, sK2861: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 32.77/9.03  thf(func_def_3796, type, sK2862: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3797, type, sK2863: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3798, type, sK2864: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3799, type, sK2865: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3800, type, sK2866: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3801, type, sK2867: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3802, type, sK2868: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3803, type, sK2869: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3804, type, sK2870: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3805, type, sK2871: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3806, type, sK2872: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3807, type, sK2873: set_complex > set_complex > (complex > real) > complex).
% 32.77/9.03  thf(func_def_3808, type, sK2874: set_complex > (complex > real) > set_complex > complex).
% 32.77/9.03  thf(func_def_3809, type, sK2875: set_int > int > (int > nat) > int).
% 32.77/9.03  thf(func_def_3810, type, sK2876: set_nat > nat).
% 32.77/9.03  thf(func_def_3811, type, sK2877: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3812, type, sK2878: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3813, type, sK2879: vEBT_VEBT > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3814, type, sK2880: vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3815, type, sK2881: vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3816, type, sK2882: vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3817, type, sK2883: nat > nat).
% 32.77/9.03  thf(func_def_3818, type, sK2884: nat > nat).
% 32.77/9.03  thf(func_def_3819, type, sK2885: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 32.77/9.03  thf(func_def_3820, type, sK2886: real > (real > $o) > (real > $o) > real).
% 32.77/9.03  thf(func_def_3821, type, sK2887: real > (real > $o) > (real > $o) > real).
% 32.77/9.03  thf(func_def_3822, type, sK2888: (set_nat > $o) > list_set_nat > nat).
% 32.77/9.03  thf(func_def_3823, type, sK2889: real > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_real) > produc8763457246119570046nteger > produc8923325533196201883nteger).
% 32.77/9.03  thf(func_def_3824, type, sK2890: real > ((code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > set_real) > produc8763457246119570046nteger > code_integer > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3825, type, sK2891: nat > nat).
% 32.77/9.03  thf(func_def_3826, type, sK2892: set_complex > (set_complex > $o) > set_complex).
% 32.77/9.03  thf(func_def_3827, type, sK2893: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3828, type, sK2894: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3829, type, sK2895: (nat > $o) > nat > nat).
% 32.77/9.03  thf(func_def_3830, type, sK2896: (nat > $o) > nat > nat).
% 32.77/9.03  thf(func_def_3831, type, sK2897: (int > nat) > (nat > nat > $o) > (int > nat) > set_int > int).
% 32.77/9.03  thf(func_def_3832, type, sK2898: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3833, type, sK2899: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3834, type, sK2900: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3835, type, sK2901: (nat > nat > $o) > nat).
% 32.77/9.03  thf(func_def_3836, type, sK2902: set_real > real).
% 32.77/9.03  thf(func_def_3837, type, sK2903: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3838, type, sK2904: vEBT_VEBT > nat > $o > nat).
% 32.77/9.03  thf(func_def_3839, type, sK2905: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3840, type, sK2906: vEBT_VEBT > nat > $o > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3841, type, sK2907: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3842, type, sK2908: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3843, type, sK2909: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3844, type, sK2910: (real > int) > real).
% 32.77/9.03  thf(func_def_3845, type, sK2911: (real > int) > real).
% 32.77/9.03  thf(func_def_3846, type, sK2912: set_nat > nat > nat).
% 32.77/9.03  thf(func_def_3847, type, sK2913: (real > real) > (nat > real) > real > nat > real).
% 32.77/9.03  thf(func_def_3848, type, sK2914: set_int > set_set_int > set_int).
% 32.77/9.03  thf(func_def_3849, type, sK2915: set_int > (int > nat) > int).
% 32.77/9.03  thf(func_def_3850, type, sK2916: int > int > int).
% 32.77/9.03  thf(func_def_3851, type, sK2917: nat > nat > nat).
% 32.77/9.03  thf(func_def_3852, type, sK2918: nat > nat > nat).
% 32.77/9.03  thf(func_def_3853, type, sK2919: set_complex > (complex > real) > set_complex > complex).
% 32.77/9.03  thf(func_def_3854, type, sK2920: set_nat > nat).
% 32.77/9.03  thf(func_def_3855, type, sK2921: real > real > real).
% 32.77/9.03  thf(func_def_3856, type, sK2922: list_nat > nat > nat).
% 32.77/9.03  thf(func_def_3857, type, sK2923: set_complex > (complex > code_integer) > complex).
% 32.77/9.03  thf(func_def_3858, type, sK2924: set_complex > code_integer > code_integer > (complex > code_integer) > complex).
% 32.77/9.03  thf(func_def_3859, type, sK2925: rat > rat).
% 32.77/9.03  thf(func_def_3860, type, sK2926: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3861, type, sK2927: vEBT_VEBT > $o).
% 32.77/9.03  thf(func_def_3862, type, sK2928: int > int > int).
% 32.77/9.03  thf(func_def_3863, type, sK2929: real > real).
% 32.77/9.03  thf(func_def_3864, type, sK2930: (nat > real) > set_nat > (nat > real) > nat).
% 32.77/9.03  thf(func_def_3865, type, sK2931: rat > rat).
% 32.77/9.03  thf(func_def_3866, type, sK2932: nat > nat).
% 32.77/9.03  thf(func_def_3867, type, sK2933: (nat > $o) > nat > nat > nat).
% 32.77/9.03  thf(func_def_3868, type, sK2934: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.03  thf(func_def_3869, type, sK2935: produc5491161045314408544at_nat > option4927543243414619207at_nat).
% 32.77/9.03  thf(func_def_3870, type, sK2936: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.03  thf(func_def_3871, type, sK2937: produc5491161045314408544at_nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3872, type, sK2938: produc5491161045314408544at_nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3873, type, sK2939: produc5491161045314408544at_nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3874, type, sK2940: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 32.77/9.03  thf(func_def_3875, type, sK2941: int > set_int > (int > nat) > int).
% 32.77/9.03  thf(func_def_3876, type, sK2942: set_int > (int > nat) > int).
% 32.77/9.03  thf(func_def_3877, type, sK2943: set_complex > (complex > real) > complex).
% 32.77/9.03  thf(func_def_3878, type, sK2944: nat > nat).
% 32.77/9.03  thf(func_def_3879, type, sK2945: nat > set_nat > nat).
% 32.77/9.03  thf(func_def_3880, type, sK2946: real > int).
% 32.77/9.03  thf(func_def_3881, type, sK2947: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3882, type, sK2948: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3883, type, sK2949: (int > $o) > int > int > int).
% 32.77/9.03  thf(func_def_3884, type, sK2950: (int > $o) > int > int > int).
% 32.77/9.03  thf(func_def_3885, type, sK2951: int > (int > $o) > int > int).
% 32.77/9.03  thf(func_def_3886, type, sK2952: int > (int > $o) > int > int).
% 32.77/9.03  thf(func_def_3887, type, sK2953: (produc8763457246119570046nteger > $o) > produc8923325533196201883nteger).
% 32.77/9.03  thf(func_def_3888, type, sK2954: (produc8763457246119570046nteger > $o) > code_integer > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3889, type, sK2955: rat > rat).
% 32.77/9.03  thf(func_def_3890, type, sK2956: (complex > real) > set_complex > set_complex > complex).
% 32.77/9.03  thf(func_def_3891, type, sK2957: (complex > rat) > set_complex > set_complex > complex).
% 32.77/9.03  thf(func_def_3892, type, sK2958: complex > product_prod_int_int > (int > int > set_complex) > int).
% 32.77/9.03  thf(func_def_3893, type, sK2959: complex > product_prod_int_int > (int > int > set_complex) > int).
% 32.77/9.03  thf(func_def_3894, type, sK2960: real > real).
% 32.77/9.03  thf(func_def_3895, type, sK2961: (rat > nat) > rat).
% 32.77/9.03  thf(func_def_3896, type, sK2962: (rat > nat) > rat).
% 32.77/9.03  thf(func_def_3897, type, sK2963: (rat > rat > $o) > rat).
% 32.77/9.03  thf(func_def_3898, type, sK2964: (option4927543243414619207at_nat > option_nat > $o) > option_nat > option4927543243414619207at_nat > nat).
% 32.77/9.03  thf(func_def_3899, type, sK2965: (option4927543243414619207at_nat > option_nat > $o) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3900, type, sK2966: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3901, type, sK2967: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > nat).
% 32.77/9.03  thf(func_def_3902, type, sK2968: set_int > (int > real) > int).
% 32.77/9.03  thf(func_def_3903, type, sK2969: (int > complex) > set_int > (int > real) > (complex > real) > set_complex > complex).
% 32.77/9.03  thf(func_def_3904, type, sK2970: int > int > set_int > int).
% 32.77/9.03  thf(func_def_3905, type, sK2971: int > int > set_int > int).
% 32.77/9.03  thf(func_def_3906, type, sK2972: real > nat).
% 32.77/9.03  thf(func_def_3907, type, sK2973: real > nat).
% 32.77/9.03  thf(func_def_3908, type, sK2974: (num > num) > num).
% 32.77/9.03  thf(func_def_3909, type, sK2975: (num > num) > num).
% 32.77/9.03  thf(func_def_3910, type, sK2976: nat > nat).
% 32.77/9.03  thf(func_def_3911, type, sK2977: nat > nat > nat > nat).
% 32.77/9.03  thf(func_def_3912, type, sK2978: nat > nat > nat > nat).
% 32.77/9.03  thf(func_def_3913, type, sK2979: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3914, type, sK2980: (rat > rat) > rat).
% 32.77/9.03  thf(func_def_3915, type, sK2981: set_int > (int > real) > int).
% 32.77/9.03  thf(func_def_3916, type, sK2982: set_complex > (complex > int) > set_complex > complex).
% 32.77/9.03  thf(func_def_3917, type, sK2983: (complex > int) > set_complex > (complex > int) > complex).
% 32.77/9.03  thf(func_def_3918, type, sK2984: real > set_real > real).
% 32.77/9.03  thf(func_def_3919, type, sK2985: produc2285326912895808259nt_int > int).
% 32.77/9.03  thf(func_def_3920, type, sK2986: produc2285326912895808259nt_int > int).
% 32.77/9.03  thf(func_def_3921, type, sK2987: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3922, type, sK2988: (int > rat) > int).
% 32.77/9.03  thf(func_def_3923, type, sK2989: (int > rat) > int).
% 32.77/9.03  thf(func_def_3924, type, sK2990: list_int > list_int > nat).
% 32.77/9.03  thf(func_def_3925, type, sK2991: real > (real > real) > real).
% 32.77/9.03  thf(func_def_3926, type, sK2992: (nat > num) > nat).
% 32.77/9.03  thf(func_def_3927, type, sK2993: (nat > num) > nat).
% 32.77/9.03  thf(func_def_3928, type, sK2994: set_VEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3929, type, sK2995: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3930, type, sK2996: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3931, type, sK2997: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3932, type, sK2998: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3933, type, sK2999: (real > real > $o) > real).
% 32.77/9.03  thf(func_def_3934, type, sK3000: set_nat > (set_nat > $o) > set_nat).
% 32.77/9.03  thf(func_def_3935, type, sK3001: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3936, type, sK3002: set_complex > (complex > nat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3937, type, sK3003: rat > rat > rat).
% 32.77/9.03  thf(func_def_3938, type, sK3004: (rat > num) > rat).
% 32.77/9.03  thf(func_def_3939, type, sK3005: (rat > num) > rat).
% 32.77/9.03  thf(func_def_3940, type, sK3006: real > set_real > real).
% 32.77/9.03  thf(func_def_3941, type, sK3007: (int > rat) > int).
% 32.77/9.03  thf(func_def_3942, type, sK3008: (int > rat) > int).
% 32.77/9.03  thf(func_def_3943, type, sK3009: int > set_int > int).
% 32.77/9.03  thf(func_def_3944, type, sK3010: nat > set_nat > nat).
% 32.77/9.03  thf(func_def_3945, type, sK3011: (int > real) > set_int > int).
% 32.77/9.03  thf(func_def_3946, type, sK3012: (real > rat) > real).
% 32.77/9.03  thf(func_def_3947, type, sK3013: (real > rat) > real).
% 32.77/9.03  thf(func_def_3948, type, sK3014: (nat > nat) > (nat > nat) > nat).
% 32.77/9.03  thf(func_def_3949, type, sK3015: real > real > real).
% 32.77/9.03  thf(func_def_3950, type, sK3016: nat > (int > $o) > int > int).
% 32.77/9.03  thf(func_def_3951, type, sK3017: (produc2285326912895808259nt_int > $o) > int).
% 32.77/9.03  thf(func_def_3952, type, sK3018: (produc2285326912895808259nt_int > $o) > produc8551481072490612790e_term > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3953, type, sK3019: (produc2285326912895808259nt_int > $o) > int).
% 32.77/9.03  thf(func_def_3954, type, sK3020: (rat > num) > rat).
% 32.77/9.03  thf(func_def_3955, type, sK3021: (rat > num) > rat).
% 32.77/9.03  thf(func_def_3956, type, sK3022: nat > (nat > $o) > nat > nat).
% 32.77/9.03  thf(func_def_3957, type, sK3023: nat > (nat > $o) > nat > nat).
% 32.77/9.03  thf(func_def_3958, type, sK3024: num > num).
% 32.77/9.03  thf(func_def_3959, type, sK3025: (complex > rat) > (complex > rat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3960, type, sK3026: set_complex > (complex > rat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3961, type, sK3027: set_complex > (complex > rat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3962, type, sK3028: set_complex > (complex > rat) > set_complex > complex).
% 32.77/9.03  thf(func_def_3963, type, sK3029: option_nat > vEBT_VEBT > nat > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3964, type, sK3030: option_nat > vEBT_VEBT > nat > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3965, type, sK3031: option_nat > vEBT_VEBT > nat > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3966, type, sK3032: option_nat > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3967, type, sK3033: option_nat > nat > vEBT_VEBT > product_prod_nat_nat).
% 32.77/9.03  thf(func_def_3968, type, sK3034: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3969, type, sK3035: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.03  thf(func_def_3970, type, sK3036: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.03  thf(func_def_3971, type, sK3037: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3972, type, sK3038: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3973, type, sK3039: vEBT_VEBT > option_nat > nat > nat).
% 32.77/9.03  thf(func_def_3974, type, sK3040: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.03  thf(func_def_3975, type, sK3041: vEBT_VEBT > nat > option_nat > $o).
% 32.77/9.03  thf(func_def_3976, type, sK3042: vEBT_VEBT > nat > option_nat > nat).
% 32.77/9.03  thf(func_def_3977, type, sK3043: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.03  thf(func_def_3978, type, sK3044: nat > vEBT_VEBT > option_nat > $o).
% 32.77/9.03  thf(func_def_3979, type, sK3045: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT).
% 32.77/9.03  thf(func_def_3980, type, sK3046: option_nat > nat > vEBT_VEBT > vEBT_VEBT).
% 32.77/9.03  thf(func_def_3981, type, sK3047: option_nat > nat > vEBT_VEBT > nat).
% 32.77/9.03  thf(func_def_3982, type, sK3048: (rat > nat) > rat).
% 32.77/9.03  thf(func_def_3983, type, sK3049: (rat > nat) > rat).
% 32.77/9.03  thf(func_def_3984, type, sK3050: list_o > ($o > $o) > $o).
% 32.77/9.03  thf(func_def_3985, type, sK3051: rat > rat > rat).
% 32.77/9.03  thf(func_def_3986, type, sK3052: (nat > int) > nat).
% 32.77/9.03  thf(func_def_3987, type, sK3053: (produc8763457246119570046nteger > $o) > code_integer > option6357759511663192854e_term).
% 32.77/9.03  thf(func_def_3988, type, sK3054: (produc8763457246119570046nteger > $o) > code_integer).
% 32.77/9.03  thf(func_def_3989, type, sK3055: (produc8763457246119570046nteger > $o) > code_integer).
% 32.77/9.03  thf(func_def_3990, type, sK3056: set_complex > (complex > rat) > complex).
% 32.77/9.03  thf(func_def_3991, type, sK3057: (int > nat) > set_int > (int > nat) > int).
% 32.77/9.03  thf(func_def_3992, type, sK3058: int > set_int > int > int).
% 33.43/9.03  thf(func_def_3993, type, sK3059: int > set_int > int > int).
% 33.43/9.03  thf(func_def_3994, type, sK3060: set_real > set_real > real).
% 33.43/9.03  thf(func_def_3995, type, sK3061: set_complex > (complex > rat) > complex).
% 33.43/9.03  thf(func_def_3996, type, sK3062: (nat > rat) > nat).
% 33.43/9.03  thf(func_def_3997, type, sK3063: (nat > rat) > nat).
% 33.43/9.03  thf(func_def_3998, type, sK3064: real > real).
% 33.43/9.03  thf(func_def_3999, type, sK3065: (nat > real) > nat).
% 33.43/9.03  thf(func_def_4000, type, sK3066: (nat > real) > nat).
% 33.43/9.03  thf(func_def_4001, type, sK3067: (set_real > $o) > set_real > set_real).
% 33.43/9.03  thf(func_def_4002, type, sK3068: rat > (rat > $o) > rat).
% 33.43/9.03  thf(func_def_4003, type, sK3069: rat > (rat > $o) > rat).
% 33.43/9.03  thf(func_def_4004, type, sK3070: (nat > int) > nat).
% 33.43/9.03  thf(func_def_4005, type, sK3071: real).
% 33.43/9.03  thf(func_def_4006, type, sK3072: (nat > $o) > nat).
% 33.43/9.03  thf(func_def_4007, type, sK3073: (int > int > $o) > (nat > int) > set_nat > (nat > int) > nat).
% 33.43/9.03  thf(func_def_4008, type, sK3074: (int > int > $o) > int).
% 33.43/9.03  thf(func_def_4009, type, sK3075: (int > int > $o) > int).
% 33.43/9.03  thf(func_def_4010, type, sK3076: (int > int > $o) > int).
% 33.43/9.03  thf(func_def_4011, type, sK3077: (int > int > $o) > int).
% 33.43/9.03  thf(func_def_4012, type, sK3078: (rat > nat) > rat).
% 33.43/9.03  thf(func_def_4013, type, sK3079: (rat > nat) > rat).
% 33.43/9.03  thf(func_def_4014, type, sK3080: nat > (nat > nat) > nat).
% 33.43/9.03  thf(func_def_4015, type, sK3081: nat > (nat > nat) > nat).
% 33.43/9.03  thf(func_def_4016, type, sK3082: (nat > nat) > nat > nat).
% 33.43/9.03  thf(func_def_4017, type, sK3083: (nat > nat) > nat > nat).
% 33.43/9.03  thf(func_def_4018, type, sK3084: (option_nat > option_num > $o) > option_nat > option_num > num).
% 33.43/9.03  thf(func_def_4019, type, sK3085: (option_nat > option_num > $o) > option_nat > option_num > nat).
% 33.43/9.03  thf(func_def_4020, type, sK3086: set_int > list_int).
% 33.43/9.03  thf(func_def_4021, type, sK3087: real > real > (real > real) > real).
% 33.43/9.03  thf(func_def_4022, type, sK3088: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 33.43/9.03  thf(func_def_4023, type, sK3089: real > (real > $o) > (real > $o) > real).
% 33.43/9.03  thf(func_def_4024, type, sK3090: real > (real > $o) > (real > $o) > real).
% 33.43/9.03  thf(func_def_4026, type, ph3092: !>[X0: $tType]:(X0)).
% 33.43/9.03  thf(f63226,plain,(
% 33.43/9.03    $false),
% 33.43/9.03    inference(avatar_sat_refutation,[status(thm)],[f62941,f62971,f63225])).
% 33.43/9.03  thf(f63225,plain,(
% 33.43/9.03    ~spl3091_4),
% 33.43/9.03    inference(avatar_contradiction_clause,[status(thm)],[f63224])).
% 33.43/9.03  thf(f63224,plain,(
% 33.43/9.03    $false | ~spl3091_4),
% 33.43/9.03    inference(subsumption_resolution,[status(thm)],[f63223,f63116])).
% 33.43/9.03  thf(f63116,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ maxs) @ X0) != $true)) ) | ~spl3091_4),
% 33.43/9.03    inference(subsumption_resolution,[status(thm)],[f63115,f63051])).
% 33.43/9.03  thf(f63051,plain,(
% 33.43/9.03    (maxs != (vEBT_VEBT_high @ ma @ m)) | ~spl3091_4),
% 33.43/9.03    inference(forward_demodulation,[status(thm)],[f63050,f54758])).
% 33.43/9.03  thf(f54758,plain,(
% 33.43/9.03    (m = na)),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f3])).
% 33.43/9.03  thf(f3,axiom,(
% 33.43/9.03    (m = na)),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_2__C8_C)).
% 33.43/9.03  thf(f63050,plain,(
% 33.43/9.03    (maxs != (vEBT_VEBT_high @ ma @ na)) | ~spl3091_4),
% 33.43/9.03    inference(forward_demodulation,[status(thm)],[f44468,f62690])).
% 33.43/9.03  thf(f62690,plain,(
% 33.43/9.03    (xa = ma) | ~spl3091_4),
% 33.43/9.03    inference(avatar_component_clause,[status(thm)],[f62689])).
% 33.43/9.03  thf(f62689,definition,(
% 33.43/9.03    spl3091_4 <=> (xa = ma)),
% 33.43/9.03    introduced(definition,[new_symbols(naming,[spl3091_4])],[avatar_definition])).
% 33.43/9.03  thf(f44468,plain,(
% 33.43/9.03    (maxs != (vEBT_VEBT_high @ xa @ na))),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f18090])).
% 33.43/9.03  thf(f18090,plain,(
% 33.43/9.03    ((ord_less_nat @ maxs @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) = $true) & (maxs != (vEBT_VEBT_high @ xa @ na))),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f18089])).
% 33.43/9.03  thf(f18089,plain,(
% 33.43/9.03    (ord_less_nat @ maxs @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) & (maxs != (vEBT_VEBT_high @ xa @ na))),
% 33.43/9.03    inference(rectify,[status(thm)],[f11])).
% 33.43/9.03  thf(f11,axiom,(
% 33.43/9.03    (ord_less_nat @ maxs @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) & (maxs != (vEBT_VEBT_high @ xa @ na))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_10_bb)).
% 33.43/9.03  thf(f63115,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ maxs) @ X0) != $true) | (maxs = (vEBT_VEBT_high @ ma @ m))) ) | ~spl3091_4),
% 33.43/9.03    inference(superposition,[status(thm)],[f63041,f48921])).
% 33.43/9.03  thf(f48921,plain,(
% 33.43/9.03    ( ! [X2 : nat,X3 : vEBT_VEBT,X0 : nat,X1 : list_VEBT_VEBT] : (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3) @ X0) = (nth_VEBT_VEBT @ X1 @ X0)) | (X0 = X2)) )),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f30243])).
% 33.43/9.03  thf(f30243,plain,(
% 33.43/9.03    ! [X0 : nat,X1 : list_VEBT_VEBT,X2 : nat,X3 : vEBT_VEBT] : ((X0 = X2) | ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3) @ X0) = (nth_VEBT_VEBT @ X1 @ X0)))),
% 33.43/9.03    inference(ennf_transformation,[status(thm)],[f25941])).
% 33.43/9.03  thf(f25941,plain,(
% 33.43/9.03    ! [X0 : nat,X1 : list_VEBT_VEBT,X2 : nat,X3 : vEBT_VEBT] : ((X0 != X2) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ X1 @ X2 @ X3) @ X0) = (nth_VEBT_VEBT @ X1 @ X0)))),
% 33.43/9.03    inference(rectify,[status(thm)],[f23])).
% 33.43/9.03  thf(f23,axiom,(
% 33.43/9.03    ! [X14 : nat,X13 : list_VEBT_VEBT,X5 : nat,X0 : vEBT_VEBT] : ((X5 != X14) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ X13 @ X5 @ X0) @ X14) = (nth_VEBT_VEBT @ X13 @ X14)))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_22_nth__list__update__neq)).
% 33.43/9.03  thf(f63041,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ ma @ m) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ ma @ m)) @ (vEBT_VEBT_low @ ma @ m))) @ maxs) @ X0))) ) | ~spl3091_4),
% 33.43/9.03    inference(backward_demodulation,[status(thm)],[f63039,f62690])).
% 33.43/9.03  thf(f63039,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ m) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ m)) @ (vEBT_VEBT_low @ xa @ m))) @ maxs) @ X0) != $true)) )),
% 33.43/9.03    inference(forward_demodulation,[status(thm)],[f48048,f54758])).
% 33.43/9.03  thf(f48048,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X0) != $true)) )),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f28053])).
% 33.43/9.03  thf(f28053,plain,(
% 33.43/9.03    ! [X0 : nat] : ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X0) != $true)),
% 33.43/9.03    inference(ennf_transformation,[status(thm)],[f14452])).
% 33.43/9.03  thf(f14452,plain,(
% 33.43/9.03    ~? [X0 : nat] : ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X0) = $true)),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f14451])).
% 33.43/9.03  thf(f14451,plain,(
% 33.43/9.03    ~? [X0 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X0)),
% 33.43/9.03    inference(rectify,[status(thm)],[f10250])).
% 33.43/9.03  thf(f10250,negated_conjecture,(
% 33.43/9.03    ~? [X17 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X17)),
% 33.43/9.03    inference(negated_conjecture,[status(cth)],[f10249])).
% 33.43/9.03  thf(f10249,conjecture,(
% 33.43/9.03    ? [X17 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ maxs) @ X17)),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',conj_0)).
% 33.43/9.03  thf(f63223,plain,(
% 33.43/9.03    ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ maxs) @ (sK2200 @ maxs)) = $true)),
% 33.43/9.03    inference(subsumption_resolution,[status(thm)],[f63202,f47822])).
% 33.43/9.03  thf(f47822,plain,(
% 33.43/9.03    ((vEBT_V8194947554948674370ptions @ summary @ maxs) = $true)),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f11713])).
% 33.43/9.03  thf(f11713,plain,(
% 33.43/9.03    ((vEBT_V8194947554948674370ptions @ summary @ maxs) = $true)),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f11712])).
% 33.43/9.03  thf(f11712,plain,(
% 33.43/9.03    (vEBT_V8194947554948674370ptions @ summary @ maxs)),
% 33.43/9.03    inference(rectify,[status(thm)],[f2])).
% 33.43/9.03  thf(f2,axiom,(
% 33.43/9.03    (vEBT_V8194947554948674370ptions @ summary @ maxs)),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062)).
% 33.43/9.03  thf(f63202,plain,(
% 33.43/9.03    ((vEBT_V8194947554948674370ptions @ summary @ maxs) != $true) | ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ maxs) @ (sK2200 @ maxs)) = $true)),
% 33.43/9.03    inference(trivial_inequality_removal,[status(thm)],[f63197])).
% 33.43/9.03  thf(f63197,plain,(
% 33.43/9.03    ((vEBT_V8194947554948674370ptions @ summary @ maxs) != $true) | ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ maxs) @ (sK2200 @ maxs)) = $true) | ($true != $true)),
% 33.43/9.03    inference(superposition,[status(thm)],[f63195,f63070])).
% 33.43/9.03  thf(f63070,plain,(
% 33.43/9.03    ($true = (ord_less_nat @ maxs @ (size_s6755466524823107622T_VEBT @ treeList)))),
% 33.43/9.03    inference(forward_demodulation,[status(thm)],[f44469,f52161])).
% 33.43/9.03  thf(f52161,plain,(
% 33.43/9.03    ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m) = (size_s6755466524823107622T_VEBT @ treeList))),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f37])).
% 33.43/9.03  thf(f37,axiom,(
% 33.43/9.03    ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m) = (size_s6755466524823107622T_VEBT @ treeList))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_36__C2_C)).
% 33.43/9.03  thf(f44469,plain,(
% 33.43/9.03    ((ord_less_nat @ maxs @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) = $true)),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f18090])).
% 33.43/9.03  thf(f63195,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (((ord_less_nat @ X0 @ (size_s6755466524823107622T_VEBT @ treeList)) != $true) | ($true != (vEBT_V8194947554948674370ptions @ summary @ X0)) | ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ (sK2200 @ X0)) = $true)) )),
% 33.43/9.03    inference(forward_demodulation,[status(thm)],[f52451,f52161])).
% 33.43/9.03  thf(f52451,plain,(
% 33.43/9.03    ( ! [X0 : nat] : (($true != (vEBT_V8194947554948674370ptions @ summary @ X0)) | ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ (sK2200 @ X0)) = $true) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)))) )),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f39256])).
% 33.43/9.03  thf(f39256,plain,(
% 33.43/9.03    ! [X0 : nat] : (((($true = (vEBT_V8194947554948674370ptions @ summary @ X0)) | ! [X1 : nat] : ($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1))) & (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ (sK2200 @ X0)) = $true) | ($true != (vEBT_V8194947554948674370ptions @ summary @ X0)))) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),
% 33.43/9.03    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2200])],[f39254,f39255])).
% 33.43/9.03  thf(f39255,plain,(
% 33.43/9.03    ! [X0 : nat] : (? [X2 : nat] : ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X2) = $true) => ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ (sK2200 @ X0)) = $true))),
% 33.43/9.03    introduced(definition,[],[choice_axiom])).
% 33.43/9.03  thf(f39254,plain,(
% 33.43/9.03    ! [X0 : nat] : (((($true = (vEBT_V8194947554948674370ptions @ summary @ X0)) | ! [X1 : nat] : ($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1))) & (? [X2 : nat] : ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X2) = $true) | ($true != (vEBT_V8194947554948674370ptions @ summary @ X0)))) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),
% 33.43/9.03    inference(rectify,[status(thm)],[f39253])).
% 33.43/9.03  thf(f39253,plain,(
% 33.43/9.03    ! [X0 : nat] : (((($true = (vEBT_V8194947554948674370ptions @ summary @ X0)) | ! [X1 : nat] : ($true != (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1))) & (? [X1 : nat] : ($true = (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1)) | ($true != (vEBT_V8194947554948674370ptions @ summary @ X0)))) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),
% 33.43/9.03    inference(nnf_transformation,[status(thm)],[f29955])).
% 33.43/9.03  thf(f29955,plain,(
% 33.43/9.03    ! [X0 : nat] : ((($true = (vEBT_V8194947554948674370ptions @ summary @ X0)) <=> ? [X1 : nat] : ($true = (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1))) | ($true != (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),
% 33.43/9.03    inference(ennf_transformation,[status(thm)],[f17320])).
% 33.43/9.03  thf(f17320,plain,(
% 33.43/9.03    ! [X0 : nat] : (($true = (ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))) => (($true = (vEBT_V8194947554948674370ptions @ summary @ X0)) <=> ? [X1 : nat] : ($true = (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1))))),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f17319])).
% 33.43/9.03  thf(f17319,plain,(
% 33.43/9.03    ! [X0 : nat] : ((ord_less_nat @ X0 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (? [X1 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X0) @ X1) = (vEBT_V8194947554948674370ptions @ summary @ X0)))),
% 33.43/9.03    inference(rectify,[status(thm)],[f14])).
% 33.43/9.03  thf(f14,axiom,(
% 33.43/9.03    ! [X6 : nat] : ((ord_less_nat @ X6 @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (? [X7 : nat] : (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ X6) @ X7) = (vEBT_V8194947554948674370ptions @ summary @ X6)))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_13__C4_C)).
% 33.43/9.03  thf(f62971,plain,(
% 33.43/9.03    ~spl3091_2),
% 33.43/9.03    inference(avatar_split_clause,[status(thm)],[f56192,f62680])).
% 33.43/9.03  thf(f62680,definition,(
% 33.43/9.03    spl3091_2 <=> (mi = ma)),
% 33.43/9.03    introduced(definition,[new_symbols(naming,[spl3091_2])],[avatar_definition])).
% 33.43/9.03  thf(f56192,plain,(
% 33.43/9.03    (mi != ma)),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f13476])).
% 33.43/9.03  thf(f13476,plain,(
% 33.43/9.03    ((ord_less_nat @ xa @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) = $true) & (mi != ma)),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f13475])).
% 33.43/9.03  thf(f13475,plain,(
% 33.43/9.03    (mi != ma) & (ord_less_nat @ xa @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 33.43/9.03    inference(rectify,[status(thm)],[f45])).
% 33.43/9.03  thf(f45,axiom,(
% 33.43/9.03    (mi != ma) & (ord_less_nat @ xa @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_44__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062)).
% 33.43/9.03  thf(f62941,plain,(
% 33.43/9.03    spl3091_2 | spl3091_4),
% 33.43/9.03    inference(avatar_split_clause,[status(thm)],[f47546,f62689,f62680])).
% 33.43/9.03  thf(f47546,plain,(
% 33.43/9.03    (xa = ma) | (mi = ma)),
% 33.43/9.03    inference(cnf_transformation,[status(thm)],[f28522])).
% 33.43/9.03  thf(f28522,plain,(
% 33.43/9.03    ((mi = (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))) = none_nat) @ mi @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na)))))))))) | (xa != ma)) & ((mi = ma) | (xa = ma))),
% 33.43/9.03    inference(ennf_transformation,[status(thm)],[f23540])).
% 33.43/9.03  thf(f23540,plain,(
% 33.43/9.03    ((xa != ma) => (mi = ma)) & ((xa = ma) => (mi = (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))) = none_nat) @ mi @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na)))))))))))),
% 33.43/9.03    inference(fool_elimination,[status(thm)],[f2752])).
% 33.43/9.03  thf(f2752,axiom,(
% 33.43/9.03    ((xa != ma) => (mi = ma)) & ((xa = ma) => ((if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))) = none_nat) @ mi @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ na)) @ (vEBT_VEBT_low @ xa @ na))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ summary @ (vEBT_VEBT_high @ xa @ na))))))))) = mi))),
% 33.43/9.03    file('/export/starexec/sandbox2/tmp/tmp.LJ3leIzvkk/DTF2THF_3754.p',fact_2751_aampt)).
% 33.43/9.03  % SZS output end Proof for DTF2THF_3754
% 33.43/9.03  % (3984)------------------------------
% 33.43/9.03  % (3984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.43/9.03  % (3984)Termination reason: Refutation
% 33.43/9.03  
% 33.43/9.03  % (3984)Memory used [KB]: 54114
% 33.43/9.03  % (3984)Time elapsed: 1.620 s
% 33.43/9.03  % (3984)Instructions burned: 5230 (million)
% 33.43/9.03  % (3984)------------------------------
% 33.43/9.03  % (3984)------------------------------
% 33.43/9.03  % (3861)Success in time 3.984 s
%------------------------------------------------------------------------------